Applied Science, Faculty of
Mechanical Engineering, Department of
DSpace
UBCO
Mohammadi, Mahsa
Doctor of Philosophy - PhD
University of British Columbia
In an era marked by rapid technological advancements, volatile market conditions, and global disruptions, effective Supply Chain (SC) management requires innovative approaches to address uncertainty, complexity, and dynamic changes. This dissertation presents the development and application of a set of novel Intelligent Decision Support Systems (IDSSs) for solving large-scale, stochastic, and dynamic SC networks under disruptions. The proposed IDSSs are validated using different case studies in diverse domains, including e-commerce, manufacturing, healthcare, and sustainability. Specifically, the research introduces four novel resilient IDSSs that integrate advanced optimization, machine learning, reinforcement learning, and logistics simulations to tackle some of the real-world challenges in the event of major disruptions in SCs. The first proposed resilient IDSS optimizes last-mile delivery in urban areas using mobile depots and crowd-shipping, achieving significant reductions in delivery time, cost, and environmental impact. The second IDSS enhances resilience in global SCs by developing a multi-stage stochastic dynamic programming to deal with disruptions and optimize logistics operations under uncertainty. The third IDSS focuses on equitable and efficient vaccine distribution, addressing demand uncertainties with a data-driven decision-making approach that significantly reduces shortages. Lastly, the fourth IDSS designs a robust and sustainable mask distribution and recycling network, balancing cost efficiency, environmental impact, and customer services. This research integrates exact methods (e.g., Parallelized Stochastic Dual Dynamic integer Programming (PSDDiP)), reinforcement learning, and hybrid optimization approaches, to enhance real-time resilient decision-making for large-scale SCs, while ensuring scalability, and computational efficiency. This is despite that most earlier IDSSs specifically reported for âresilienceâ SC design, lack such integration, assume no disruptions, or they have not been assessed for large systems in real-time. The findings demonstrated the potential of resilient IDSSs to improve responsiveness, time management, and cost-effectiveness in selected SC networks. Addressing critical gaps in data availability during disruption events and dynamic adaptation of the decisions can also potentially provide practical new insights for policymakers and practitioners. For example, the proposed Online Reinforcement Driven Adoptive Optimization (ORDAO) showed the applicability to generate delivery tours to fulfill the same number of customer orders in almost 11% less delivery time in comparison to the Interactive Multi-Agent Simulation IMAS.
Integrating Resiliency in IntelligentDecision Support Systems forReal-Time Management of Disruptionsin Large-Scale Supply ChainsbyMahsa MohammadiB.Sc., Zanjan University, 2016M.Sc., Azad University, 2019A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)April 2025© Mahsa Mohammadi, 2025The following individuals certify that they have read, and recommend to the College of GraduateStudies for acceptance, a dissertation entitled:Integrating Resiliency in Intelligent Decision Support Systems for Real-TimeManagement of Disruptions in Large-Scale Supply Chainssubmitted byMahsa Mohammadi in partial fulfilment of the requirements of the degree of Doctor of PhilosophyDr. Lukas Bichler, School of EngineeringSupervisorDr. Abbas Milani, School of EngineeringCo-SupervisorDr. Jahangir Hossain, School of EngineeringSupervisory Committee MemberDr. Mahmudur Fatmi, School of EngineeringSupervisory Committee MemberDr. Harish Krishnan, University of British Columbia- VancouverUniversity ExaminerDr. Guoqing Zhang, Faculty of Engineering, University of WindsorExternal ExamineriiAbstractIn an era marked by rapid technological advancements, volatile market conditions, and globaldisruptions, effective Supply Chain (SC) management requires innovative approaches to addressuncertainty, complexity, and dynamic changes. This dissertation presents the development andapplication of a set of novel Intelligent Decision Support Systems (IDSSs) for solving large-scale,stochastic, and dynamic SC networks under disruptions. The proposed IDSSs are validated usingdifferent case studies in diverse domains, including e-commerce, manufacturing, healthcare, andsustainability. Specifically, the research introduces four novel resilient IDSSs that integrate ad-vanced optimization, machine learning, reinforcement learning, and logistics simulations to tacklesome of the real-world challenges in the event of major disruptions in SCs. The first proposedresilient IDSS optimizes last-mile delivery in urban areas using mobile depots and crowd-shipping,achieving significant reductions in delivery time, cost, and environmental impact. The second IDSSenhances resilience in global SCs by developing a multi-stage stochastic dynamic programming todeal with disruptions and optimize logistics operations under uncertainty. The third IDSS focuseson equitable and efficient vaccine distribution, addressing demand uncertainties with a data-drivendecision-making approach that significantly reduces shortages. Lastly, the fourth IDSS designs arobust and sustainable mask distribution and recycling network, balancing cost efficiency, environ-mental impact, and customer services. This research integrates exact methods (e.g., ParallelizedStochastic Dual Dynamic integer Programming (PSDDiP)), reinforcement learning, and hybridoptimization approaches, to enhance real-time resilient decision-making for large-scale SCs, whileensuring scalability, and computational efficiency. This is despite that most earlier IDSSs specifi-cally reported for âresilienceâ SC design, lack such integration, assume no disruptions, or they havenot been assessed for large systems in real-time. The findings demonstrated the potential of resilientIDSSs to improve responsiveness, time management, and cost-effectiveness in selected SC networks.Addressing critical gaps in data availability during disruption events and dynamic adaptation of thedecisions can also potentially provide practical new insights for policymakers and practitioners. Forexample, the proposed Online Reinforcement Driven Adoptive Optimization (ORDAO) showediiithe applicability to generate delivery tours to fulfill the same number of customer orders in almost11% less delivery time in comparison to the Interactive Multi-Agent Simulation IMAS .ivLay SummaryThis dissertation advances logistics operations in large-scale supply chains by developing IDSSsthat integrate data-driven models, optimization, simulation, and machine learning to enhance re-silience and sustainability. Chapter II introduces an IDSS for last-mile delivery using stochasticmodeling, travel time simulation, deep learning for crowd-shipper availability, and reinforcementlearning. Chapter III presents a multi-stage stochastic model for manufacturing supply chains withhedging policies and a parallel SDDiP algorithm. In healthcare, Chapter IV proposes a vaccinedistribution system with real-time demand forecasting and dynamic inventory. Chapter VI devel-ops a robust-stochastic model for sustainable mask distribution and recycling within a closed-loopsupply chain. Chapter V summarizes the findings, outlines key contributions, discusses model limi-tations, and suggests future research directions. Overall, the research offers a unified framework forsector-specific IDSSs, improving adaptability and responsiveness under uncertainty.vPrefaceThis dissertation is conducted by Mahsa Mohammadi under the supervision of Dr. BabakMohamadpour Tosarkani at the Industrial & Systems Engineering (ISE) Research Group at TheUniversity of British Columbia. The original research carried out in this dissertation has led tomultiple submitted journal publications and conference presentations. No generative AI was usedfor any aspects of this work. The details of all publications extracted from this dissertation arelisted below:Journal Publicationsâ Mohammadi, M., & Tosarkani, B. M. (2024). Crowd-Shipper or Hyper-Local Driver?A Journey Beyond Delivery Policies. Transportation Research Part E (Under Review).(Manuscript Number: TRE-D-24-02955 ).â Mohammadi, M., & Tosarkani, B. M. (2024). Green Horizons: Sustainable Global Logis-tics in Dynamic Supply Chain Management. Computers & Operations Research (RevisionSubmitted). (Manuscript Number: CAOR-D-24-01344).â Mohammadi, M., Ghiasvand, M. R., & Tosarkani, B. M. (2024). Timing the Vaccine Flow:An Intelligent Navigator for Strategic Delivery and Coverage. OMEGA (Revision Submitted),(Manuscript Number:OMEGA-D-24-01034).Mohsen Roytvand Ghiasvand helped me in data-driven module of the manuscript.â Mohammadi, M., & Tosarkani, B. M. (2024). Harmonizing Sustainability and Resiliency:A Novel Robust-Stochastic Decomposition Approach for Effective Mask Distribution and Re-cycling. Computer & Industrial Engineering (Under Review). (Manuscript Number: CAIE-D-24-04322)Additionally the following papers have been prepared as a side project during myPhD journey:â Shahparvari, S.,Mohammadi, M., Peszynski, K. (2024). How contraflow enhances clearancetime during assisted mass evacuation - A case study exploring the Australian 2013-14 Gipps-land bushfires, Transportation Research Part A. https://doi.org/10.1016/j.tra.2024.104197.viâ Moghaddas, Z., Yousefi, S., Mohammadi, M., & Tosarkani, B. M. (2023). A hybrid returnsto scale-DEA model for sustainable efficiency evaluation of urban transportation systems.International Journal of Systems Science: Operations & Logistics.https://doi.org/10.1080/23302674.2023.2221364.â Mohammadi, M., Ghiasvand, M. R., & Tosarkani, B. M. Resilient vaccine immunogenicityresponse in epidemic outbreaks using a novel Lagrangian algorithm, Healthcare ManagementScience, (Under Review), (Manuscript Number: HCMS-D-24-00569)Conferencesâ Mohammadi, M., Tosarkani, B. M. , An Intelligent Decision Support System for Last-MileDelivery Optimization Under Uncertainty, 18th INFORMS Computing Society (ICS), 2025,Toronto, Canadaâ Tosarkani, B. M., & Mohammadi, M. (June 25-27, 2024). Enhancing Sustainable Large-ScaleLogistics Planning with a Hybrid Machine Learning Decomposition Approach, 2024 POMSInternational Conference, Istanbul, Turkey.â Mohammadi, M., & Tosarkani, B. M. (May 31- June 3, 2024). Market-Ready: Boosting E-Commerce Logistics with Intelligent Decision Support System. Innovative Topics in SupplyChain Session, IISE Annual Conference & Expo 2024, Montre´al, Canada.â Mohammadi, M., & Tosarkani, B. M. (May 30- June 3, 2023). Sustainable mask distributionplanning and recycling under uncertainty: A novel graph theory-based clustering algorithm.Production & Operations Management Division, ASAC 2023 Conference, Toronto, Canada.(Best Paper Award)â Mohammadi, M., & Tosarkani, B. M. (May 29- 31, 2023). Not anymore impacts in shadowsof disaster. Disruption Management, 2023 CORS-Optimization Days conference, Montreal,Canada.â Mohammadi, M., & Tosarkani, B. M. (June 5-8, 2022). Online-offline Vehicle Routing UsingReinforcement Learning: A Markov Decision Process Model. Innovative Models on SupplyChain Risk Mitigation Track, 2022 CORS/INFORMS International Conference, Vancouver,Canada.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Supply Chain Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Intelligent Decision Support System . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 A Synopsis of Relevent Past Research . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Supply Chain Management and Sustainability . . . . . . . . . . . . . . . . . . 61.3.2 Decision Support System Design for Supply Chain Networks . . . . . . . . . 71.4 Research Gaps and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4.1 Gap 1: Real-Time Decision-Making . . . . . . . . . . . . . . . . . . . . . . . 81.4.2 Gap 2: Integrated Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.3 Gap 3: Scalability of the Optimization Models . . . . . . . . . . . . . . . . . 91.4.4 Gap 4: Sustainability Consideration . . . . . . . . . . . . . . . . . . . . . . . 9viii1.5 Objectives and Expected Research Contributions . . . . . . . . . . . . . . . . . . . . 121.5.1 Methodological Enhancement Aimed . . . . . . . . . . . . . . . . . . . . . . . 121.5.1.1 Aim 1: Resilient and Intelligent Decision Support Systems Design . 121.5.1.2 Aim 2: Including Real-Time Decision-Making . . . . . . . . . . . . . 121.5.1.3 Aim 3: Enhancing Time Management in SC Management . . . . . 121.5.1.4 Aim 4: Cost-effectiveness . . . . . . . . . . . . . . . . . . . . . . . . 131.5.2 Aim 5: Sustainability Consideration . . . . . . . . . . . . . . . . . . . . . . . 131.5.3 Overview of Methodologies of the Proposed IDDSs: Expected Contributions 141.5.3.1 Chapter 2: IDSS 1 E-commerce Business Logistics . . . . . . . . . . 151.5.3.2 Chapter 3: IDSS 2 Resilient Global Supply Chain Logistics . . . . . 151.5.3.3 Chapter 4: IDSS 3 Healthcare Logistics-Vaccine Distribution Planning 161.5.3.4 Chapter 5: IDSS 4 Healthcare Logistics-Mask Distribution and Re-cycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.6 Dissertation flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Chapter 2: Intelligent decision support system for e-commerce logistics resiliency:crowd-shipper or hyper-local driver? . . . . . . . . . . . . . . . . . . . . 202.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.1 Innovative Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 EDI and SET in the Proposed Last-Mile Delivery Business Model . . . . . 242.2.3 Aims and Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4 Intelligent Decision Support System . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.1 Online Reinforcement-Driven Adaptive Optimization . . . . . . . . . . . . . . 342.4.2 Markov Decision Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.4.3 Optimization Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.4.3.1 Risk-Averse Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.4.4 Interactive Multi-Agent Simulation Module . . . . . . . . . . . . . . . . . . . 462.4.5 EDI -SET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.4.5.1 Crowd-Shippers Success Rate of Delivery . . . . . . . . . . . . . . . 482.4.5.2 Deep Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48ix2.4.5.3 An Integrated Ensemble Model . . . . . . . . . . . . . . . . . . . . . 492.5 Numerical Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.6 Case Study and Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.6.1 Analysis of Stochastic Solution Quality . . . . . . . . . . . . . . . . . . . . . 562.6.2 Innovative Policies Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 572.7 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.8 Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.8.1 The Impact of Selected Features on Delivery Success Rate . . . . . . . . . . . 622.8.2 The Impacts of Selected Features on Last-Mile Delivery Business Model Per-formance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642.8.3 Hyper-Local Drivers Reimbursement Policy . . . . . . . . . . . . . . . . . . . 672.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Chapter 3: Intelligent decision support system for global dynamic supply chainlogistics resiliency in manufacturing sector . . . . . . . . . . . . . . . . 763.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.2.1 Supply Chain Resiliency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.2.2 Multi-Sourcing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.2.3 Long-Term Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.2.4 Parallel Stochastic Dual Dynamic Integer Programming . . . . . . . . . . . . 803.2.5 Aims and Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.4 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.4.1 Hedging Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.4.1.1 Multiple Sourcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.4.1.2 Long-Term Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.4.1.3 Consignment Inventory . . . . . . . . . . . . . . . . . . . . . . . . . 903.5 Solution Approach: The Proposed Parallel Stochastic Dual Dynamic Integer Pro-gramming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.5.1 Forward Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.5.1.1 First Stage Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93x3.5.1.2 Middle Stages Model . . . . . . . . . . . . . . . . . . . . . . . . . . 943.5.1.3 Last Stage Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.5.2 Backward Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.5.2.1 Cut Families: Multi-Cut SDDiP . . . . . . . . . . . . . . . . . . . 953.5.2.1.1 Benders Optimality Cut . . . . . . . . . . . . . . . . . . . . 953.5.2.1.2 Stage-Wise Lagrangean Dual Cuts . . . . . . . . . . . . . . 963.5.2.1.3 Mixed-Integer Rounding Cuts . . . . . . . . . . . . . . . . 973.5.3 Parallelization in Large-Scale Multi-Stage Stochastic Models . . . . . . . . . 983.6 Numerical Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003.6.1 Advance Scenario Sampling: Importance Sampling . . . . . . . . . . . . . . . 1013.6.2 Resiliency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.6.3 Scenario I: Baseline Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.6.4 Scenario II: Supplier Unavailability . . . . . . . . . . . . . . . . . . . . . . . . 1103.6.5 Scenario III: Delays in Sourcing the Productâs Components . . . . . . . . . . 1123.7 Managerial Implications: Discount Rate Model . . . . . . . . . . . . . . . . . . . . . 1143.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Chapter 4: Intelligent decision support system for healthcare sector logistics re-siliency: timing the vaccine flow . . . . . . . . . . . . . . . . . . . . . . . 1194.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.2.1 Vaccine Supply Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.2.2 Employing Machine Learning to Tackle Uncertainty . . . . . . . . . . . . . . 1234.2.3 Aim Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.3 Systematic Decision Support System Design . . . . . . . . . . . . . . . . . . . . . . . 1264.3.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.3.2 Systematic Decision Support System Design for Vaccine Distribution Plan-ning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1284.4 Data-Based Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1294.4.1 Data Generation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.4.1.1 Noise Range Random Injection Algorithm . . . . . . . . . . . . . . . 1324.4.1.2 Density-based Random Injection Algorithm . . . . . . . . . . . . . . 133xi4.4.1.3 SKL- and MKL-based WOC-SVM . . . . . . . . . . . . . . . . . 1354.4.1.4 Weight Parameter Setting . . . . . . . . . . . . . . . . . . . . . . . . 1384.5 Model-Based Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.5.1 Developed Robust Counterpart Model . . . . . . . . . . . . . . . . . . . . . . 1424.5.2 Vaccine Distribution Planning Model . . . . . . . . . . . . . . . . . . . . . . . 1434.5.2.1 Lineralization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464.5.2.2 Distance-Based Approach . . . . . . . . . . . . . . . . . . . . . . . . 1474.5.3 Assignment Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1484.5.4 Update Candidate Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.6 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1504.6.1 Supporting Data of Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . 1514.6.2 Numerical Analysis of the Data-Based Framework . . . . . . . . . . . . . . . 1524.6.2.1 How Many Data Samples Should be Generated? . . . . . . . . . . 1574.6.3 Numerical Analysis of the Model-Based DSS . . . . . . . . . . . . . . . . . . 1604.6.3.1 Overview of Scenarios and Approaches for Comparison . . . . . . . 1604.6.4 Determining the Optimal Location of Stationary PHUs . . . . . . . . . . . . 1664.6.5 Managing the Optimal Location of Mobile PHUs . . . . . . . . . . . . . . . 1714.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Chapter 5: Intelligent decision support system for healthcare sector logistics re-siliency: harmonizing sustainability for mask distribution and recycling1775.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1775.1.1 Aims and Novelty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1795.2 Research Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1815.2.1 PPE Supply Chain Network Design . . . . . . . . . . . . . . . . . . . . . . . 1815.2.2 Large-Scale Optimization Under Uncertainty . . . . . . . . . . . . . . . . . . 1845.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1875.4 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1925.4.1 Robust Counterpart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1975.4.2 Robustness Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1985.5 Solution Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2005.5.1 Sample Average Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 201xii5.5.2 Graph Theory-Based Clustering Algorithm . . . . . . . . . . . . . . . . . . . 2045.5.2.1 The Graph Theory-based Clustering Algorithm Performance Mea-surement (Silhouette Analysis) . . . . . . . . . . . . . . . . . . . . . 2125.5.3 Accelerated Scenario Decomposition . . . . . . . . . . . . . . . . . . . . . . . 2155.6 Numerical Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2165.7 An Extension of Multi Objective Optimization . . . . . . . . . . . . . . . . . . . . . 2195.7.1 ϵ-Constraint Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2205.7.2 Scenario and Computational Time Analysis . . . . . . . . . . . . . . . . . . . 2205.8 Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2215.8.1 Case Study: Baseline Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 2215.8.2 Case Study: Scenario I-Resource Unavailability . . . . . . . . . . . . . . . . . 2245.8.3 Case Study: Scenario II-Workforce Unavailability . . . . . . . . . . . . . . . . 2255.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Chapter 6: Conclusions and Future Work Recommendations . . . . . . . . . . . . 2286.1 Summary of Research Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2286.2 Categorization of Contributions to the Knowledge . . . . . . . . . . . . . . . . . . . 2306.2.1 Advancement of Intelligent Decision Support Systems . . . . . . . . . . . . . 2306.2.2 Advancement of Stochastic and Dynamic Modeling in SC Management . . . 2316.2.3 Development of Scalable Solution Approaches . . . . . . . . . . . . . . . . . . 2326.2.4 Addressing Real-World Challenges in Supply Chain Management . . . . . . . 2326.2.5 Some Practical Insights for Decision-Makers . . . . . . . . . . . . . . . . . . . 2336.2.6 Impact on Sustainability and Resiliency . . . . . . . . . . . . . . . . . . . . . 2346.3 Limitations and Future Work Recommendations . . . . . . . . . . . . . . . . . . . . 2346.3.1 Possible Extensions for E-commerce Business Logistics . . . . . . . . . . . . . 2346.3.2 Possible Extensions for Resilient Global Supply Chain Logistics . . . . . . . . 2346.3.3 Possible Extensions for Healthcare Logistics: Vaccine Distribution . . . . . . 2356.3.4 Possible Extensions for Healthcare logistics: Mask Distribution and Recycling 235Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237xiiiList of TablesTable 2.1 The Most Relevant Research Reviews . . . . . . . . . . . . . . . . . . . . . . 26Table 2.2 Nomenclature Specific to Models in This Chapter . . . . . . . . . . . . . . . 43Table 2.3 Numerical Experiments Results (highlighted rows show the Toronto case study) 50Table 2.4 The Impacts of Risk Parameters on Risk-Neutral and Risk-Averse Models inDifferent Instances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Table 2.5 Analysis of Quality of Stochastic Solution (highlighted rows show the Torontocase study) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Table 3.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Table 3.2 Numerical Experiments Results . . . . . . . . . . . . . . . . . . . . . . . . . . 104Table 3.3 Summary of the Scenario I (Baseline) Results . . . . . . . . . . . . . . . . . . 109Table 3.4 Summary of the Scenario II Results . . . . . . . . . . . . . . . . . . . . . . . . 111Table 3.5 Summary of the scenario III results . . . . . . . . . . . . . . . . . . . . . . . . 113Table 4.1 List of Sets, Indices, Parameters, and Decision Variables . . . . . . . . . . . . 144Table 4.2 List of Sets, Indices, Parameters, and Decision Variables . . . . . . . . . . . . 149Table 4.3 Similarity Measurements for the Generated Data Samples . . . . . . . . . . . 157Table 4.4 Summary of Scenarios, Region Performance, and Improvement . . . . . . . . 163Table 4.5 The Effect of BM Parameter on the Optimal Solution of the VDP Model . . 168Table 5.1 The Most Relevant Research Reviews . . . . . . . . . . . . . . . . . . . . . . 186Table 5.2 Nomenclature: Indices & Sets, Parameters, and Decision Variables . . . . . . 193Table 5.3 Robustness Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199Table 5.4 Graph Theory-Based Clustering Algorithm Validation . . . . . . . . . . . . . 218Table 5.5 Disruption and Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . 225Table 5.6 Disruption and Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . 226xivList of FiguresFigure 1.1 Overall components of the IDSSs Designed in the Present Research . . . . . 14Figure 1.2 The Illustration of the Research Gaps, Aims, and Novelty of the PresentWork. In essence, the methodological novelty of the present work lies on in-tegration of different solution approaches shown in the last three columns (ex-act methods, reinforcement learning, simulation) under each chapter IDDS ,along with the proof/validation of each IDSS through a demonstrative casestudy. Each IDSS addresses the four key gaps identified in Section 1.4,applying them to various application sectors PHUs . . . . . . . . . . . . . 18Figure 2.1 Last-Mile Delivery Operations with Mobile Depot, Crowd-Shippers, and Hyper-Local Drivers for Online and Offline Orders for for E-commerce LogisticsApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.2 The Proposed Intelligent Decision Support System . . . . . . . . . . . . . . . 32Figure 2.3 The Illustrative Case Study (Orders Density) . . . . . . . . . . . . . . . . . . 52Figure 2.4 Scenario I Configuration: Mobile Depot, Crowd-Shipper, and Hyper-LocalDrivers Deliver Tours Configurations . . . . . . . . . . . . . . . . . . . . . . 59Figure 2.5 Scenario II Configuration: Mobile Depot, Crowd-Shipper, and Hyper-LocalDrivers Deliver Tours Configurations . . . . . . . . . . . . . . . . . . . . . . 60Figure 2.6 Performance Evaluation of the Proposed ORDAO . . . . . . . . . . . . . . 61Figure 2.7 Impacts of Selected Features by Developed Ensemble on Success Delivery Rate 63Figure 2.8 The Impacts of Selected Features on the Overall Performance of Last-MileDelivery Network (T.C , CVaR, E.V , T.D , F.S , S.S , and T.S) . . . . . 66Figure 2.9 Sensitivity Analysis on Hyper-Local Drivers Reimbursement Policy (fjdj) . . . 68Figure 2.10 Sensitivity Analysis on Hyper-Local Drivers Reimbursement Policy (fjdâ²j) . . . 70Figure 2.11 Sensitivity Analysis on Hyper-local Drivers Reimbursement Policy (fjcâ²ijk) . . 71xvFigure 3.1 Sequential Decision-Making for Resilient Stochastic-Dynamic Global SupplyChains: Strategic Supplier Selection, Tactical Renting and Shipment, andOperational Manufacturing and Inventory Management . . . . . . . . . . . . 84Figure 3.2 The Proposed Decision Support System for Global Supply Chain Logisticsin Manufacturing Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 3.3 The Illustrative Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Figure 3.4 Gantt Charts Comparing Baseline and Scenario Estimates in Multiple Regions116Figure 3.5 Comparison of Costs Across Different Scenarios . . . . . . . . . . . . . . . . 117Figure 4.1 The Overall Procedure of the Proposed Data-Driven DSS for the VDPProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 4.2 The Overall Procedure of the Data-based Framework . . . . . . . . . . . . . 130Figure 4.3 The Overall Procedure of the Model-based Framework . . . . . . . . . . . . 141Figure 4.4 Weekly Vaccination Demand of Canada and the USA . . . . . . . . . . . . . 151Figure 4.5 Candidate Locations for Establishing Stationary and Mobile PHUs . . . . . 152Figure 4.6 Historical Vaccine Demand of Two Different Regions of GTA . . . . . . . . 153Figure 4.7 Data-Driven Uncertainty Using MSC Algorithm for Limited Data . . . . . 154Figure 4.8 Data-Driven Uncertainty Sets using the MSC Algorithm with New Gener-ated Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Figure 4.9 Impact of Generated Dataset Size on Uncertainty Set Construction and FinalDemand Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Figure 4.10 The Overall Procedure of the Proposed Scenario 6 (Actual Demand) . . . . 162Figure 4.11 Comparison of Data-based Framework Compared to Different Approaches . 165Figure 4.12 Selected Locations for Stationary PHUs . . . . . . . . . . . . . . . . . . . . 170Figure 4.13 Selected Locations for Stationary and Mobile PHUs for Different Time Periods172Figure 4.14 The Impact of the Proposed Data-based Framework on the Vaccination Net-work Compared to Predicted Values . . . . . . . . . . . . . . . . . . . . . . . 173Figure 4.15 Impact of Mobile PHUs on the Overall Performance . . . . . . . . . . . . . 174Figure 4.16 Impact of Assignment on the Overall Performance . . . . . . . . . . . . . . . 174Figure 5.1 Municipal District of the Case Study . . . . . . . . . . . . . . . . . . . . . . 188Figure 5.2 Simplified Illustration of the Sustainable Mask Distribution Planning . . . . 189Figure 5.3 The Architecture of the Proposed DSS Platform for the Sustainable CLSCN 191xviFigure 5.4 Graph Theory-Based Clustering Algorithm Comparison with Six Top Ma-chine Learning Clustering Algorithms . . . . . . . . . . . . . . . . . . . . . . 210Figure 5.5 Graph Theory-Based Clustering Algorithm . . . . . . . . . . . . . . . . . . . 211Figure 5.6 Parameter Tuning for the k-means and DBSCAN . . . . . . . . . . . . . . 211Figure 5.7 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214Figure 5.8 Sensitivity Analysis for the Proposed Graph Theory-Based Clustering Algo-rithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Figure 5.9 Scenario and Computational Time Analysis . . . . . . . . . . . . . . . . . . . 221Figure 5.10 Baseline Scenario Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 223Figure 5.11 Scenario I (Resource Unavailability) Configuration . . . . . . . . . . . . . . . 225xviiNomenclatureAP Affinity PropagationAC Assembly CenterACA Available CapacityADDRO Augmented Data-Driven Robust OptimizationARIMA Auto Regressive Integrated Moving AverageBSV Boundary Support VectorBIRCH Balance Iterative Reducing And Clustering HierarchiesC.T Computational TimeCVaR Conditional Value at RiskDDSS Data-Driven Decision Support SystemDDRO Data-Driven Robust OptimizationDSS Decision Support SystemDRI Density-Based Random InjectionDBSCAN Density-Based Spatial Clustering Applications With NoiseDFFNN Deep Feed Forward Neural NetworkDRC Developed Robust CounterpartDPA Dynamic Public Health Units AllocationEOL End Of LifeEOU End Of UseEV Expected ValueEVPI Expected Value of Perfect InformationEDI Equity, Diversity, and InclusionED Expected DemandFED Federal Electoral DistrictsF.S First StageGTC Graph Theory-Based ClusteringxviiiGTA Greater Toronto AreaGM Gaussian MixtureID Inlier Data pointIS Importance SamplingIBA Indefinitely Binding AgreementIDSS Intelligent Decision Support System DesignIMAS Interactive Multi-Agent SimulationKDE Kernel density EstimationKPI Key Principal FactorLR Linear RegressionLSTM Long Short-Term MemoryLB Lower BoundMDP Markov Decision ProcessMLE Maximum Likelihood EstimationMS Mean ShiftMSE Mean Squared ErrorMBGD Mini-Batch Gradient DescentMIR Mixed-Integer RoundingMILP Mixed-Integer Linear ProgrammingMSC Multi-Stage ClusteringMKL-OC-SVM Multiple Kernel Learning-based One-Class Support Vector MachineNRRI Noise Range Random injectionOC-DNN One-Class Deep Neural NetworkORDAO Online Reinforcement-Driven Adaptive OptimizationPSDDiP Parallel Stochastic Dual Dynamic integer ProgrammingPPE Personal Protective EquipmentPCA Principal Component AnalysisPHUs Public Health UnitsRL Reinforcement LearningRHS Right Hand SideREI Risk Exposure IndexRC Robust CounterpartxixRO Robust OptimizationSAA Sample Average ApproximationS.S Second StageSD Scenario DecompositionSET Social Exchange TheorySKL-OC-SVM Single Kernel Learning-based One-Class Support Vector MachineSWLDC Stage-Wise Lagrangian Dual CutSDDP Stochastic Dual Dynamic ProgrammingSVC Support Vector ClusteringSK Support KernelsSVM Support Vector MachineSCN Supply Chain NetworkSSCN Sustainable Supply Chain NetworkST Supplier TypeTBA Temporary Binding AgreementT.S Third StageTTR Time To RecoverTTS Time To SurviveT.C Total CostT.D Total DistanceTTS Transportation Tomorrow SurveyUB Upper BoundVDP Vaccine Distribution PlanningVaR Value at RiskVSS Value of Stochastic SolutionWGIK Weighted Generalized Intersection KernelWHO World Health OrganizationxxAcknowledgementsI would like to express my deepest gratitude to all those who have supported me throughout myPh.D. journey.First and foremost, I am profoundly grateful to my former supervisor, Dr. Babak Tosarkani, forhis invaluable guidance, insight, and unwavering support. His expertise and encouragement wereinstrumental in shaping the direction of this research. I would like to thank Dr. Lukas Bichler andDr. Abbas Milani as my supervisor and co-supervisor from November 2024 to January 2025 fortheir feedback. I would also like to thank the members of my dissertation committee, Dr. JahangirHossain and Dr. Mahmudur Fatmi, for their feedback.I extend my sincere thanks to Natural Sciences and Engineering Research Council of Canada(NSERC), whose financial support made this research possible.Special thanks to my partner, whose unwavering support, patience, and love have been mygreatest source of strength throughout this journey. Their encouragement and understanding duringthe challenging times have been invaluable, and their belief in my abilities has kept me motivated.I am also deeply grateful to my family, my father, mother, and my brother whose constantsupport and encouragement have been the foundation of my perseverance. Their understandingand sacrifices have allowed me to focus on my research with peace of mind. Their love and pride inmy achievements have been a continuous source of inspiration.Thank you all for your enduring support and for being a pivotal part of this journey.xxiDedicationTo my family, whose sacrifices, encouragement, and unconditional support have been the foun-dation upon which I have built this achievement. Your dedication and faith in my abilities haveinspired me every step of the way. To my friend Elnaz, your constant encouragement and unwaveringfriendship have been invaluable.This work is dedicated to you, with profound gratitude and deep affection.xxiiChapter 1IntroductionThis chapter presents an overview of the present research background and identifies the researchgaps that led to the development of resilient IDSS for large-scale optimization problems underlarge-scale SC disruptions/uncertainty. It outlines the primary objectives and research expectedcontributions, followed by a summary of the outline of the dissertation. This dissertation presentsthe development of four new IDSSs tailored to various application sectors including e-commercelogistics, global SC logistics in manufacturing, and two healthcare logistics, to address contempo-rary challenges/disruptions in SC s (e.g., due to wildfires, COVID-19 pandemic, and geopoliticalissues). These challenges, present unique complexities that require integrated SC managementmethodologies. As a result, herein, different combinations of solution approaches, including exactalgorithms, reinforcement learning, and other data-driven methods, have been incorporated intodifferent modules of the IDSSs to tackle each real-world problem under unseen SC disruptions.1.1 Supply Chain ManagementA SC represents a highly complex network including various processes, from sourcing rawmaterials to delivering finished goods to end consumers. It involves numerous entities, such asmanufacturers with distinct roles, and often spans diverse geographic regions. Effective managementof such a complex system requires addressing challenges posed by global markets, dynamic customerdemands, competitors, and regulatory frameworks. This calls for a strategic approach to planning,execution, and control [1]. The SC network design primarily includes determining the configurationof a SC , which involves various critical decisions. These include estimating operational time andcosts, selecting facility locations, determining capacities and the number of facilities, allocatingareas and technology for production and processes, and choosing suitable suppliers [2]. The SCmanagement is a vital operational process with a significant impact on the economy, environment,and society [3].The importance of sustainability in SC management has grown significantly in recent years, due1to a combination of environmental, social, economic, and technological factors [4]. Sustainability-driven pressures from both internal and external stakeholders increase firmsâ awareness of sustain-ability issues, motivating them to adopt and integrate sustainable practices within their SC [5].The objective is to support firmsâ sustainable growth while ensuring that future generations canmeet their own needs [6]. The SC sustainability aims to maximize business profit and minimizeenvironmental and social impacts, simultaneously [7]. Sustainable SC management allows orga-nizations to evaluate the social, environmental, and economic impacts of their operations, trackprogress toward sustainability goals, and make informed decisions about resource allocation andperformance assessment [8].SC s typically do not always operate in a stable, steady state, as they are continuously exposedto risks arising from uncertainty and a dynamically changing environment that can alter theirconditions [9]. These risks stem from the uncertainty of incidents taking place, which can lead toconsequences that are often difficult to quantify in advance [10]. The impacts of such risks caninfluence the performance of individual entities within a SC , as well as other entities connectedto the affected one, potentially extending to multiple SC [11]. Disruptions in SC s can result insevere economic, environmental, and social repercussions. Therefore, it is essential for managersto implement effective strategies within SC s to minimize the negative impacts of such disruptions(e.g., wildfires, flood, droughts, and political issues). As these disruption have emerged, factors suchas robustness, agility, responsiveness, and visibility have become crucial for managers to ensure theresilience and effectiveness of their SC . The process of analyzing and addressing these disruptionsand associated risks is referred to as resiliency, a concept that has garnered increasing attentionfrom managers across various industries [12]. Conventional and contemporary SC s are increasinglyunable to keep pace with the demands of future business environments. Conventional SC s struggleto meet the demands of modern business environments due to rapid technological advancements,globalization, and uncertain demand patterns. These challenges highlight the need for agility,innovation, and sustainability that traditional SC s often lack. Additionally, while vast amounts ofdata are now available, many SC s fail to use it effectively for predictive and prescriptive decision-making. Unlike traditional SC s, which rely on isolated and segmented processes, integrated DSSsto SC can eliminate these barriers, creating a unified and continuous resilient system [13].A SC must meet customer expectations by ensuring timely delivery, cost efficiency, and high-quality products. Responsiveness is a critical factor in ensuring the agility and effectiveness of SC .In an environment characterized by rapid changes in customer preferences, market dynamics, and2external factors such as disruptions or regulatory changes, SC s must be able to react quickly tochanging demands. This requires real-time data access, advanced forecasting models, and flexibleoperational structures that can adjust quickly to dynamic conditions [14]. By prioritizing respon-siveness, companies can minimize the impact of uncertainties, ensure timely deliveries, and maintainhigh levels of customer satisfaction. In a responsive SC , decision-making processes are streamlined,enabling quick adjustments to inventory levels, transportation routes, and production schedules inresponse to customer needs or unforeseen events, making it a key pillar for maintaining competitiveadvantage [15].The effectiveness of SC operations is increasingly reliant on efficient time management, which,when properly controlled, offer a significant competitive advantage in todayâs business environ-ment [16]. Time management plays a pivotal role in optimizing the flow of goods and informationthroughout the SC . Effective time management ensures that products are delivered on time, whichis essential for meeting customer expectations and maintaining operational efficiency. Time man-agement involves coordinating various tasks, such as sourcing, production, and distribution, in amanner that minimizes delays and enhances throughput. This requires precise scheduling, accuratedemand forecasting, and seamless communication across all entities involved in the SC [17]. Theimplementation of technologies such as automated inventory management and transportation plan-ning can significantly improve time management, reducing lead times and improving the overallresponsiveness of the SC [18]. In this dissertation, time management is also demonstrated throughthe results of each IDSS application. For instance, in Chapter 2, the findings indicate an averagereduction in delivery time by 11%.SC challenges have long been a key focus in research, underscoring the vital need for DSSs tomanage these complex issues effectively [19]. Cost-effectiveness is at the heart of SC management,as organizations constantly seek ways to reduce costs while maintaining or improving service quality.A cost-effective SC minimizes unnecessary expenses at every stage of the process, from raw materialprocurement to final delivery [20]. Efficient procurement strategies, optimized transportation, andwarehouse operations, and the use of automation are critical in achieving cost savings. By developingDSSs and including predictive analytics and machine learning methods, companies can betterforecast demand, optimize inventory, and reduce the risk of overstocking or stockouts, both ofwhich can be costly [21]. Additionally, outsourcing and long-term contract with strategic supplierscan lead to further cost reductions [22]. By ensuring cost-effectiveness across the SC , organizationscan improve their profitability, offer competitive pricing, and maintain high service levels, ultimately3contributing to their long-term success.To navigate these challenges and ensure cost-effectiveness, responsiveness, time management,and sustainability, companies are increasingly relying on advancedDSS to improve decision-makingprocesses. The term advanced DSS refers to DSSs that incorporate more sophisticated method-ologies compared to regular DSS . While regular DSS typically focuses on providing support fordecision-making using historical data and basic optimization techniques, advanced DSS integratescutting-edge methodologies such as machine learning, predictive analytics, real-time data process-ing, and accelerated optimization algorithms. These systems are capable of handling large-scale,dynamic, and uncertain environments, offering more accurate forecasts, adaptive decision-making,and real-time responses to changing conditions in the SC . These systems not only support efficientmanagement but also enable real-time responses to the dynamic and complex nature of contempo-rary SC s. As a result, the integration of DSS has become essential for maintaining profitabilityand service quality in a competitive market.1.2 Intelligent Decision Support SystemThe growing need to make real-time decisions based on the dynamic nature of the environmenthas led to the adoption of advanced information systems and innovative techniques [23]. Advance-ments in information systems have significantly transformed traditional decision-making processes[24]. Today, systems have become more complex due to the need for dynamic real-time decision-making, the continuous flow of data into the system, and extensive data generation tools [25].Therefore, a DSS must be robust and adaptable, capable of handling complex and dynamic data inreal-time. It should provide reliable insights in dynamic conditions and support effective decision-making by integrating diverse data sources and responding to changing circumstances. The DSSshould also be resilient to changes in the environment, ensuring that it can continue to providevaluable support even in the face of uncertainty or unexpected events.Extensive research has been conducted in the pas to develop robust DSSs that assist in mak-ing effective managerial decisions. These systems represent a specialized category of computerizedinformation systems designed to support various management decision-making processes [26]. Theconcept of DSS is rooted in integrating human judgment with computerized information process-ing. DSSs support management across various activities, from strategic planning to the executionof operations throughout the value chain. Over time, the focus of DSS has shifted from be-4ing purely computer-based decision-making tools to systems capable of acquiring, adapting, andself-organizing in uncertain and dynamic environments. These systems now offer more flexibility,enabling them to continuously adjust and respond to dynamic conditions, making them essentialfor effective decision-making in complex and dynamic business settings [27]. DSSs consist of threecore components. The first is the database management system, which serves as the data repositoryfor the DSS . The second is the model-based management system, which performs a role similar tothe database management system but focuses on managing analytical and decision models. Lastly,the dialog generation and management system facilitates user interaction with the system, enablingseamless communication and decision-making processes [28]. DSSs process and analyze large vol-umes of data while also capturing, storing, and retrieving information. They incorporate a feedbackcontrol mechanism to promote continuous improvement and ensure adaptability in decision-makingprocesses [29, 30].Effective decision-making is crucial in managing SC networks, as it supports business stabil-ity, minimizes risks, and enhances sustainability. Well-designed DSSs ensure that decisions areinformed, timely, and aligned with organizational goals, thereby fostering stability and long-termsuccess [31]. To support decision-makers in addressing the complexities of SC s, DSSs have beenproposed, which help solve real-world challenges in an effective and efficient manner [32]. However,conventional DSSs may face challenges in managing the inherent uncertainties and complexitiesof SC s. To overcome these limitations, a smart version known as IDSSs have been developed.An IDSS uses artificial intelligence and machine learning techniques to handle imprecisions anduncertainties, making it particularly suited for the dynamic and complex nature of SC networks.This enables more accurate and adaptive decision-making, especially in situations involving riskmanagement and sustainability objectives [33].1.3 A Synopsis of Relevent Past ResearchThis section provides a review of relevant studies on SC management and the design of DSS forSC management. The first subsection focuses on research related to SC networks and sustainabilityconsiderations, while the second subsection offers a thorough examination of the design of decisionsupport systems for SC networks. This review also identifies existing gaps, motivations, and thecontributions of this dissertation. More detailed literature review for each proposed IDSS in thefield will be presented in the subsequent chapters.51.3.1 Supply Chain Management and SustainabilitySustainability refers to the ability to meet the needs of the present without compromising theability of future generations to meet their own needs. It involves balancing economic, environmental,and social factors to ensure long-term well-being [6]. Sustainability has become a cornerstone ofSC design, with researchers emphasizing the integration of environmental, social, and economicdimensions. [34] highlighted the need for carbon emissions assessment and management withinproduct SC s, proposing a framework that provides businesses with a comprehensive view of theiroperations. Building on the concept of sustainable SC s, [35] focused on the probabilistic lot-sizingproblem with service-level constraints, testing parameters such as demand uncertainty, service levels,cost factors (ordering, holding, and shortage costs), and lead time uncertainty. Their simulation-based approach explored how these factors influence inventory decisions and lot-sizing policies underuncertainty. Similarly, [36] proposed a stochastic bi-objective optimization model to maximizesustainability while minimizing costs. Their two-step approach aggregated sustainability dimensionsthrough fuzzy c-means clustering and incorporated resilience strategies to mitigate disruptions.To address uncertainties and risks, several researchers have developed stochastic and multi-objective optimization models. [37] developed a model that incorporated sustainability indicatorssuch as emissions, waste, energy consumption, and job creation, addressing risks associated withtransportation costs and demand variability. Similarly, [38] integrated system dynamics with multi-objective optimization, enabling contingency planning for disruptions while balancing cost efficiencyand resource flow. [39] developed an approach in the chemicals production sector by consideringenvironmental impacts and economic objectives to minimize financial risks. These studies underlinedthe critical role of advanced optimization techniques in managing complex and uncertain SC s.Sector-specific applications have further demonstrated the versatility of sustainable SC designmodels. [40] proposed a robust-stochastic optimization model for the automotive sector, focusingon minimizing costs, emissions, and energy consumption while enhancing job creation. However,challenges included the computational complexity of solving large-scale problems and balancingconflicting objectives such as cost reduction and job creation. Limitations also arose from the re-liance on accurate scenario generation, which can be difficult in uncertain environments. Despiteits strengths, the model required further refinement for scalability. For fuel SC s, [41] addressedeconomic, environmental, and social dimensions, incorporating uncertainty to handle demand fluc-tuations. In healthcare, [42] tackled vaccine distribution challenges with a stochastic model thatminimized costs and emissions while enhanced social welfare and job creation. Their study did pro-6pose any innovative approaches by integrating sustainability and efficiency into vaccine distribution.It did not also deeply explore specific policy frameworks or new policy recommendations beyondthe model itself. The model emphasized minimizing logistical costs and environmental impacts butdid not detail large-scale, real-world policy solutions for tackling the vaccine distribution process.As for shortages, the research considered the potential for supply chain disruptions , especiallyduring a global health crisis, but did not explicitly model vaccine shortages or how to handle themwithin the distribution framework. Furthermore, [43] applied a hybrid genetic algorithm to theagricultural sector, balancing sustainability objectives while improving resilience against demanduncertainties. These efforts highlight the growing recognition of sustainability and resilience asessential components in contemporary SC networks.1.3.2 Decision Support System Design for Supply Chain NetworksSeveral studies have focused on developing DSS for various SC applications, especially in thecontext of improving efficiency, sustainability, and risk management. For instance, [44] proposeda DSS for packaged fresh and perishable products that combined sales forecasting with an orderplanning system. This system optimized computational efficiency and achieved acceptable fore-casting accuracy (i.e., the forecasting accuracy was found to be within 90% when compared to testdata), which ultimately helped meet performance expectations. Similarly, [45] introduced a dynamicDSS designed for sustainable supplier selection within circular SC s. Their system incorporatedfuzzy methods to prioritize economic, social, and circular criteria, enabling more informed supplierdecisions. The use of fuzzy methods could be computationally intensive, potentially limited its scal-ability in real-world applications. Additionally, the model did not fully address market fluctuationsor real-time disruptions that were common in dynamic SC s. In a broader context, [19] developed asimulation-based DSS for a Portuguese wine SC network, analyzing various configurations underrisk scenarios and sustainability objectives. Their results demonstrated that transportation riskswere particularly impactful on SC performance, more so than risks related to energy or raw materialprices. Specifically, transportation disruptions led to a 15-20% reduction in SC performance, pri-marily due to delays and increased transportation costs. In terms of cost increases, transportationrisks were found to raise overall SC costs by 10-12% due to the delays, rerouting, and additionalfreight charges.Moreover, DSS applications extend beyond SC configuration to include areas such as priceoptimization [33], inventory management [46], and transportation planning [47], as well as overall7SC performance [32]. For example, [48] focused on optimizing the efficiency and sustainabilityof the sugarcane agroindustry SC . Their developed DSS was validated through rigorous testingand showed potential for real-world application, contingent on addressing the modelâs underlyingassumptions (i.e., steady supply and demand conditions, homogeneous production units, linearrelationships between variables, and perfect data availability). Similarly, [12] developed a two-stageDSS for resilient supplier selection and order allocation in multi-echelon SC s. Their case studyon the COVID-19 vaccine distribution highlighted the effectiveness of their methodology, whichoptimized the vaccine SC by identifying Germany as a primary supplier. Lastly, [49] employeda Bayesian network-based DSS to support operations managers in selecting effective sustainablegovernance approaches in multi-tier SC s. Their system was applied to a multinational company inChina, demonstrating the systemâs practical value in navigating complex, risk-laden environments.1.4 Research Gaps and MotivationThe challenges of SC network design have been widely studied [2, 50â52]. One critical gapidentified is the need for real-time decision-making.1.4.1 Gap 1: Real-Time Decision-MakingThe limited focus on real-time decision-making in SC network design arises from several sig-nificant challenges. SC s operate in dynamic and uncertain environments, making it challenging todevelop models that can adapt quickly to disruptions such as demand fluctuations or transporta-tion delays. The computational complexity of solving large-scale optimization problems in real-timeadds another layer of difficulty, as traditional methods are often too slow to deliver timely solu-tions. Furthermore, the absence of standardized frameworks for real-time decision-making forcesresearchers to develop tailored approaches, increasing the complexity of the task. In the literature,these challenges, such as data synchronization, computational complexity, and adaptation to dy-namic environments, have often been considered individually rather than addressing all the dynamicfeatures of real-world systems collectively. In addition, many studies in the literature have focusedon either technical or conceptual contributions, prioritizing specific aspects like algorithm develop-ment or theoretical frameworks rather than creating holistic, real-time solutions. In dynamic SCenvironments, decision-makers must respond quickly to changing conditions, such as disruptions,demand fluctuations, and new data inputs. Traditional DSSs often fail to accommodate this real-8time need, leaving SC managers with outdated or incomplete information when making decisions.Therefore, an effective DSS should be capable of integrating data in real time, allowing managersto make timely, well-informed decisions even in the face of uncertainty and disruptions.1.4.2 Gap 2: Integrated MethodologiesAnother significant gap in the literature lies in the integration and methodology of DSS mod-ules. Many existing DSSs tend to focus on individual approaches, such as optimization or simula-tion, but they often do not integrate these methods into a single, cohesive decision-making frame-work. This approach can limit the DSS âs ability to effectively support complex decision-making indynamic environments. In contrast, a robust DSS should seamlessly combine multiple techniques,such as optimization, simulation, machine learning, and data-driven models into a unified system.This integration allows for more comprehensive, informed decisions by focusing the strengths ofeach method.1.4.3 Gap 3: Scalability of the Optimization ModelsMost existing DSS solutions are designed for small-scale, relatively simple problems, whichmay not fully capture the complexity of real-world SC challenges. These solutions often rely onheuristics or simplified models that cannot handle the scale and intricacies of large, real-worldSC networks. This is particularly problematic when dealing with large-scale SC problems thatrequire exact algorithms for informative and optimal decision-making. Real-world SC s are complex,involving numerous variables and uncertainties that require exact and robust solutions rather thanapproximate ones.1.4.4 Gap 4: Sustainability ConsiderationIn addition, most decisions in SC s have typically focused primarily on economic considerations[53]. Although an efficient SC network design based on economic objectives presents a considerablechallenge, including environmental and social dimensions adds further complexity to the problem[54]. As a result, the growing focus on the remaining two pillars of the Triple Bottom Line inthe sustainability concept has attracted significant attention from the community, leading to thedevelopment of different approaches to address this problem [55]. While economic objectives havebeen the primary focus in most SC network design studies, this does not mean the environmentaland social pillars of sustainability have been entirely overlooked. Researchers have addressed these9dimensions, but their inclusion is often limited in scope or based on simplifying assumptions. Forexample, sustainability has rarely been fully integrated into DSSs for specific applications such aslast-mile delivery, leaving significant gaps in practical implementation. Additionally, while socialobjectives are usually considered, they are often treated simplistically. The approach in this disser-tation goes further by incorporating established theories, such as social exchange theory, to identifyand analyze social features. For instance, detailed aspects such as participation rates among malesand females, different age groups, and other social factors are considered. This methodology ensuresa deeper, theory-driven understanding of the social dimension, providing a more comprehensive viewof sustainability within SC network design. Although there is a rising focus on sustainability inSC network design, these networks continue to face significant vulnerabilities to various risks [56].Recent disruptions impacting the efficiency of global SC s can be referred to the COVID-19 pan-demic, the Russia-Ukraine war, and the subsequent surge in energy and raw material costs resultingfrom such disruptions [57]. As a result, the intricate challenge of creating SC s with sustainabilityobjectives becomes even more demanding, as these networks must address economic, social, andenvironmental goals while also managing uncertainty and disruptions [36]. While there has beengrowing interest from both academics and practitioners in general SC risk management in recentyears, limited research has been conducted on the impact of sustainability-related practices on SCrisks, particularly with a focus on suppliers. The specific focus on supplier selection and sourcingstrategies to address disruption risks, especially in the context of sustainability, is rarely inves-tigated. While much of the literature addresses supplier selection from cost, quality, or deliveryperspectives, there is a lack of research that integrates sustainability practices into supplier selec-tion and sourcing strategies aimed at managing disruptions. The challenge is that many studiesfocus on traditional sourcing strategies without considering how other sourcing strategies can beadapted or optimized to reduce the risks associated with disruptions, particularly in the contextof sustainability. Therefore, SC managers and decision-makers need effective DSSs to redesigntheir SC networks, taking into account economic, social, and environmental objectives, while alsoenabling real-time decision-making in the dynamic nature of the environment.The identified gaps in current literature about DSS for SC network design can have significantand far-reaching consequences for the efficiency, sustainability, and resilience of SC s. The lackof real-time decision-making capabilities in many existing DSSs is particularly problematic. Forexample, failing to account for real-time disruptions in the SC may result in delayed responses,increased costs, missed opportunities, and ultimately, reduced service levels to customers. This lag10in decision-making can also exacerbate the vulnerability of the SC to risks, leading to inefficiencies,waste, and missed opportunities for improvement.Additionally, the absence of an integrated DSS that combines optimization, simulation, ma-chine learning, and data-driven models into a cohesive system further limits the effectiveness ofDSS . Isolated approaches to decision-making fail to address the complexity of modern SC s, whichrequire a holistic perspective. Without integration, decision-makers may overlook critical interde-pendencies between different parts of the SC , leading to decisions that optimize one aspect of thesystem at the cost of others. For instance, failing to incorporate accurate demand prediction usingmachine learning methods into the decision-making process could lead to overstocking or stockouts,disrupting the SC âs balance. Overstocking results in increased holding costs and potential waste,while stockouts can lead to lost sales, reduced customer satisfaction, and damage to the companyâsreputation. These inefficiencies compromise the long-term sustainability and resilience of the SC .Furthermore, the reliance on small-scale or simplified models in existing DSS solutions presentsanother significant consequence, the inability to accurately model large, real-world SC networks.Real-world SC s are typically vast, multi-tiered, and include a wide array of variables and uncer-tainties. The use of heuristic methods or approximate solutions for such complex systems can leadto poor decision-making and missed opportunities for optimization. For instance, oversimplifiedmodels may fail to account for key factors such as supplier disruptions, changing regulations, or en-vironmental considerations, leading to inefficiencies and vulnerabilities that could have been avoidedwith more precise, data-driven models.Finally, the insufficient integration of sustainability objectives into DSS solutions for SC net-work design is a critical shortcoming. While many DSS solutions focus on economic factors suchas cost reduction and efficiency, they often neglect the environmental and social dimensions of SCmanagement. This is problematic, especially in todayâs world where sustainability is becoming anincreasingly important criterion for both business success and regulatory compliance. SC managerswho lack tools to consider sustainability in their decision-making are at risk of overlooking criticalissues such as carbon emissions, waste management, and social responsibility, all of which are crucialfor ensuring long-term SC viability and compliance with emerging regulations.These challenges and their consequences in contemporary SC network design motivated me tofocus on this area for my dissertation.111.5 Objectives and Expected Research ContributionsThe overreaching objective of this dissertation is to develop a series of resiliency-focused IDSSsand demonstrate their diverse applications by integrating advanced optimization, exact algorithms,machine learning, and logistics simulation techniques. The selected demonstrative case studies,include (i) e-commerce logistics, (ii) global supply chain logistics in manufacturing, and two health-care logistics concerning (iii) vaccine distribution, and (iv) mask distribution (including recyclingaspects). The primary motivation for these IDSSs is to assist decision-makers in managing un-expected operational uncertainties, such as resource or logistics disruptions, in real time withinlarge-scale SC s. This section outlines the overall objectives and contributions. Each IDSS ad-dresses the four key gaps identified in Section 1.4, applying them to various application sectors asdescribed below:1.5.1 Methodological Enhancement Aimed1.5.1.1 Aim 1: Resilient and Intelligent Decision Support Systems DesignThe primary objective of this dissertation is to develop resilient IDSSs, that addresses criticalgaps in SC network management modeling, ensuring resilience, sustainability, and adaptability indynamic environments (i.e., responsiveness, cost effectiveness, time management, and sustainabil-ity).1.5.1.2 Aim 2: Including Real-Time Decision-MakingThis dissertation for each given application aims to develop an IDSS capable of real-timedecision-making, enabling SC managers to respond quickly and effectively to changing circum-stances. By integrating different modules and advanced data-driven methodologies, this objectiveminimizes inefficiency in decision-making and ensure SC resilience under varying conditions.1.5.1.3 Aim 3: Enhancing Time Management in SC ManagementAnother key objective is to improve time management across SC operations. Efficient timemanagement is critical to maintaining the flow of goods, meeting customer expectations, and re-ducing operational bottlenecks. This dissertation emphasizes on developing systems that optimizescheduling, resource allocation, and transportation planning. By addressing delays and enhanc-ing synchronization across various SC echelons, this objective ensures cohesive and uninterrupted12operations and maximizes operational efficiency in the face of challenges or disruptions.1.5.1.4 Aim 4: Cost-effectivenessCost-effectiveness is also a central focus of this dissertation. SC managers often face the chal-lenge of balancing costs with other operational goals. This dissertation aims to design IDSS modelsthat incorporate multi-objective optimization techniques, allowing for cost minimization withoutcompromising on quality, timeliness, or sustainability. The proposed IDDS reduces unnecessaryexpenditures related to inventory management, transportation, procurement, and resource utiliza-tion, while ensuring overall efficiency and profitability.1.5.2 Aim 5: Sustainability ConsiderationFinally, this dissertation advances sustainability in SC networks by integrating economic, so-cial, and environmental objectives into the decision-making process. Traditional approaches oftenprioritize economic outcomes. By addressing the three pillars of sustainabilityâeconomic, envi-ronmental, and socialâthis research contributes to building SC s that align with long-term globalsustainability goals. While integrating the three pillars of sustainability, economic, environmental,and social, is not entirely new in SC research, many existing studies incorporate environmentaland social objectives using simplified assumptions or limited metrics. This dissertation addressesthese objectives through the application of comprehensive theories, such as social exchange theory,to address social factorsThese interconnected objectives collectively address the pressing challenges in contemporary SCmanagement, providing a robust framework to improve responsiveness, manage time effectively,reduce costs, and ensure sustainable practices.Figure 1.1 provides a better understanding about the challenges, objectives, methodologies, andimplementation in the selected case studies.13Figure 1.1: Overall components of the IDSSs Designed in the Present Research1.5.3 Overview of Methodologies of the Proposed IDDSs: ExpectedContributionsAccording to the above mentioned research gaps and objectives, this dissertation develops fourdifferent IDSSs for SC network management, and validates their applications across differentsectors. These application sectors include e-commerce SC , manufacturing SC , and healthcare14SC . The summary of these IDSSs and their novelty are summarized in Figure 1.2.1.5.3.1 Chapter 2: IDSS 1 E-commerce Business LogisticsIn recent years, the e-commerce market has established itself as the dominant and consistentlyexpanding segment of the retail industry [58]. The surge in online demand has significantly boostedrevenue for the online marketplace, reaching $4,938 in 2021. This growth has led to increasedattention towards the last-mile delivery problem [59]. Given that this sector stands as the costliestsegment in the entire supply chain network, there is a need to implement effective policies (e.g.,mobile depot and crowd-shipping) [60]. During 2020, a total of $131 billion worth of packages wasdelivered worldwide, and this value is projected to double by 2026 [61]. There has been a growingtrend in customer expectations regarding the delivery of online orders, including fast deliveries,same-day delivery, and customized online deliveries in terms of timing and location [62]. In thisregard, specific challenges arise from inaccurate delivery time estimates, particularly when real-timetraffic and weather conditions are overlooked. This gives rise to delivery delays, inefficient resourceallocation, higher delivery cost, and customer dissatisfaction. A practical illustration is the GTA,which faces numerous challenges in last-mile deliveries during winters due to disruptions stemmingfrom cold temperature and snowy conditions. Such circumstances lead to slower delivery process,longer service time, and delays which are investigated in Chapter 2.The research gap in e-commerce business logistics highlights several potential areas for inves-tigation. These areas encompass the lack of investigation into dynamic same-day deliveries, thesequential decision-making process, the incorporation of EDI factors, and large-scale multi-stagestochastic dynamic models. These aspects serve as motivation to develop an IDSS for the last-miledelivery problem, including four main modules of risk-averse multi-stage stochastic dynamic model,IMAS (traffic simulation, analytical simulation model), SET-EDI, and ORDAO in Chapter 2.1.5.3.2 Chapter 3: IDSS 2 Resilient Global Supply Chain LogisticsThe global economy is experiencing significant disruptions, impacting global supply chain strate-gies across all industries. In recent decades, businesses are under intense pressure to restructure,redesign, and reconsider the locations, sourcing and manufacturing strategies, and demand fulfill-ment. The factors driving this transformation include typical elements such as market volatility,varying costs, and technological disruptions [63]. The complexity and diversity of global supplychains make them vulnerable to a variety of logistical, natural, geopolitical, and industrial disrup-15tions that can temporarily restrict sourcing [64]. Such disruptions occur for reasons beyond thefirmâs control, and their frequency cannot be easily managed. However, effective supply chain man-agement practices can mitigate the negative consequences of such interruptions. For example, amore resilient supply chain may be able to recover more quickly from a disruption, returning to itsnormal full operational capacity sooner than a less resilient one [65]. Over the past decade, supplychain disruptions including supplier bankruptcies, natural and man-made disasters, labor strikes,and public health crises, have posed serious concerns to firms [66]. Notable cases of supply chaindisruption (e.g., bankruptcy and natural disaster) include the bankruptcy of 30% of existing NorthAmerican automotive suppliers in 2008 [67]. In July 2021, Pipeline Foods, a Minnesota organicfood company filed for bankruptcy due to the reduced customer orders during the COVID-19 pan-demic. Many farms were severely impacted by this bankruptcy. These challenges and disruptionsare examined in Chapter 3.The research gap in resilient global supply chain logistics opens several avenues for investigation.The first research gap lies in the lack of an integrated approach to managing order scheduling (logis-tics), production planning, and inventory management within global supply chains. Traditionally,these areas have been studied in isolation, leading to inefficiencies and missed opportunities foroptimization. In a global supply chain, these functions are highly interdependent, and decisions inone area can significantly impact the others. For example, production planning without consideringorder scheduling for bills of materials can lead to delays, increased costs, and inventory imbalances.Another key research gap is the insufficient exploration of the dynamic nature of global supply chainsand the role of hedging policies in enhancing resilience. Global supply chains are subject to frequentdisruptions and uncertainties, such as fluctuating demand, supply shortages, and geopolitical risks.Existing studies often overlook the need for adaptive strategies that can respond to these dynamicchanges. Chapter 3 fills this gap by investigating the impact of hedging policies, such as multiplesourcing, consignment inventory, and long-term contracts, on global supply chain resilience. In thischapter, a novel solution approach, PSDDiP , is developed for addressing a large-scale multi-stagestochastic dynamic model.1.5.3.3 Chapter 4: IDSS 3 Healthcare Logistics-Vaccine Distribution PlanningThe rise and spread of infectious disease, such as the COVID-19, and Ebola have put peopleâshealth and lives at risk. Annually, 5â15% of the global population has been infected with theflu, resulting in 3â5 million severe cases and 290,000-650,000 deaths [68]. The drastic impact of16the COVID-19 pandemic has also dramatically affected healthcare systems, economies, and variousindustries all over the world. More than 775 million COVID-19 cases have been confirmed globally,and the mortality rate has been more than 7 million until April 2024 [68]. Due to the severity of thisinfectious disease, the WHO and pharmaceutical companies have been seeking ways to tackle thespread of the pandemic. While healthcare scientists have focused on developing effective vaccines,supply chain practitioners have investigated ensuring the timely delivery of vaccines to health centers[69]. Vaccine manufacturing and distribution are crucial steps in mass immunization that requirethorough planning due to high and unpredictable demand [70]. Moreover, ensuring equitable vaccinedistribution across various situations necessitates creating a resilient SCN capable of withstandingfluctuations in demand, as discussed in Chapter 4.The research gap in healthcare logistics operations provides multiple opportunities for investi-gation. The VDP problems face challenges due to limited initial data, leading to potentially in-accurate or overly conservative solutions. To address this, an ADDRO approach (i.e., data-basedframework and model-based framework) is proposed in Chapter 4. Data-based framework integratesSVM -based techniques, data generation algorithms, and prediction values to create dynamic un-certainty sets and improve out-of-sample performance. The model-based framework includes abi-objective VDP model to optimize vaccine distribution by minimizing costs and maximizing cov-erage of PHUs, ensuring equitable access. To handle complexity, a DRC model determines robustdemand values, which are then applied to the VDP model. Additionally, a DPA algorithm dy-namically updates mobile PHU locations based on real-time demand, enhancing the effectivenessand equity of vaccine distribution. This comprehensive approach ensures robust, adaptable, andfair vaccine distribution even with limited data availability.1.5.3.4 Chapter 5: IDSS 4 Healthcare Logistics-Mask Distribution and RecyclingPPE has been recommended by health organizations as a control measure and precautionagainst the spread of the COVID-19 outbreak. One key preventive measure is the use of face masks,which help reduce the prevalence of viral diseases. Wearing face masks has become mandatory inpublic indoor spaces to decrease the high number of fatalities. However, these mandatory face maskpolicies have created a new environmental challenge regarding the effective and efficient managementof face mask waste. Therefore, it is crucial for decision-makers to properly manage this waste tominimize environmental pollution and reduce supply chain costs, which are examined in Chapter5.17In terms of mask distribution and recycling, sustainability in PPE supply chain design, in-cluding economic, environmental, and social aspects, is crucial. This involves creating a resilientand sustainable CLSCN for recycling COVID-19 masks using a robust-stochastic multi-objectivemixed-integer linear programming model. The approach proposed in Chapter 5 aims to minimizecosts and environmental impact while maximizing social benefits. The SAA integrated with the SDalgorithm tackles large-scale instances, while the GTC algorithm clusters high-dimensional data,reduces model complexity, and enhances cluster performance using Silhouette analysis, resulting asignificant improve in SAA-SD algorithm.(a) Supply Chain Overall FeaturesConsidered(b) Challenges and Gaps Addressed(c) Methodologies/Modules UsedFigure 1.2: The Illustration of the Research Gaps, Aims, and Novelty of the Present Work. Inessence, the methodological novelty of the present work lies on integration of different solutionapproaches shown in the last three columns (exact methods, reinforcement learning, simulation)under each chapter IDDS , along with the proof/validation of each IDSS through a demonstrativecase study. Each IDSS addresses the four key gaps identified in Section 1.4, applying them tovarious application sectors PHUsFigure 1.2 summarizes the research gaps, proposed approaches, and contributions of each chap-ter. The detailed literature review research gaps, contributions, and proposed methodologies re-garding each topic are provided in more details in each respective chapter.181.6 Dissertation flowThis dissertation is organized into six chapters. Chapter 2 presents the proposed IDSS designfor the e-commerce logistics considering novel delivery policies, such as crowd-shippers, hyper-localdrivers, and mobile depot. The designed IDSS includes four main modules, risk-averse multi-stagestochastic dynamic model, IMAS (traffic simulation, analytical simulation model), SET-EDI, andORDAO . Chapter 3 presents the designed IDSS for the resilient global supply chain logistics inmanufacturing considering the hedging policies to improve resiliency by developing an acceleratedPSDDiP approach. Chapter 4 proposes a IDSS for the healthcare logistics, specifically focusingon vaccine distribution planning considering novel policies such as mobile PHU s. Chapter 5presents the proposed IDSS the PPE distribution, particularly mask distribution and recycling,by developing an integrated solution approach. A two-stage stochastic model is developed andsolved using integrated SD and SAA algorithm. A novelGTC algorithm is proposed to reduce thenumber of scenarios, enhancing the performance of SAA-SD algorithm in terms of computationalburden. Finally, Chapter 6 denotes concluding remarks and future research directions.19Chapter 2Intelligent decision support system fore-commerce logistics resiliency:crowd-shipper or hyper-local driver?2.1 IntroductionIn recent years, the e-commerce market has established as the dominant and consistently ex-panding segment of all retail sales [58]. The surge in online demand has significantly boostedrevenue for the online marketplace, reaching $4,938 in 2021. This growth has led to increased at-tention towards the last-mile delivery problem [59]. Given that this sector stands as the costliestsegment in the entire supply chain network, there is a need to implement effective policies (e.g.,mobile depot and crowd-shipping) [60]. During 2020, a total of $131 billion worth of packages wasdelivered worldwide, and this value is projected to double by 2026 [61]. There has been a growingtrend in customer expectations regarding the delivery of online orders, including fast deliveries,same-day delivery, and customized online deliveries in terms of timing and location [62]. In thisregard, specific challenges arise from inaccurate delivery time estimates, particularly when real-timetraffic and weather conditions are overlooked. This gives rise to delivery delays, inefficient resourceallocation, higher delivery cost, and customer dissatisfaction. A practical illustration is the GTA,which faces numerous challenges in last-mile deliveries during winters due to disruptions stemmingfrom cold temperature and snowy conditions. Such circumstances lead to slower delivery process,longer service time, and delays.Given these circumstances, the implementation of innovative urban freight delivery policies, suchas crowd-shipping, holds a crucial role in addressing the impact of such challenges. Furthermore,these new delivery policies help mitigate potential adverse societal and environmental impacts ofurban freight transportation, including emissions, noise, and safety issues [71]. This approach20enables individuals to actively participate in the package delivery process from the main depot(hub) to the customer zones. Owing to the various social, economic, and environmental benefits ofcrowd-sourcing, e-commerce companies such as Amazon and Flex have incorporated crowd-shippingpolicies into their last-mile delivery operations [72]. Furthermore, the mobile depot policy aims toenhance consolidation and coordination between logistics service providers and customers, whileminimizing truck travels in urban areas [73]. A mobile depot refers to a customized trailer servingas both a loading dock and a depot facility equipped with an office [74]. This approach effectivelyreduces the number of required delivery vehicles and mitigates the heavy traffic congestion andenvironmental impacts stemmed from transportation. The adoption of this policy by the US PostalService, Royal Mail, and Hong Kong Post in densely populated urban areas has effectively eliminatedthe need for substantial investments in establishing static depots [75]. The concept of âcollaborativeconsumptionâ or âdistributed economyâ (e.g., Uber) entails the idea of sharing underutilized assets,such as car sharing, or ride pooling among individuals. This idea has the dual purpose of makingprofit and reducing ownership costs. In this context, Walmart has implemented the same-daydelivery policy by utilizing the assistance of in-store customers to deliver online orders on theirway home (i.e., in proximity to their residential areas) [76]. The adoption of such policies enablese-commerce stakeholders to expedite their service to customers.Beyond the mentioned policies, the concept of EDI holds a significant impact on the efficiencyof the last-mile delivery system, particularly on the availability of crowd-shippers. According tothe SET , factors such as demographic attributes, educational level, income, and occupation areidentified as the influential factors, determining individuals willingness to be engaged in last-miledelivery services (e.g., crowd-shipping). The interrelated connection between EDI and the avail-ability of crowd-shippers not only reinforce the crowd-shippers community but also guarantees theadaptability and responsiveness of the last-mile delivery system to the uncertain and dynamic en-vironment. Since the demographic attributes, income, educational level, and occupation have beenappeared as influential features based on the SET , supporting EDI is a strategic scheme in en-couraging individuals from diverse background to involve in crowd-shipping services. It ensures thecontribution of benefits, services, and support (inclusion) in an equitable environment (equity) forall crowd-shippers from diverse background (diversity), leading to improved participation, expandedcoverage, and persistent growth. In this study, I propose an IDSS designed for a last-mile deliverybusiness model, comprising four main modules: (i) In optimization module, a multi-stage stochasticdynamic risk-averse model is developed to effectively manage uncertainties associated with stochas-21tic pre-scheduled orders and availability of crowd-shippers, (ii) In simulation module, an IMASis utilized to estimate travel times based on dynamic traffic congestion and weather conditions,(iii) In RL module, an ORDAO is proposed to generate high-quality optimal routing policies asinitial solutions for the RL module, (iv) In SET-EDI module, an integrated approach, includinga deep learning and an ensemble model, is developed to identify the EDI features influencing thedelivery success rate. By leveraging the proposed IDSS , decision-makers can account for stochasticpre-scheduled orders and dynamic same-day orders when planning the last-mile deliveries.2.2 BackgroundThe last-mile delivery problem, as a main part of the delivery process, has received growingattention from e-commerce stakeholders due to the significant increase in online shopping [59]. Theâshared mobility serviceâ idea is by no means new, and the crowd-sourcing policy has inspiredboth e-commerce business owners and academia to explore various policies for the last-mile deliveryproblem. These policies include, strategic policies (e.g., stopping location of mobile depots), tacticalpolicies (e.g., order assignment and delivery planning), and operational policies (e.g., vehicle routing)[77, 78]. In this section, I review the existing research investigating last-mile delivery problems interms of innovative policies, EDI , and SET .2.2.1 Innovative PoliciesThe first innovative policy (i.e., hyper-local drivers or in-store customers), implemented byWalamrt in 2013, was investigated by [79]. A multi-start heuristic algorithm, combination of variableneighborhood search algorithm and Tabu search algorithm, was developed to solve the problem. [80]developed a stochastic optimization model that considers the availability probability of hyper-localdrivers. An extension of the [79]âs study was conducted by [81], enabling âmultiple deliveryâ policyfor hyper-local drivers. Based on this policy, hyper-local drivers were empowered to contribute toa bidding system by placing their bids for bundles of delivery services. They generated valuablebundles of customers using two developed heuristic algorithms. Later in 2017, a general last-miledelivery problem was studied by [82], taking into account time windows to explore two main policies.The first policy enables each hyper-local driver to deliver multiple packages, and the second policyâsplits deliveriesâ policy. The first policy was further examined by [83] using a combined machinelearning technique with variable neighbourhood search algorithm to identify the most promising22search areas. In a subsequent study in 2022, [84] developed a novel hybrid solution approach(i.e., including the variable neighbourhood search algorithm with the greedy randomized adoptivesearch) for the same policy. Similarly, two dynamic models and the rolling-horizon methodologywere applied by [85] to investigate the dynamic variant of the last-mile delivery problem. [86]developed a novel robust optimization model (i.e., including the robust routing policies, robustqueuing, and crowd-sourcing) to study the last-mile delivery problem, ensuring the timely deliveryof online orders. [87] developed a heuristic algorithms, to maximize the profit and the total numberof served orders for the integrated item-sharing and crowd-sourcing delivery problem.Mobile depots offer several advantages compared to static depots in terms of flexibility, costs,and delivery time. The mobile facility problem was introduced by [75] to model the mobile facilityrouting problem, specifically to address dynamic demand. Three heuristic algorithms were devel-oped to find high quality solutions for dynamic demands with high variance and maximize the totalnumber of served orders. Although there have been extensive well-studied investigations focusing onthe truck delivery with transshipment points, the literature on the mobile depot with crowd-sourcinghas relatively remained limited and scarce [88]. [89] pioneered the inclusion of transshipment pointsin the last-mile delivery problem with crowd-shippers. The proposed model integrated deliveryservices by different transportation modes (e.g., trucks and cyclists) from transshipment point (mo-bile depot) to customer zones. In [90]âs study, transshipment nodes were considered as automaticpickup and drop off nodes and a stochastic dynamic programming model was developed to optimizepackage deliveries. Their study was extended by [91] by incorporating the crowd-shippers and theirtime windows, enabling them to pickup customersâ packages from the main depot or transshipmentpoints and provide delivery services. The crowd-sourcing policy has been considered in the last-miledelivery problem where pickup and delivery locations of packages are predetermined. There havebeen limited studies focused on investigating the two-tier last-mile delivery problem with crowd-sourcing based on the traditional âtruck-only deliveryâ policy. [92] introduced a simplified two-tierlast-mile delivery problem with crowd-sourcing by integrating two policies (i.e., home delivery andout-of-home delivery). In the second policy, a drop off policy was followed by delivery vehicles (i.e.,dropping off packages at designated pickup locations), and customers were responsible for retrievingtheir packages from these locations. [91]âs study was extended by incorporating multiple deliveryoptions. They developed a mixed-integer linear programming model and employed the adaptiveneighbourhood search algorithm as a solution approach. In a similar study by [93], the secondpolicy (crowd-shippers) was integrated into the last-mile delivery problem. Accordingly, packages23were allocated to âpickup own packageâ located in proximity to the demand points.2.2.2 EDI and SET in the Proposed Last-Mile Delivery Business ModelIntegrating EDI into crowd-shipping services within the last-mile delivery system is crucial forcreating fair opportunities for people from various backgrounds to engage in these services. This re-quires investigating different demographic attributes, educational background, employment status,religious, tradition and culture, and perspectives. To gain a complete understanding of how the effi-ciency of the delivery process is related to the behavior of crowd shippers, it is essential to investigaterelevant theoretical concepts. Notably, SET [94] offers an opportunity to understand how individu-als engage in social activities by considering potential benefits and drawbacks [95]. [96] investigatedthe crowd-shippers participation motivations based on the SET for the last-mile delivery problem.They concluded that financial incentives, satisfaction, and confidence have the significant impactson the availability of crowd-shippers. Extrinsic incentives affecting âuser-generated contentâ onbusiness websites based on the voluntary crowd-shipping were examined by [97]. They developed aconceptual model for knowledge sharing in âuser-generated contentâ-based websites and concludedthat reciprocity, awareness of rewards, and prestige are the main extrinsic motivations for users toadd content. Extrinsic and intrinsic motivations in crowd-shipping services were studied by using adeveloped mediated moderation model by [98]. They found a negative correlation between extrinsicand intrinsic motivations, implying that the impact of intrinsic incentives is weak when the levelof extrinsic motivation is high. [99] examined the participation of individuals in crowd-shippingby focusing on behavioral factors and developing two models (i.e., a binary logit model and anordinary least-square regression model). [100] investigated the engagement of Indian in urban andsemi-urban areas in crowd-shipping services in the last-mile delivery network by adopting a frame-work that incorporates the mediating roles of âtrustâ and âattitudeâ. In another study, [101] studiedthe potential willingness of crowd-shippers to participate in crowd-shipping operations and incentivefactors for the sustainable last-mile delivery. They utilized both âGoogle Trends Analysisâ and asurvey to validate their respective theoretical model. The results indicated a positive and strongcorrelation between young age groups participation in crowd-shipping operations and factors suchas social interaction and trust. However, a negative significant correlation was observed betweenthe impact of monetary rewards on trust and young age groups participation in crowd-shippingoperations. The characteristics of crowd-shippers and their perceptions in involving crowd-shippingoperations were investigated by [102]. They analyzed narratives from 55 crowd-shippers signed up24on âAmazon Mechanical Turkâ by using causal mapping method. Personal necessities, occupationautonomy, task diversity, job significance, job instruction, and compensation were identified as sig-nificant factors in crowd-shipping operations based on demographic features, such as gender, agegroup, income, and education level. Similarly, an analysis was adopted by [101] to investigate thefactors affecting the participation of individuals in crowd-shipping operations. Their study con-sidered features such as gender, age, income, occupation, education, and participation period incrowd-shipping services. Their investigation revealed a positive and strong correlation between par-ticipation in crowd-shipping and factors such as monetary rewards and trust. However, they founda significant and negative correlation between enjoyment from previous work and participation incrowd-shipping. [103] studied different incentive factors that influence the continued involvement ofcrowd-shippers. In their theoretical model, four theories (i.e., expectancy theory, self-determinationtheory, organizational justice theory, and self-efficacy theory) were utilized to investigate the sus-tained participation of crowd-shippers in last-mile delivery services.25Table 2.1: The Most Relevant Research ReviewsStudies Order Theory Policies Solution Approach Weather ConditionScheduled Same-Day EDIâ Mobile Depot Crowd-shipping Hyper-Local Drivers Machine Learning Traffic[104] â â â â â â Traffic management system â[105] â â â â â â â[91] â â â â â â â[74] â â â â â â[106] â â â â â â â[107] â â â â â â â â[108] â â â â â â â[77] â â â â â â â[109] â â â â â â Simulation â â[58] â â â â â â[110] â â â â â â[111] â â â â â â â[112] â â â â â â â â[113] â â â â â â â[114] â â â â â â â â[115] â â â â â â â[116] â â â â â Traffic factor â[117] â â â â â â âCurrent study Social Exchange Theory Online Reinforcement-Driven Optimization Interactive Multi-Agent Simulation26As indicated in Table 2.1, unlike the few studies on last-mile delivery problems, particularly incrowd-shipping where drivers are contracted and paid a fixed rate, there hasnât been a comprehensiveanalysis of crowd-shipper availability. Furthermore, there is a lack of research investigating theinfluential EDI factors that affect the availability of crowd-shippers. The utilization of hyper-local driver policies and the associated reimbursement fee in a stochastic and dynamic environmenthas not been addressed in the last-mile delivery problem. Although some studies have considereduncertainty and utilized robust optimization or stochastic programming techniques to manage it,they have overlooked the dynamic nature of the problem (e.g., same-day deliveries, traffic congestion,and weather conditions). The literature review of RL approaches employed for sequential decision-making highlights the existence of an extensive huge solution space, resulting in slow convergenceand requiring high volume of training data. In addition, integrating an IMAS to estimate realtravel times based on dynamic traffic and weather conditions are rarely observed in the last-miledelivery problem.2.2.3 Aims and NoveltyIn this chapter the main aim is to design an IDSS for the e-commerce logistics resiliency con-sidering novel policies such as mobile depot, crowd-shippers, and hyper-local drivers. The aboveresearch gap highlights several potential areas for investigation. These areas encompass the simulta-neous investigation of two deliveries types (i.e., stochastic scheduled orders and dynamic same-daydeliveries), the study of the sequential decision-making process while accounting for spatiotemporalheterogeneity along with associated risks (incorporating CVaR), the implementation of innova-tive delivery policies, the utilization of influential EDI factors based on the SET attributes, andthe development of large-scale multi-stage stochastic dynamic models. These aspects serve as mo-tivation to develop an IDSS for the last-mile delivery problem, including four main modules ofrisk-averse multi-stage stochastic dynamic model, IMAS (traffic simulation, analytical simulationmodel), SET-EDI, and ORDAO . The main contributions of this study are as follows:â A risk-averse multi-stage stochastic dynamic programming model is developed for the pro-posed last-mile delivery business model, integrating three innovative policies. The risk-aversestochastic model is equipped to manage stochastic orders. Among these, pre-scheduled orders,crowd-shipper availability, and hyper-local drivers fall under stochastic category, while same-day delivery orders, traffic, and weather conditions are dynamic. Furthermore, an IMASmodule is developed to estimate travel times based on the real-time, real-location traffic, and27weather conditions.â The incorporation of the hyper-local driver policy into the proposed last-mile delivery businessmodel is accompanied by an investigation of the two-part reimbursement fee. The availabilityof crowd-shippers is estimated by developing a deep learning model, with a focus on extractingthe most influential EDI factors that affect individual willingness to participate in last-miledelivery. These factors are derived from the SET and include demographics attributes, such aseducational background, income, occupation, and overall reliability. Then, an ensemble modelembedded in SET-EDI module, including Ridge Regression, Support Vector Regression, andRandom Forest Regression, is developed to identify the most influential EDI features.â A hybrid approach, referred to ORDAO , is proposed to address sequential decision-makingwhile considering spatiotemporal homogeneity. This approach involves collaborative interac-tion between the RL module and the optimization module to effectively handle complexitiesposed by stochastic and dynamic nature of the last-mile delivery business model. In thisregard, the risk-averse multi-stage stochastic model generates preliminary policies for the RLmodule. Then, the initial policies are refined by the RL module based on the inherent uncer-tainty stemming from the dynamic or stochastic nature of the parameters. This collaborativeprocess leverages the strengths of both approaches: the risk-averse multi-stage stochasticmodelâs capability to provide robust preliminary solutions and the adaptability of the RLmodule in fine-tuning these policies to deal with uncertainty.The rest of this chapter is structured as follows: Section 2.3 presents the problem statement. InSection 2.4, the proposed IDSS is outlined. Numerical experiment, case study, and sensitivityanalysis are presented in Sections 2.5 and 2.6, respectively. Section 2.7 discusses the performanceevaluation, and managerial implications is discussed in Section 2.8. Finally, Section 2.9 concludesthe research.2.3 Problem DefinitionIn this case study, I focus on a stochastic dynamic last-mile delivery of offline (scheduled) andonline (same-day deliveries) orders, comprising three distinct stages. Offline orders refer to pre-scheduled orders that are known in advance before the working day. Such pre-scheduled orders areassigned to crowd-shippers for delivery. However, online orders are not pre-scheduled and are placedon the working day, requiring delivery within the same day. In this regard, the first stage investigates28the strategic placement of mobile depot to facilitate the delivery of orders. While the second andthird stages analyze the tactical and operational policies related to offline and online orders in termsof service coverage, delivery scheduling, and route planning. In this context, the mobile depotsare dispatched from main depot (central hub) to specific stopping locations, waiting for crowd-shippers to pick up and deliver offline orders. When delivery attempts fail, crowd-shippers reportthe unsuccessful deliveries to the mobile depot authority, leading to notifications being issued tocustomers. In reality, the success rate of deliveries, stemming from the availability of crowd-shippers,is uncertain. Due to last-minute schedule changes, crowd-shippers might decide not to participatein the deliveries. In such cases, same-day delivery orders are offered to those customers who arriveto collect their orders and are willing to serve as hyper-local drivers, within close proximity to theirdestinations. To support these hyper-local drivers, they are provided with reimbursement fee topartially offset their delivery costs.The first stage decisions are made, focusing on the strategic placement of the mobile depots,before any deliveries are carried out by crowd-shippers. In the second stage, decisions are madeto facilitate routing decisions based on the placement of the mobile depot. Finally, the decisionsin the third stage are linked to the provision of same-day delivery services by hyper-local drivers,stemming from the unsuccessful delivery attempts of crowd-shippers in the second stage. The secondand third stages involve the investigation of large number of routing decisions (i.e., all potentialpermutations of delivery sequence), posing a significant challenge. Same-day delivery orders areaffected by dynamic changes and require sequential decision-making in a dynamic and stochasticenvironment. It is notable that online orders are processed for the same-day delivery only if anavailable hyper-local driver is located in close proximity to the delivery destination. A strongcorrelation exists between the reimbursement fee policy and the acceptance rate of delivery amonghyper-local drivers. The integrated novel policies within the developed model serve as an incentivefor e-commerce business stakeholders to implement such policies, aiming to gain dominant marketshare with minimum delivery cost, CO2 emissions, and traffic congestion. Figure 2.1 provides abetter understanding about the problem. In the first decision epoch (kâ²0), the model deals with thestrategic decisions including strategic placement of mobile depot i, and decisions about fulfilling,postponing, and rejecting orders. The delivery operations (operational decisions) are started fromthe decision epoch (kâ²1). The prescheduled orders (j1, j2, and j4) are fulfilled by crowd-shipperk1 at decision epoch kâ²1, while order j3 is postponed and a new same-day delivery order is placed.There is a failed delivery j2 that poses dâ²j refusal costs to the system. In the last decision epoch29kâ²4, the customer j2 travels to the mobile depot location to collect her order that has been notified,and the mobile depot authorities offer same-day deliveries in the vicinity of his destination. Theoffer is accepted and same-day delivery orders j6 and j7 are serviced by hyper-local driver (j2 faileddelivery customer).Figure 2.1: Last-Mile Delivery Operations with Mobile Depot, Crowd-Shippers, and Hyper-LocalDrivers for Online and Offline Orders for for E-commerce Logistics ApplicationsThe research conducted by [74] closely aligns with our study, as they investigated the chal-lenges of last-mile deliveries by incorporating crowd-shipping and mobile depot operations. Theydeveloped a sample average approximation algorithm to solve a risk-averse two-stage stochasticmodel. However, this study distinguishes itself in various significant aspects. Firstly, a hyper-localdriver policy is incorporated into the proposed last-mile delivery business model and a two-partreimbursement scheme is investigated. Secondly, the availability of crowd-shippers is estimated bydeveloping a deep learning model, with EDI features extracted from the SET incorporated into thenetwork. Furthermore, an ensemble model, including Ridge Regression, Support Vector Regression,and Random Forest Regression, is developed to identify the most impactful EDI features. Thirdly,30this study proposes a hybrid approach (i.e., ORDAO) to deal with stochastic pre-scheduled ordersand dynamic factors (e.g., same-day delivery, traffic, and weather conditions). This approach takesinto account spatiotemporal homogeneity to make decisions sequentially. Finally, an IMAS mod-ule is developed to estimate travel times based on the real-time, real-location traffic and weatherconditions.2.4 Intelligent Decision Support SystemThe overreaching objective of this dissertation is to develop an IDSS for the last-mile deliveryproblem, including four main modules of risk-averse multi-stage stochastic dynamic model, IMAS(traffic simulation, analytical simulation model), SET-EDI, and ORDAO . In Module I, an IMASsimulation model is developed to estimate travel times based on the real-time, real-location traffic,and weather conditions. The incorporation of the hyper-local driver policy into the proposed last-mile delivery business model is accompanied by an investigation of the two-part reimbursement fee.The availability of crowd-shippers is estimated by developing a deep learning model (Module II),with a focus on extracting the most influential EDI factors that affect individual willingness toparticipate in last-mile delivery. These factors are derived from the SET and include demographicsattributes, such as educational background, income, occupation, and overall reliability. Then, anensemble model embedded in SET-EDI module, including Ridge Regression, Support Vector Re-gression, and Random Forest Regression, is developed to identify the most influential EDI features.In Module III, a risk-averse multi-stage stochastic dynamic programming model is developed for theproposed last-mile delivery business model, integrating three innovative policies. The risk-aversestochastic model is equipped to manage stochastic orders. Among these, pre-scheduled orders,crowd-shipper availability, and hyper-local drivers fall under stochastic category, while same-daydelivery orders, traffic, and weather conditions are dynamic. Module Iv deals with the developmentof a hybrid approach, referred to ORDAO , is proposed to address sequential decision-making whileconsidering spatiotemporal homogeneity. This approach involves collaborative interaction betweenthe RL module and the optimization module to effectively handle complexities posed by stochas-tic and dynamic nature of the last-mile delivery business model. In this regard, the risk-aversemulti-stage stochastic model generates preliminary policies for the RL module. Then, the initialpolicies are refined by the RL module based on the inherent uncertainty stemming from the dy-namic or stochastic nature of the parameters. This collaborative process leverages the strengths of31both approaches: the risk-averse multi-stage stochastic modelâs capability to provide robust pre-liminary solutions and the adaptability of the RL module in fine-tuning these policies to deal withuncertainty. Figure 2.2 provides a better understanding of the proposed IDSS .Figure 2.2: The Proposed Intelligent Decision Support SystemThe core question of this chapter is: How a resilient and intelligent decision support system canbe designed that ensures reliable last-mile delivery by dynamically adapting to changing conditionssuch as traffic, weather, and the availability of human delivery agents?The choice of an interactive simulation framework, comprising both a data-driven interactivesimulator and an analytical multi-agent simulator, enables detailed modeling of agent behaviors andenvironmental interactions over time. This module provides valuable insights into travel times anddelivery scheduling under varying scenarios, supporting the need for a simulation-based evaluationof operational feasibility in highly dynamic contexts. A traditional static model (e.g., linear pro-gramming) would be inadequate for this, as it cannot capture the behavioral interactions among32agents or temporal fluctuations. The choice of a hybrid interactive-analytical simulator allows forboth exploratory (what-if) analysis and structured evaluation of delivery schedules, enabling moreinformed decision-making. Simulation was selected over discrete-event or system dynamics modelsbecause it offers greater flexibility in modeling agent-specific behavior and decentralized decision-making. An integrated ensemble learning model is used to identify the most important predictors ofparticipation, leveraging methods such asRR, SVR, andRFR. These models were chosen for theircomplementary strengths: Ridge is robust to multicollinearity, SVR handles high-dimensionalityand non-linearity, and RR captures interactions and nonlinearities while being less prone to overfit-ting. Simpler models such as linear regression were rejected due to their inability to handle complexfeature interactions, while more complex models were excluded due to interpretability concerns atthis exploratory stage. The second part of the module uses a deep learning model to forecastavailability patterns using socio-economic and behavioral features. Deep learning was chosen herebecause it excels in learning intricate, nonlinear dependencies from high-dimensional, unstructureddatasets especially when behavioral data is involved. While classical machine learning models couldalso offer predictions, they often require more feature engineering and struggle with generalizationin data-rich contexts. Hence, deep learning provides a more scalable and adaptive solution for be-havioral modeling. A risk-averse framework is preferred over risk-neutral models because it accountsfor extreme outcomes (e.g., delivery failures or driver shortages), aligning better with the resiliencegoals of the study. Deterministic models were not considered suitable, as they ignore the variabil-ity and randomness intrinsic to urban logistics. Reinforcement learning was selected because it isuniquely capable of learning optimal policies in sequential decision environments with delayed feed-back. Unlike supervised learningâwhich requires labeled datasetsâor optimization modelsâwhichrequire prior knowledge of all system parameters, RL allows the system to learn by interactingwith its environment over time. Classical approaches like Q-learning or SARSA were not suitabledue to their inefficiency in high-dimensional, continuous action spaces. Instead, a more scalableand accelerated RL framework is used to ensure timely policy updates and convergence. Heuristicsearch or rule-based systems were not adopted due to their rigidity and inability to generalize acrosschanging real-world scenarios.The selection of each model is guided by the nature of the data, the complexity of the sub-problem, and the need for dynamic adaptability and risk-aware decision-making. Collectively, thesystem responds to the core research question by demonstrating how a modular, learning-based,and resilient optimization framework can significantly improve the reliability and efficiency of last-33mile logistics. Therefore, each model was selected not in isolation, but as part of a unified strategyto address the intricacies of last-mile delivery under uncertainty. Models were chosen for theirability to integrate with real-time data, support learning and adaptation, and accommodate riskand human behavior. Alternative methods were considered but dismissed if they lacked flexibility,interpretability, computational efficiency, or the ability to generalize across complex operationalsettings.2.4.1 Online Reinforcement-Driven Adaptive OptimizationE-commerce last-mile delivery business models are undergoing a paradigm shift in terms ofreal-time decision-making. The challenges in last-mile delivery highlight the need for frequentupdates for routing decisions, and in some cases, even the need for re-scheduling. Such sequentialdecision-making processes can be modeled using various strategies in MDP . One of these solutionapproaches involves incorporating a safety buffer or applying a penalty term to prevent the makingmyopic decisions (i.e., prioritizing short-term benefits without adequately considering the potentiallong-term consequences) [118]. Although such methodologies can replicate future details, theyhave the potential to be computationally demanding and may deviate from real-world instances, asthe scenario horizon extends longer [119]. To address these inefficiencies, RL methods have beenintroduced. An example of these methods is policy-gradient techniques, which focus on exploring anoptimal policy rather than engaging with the value function [120]. A hybrid approach integratinga machine learning method and an exact algorithm (i.e., column generation) was proposed by [121]to address the crew-pairing problem. The probability of selecting each arc was estimated using adeep neural network to enhance the computational efficiency of finding near optimal solutions. [122]investigated the crew scheduling problem integrated with the vehicle routing problem by utilizinga column generation-based binary classification model. In the study conducted by [123], a selectionapproach using binary classification was applied to identify arcs with a higher chance of beingincluded in the optimal solution. [124] focused on the application of machine learning techniques toinvestigate human pickup behaviour at depot. Their main objective was to forecast the processingtime of orders based on the historical data. A solution framework including a set partitioning modeland the branch and price algorithm was developed to solve the problem. Moreover, [125] developed anovel RL solution approach to solve the last-mile delivery problem considering crowd-sourcing withthe same settings as the study conducted by [86]. An actor-critic solution framework (i.e., a policy-based RL method) was developed by [126] for the last-mile delivery problem. This framework34enabled customers to pick up their packages, considering dynamic orders. In this research, theobjective was to identify the optimal policy for a single vehicle and then extend this policy to allvehicles involved in the delivery process.2.4.2 Markov Decision ProcessIn this study, the stochastic dynamic last-mile delivery problem is investigated by consideringthree integrated innovative policies, which are modeled as an MDP . The problem is framed as asequential decision-making process including a sequence of states linked by actions, policies, rewardsor penalties, and transitions. The set of decision points is defined by kâ² â K â², representing timewhen decisions are made. At each decision point kâ², the recourse model executes an optimal actionrelating to the first stage decision, and revealed state. This state represents the dynamic onlineorders, the availability of crowd-shippers and hyper-local drivers. The model receives a reward orpenalty as a result of decisions and scenario realization. A new state is defined as a transitionbetween decision points. The episode is characterized by occurring a group of decision points,and the total return is defined as the cumulative sum of all rewards in each episode. The maincomponents of the MDP is given as follows:â Decision point : A decision point is activated by the placement of a new order, resulting in anew scenario realization and subsequently, a vehicle routing problem.â States: A state is defined by a realized scenario just before decision point kâ². Each state isrepresented as a tuple including the time of decision point kâ², the number of available crowd-shippers and hyper-local drivers, planned routes, the set of failed deliveries, and orders (onlineand offline).â Actions: Action akâ²at decision point kâ² includes both tactical decisions (i.e., orders as-signments to crowd-shippers and hyper-local drivers) and operational decisions (i.e., crowd-shippers and hyper-local drivers routing decisions). These decisions are made by solving themulti-stage stochastic dynamic model. In addition, the acceptance of a placed order and itsassignment to either a crowd-shipper or a hyper-local driver is defined as an action at decisionpoint kâ². This is performed by utilizing ϵ-soft policy defined by the second and third stagedecisions of the recourse model.â Reward function: The reward function estimates the impact of an action on the objective func-tion value. The reward function is highly correlated to the recourse model decision variablesand state (scenario) since each action is tied to a multi-stage stochastic dynamic programming35model. The reward function accounts for the crowd-shippers delivery compensation fee andhyper-local drivers reimbursement fee , contributing to the objective function of the recoursemodel.â Transition: Transitions happen as a result of a scenario realization (i.e., stochastic offline anddynamic online orders). The transition between states is associated with the spatiotemporalcorrelation between scenarios. The Monte Carlo simulation is implemented to simulate thevalue function of the MDP model through scenarios.â Episode: An episode is defined as a day at mobile depots comprisingK â² time steps (K â² decisionpoints), generating scenarios and actions occurring throughout the day.The ORDAO involves a joint interaction between the RL module and the risk-averse multi-stage stochastic dynamic module to provide optimal delivery policies in a stochastic dynamic envi-ronment. The risk-averse multi-stage stochastic dynamic module plays a crucial role by recurrentlygenerating initial policies for the RL module. The generated policies consistently originate fromthe risk-averse multi-stage stochastic dynamic module, which is efficiently capable of making strate-gic, tactical, and operational decisions with respect to constraints and objective. The RL modulederives the generated initial policies and refines them based on the dynamic same-day deliveries,traffic congestion, and weather conditions requiring spatiotemporal sequential decision-making. Thegenerated policies can vary from high-quality policies to feasible policies based on the risk-aversemulti-stage stochastic dynamic module properties. The RL module refines the policies generatedby the risk-averse multi-stage stochastic dynamic module. This refinement is necessary as therisk-averse multi-stage stochastic dynamic module is unable to deal with a dynamic environment.Therefore, these policies are improved through interactions with the dynamic environment over time.The refined policies are subsequently evaluated by the risk-averse multi-stage stochastic dynamicmodule to ensure their alignment with constraints. This joint interaction highlights the strengthsof both modules, (i.e., the RL module and the risk-averse multi-stage stochastic dynamic module).Algorithm 1 provides a detailed explanation about the main steps of the proposed ORDAOalgorithm. First, it creates an initial state (decision point kâ² = 0) with stopping location of mobiledepot (at central hub), crowd-shippers, hyper-local drivers drivers, planned routes (empty set),and stochastic offline and dynamic online orders. Then, the algorithm decides to take an action(i.e., accept, reject, or postpone an order) based on the availability of crowd-shippers, hyper-localdrivers, traffic congestion, weather condition, and associated costs for each action types. For theaccepted orders (either online or offline), it assigns them to the available crowd-shippers or hyper-36local drivers considering the defined factors and updates the availability of crowd-shippers andhyper-local drivers.The total distance covered by each vehicle (crowd-shipper or hyper-local driver)is calculated based on their assigned orders to estimate the compensation fee for crowd-shipper andreimbursement fee for hyper-local drivers.The reward function, calculates the reward for current state sâ². The reward function Râ² isdefined as an utility function including acceptance-based reward, lost reward due to the rejection,lost reward due to postponement. It takes parameters such as acceptance, rejection, delivery,reimbursement, postponement, and rejection costs, along with the current state and a parameterK â².The acceptance-based reward utility function iterates through the planned routes, which representsthe routes assigned to different vehicles (crowd-shipper or hyper-local driver). For each route, itchecks the action type of the corresponding vehicle. If the vehicle is a crowd shipper, it increasesthe regular delivery profit. If the vehicle is a hyper-local driver driver, it increases the same-daydelivery reward. In rejection based reward utility function, similar to the acceptance-based reward,the function iterates through planned routes and for each route, it checks the action type of thecorresponding vehicle. If the vehicle is a hyper-local driver, it decrements lost reward of rejectionby a hyper-local driver. If the vehicle is a crowd-shipper, it decreases the lost reward of rejection bya crowd-shipper. Finally, delivery cost function, decreases the delivery costs from the total profitof the network. The defined utility function as the reward function in the proposed ORDAOcombines these components to provide a comprehensive measure of the reward for a given state.Iterations over decision points shows how the agent evolves over multiple decision points andupdates the state, assigns orders, and calculates rewards for each iteration. In each decision point,offline orders are added to the system stochasticly (i.e., N(J), the total number of stochastic offlineorders) and online orders are entered to the system dynamically (N(J â²), the total number of onlineorders) using the Bionomial distribution with success delivery probability 0.65 (see Section 2.4.5.1).In summary, the proposed algorithm simulates a real-word agent with crowd-shippers, hyper-localdrivers, and stochastic offline and dynamic online orders. The reward function considers variouscosts and factors related to the acceptance, rejection, and utility of orders. The delivery cost andtour distances are also considered in the overall analysis of the system.37Algorithm 1 Online Reinforcement-Driven Adaptive OptimizationInputs : J Set of regular deliveries;J â² Set of same-day deliveries;K â² Set of decision points;K Set of crowd-shippers;K â²â² Set of hyper-local drivers;Parameters: dj Order postponement cost;dâ²j Order cancellation cost;câ²ijk Crowd-shipper compensation fee;fj Hyper-local drivers reimbursement fee;Outputs : Qâ, RâGenerating Initial Policies: Optimization module (multi-stage risk-averse stochastic model)Solve risk-averse model;Save the initial action (Xi, Wj , Wâ²j , Yij , Sijk, Pj);Initialization:kâ² = 0, sâ² {â}, N(J) = 0, N(J â²) = 0, Ï = {â}, Râ² = 0, aâ²kâ²=0 = 0, aâ²kâ²=1 = Xi, Wj , W â²j , Yij , Sijk, Pjfor kâ² = 1 : K â² do(N(Jâ²)+N(J)N(Jâ²))pN(J)(1â p)N(Jâ²);while |Ïkâ²+1 â Ïkâ² | < δ or |Râ²kâ²+1 âRâ²kâ² | < δ doUpdate sâ² + 1;Taking strategic action (aâ² = Xi);Taking tactical actions (aâ² =Wj , W â²j , Yij);Taking operational decisions (aâ² = Sijk, Pj);Calculate Râ²;Update sâ², N(J), N(J â²), Ï, Râ², aâ²;Refined aâ²;Update sâ², N(J), N(J â²), Ï, Râ², aâ² based on the refined action aâ²refined;endCheck the feasibility of the refined action aâ² using the optimization module;if Ï is feasible thenif Râ²aâ² â¤Râ²aâ²refinedthenChoose aâ²refinedelsekâ² = kâ² + 1endelsekâ² = kâ² + 1endendIn general, theORDAO module provides a comprehensive framework to solve complex problemsby combining the robustness of the risk-averse multi-stage stochastic dynamic module with theadaptability of the RL module. The optimal solution is characterized by an optimal policy Ïâ thatdecides whether to serve (i.e., postpone or cancel) order. The policy assigns the tasks to an availablecrowd-shipper or a hyper-local driver if the decision is to proceed, aiming to maximize the totalexpected rewards. Since the proposed ORDAO module involves iterative updates or learning, it isrequired to demonstrate that, the ORDAO module converges to an optimal policy (i.e., the refinedpolicies are optimal). Proposition 2.1 proves the convergence of the proposed ORDAO .38Proposition 2.1. For a given policy iteration Step kâ², letâs Qâ²Ïkâ² be the Q-values associated withthe policy Ïkâ². If the exploration-exploitation trade-off is balanced, considering 0 < Î±â² â¤ 1 (learningrate), and the environment dynamics are Markovian, then the Qâ²Ïkâ² converge to Qâ, (i.e., the optimalQ-values).Proof. Letâs Ïinit be the set of initial provided actions by the optimization module, Ïref be the re-fined action obtained through reinforcement learning, and Qâ²Ï represent the Q-values associated withpolicy Ï. The learning rate Î±â² used in updating Q-values is constant and exploration-exploitationtrade-off is maintained based on the epsilon-greedy strategy. The environment dynamics showMarkovian behavior, with the transition probabilities following specific regularity conditions.First, I start by initializing the Q-values arbitrarily or setting them to zero (Set kâ² = 0). Thenpolicy evaluation is implemented to update Qâ²Ïkâ² using Bellman equation, following by policy im-provement to find a new policy Ïkâ²+1. Then, next step is to increase kâ². The mathematical inductionis used to show that Qâ²Ïkâ² improves over iterations, and the Limit Theorem (i.e., Banach Fixed-Pointtheorem) is used to demonstrate the existence of a fixed point. Based on this theorem, (Ï, β) isa complete metric space, where Ï and β represent the set of Qâ²-value functions and the metric,respectively (T â² : Ï â Ï is a contracting mapping). Therefore, T â² has a fixed point in Ï. Toshow convergence, it is required to ensure that the learning rate Î±â² is appropriately chosen (i.e.,Robbins-Monro condition [127]). According to the Robbins-Monro condition,ââkâ²=0 Î±â²kâ² = â andââkâ²=0(Î±â²kâ²)2 <â, the learning rate is large enough to explore the entire state space while diminish-ing over time. Therefore, under the specified mentioned assumptions and Robbins-Monro condition,Qâ²Ïkâ² converges to the fixed point Qâ.Proposition 2.2. For any policy Ï generated by the ORDAO, P â²Ï (i.e., performance metrics)maintains certain desirable properties defined by the MDP and risk-averse stochastic mode underuncertainties (i.e., dynamic same-day deliveries, stochastic offline deliveries, traffic congestion, andweather conditions).Proof. Letâs P â²Ï shows the performance metric associated with policy Ï such as expected rewardand satisfaction of constraints, and U â² demonstrates the set of uncertainties in the environment.The desirable properties to evaluate the robustness of the generated policies are defined as follows:Stability: A policy is considered stable if small perturbations Ïµâ² in the environment or input con-ditions do not lead to drastic changes in the systemâs behavior (i.e., less than meaningful threshold39of Î´â²).â Ïµâ² > 0, â Î´â² > 0, |P â²Ï+Ïµâ² â P â²Ï < Î´â²| (2.1)Optimality: An optimal policy maximizes the expected rewards or minimizes the expected costsover the long-term. In this study, a utility function Râ² is defined based on the delivery costs, post-ponement costs, order cancellation costs, compensation fee for crowd-shippers, and reimbursementfee for hyper-local drivers.Ïâ =Ï E[Râ²Ï ] (2.2)Constraint Satisfaction: A policy satisfies constraints if it adheres to specified requirements,ensuring the system operates within acceptable bounds. In this study, the limitations are definedin the proposed ORDAO and are checked by risk-averse stochastic model. The ð­ is a constraintfunction that depends on the system state sâ²kâ² and policy Ï.âkâ²,ð­(sâ²kâ² , Ï) â¤ 0 (2.3)Consistency: A consistent policy yields similar outcomes for similar situations, ensuring reli-ability and predictability. For s1 and s2 with similar environment (s1, s2), where (.) defines thesimilarity between states, the following equation:P â²Ï(s1) â P â²Ï(s2) (2.4)The Bellman optimality equation, is a powerful tool in the policy generation process in MDPs.The process involves iteratively updating the value functions until convergence, where the optimalpolicy and corresponding value functions are obtained. In the following, Proposition 2.4 proves thatthe policies generated by the ORDAO module satisfy the formulated robustness criteria-stability(Equations (2.1), (2.3), and (2.4)), Proposition 2.3. Additionally, Proposition 2.4 proves that the40policies generated by the ORDAO module satisfy the formulated robustness criteria-optimality(Equation (2.2)).Proposition 2.3. The policies generated by the ORDAO module satisfy the formulated robustnesscriteria defined by Equations (2.1) to (2.4).Proof. Letâs V â²sâ² denotes the state value function, and â(vâ²) shows the deviation in stability. Itshould be proved that â(vâ²) remains bounded under different scenarios. The Lyapunov stabilityanalysis is used to prove the stability (i.e., the policies generated by theORDAO module satisfy theformulated robustness criteria). The Lyapunov function W â²sâ² is selected such that Wâ²sâ² > 0 âsâ² Ì¸= 0and W â²(0) = 0. The derivative of the W â² should be negative semi-definite. Letâs V â²sâ² = Wâ²sâ² ,this choice aligns with stability analysis in ORDAO , where value function serves as a candidatefor Lyapunov functions. The derivative of W â² is as follows: dWâ²dt =dV â²dt . To prove that Wâ² isnegative semi-definite, I need to show that W â² â¤ 0 for all sâ², and W â² = 0 only when sâ² is at anequilibrium point. Assume that W â²(sâ²) is a continuously differentiable function defined over thestate space sâ², and it satisfies W â²(sâ²) â¥ 0 for all sâ². According to the Lyapunov function properties,W â²(sâ²) decreases or remains constant along the trajectories of the system. In mathematical terms,W â²(sâ²) â¤ 0 demonstrates its negative semi-definiteness. Furthermore, it should be proved thatW â²(0) = 0 when sâ² is an equilibrium point. Typically, the equilibrium points of a dynamical systemare characterized by the condition when W â²(0) = 0. Moreover, according to the Lyapunov theorem(i.e., if a Lyapunov function V â²(sâ²) exists in the neighbourhood U of the zero solution sâ² = 0 for anautonomous system, then the systemâs equilibrium point sâ² is Lyapunov stable.Finally, according to the Lyapunov direct method LDM , â(vâ²) which is proportional to W â²(sâ²)is bounded, demonstrating that W â²(sâ²) is bounded for all sâ². This guarantees the stability of thesystem.Proposition 2.4. The policies generated by the ORDAO module satisfy the robustness criteriaoptimality as defined by Equation (2.2).Proof. Letâs J â²(Ï) be the expected cumulative reward, and maxÏJ(Ï) be the optimality metric. Itshould be proved that the generated policies i) converge toward Jâ under uncertainty, and ii) thesystem achieves the optimal policy. In Proposition 2.1, it is proved that the generated policies underthe specified assumptions and Robbins-Monro condition, converge towards the optimal policy.412.4.3 Optimization ModuleThe proposed last-mile delivery model, including the mobile depot location problem and theorder assignment problem to crowd-shippers and hyper-local drivers, is formulated as a multi-stage stochastic dynamic model. The delivery success rate (i.e., availability of crowd-shipper) isstochastic and modeled as a random vector α = (α1, ..., αk) where αk represents the availability ofcrowd-shipper k. The first stage decisions, denoted by binary variables Xi, Wj , and Yij , determinethe optimal location of mobile depots, the allocation of packages to mobile depots, and the choiceof whether to postpone the placed order, respectively. Such deterministic decisions are made priorto the scenario realization (i.e., the availability of crowd-shippers). The subsequent stage decisions,represented by Pj , Sijk, and Wâ²j , are made after scenario realization, implying the offline andonline order assignments to crowd-shippers and hyper-local drivers, respectively. The multi-stagestochastic dynamic integer programming model is defined as follows:The following assumptions are considered in the model:â Stochastic uncertainty of offline orders and dynamic uncertainty of online orders.â Traffic and weather are modeled as real-time, real-location data, assuming the availabilityof accurate and up-to-date information from external sources (e.g., traffic APIs or weatherforecasts).42Table 2.2: Nomenclature Specific to Models in This ChapterIndices & SetsI Set of potential stopping locations for the mobile depotJ Set of ordersK Set of crowd-shippersi Index of potential stopping locations for the mobile depot i â {1, 2, ...,I }j Index of orders j â {1, 2, ...,J }k Index of crowd-shippers k â {1, 2, ...,K }Parametersci The placement cost of a mobile depot to an optimal location icâ²ijk The order jâs delivery cost by crowd-shipper k through mobile depot idj The cost of postponing order jdâ²j The order jâs delivery refusal costE The mobile depot capacityfj The reimbursement fee of hyper-local drivers for order jrk The availability of crowd-shipper k in the morning or eveningrâ²i The operation window of mobile depot at location i in the morning or eveningαk The availability of crowd-shipper kζj The hyper-local driver acceptance rate for order jDecision VariablesPj Binary variable, equals 1 if order jâs delivery is failed, otherwise 0.Sijk Binary variable, equals 1 if order jâs assigned to mobile depot i is successful by crowd-shipper kWj Binary variable, equals 1 if order jâs delivery is postponed, otherwise 0.W â²j Binary variable, equals 1 if order j is serviced by a hyper-local driver, otherwise 0.Xi Binary variable, equals 1 if mobile depot i is positioned in location i, otherwise 0.Yij Binary variable, equals 1 if order j is assigned to mobile depot i, otherwise 0.Min Z =F (X) + Eα[Q(W,Y, α) + EÎ±[Qâ²(W â², α)]](2.5)Subject to:Yij â¤ Xi âi â I , j âJ (2.6)âiâIYij +Wj = 1 âj âJ (2.7)âjâJYij â¤ E âi â I (2.8)The first-stage cost function Z = F (X) is defined as:43Min F (X) =âiâIXici (2.9)The second and third stage cost functions are defined as:Min Q(W,Y, α) =âjâJWjdj +âiâIâjâJâkâKcâ²ijkSijk +âjâJPjdâ²j (2.10)Min Qâ²(W â², α) =âjâJfjWâ²j (2.11)Subject to:âiâIâjâJSijk â¤ αk âk â K (2.12)âiâIâkâKSijk + Pj = 1âWj âj âJ (2.13)âkâKSijk â¤ Yij âi â I , j âJ (2.14)Sijk = 0 âj âJ , (i, k) â I ÃK , rk Ì¸= râ²i (2.15)W â²j +âiâIâkâKSijk â¥ ζj âj âJ (2.16)W â²j +âiâIâkâKSijk â¤ 1 âj âJ (2.17)W â²j â¤ ζj âj âJ (2.18)âiâIâkâKSijk â¤ αk âj âJ (2.19)Pj ,Wj ,Wâ²j â [0, 1] âj âJ (2.20)Xi â [0, 1] âi â I (2.21)Sijk â [0, 1] âi â I , j âJ , k â K (2.22)Yi,j â [0, 1] âi â I , j âJ (2.23)The first-stage objective function (Equation (2.9)) aims to minimize operational cost of themobile depot such as parking and fuel expenses. The second-stage objective (Equation (2.10))44aims to minimize penalty cost for order delay, the crowd-shipper delivery cost (i.e., compensationfor crowd-shippers), and the penalty cost for failed deliveries. The third-stage objective function(Equation (2.10)) aims to minimize the reimbursement fee for hyper-local drivers. Constraint (2.6)guarantees that processed orders are only allocated to dispatched mobile depots. Constraint (2.7)determines whether to allocate a order j to a mobile depot i or to postpone to a different day.Constraint (2.8) ensures that the maximum number of assigned orders to mobile depot i does notexceed its capacity. Constraint (2.12) guarantees that the order j is only allocated to availablecrowd-shippers. Constraint (2.13) ensures the assignment of order j to available crowd-shippersand keeps a record of failed deliveries. Constraint (2.14) implies that order j is not delivered bycrowd-shipper k unless mobile depot i is sent to the optimal location. Two operational time framesare defined; one for the morning and one for the evening. Such time frames integrate the temporalmovement behaviour patterns of crowd-shippers (e.g., rush hours) and the active operating timeframe of mobile depots. Constraint (2.15) explains that in case of failed deliveries, there is nooption to drop-off packages beyond the defined operating hours. Constraint (2.16) characterizesorder j delivered by crowd-shippers as scheduled orders and those delivered by hyper-local driversas same-day delivery orders. Constraint (2.17) guarantees that order j is assigned to a hyper-localdriver only when it is the same-day delivery order (ζj = 1). Constraints (2.18) and (2.19) ensurethat customer j is not served by a hyper-local driver and crowd-shipper k if ζj = 0 and αk = 0,respectively. Constraints (2.20) to (2.23) are binary variables.2.4.3.1 Risk-Averse ModelThe delivery operations of the stochastic dynamic last-mile delivery problem are subject to sub-stantial penalties for failed and postponed deliveries. The proposed risk-neutral model exclusivelyemphasizes on minimizing the expected penalty. The risk-neutral model performs well when thespecifications of the last-mile delivery network (e.g., the availability of crowd-shippers and hyper-local drivers, offline and online orders) experience negligible perturbations and remain relativelystable. Nonetheless, in real-world cases, the customer location, the availability of crowd-shippers,and hyper-local drivers vary from day to day (e.g., holiday season). Accordingly, the risk-neutralmodel may not perform efficiently in some specific scenarios. The risk of the worst-case scenarioscan be mitigated by incorporating risk measures such as VaR, CVaR, and TVaR. In this section,the CVaR is incorporated into the risk-neutral multi-stage stochastic dynamic model to extend itto a risk-averse setting.45Min Z =F (X,W ) + (1â λ)Eα[Q(W,Y, α)]+ λ CV aRÏ[Q(W,Y, α)](2.24)Subject to:Equations (2.6) to (2.23) (2.25)Where CV aRÏ demonstrates the CVaR at a confidence level Ï, which defines a threshold for100(1â Ï)% of the worst scenarios, and λ denotes the non-negative coefficient risk part.2.4.4 Interactive Multi-Agent Simulation ModuleIn this section, a novel IMAS model is developed to integrate the dynamic traffic and weatherpatterns into the last-mile delivery network. The IMAS is capable of modeling complex systems,including several independent entities (agents). Each agent is characterized by its unique behaviourand decision-making proficiency [128]. The uncertainty of the dynamic traffic and weather pat-terns give rise to significant barriers during the last-mile delivery phase. The congested traffic andadverse weather pose substantial challenges to the last-mile delivery network, resulting in deliv-ery delays, escalated network costs, drop in market share, increased fuel consumption, and CO2emissions, and customer dissatisfaction. These challenges drive the incorporation of dynamic trafficand weather patterns into the IMAS to deal with such complexities in last-mile delivery networks.The developed model aims to provide e-commerce business stakeholders with a systematic approachto evaluate various delivery policies, resembling real-world scenarios, and identifying potential im-provements.In the developed IMAS , each agent demonstrates a delivery driver (i.e., crowd-shippers andhyper-local drivers), equipped with the travel time adjustment mechanism to deal with real-timetraffic status. The impacts of weather conditions on the travel time (i.e., delivery vehicles speed)and, accordingly, the last-mile delivery network are assessed by integrating weather patterns intothe simulation model. The developed IMAS simulates last-mile delivery operations over multipletime steps, generating various real-world scenarios to evaluate the overall efficiency of the last-miledelivery network under dynamic traffic and weather patterns. This analysis includes assessing theaverage speed or travel time of vehicles, the success rate of deliveries, the total delivery cost, andthe total number of failed deliveries. The simulation results are compared to the baseline scenariowithout incorporating the dynamic traffic and weather patterns. This highlights the importance of46incorporating real-time traffic and weather patterns on the last-mile delivery problem.The simulation is started by generating a set of virtual crowd-shippers with a distinct identifier(agents). These delivery agents are capable of making decisions independently based on the dynamicenvironment and predefined policies. Each agent is able to fulfill an order from a list of placed ordersand estimate the travel time by considering the real-time traffic and weather patterns. The Haversineformula is employed to estimate the travel distance based on the geospatial coordinates of locationsby taking into account the real-time traffic and weather patterns. A MultiGrid, as a geospatial datastructure, is utilized to demonstrate a grid-like world, aiming to model the actual environment andsimplify the agent mobility. The MultiGrid is capable of managing the locations of crowd-shippersand customers within the physical environment. It facilitates navigation of crowd-shippers acrossthe grid and simulates their mobility behaviour through the landscape. In each simulation epoch,crowd-shippers sequentially make decisions about their next trip based on their real-time locationand predetermined policies (network constraint). Therefore, the developed IMAS simulates traveltimes for each crowd-shipper in a dynamic environment. Simulated travel times are analyzed toevaluate the overall performance of the last-mile delivery network under different real-time trafficand weather pattern scenarios. This analysis aims to identify urban zones with lengthy travel times(delivery time) due to heavy traffic congestion, facilitating efficient delivery scheduling to minimizedelivery time and costs (e.g., compensation and fuel costs). In addition, it supports to identifypotential bottlenecks, enabling courier companies to avoid delays, improve on-time deliveries, andauthorize flexible scheduling in response to the uncertainty. The analysis of simulated travel timealso provides benefits in terms of resource management (i.e., delivery vehicles and drivers), high-levelcustomer services, and reduced environmental impacts.2.4.5 EDI -SETAccording to the reviewed literature, the investigation of factors such as demographics andeducational factors, income, and overall reliability in crowd-shippers willingness to participate inlast-mile delivery services are still scarce. Such factors are emphasised in the SET , interpreting thecrowd-shippers behaviour regarding their willingness to participate in crowd-shipping. Therefore,these features are extracted, and the availability of crowd-shippers is estimated using a developedneural network model. Then, importance feature analysis is performed to identify the most impactfulfeatures.472.4.5.1 Crowd-Shippers Success Rate of DeliveryThis section estimates the delivery success rate using a neural network and investigates its im-pacts on the delivery network capacity, traffic congestion, customer service level, and CO2 emissions.The dataset includes samples with different features, such as âAge groupâ, âGenderâ, âIncomeâ, âEdu-cational Levelâ, âOccupationâ, and âProfileâ [101, 102]. According to the 2021 Canada census report,the population of males and females within the age groups [16-20], [20-24], [25-29], and [30-35] havebeen recorded as 2,091 males and 1,964 females, 93,740 males and 91,915 females, 121,370 malesand 122,585 females, and 2,662 males and 2,566 females, respectively [129]. The crowd-shippingcommunity forms almost 20% of this population, with 83.97% and 16.03% males and females en-gagement, respectively [130]. In addition, individuals aged 18 to 25 years old constitute 70.73% ofthe crowd-shipping community. Educated crowd-shippers (holding bachelorâs degree) account for47.38% of the crowd-shipping community, and 32.40% have monthly income less than CAD $10, 000[131].2.4.5.2 Deep LearningAn artificial neural network, as a powerful machine learning method, imitate humanâs brain interms of data storage and process capabilities [132]. A neural network is modeled to forecast theavailability of crowd-shippers and hyper-local drivers. Given a set of input neurons yâ²(yâ²1, yâ²2, ..., yâ²m),a dataset (yâ², Î³â²) is used to train a binary classifier that approximates the distribution Ï â²(Î³â²nâ² |Ï â², yâ²nâ²),where yâ² represents the input neuron, and Î³â² represents the corresponding desired output. Thebinary classifier is parameterized by Ï â², and once parameters are determined using the MLE , abinary classifier is derived to predict the availability of crowd-shippers and hyper-local drivers.ÏË â² = argmaxÏ â²N â²ânâ²=1Ï â²(Ï, yâ²nâ²)Î³â²nâ² (1â Ïâ²(Ï, yâ²nâ²)1âÎ³â²nâ² ) (2.26)Where nâ² is the sample counter in the dataset, N â² is the total number of samples, and Ï â²(Î³â²nâ² |Ï â², yâ²nâ²)is the parameterized approximation distribution function. The MLE solves a maximization prob-lem considering unidentified coefficients. However, finding the global maximum of a function isnot always straightforward, especially when dealing with high uncertainty. The consistency of theneural network estimator should be assured by checking the concavity of the objective function[133]. Natural logarithms of many distributions with non-concave density functions are log-concave48[134]. Thus, training a binary classifier with parameters Ï â² is equivalent to solving the followingoptimization problem:minÏ â²Lâ²(Ï â²) = â 1N â²[N â²ânâ²=1(Ïâ²nâ² log Ï â²(Ï â², yâ²nâ²) + (1â Ïâ²nâ²) log(1â Ï â²(Ï â², yâ²nâ²)))](2.27)The DFFNN is developed with high capacity, flexibility, and rich toolkits, capable of learningcomplex distributions through nonlinear activation functions [135â137]. The hyper-parameters ofDFFNN (i.e., the number of layers, the number of neurons per layer, and the type of activationfunction), are tuned to learn the desired distribution. Hyper-parameter tuning makes DFFNNmore flexible in balancing the capacity and speed. The DFFNN is optimized using MBGDalgorithm that samples a subset of training data to perform gradient descent. This approach leadsto faster convergence and the ability to escape local minima [138]. TheMBGD is the most commonoptimization algorithm for training artificial neural networks [139].2.4.5.3 An Integrated Ensemble ModelThe primary focus of this section is to identify the most imperative features, influencing thedelivery success rate. Accordingly, feature importance approaches are applied to enhance the neuralnetwork performance. Key features, such as demographic attributes (âGenderâ and âAge Groupâ),educational background (âEducational Levelâ), employment status (âOccupationâ), monthly income(âIncomeâ), and the overall reliability (âProfileâ), are investigated. Data preprocessing is performed toguarantee the quality of data and prevent issues with logarithmic calculations. Subsequently, featureengineering is implemented to generate new variables and identify potential non-linear correlationsto augment the dataset. An ensemble model is developed by incorporating Ridge Regression,Support Vector Regression, and Random Forest Regression.The ensemble model and cross-validation results provide useful information for courier compa-nies. The results verify the negative coefficient of the feature âIncomeâ, explaining that the lowerdelivery success rate arises from higher income values. The higher-income crowd-shippers demon-strate lower inclination for delivery which is reasonable. In contrast, there is a positive coefficientfor feature âAge Groupâ, implying that age groups [18-24] and [24-30] indicate a higher interestin delivery. The third selected feature is âGenderâ, resulting that males have shown more inten-tion to involve in delivery operations. The MSE and R-squared R2 scores are used to implement49cross-validation and evaluate the ensemble model performance. The range of the cross-validatedMSE values and the cross-validated R2 values are between 0.0648 to 0.3085 and 0.5988 to 0.8341,respectively. The closeness of the modelâs prediction to the actual delivery success rate is confirmedby lower MSE values and high R2 scores, indicating a better fit of the model to the data.2.5 Numerical ExperimentA set of instances is generated based on different sizes (i.e., small-size, middle-size and large-size)to validate the performance of the risk-averse model in dealing with high-risk scenarios. Despite therisk-neutral model that minimizes the expected penalty, the risk-averse model efficiently managesworst-case scenarios. The key features of the developed models, indicating the problem complexity(e.g., the number of mobile depots, and the number of available crowd-shippers), are incorporatedto generate instances.Table 2.3: Numerical Experiments Results (highlighted rows show the Toronto case study)No Instance Size Risk-Neutral Risk-Averse (CVaR)I J K S â² C.T(s) O.F.V C.T(s) O.F.V1 2 10 2 3 0.00 395.31 0.00 412.912 4 50 4 3 0.00 2,102.57 0.00 2,306.103 6 150 8 3 0.00 7,536.33 0.00 8,307.714 30 40 160 3 3.00 5,968.13 4.00 6,019.895 15 500 15 3 6.00 26,493.82 7.00 26,623.206 20 1,000 20 10 115.00 55,383.68 366.00 56,106.107 20 1,000 60 10 136.00 55,416.19 265.00 55,977.708 20 1,000 20 90 190.00 55,506.50 350.00 56,102.919 20 3,000 20 20 735.00 175,371.64 2,246.00 177,112.7810 60 1,000 20 10 959.20 46,637.66 1,715.00 47,252.1311 40 2,000 40 20 1,120.00 112,992.83 2,080.00 113,597.0812 50 2,500 50 10 4,666.00 110,993.43 5,810.00 118,820.00As illustrated in Table 3.2, this investigation includes 12 instances in different sizes, with an em-phasis on the real-word case study (City of Toronto), highlighted in yellow. Two different multi-stagestochastic models, risk-neutral and risk-averse are developed to efficiently deal with uncertainties.Table 3.2 demonstrates that both models offer almost the same solutions with negligible computa-tion time for small-size instances (i.e., Instances 1 to 3). While increasing the instance size (e.g.,Instance 6) results in a sharp rise in computational time, this effect is particularly noticeable in therisk-averse model. This is due to the exploration of a large allocation and routing decision space,50since all delivery sequence permutations are investigated. The results in Table 3.2 imply that therisk-averse model offers several key benefits not found in the risk-neutral model. One major advan-tage of the risk-averse model is its ability to produce robust solutions, thus minimizing the impactof worst-case scenarios. The incorporation of the CVaR as a risk measure introduces a prioritiza-tion feature to the risk-averse model, mitigating the adverse impacts of worst-case scenarios. Thisguarantees the robustness of the risk-averse model solutions in uncertain and dynamic environmentof the last-mile delivery network. To put it more precisely, the risk-averse model demonstratesenhanced flexibility in handling unanticipated disruptions, uncertainties in delivery success rates,stochastic offline orders, and dynamic online orders. Accordingly, the risk-averse model is able toprovide the optimal delivery schedule with minimum failed and postponed deliveries, particularlyin worst-case scenario, validating its applicability in real-world scenarios. The average gap betweenthe risk-neutral and risk-averse model is approximately 2%, indicating that by imposing an addi-tional 2% more cost to the network, the risk-averse model can effectively manage high-risk scenarios,leading to significant cost savings.2.6 Case Study and Sensitivity AnalysisThe case study (benchmark instance), along with various instances of different sizes, is derivedbased on data from the Toronto city (Figure 2.3). The case study and related instances are generatedbased on data from 2023 version of the TTS [140] (i.e., a comprehensive mobility survey conductedat a five-year intervals in the GTA. Overall, 625 traffic zones have been identified for the City ofToronto [141], and these zones account for approximately 20% of non-zero demand origin-destinationpairs [74]. The benchmark instance and corresponding instances are derived based on differentcombinations of the customer locations, mobile depot stopping locations, the number of availablecrowd-shippers, and the number of scenarios. Customer locations and the number of crowd-shippersare derived from [142] and TTS based on demand and past records for origin-destination pairs,respectively. The primary factors for selecting potential mobile depot stopping locations are theirproximity to local communities and the availability of a spacious open-air parking lot. In this casestudy, the central hub is located in the Peel territory (Torontoâs western side), which is the NorthAmericaâs freight logistics central hub. Moreover, the clustering of customer locations results ina total of 40 customer locations along with 30 potential stopping locations for mobile depots [74].The placement cost of a mobile depot, denoted as ci, is estimated based on the shortest travel path51taken by a truck from the Peel central hub to the designated stopping location. This cost alsoincludes an expense rate related to reimbursing a mobile depot to a crowd-shipper. The mobiledepot occupies merely 50 m3 that can hold 3,000 - 4,000 m3 once deployed [143]. The capacity ofthe mobile depot is consistently set 3,000 for all instances. The postponement cost of delivery dj isestimated to be 0.6 times the shortest path distance between the mobile depot and the respectivecustomers location. Accordingly, the unfulfilled customers delivery dâ²j is approximated to be 1.5times postponement cost of the delivery. [144] proposed the framework for reimbursement schemes.In this framework, crowd-shipping companies attain the highest cost savings through the adoptionof the two-part reimbursement scheme. Therefore, I employ the two-part reimbursement approachin which crowd-shipper compensation is computed with a weight of 1 assigned to delivery costs anda weight of 0.6 to deviations in distance due to the traffic congestion or weather patterns. Theavailability of each crowd-shipper is modeled using binary classification model, where the successrate of delivery is estimated based on the past availability of crowd-shippers. The main case studyand all the respective generated instances are implemented on macOS with Apple 10 core, M1 Prochip, and 32 GB RAM.Figure 2.3: The Illustrative Case Study (Orders Density)The proposed model aims to investigate a novel variant of the dynamic last-mile delivery prob-52lem, integrating mobile depot stopping locations, utilizing crowd shippers and hyper-local driversfor distributing customer packages. However, the availability and willingness of crowd shippers andhyper-local drivers to undertake the delivery tasks remain uncertain. To address this, the mathemat-ical model incorporates risk measures to account for this uncertainty. Therefore, a comprehensivesensitivity analysis of risk parameters (Ï and λ) is conducted on three instances to compare therisk-averse model with the risk-neutral approach. The analysis investigates the consequence of high-risk scenarios in the proposed policies (i.e., crowd-shipping, mobile depot locations, and hyper-localdrivers). Furthermore, the impact of such scenarios is analyzed on various cost measures, includingthe first, second, and third stage costs of the delivery network. This study also explores the effectof the risk-averse model on traffic management and CO2 emissions, considering the dynamic trafficand weather patterns that play pivotal role during last-mile delivery. As indicated in Table 2.4, thesensitivity analysis is performed on the case study, Sample 6, and Sample 8 using parameter valuesof λ = {0.25, 0.50, 0.75, 1} and Ï = {0.25, 0.50, 0.75, 1}. This analysis is crucial to achieve optimalstrategic, tactical, and operational decisions in the proposed model.The outcomes of sensitivity analysis demonstrate that decision-making in last-mile deliverybecomes more conservative as Ï and λ values increase, resulting in high-risk scenarios. In suchhigh-risk scenarios, stemming from volatile traffic flow and unpredictable weather patterns, crowd-shippers incline to select reliable and risk-free tours. While this approach may result in longerdistances, as elaborated in the explanation of Figure 2.8, it effectively mitigates the uncertaintiesand dynamic impacts of traffic and weather conditions. As a result, crowd-shippers may be lessavailable during traffic congestion or adverse weather conditions. Such behaviour can be justified bythe uncertainties and challenges related to navigation during traffic congestion or extreme weather,which may give rise to potential delays and inefficiencies in delivery operations.53Table 2.4: The Impacts of Risk Parameters on Risk-Neutral and Risk-Averse Models in Different InstancesÎ»Ï0.25 0.5 0.75T.C CVaR F.S S.S T.S T.C CVaR F.S S.S T.S T.C CVaR F.S S.S T.SCaseStudy 0.25 6,960 4,126 1,802 1,204 5,328 7,033 4,218 1,803 1,254 6,074 7,068 4,209 1,822 1,332 8,1120.5 8,043 4,099 1,756 2,265 6,778 8,103 4,161 1,876 2,316 8,056 8,175 4,209 1,884 2,497 12,1630.75 9,130 4,058 1,866 3,279 8,060 9,207 4,136 1,866 3,452 10,873 9,148 4,190 1,834 3,663 16,1811 10,977 4,026 1,887 5,179 10,515 10,094 4,003 1,760 4,489 12,171 10,187 3,990 1,831 4,830 20,214Sample6 0.25 61,748 52,964 2,501 43,411 40,335 61,693 53,059 2,427 48,172 44,498 61,775 53,099 2,504 62,087 56,9990.5 68,036 52,949 2,514 58,909 55,544 68,161 53,015 2,503 68,511 64,062 68,094 52,995 2,486 96,309 89,1010.75 74,420 52,935 2,596 74,575 70,897 74,382 52,951 2,538 88,542 83,423 74,429 52,021 2,466 130,600 121,1981 80,717 52,948 2,534 90,094 86,275 80,645 52,931 2,460 108,672 103,004 80,554 52,975 2,398 164,900 152,889Sample8 0.25 61,758 53,081 2,425 43,629 40,279 61,760 53,150 2,365 48,358 44,534 61,874 53,183 2,445 62,454 61,8910.5 68,165 53,129 2,447 59,272 55,687 68,299 53,131 2,613 68,670 63,986 68,276 53,167 2,551 96,791 89,0650.75 69,883 53,088 2,457 63,602 59,933 69,946 53,115 2,491 74,322 69,475 69,941 53,106 2,502 106,367 97,9471 80,894 53,079 2,589 66,961 62,933 80,863 53,086 2,445 109,399 103,221 80,876 52,945 2,515 165,526 153,19554As mentioned previously, failed delivery orders, reported by crowd-shippers to mobile depotauthority, are offered as the same-day delivery orders to customers (i.e., by hyper-local drivers).The policy regarding hyper-local drivers (i.e., failed delivery customers visiting the mobile depot tocollect their package) is influenced by risk parameters in the last-mile delivery problem. In high-riskscenarios, the risk-averse model offers more same-day deliveries by hyper-local drivers to assure agile,collaborative, and flexible delivery options. In such high-risk scenarios, if contracted crowd-shippersannounce unavailability due to dynamic factors (e.g., traffic congestion or adverse weather condition)decision-makers can rely on hyper-local drivers to execute the delivery operations, preventing delaysand customer dissatisfaction. In contrast, under lower uncertainty (risk), decision-makers prefer torely on contracted crowd-shippers rather than having a large number of hyper-local drivers. Insummary, decision-makers preference is to maintain a core team of crowd-shippers with predefinedavailability schedules and commitments to ensure more reliable and consistent delivery operations.The mobile depot policy flexibility (i.e., the availability of crowd-shippers and hyper-localdrivers) is highly correlated with coefficient risk λ and confidence level Ï, particularly during dy-namic traffic flow. To prepare the mobile depots for a high-risk environment, including factorssuch as volatile crowd-shipper availability, traffic congestion, and adverse weather conditions, amore risk-averse model should be developed, leading to higher values of Ï and λ. This results inconservative routing and allocation policies, enabling time and resource reservation to manage un-predictable delays. Consequently, incentives and compensations for crowd-shippers and hyper-localdrivers in mobile depot policy should be adjusted in response to traffic flow or extreme weatherconditions to mitigate the risk of delivery delays.The parameter Ï represents the risk preference in percentage. An increase in the Ï value leadsto a higher value-at-risk, and CV aRÏ tries to mitigate the high-risk scenarios. This leads to focusmore on conservatives policies to handle high-risk scenarios. As Ï increases, both the total expectedcost and CVaR cost rise, indicating that the model allocates additional resources to the secondand third stages. This mitigates the substantial cost of high-risk scenarios arising from the largevolume of offline and online orders. Similarly, the higher values of λ increase the significance of therisk measure, resulting in the formulation of more risk-averse policies. Therefore, the risk-aversemodel allocates more resources to the first stage (i.e., strategic placement of the mobile depot)or postpones customer orders to mitigate the uncertainty associated with crowd-shippers. Theaccurate estimation of the λ and Ï provides a managerial insight for crowed-shipping company indecision-making. For example, analyzing two different scenarios (Ï = 1, λ = 0.25, and λ = 1) in55the case study shows that a 1.3% rise in the expected total cost leads to a 4.6% decrease in theCVaR value. Increasing both Ï and λ results in a higher total cost of the network, with negativeand positive correlations existing between CVaR cost and Ï, respectively. The results validate theimportance of incorporating the risk measure in the stochastic dynamic last-mile delivery problem,providing meaningful insights for courier companies.2.6.1 Analysis of Stochastic Solution QualityThe assessment of stochastic and deterministic solutions quality is performed through two met-rics, the EVPI [145, 146], and the VSS [147, 148]. The EVPI is defined as the maximum costa decision-maker would incur to acquire the perfect information about possible uncertainties. TheEVPI metric estimates the highest potential saving in case a decision-maker had complete andaccurate information about uncertain factors [149]. According to the Equation (2.28), the EVPIis defined as the difference between the here-and-now value (i.e., the expected value of the recourseproblem), and wait-and-see value (i.e., the expected value of reacting with perfect information).EV PI =Min Eα[Q(W,Y, α) + EÎ±[Qâ²(W â², Î±)]]â E[Min Q(W,Y, α) + EÎ±[Qâ²(W â², α)]](2.28)Equation (2.28) measures the value of a perfect estimate for future uncertainties. TheVSS met-ric assesses the benefits of employing a stochastic model instead of a deterministic one in decision-making within an uncertain environment. The VSS is estimated based on the [150â152] thatdemonstrates the potential cost-saving percentage of adopting a stochastic model instead of a de-terministic one. Table 2.5 compares eight instances with different probabilities for success rate ofdelivery (i.e., the availability of crowd-shippers).V SS = Eα[Q(W,Y, α¯) + EÎ±[Qâ²(W â², Î±¯)]]â Eα[Q(W,Y, α) + EÎ±[Qâ²(W â², α)]](2.29)56Table 2.5: Analysis of Quality of Stochastic Solution (highlighted rows show the Toronto case study)No Instance SizeI J K S â² αk EVPI VSS1 2 10 2 3 0.66 0.462 0.1422 2 10 2 3 0.79 0.466 0.1333 4 50 4 3 0.66 0.465 0.1224 4 50 4 3 0.79 0.475 0.1455 30 40 160 3 0.66 0.513 0.0006 30 40 160 3 0.79 0.530 0.0047 15 500 15 3 0.66 0.469 0.1218 15 500 15 3 0.79 0.471 0.121According to Table 2.5, although the VSS and EVPI represent relatively small percentagevalues, they carry significant economic implications. Instances with comprehensive and accurateinformation regarding uncertain parameters (e.g., success rates of delivery, stochastic offline orders,dynamic online orders, and travel time) have the potential to save an average of 48%. On average,stochastic solutions outperform deterministic ones by 9.85% due to the lack of complete and accurateinformation in the deterministic model. In reality, gaining access to such information is challenging,however the integration of efficient policies in the developed stochastic model provides solutions thatare, on average, 9.85% less costly than the deterministic model. Even in high-risk environments,the CVaR-VSS confirms that the solutions obtained mitigate risks by achieving resilience valuesclose to those of wait-and-see solutions. Increasing the instance size, such as adding more crowd-shippers, leads to a decrease in theVSS , and this difference becomes more evident as the probabilityincreases. This implies that a higher VSS value is achieved when the network has the lower numberof crowd-shippers with higher success rate of delivery.2.6.2 Innovative Policies ComparisonAs discussed in Section 2.6, the hyper-local driver policy yields multiple benefits, resultingin economic, environmental, and societal advantages by reducing the total cost, CO2 emissions,delivery time, and traffic congestion. Two scenarios are designed to evaluate the performance ofproposed policies integrated into the stochastic dynamic last-mile delivery problem. Figures 2.4 and2.5 provide a better understanding of these two scenarios.In the first scenario, both online and offline orders are delivered by crowd-shippers, while in thesecond scenario, a portion of online orders is handled by hyper-local drivers. To provide a clearillustration, a small-scale scenario is selected to investigate these two scenarios thoroughly. In both57scenarios, there is no unfulfilled order. In the first scenario, mobile depot i2 is strategically placed onHeward Avenue from Peel region, which serves as the freight central hub in North America locatedon the western side of the City of Toronto. This setup incurs an approximate cost of 105 units forthe last-mile delivery network. All deliveries in this scenario are fulfilled by two crowd-shippers,k1 and k2. The mobile depot i2 is placed on Heward Avenue before the beginning of the workingshift, ensuring its presence before 8 AM. The first crowd-shipperâs tour initiates from mobile depoti2 on Heward Avenue at the beginning of the working shift at 8AM, continued to Empire Avenueto deliver customer j1âs package in almost 11 minutes. Subsequently, customer j2 is serviced onSaulter Street by crowd-shipper k1 in about 8 minutes. Following that, the tour continues withcustomer j4 on Hamilton Street, and customer j10 on Carrol Street, taking almost 9, and 8 minutes,respectively. Customers orders j3, j5, j6, j7, j8, and j9 are assigned to the second crowd-shipper k2.The second crowd-shipperâs tour initiates by servicing customer j3 at 8:10 AM on Pape Avenue, andcontinues along Dundas Street to serve customers j6, j7, j8, and j9, consecutively after deliveringthe customer j5 on Coady Avenue. The crowd-shipper arrives on Mallon Street at 8:22 AM to servecustomer j6, and delivers the customer j7âs package on Dundas Street in almost 9 minutes. Thetour is finalized by delivering customers j8 and j9 packages in nearly 20 minutes on Dundas Streetand Prust Avenue, respectively. The total tour duration for the first crowd-shipper is estimated 45minutes, while the second crowd-shipperâs tour takes 55 minutes, travelling approximately 37 kmdistance with 80 units crowd-shippersâ compensation delivery cost. This scenario is characterizedby the total delivery cost of 176.37 units and the traveled distance of 75.61 km under three deliverysuccess rate scenarios.58Figure 2.4: Scenario I Configuration: Mobile Depot, Crowd-Shipper, and Hyper-Local DriversDeliver Tours ConfigurationsIn the second scenario, mobile depot i1 departs Peel region before the start of the working day at8 AM and travels to Booth Avenue. The crowd-shipper k2 is assigned to serve customers j1, j2, j4,and j10. Orders j3, j5, j6, j7, j8, and j9 are included in the crowd-shipper k1âs tour. At 8 AM,crowd-shipper k1 begins the delivery tour from Booth Avenue, following the first stop on HamiltonAvenue, and delivers the customer j4âs package in approximately 6 minutes. Then, crowd-shipperk1 serves customer j10 at Carrol Street at 8:15 AM before arriving on Saulter Street to deliverthe customer j2âs package, which takes nearly 7 minutes. Unfortunately, there has been a faileddelivery in the crowd-shipper k1âs tour in his attempt to serve customer j1 (online order) on EmpireStreet. After 10 minutes, crowd-shipper k1 reports the failed delivery, and returns the package toBooth Avenue (mobile depot i1), and notifies customer j1. Accordingly, the customer j1âs same-daydelivery order is offered to a hyper-local driver, incurring 6-units reimbursement fee to the deliverynetwork. Meanwhile, customer j3 on Pape Avenue is the first customer that should be visited in thesecond crowd-shipper k2âs tour, initiating at 8 AM on Booth Avenue. The next planned customeron the crowd-shipper k2âs route is customer j5 on Coady Avenue, which is served in 5 minutes.59Customers j6, j7, and j8, located on Dundas Street, are received their packages in about 20 minutesby crowd-shipper k2. The failed delivery by crowd-shipper k2 to customer j9 results in an extra costof 5 units to the delivery network as reimbursement for a hyper-local driver. It should be noted thatthese scenarios are investigated under light traffic and without extreme weather conditions. Thesefactors can significantly impact the delivery time, cost, the customer service level, and the successrate of delivery. In this scenario, the total cost of the network is estimated at 179 units, with 75units is related to the delivery by crowd-shippers, covering a total distance of 33 km.Figure 2.5: Scenario II Configuration: Mobile Depot, Crowd-Shipper, and Hyper-Local DriversDeliver Tours ConfigurationsAccording to the obtained results, it is notable that there has been an identical placement costfor mobile depot locations (i1 and i2) on Heward Avenue (first scenario) and Booth Avenue (secondscenario), respectively. As expected, the total delivery time and distance in the second scenarioare decreased by 12% in the small-size case. This reduction becomes more meaningful in the large-size cases, leading to lower CO2 emissions and reduced traffic congestion. In the second scenario,there has been an approximate 6% drop in the total delivery cost carried out by crowd-shippers.However, incorporating the hyper-local driver policy to the crowd-shipper policy imposes a negligible1% rise in the total cost of the network. The cold and snowy winters in the GTA, lasting from60December to March, with temperatures often dropping below freezing, make the delivery processvery challenging, particularly due to the high delivery orders during holiday season. Integratingthe hyper-local driver policy into the crowd-shipper policy in the last-mile delivery problem withmobile depot can significantly alleviate the mentioned challenges.2.7 Performance EvaluationIn this section, the performance of the proposed ORDAO is validated by comparing it withthe IMAS . The proposed ORDAO exhibits promising performance when compared to the sim-ulation results for the last-mile delivery problem. Notably, the proposed ORDAO consistentlydemonstrates improved delivery times as shown in Figure 2.6. The number of packages handledby the ORDAO algorithm aligns with the IMAS , with both models meet all the demand points,respectively. The observed reduction in travel times, by almost 11%, suggests that the proposedORDAO effectively optimizes delivery routes and adapts to dynamic online orders, demonstratingits ability to outperform the IMAS in realistic last-mile delivery scenarios.[1800-1850] [1850-1900] [1900-1950] [1950-2000] [2000-2050]Travel Time (seconds)681012141618umber of Packages((a)) Average Travel Time IMAS[1600-1650] [1700-1750] [1800-1850] [1900-1950] [2000-2050]Travel Time (seconds)681012141618umber of Packages((b)) Average Travel Time ORDAOFigure 2.6: Performance Evaluation of the Proposed ORDAOThe superior performance of the proposed ORDAO becomes even more evident when consid-ering its approach to handling dynamic online orders (same-day delivery orders) compared to theIMAS . While the IMAS incorporates dynamic online orders into a pre-scheduled set of stochasticoffline orders, the proposed ORDAO deals with online orders by dynamically reoptimizing andrescheduling the offline stochastic orders at each decision point triggered by the placement of adynamic online order. This adaptability to real-time changes allows ORDAO to continually refineits decision-making process, optimizing delivery routes in response to incoming online orders. This61contrasts with the static nature of the IMAS , which does not fully capture the dynamic natureof last-mile delivery scenarios. The ability of the ORDAO to reoptimize and reschedule its de-livery routes in response to new information positions it as a more agile and responsive solutionfor last-mile delivery challenges. This dynamic reoptimization mechanism not only contributes tothe observed improvements in delivery times but also reflects the ORDAO âs capacity to deal withthe inherent uncertainties and fluctuations in the last-mile delivery environment. This crucial dis-tinction highlights the practical advantages of the ORDAO in scenarios where adaptability andreal-time responsiveness play a significant role in achieving efficient and timely deliveries.2.8 Managerial Implications2.8.1 The Impact of Selected Features on Delivery Success RateIn this section, the impacts of selected features on delivery success rate are investigated. Anensemble model integrating Ridge Regression, Support Vector Regression, and Random Forest Re-gression is utilized to identify the most impactful features, including âIncome,â âAge Group,â andâGender.â The investigation involves creating three main scenarios, each emphasizing the influence ofone selected feature on the delivery success rate, while keeping the values of the other two featuresconstant. The developed neural network provides identical, high training, and testing accuracy.The results validate the model generalization ability, and there is no overfitting sign in trainingdata. They also indicate that selected features have different degrees of impacts on the deliverysuccess rate. The correlation between the selected features and delivery success rate verifies theirimportance in estimating the accurate delivery success rate in each generated scenario. Finally, themodel performance is validated by the consistency between training and testing accuracy for allscenarios. The delivery success rate for the baseline Scenario, Scenario I, Scenario II, and ScenarioIII are estimated 0.66, 0.79, 0.69, and 0.72, respectively.62Low Income Medium Income High Income0.00.20.40.60.81.0Success Delivery RateIncome ImpactAverage Success Rate((a)) Income18-24 24-30 30-400.00.20.40.60.81.0Success Delivery RateAge Group ImpactAverage Success Rate((b)) Age GroupMale Female0.00.20.40.60.81.0Success Delivery RateGender ImpactAverage Success Rate((c)) GenderFigure 2.7: Impacts of Selected Features by Developed Ensemble on Success Delivery RateFigure 2.7 provides a simple visualization of the obtained results. Briefly, the average deliverysuccess rate, represented by the gray dashed line, is approximately 66%. According to Figure2.7(c), the impact of âGenderâ feature is relatively small, with a difference of only 3% between thedelivery success rate by males and females. Both genders are close to the average delivery successrate, indicating that gender has a minimal effect on the overall delivery success rate. However,their participation percentage is different. The Figure 2.7(b) illustrates the impact of âAge Groupâfeature on delivery success rate. The [24-30] age group has a negligible impact on the deliverysuccess rate. In contrast, the [18-24] age group has a delivery success rate that is almost 6% higherthan the average, while the [30-40] age group has a delivery success rate that is almost 6% lower thanthe average. The Figure 2.7(a) demonstrates the impact of feature âIncomeâ levels on the deliverysuccess rate. The delivery success rate for âLow Incomeâ is approximately 79%, which is higher thanthe average delivery success rate. This indicates that individuals with low income have a highermotivation for crowd-shipping. The delivery success rate for âMedium Incomeâ is approximately72%, closer to the average delivery success rate, but still higher than the delivery success rate forâHigh Incomeâ. The delivery success rate for âHigh Incomeâ is approximately 53%, significantlybelow the average delivery success rate, implying that individuals with high income are less likelyto be available for crowd-shipping.The identified significant features, including âIncomeâ, âAge Groupâ, and âGenderâ, provide valu-able insights for decision-makers at courier companies about the delivery success rate. The negativecorrelation between âIncomeâ and the delivery success rate represents that individuals with higherincome may have different priorities or preferences when they want to participate in delivery oper-ations. Individuals with higher income may have less time available for delivery activities due to63rigorous working hours and commitments and may prefer to involve in other profitable operationsand investments. The analysis demonstrates a more inclination among younger people to involve inflexible money-making opportunities, such as part-time deliveries. It can be interpreted that youngindividuals aged [18-24] (e.g., university students and early-career professionals pursuing flexibletime job) find the delivery operations suitable. Their comfort with technology and online deliveryapplications may make it easier for them to engage in such operations. This insight provides abetter understanding for courier companies in terms of targeting and recruiting employees in thespecific age group. The analysis also showed that women are less likely to participate in deliveryoperations. This finding can be justified with gender disparities or barriers in delivery operations.Such barriers might include safety issues, as women believe that delivery operations involve interac-tions and communications with strangers. Furthermore, the perception that unknown and distantplaces are unsafe affects their decision to participate in crowd-shipping. Other factors impactingwomen participation rate in crowd-shipping can be referred to societal culture, traditions, and cul-tural gender roles, which have formed the perception of specific jobs as more acceptable and suitablefor men. Recognizing such gender disparities provides insights for decision-makers in courier com-panies to establish a supportive and safe environment, which encourages all genders to involve incrowd-shipping services. These potential challenges can be mitigated by specifying safety measures,ensuring supportive services, and providing flexible working hours.2.8.2 The Impacts of Selected Features on Last-Mile Delivery Business ModelPerformanceThis section investigates the impacts of selected features, based on the outlined scenarios inSection 2.8.1 and the estimated delivery success rate, on the overall performance of proposed last-mile delivery model. This investigation is implemented on the case study (highlighted in yellowin Table 2.3). The overall performance of proposed last-mile delivery model is evaluated based onthe T.C , CVaR, E.V , T.D , F.S , S.S , T.S , CO2 emissions, and traffic congestion. Figure 2.8visualizes the overall performance of proposed last-mile delivery model for the baseline Scenario,Scenario I, Scenario II, and Scenario III based on the T.C , CVaR, E.V , T.D , F.S , S.S , andT.S .In the first scenario, the focus is on the impact of âIncomeâ on the proposed last-mile deliverymodel. The results reveal that fluctuations in income have a significant impact on multiple aspectsof the proposed model. There is a negative correlation between the changes in income and the64availability of crowd-shippers. This gives rise to a higher level of unfulfilled order and, consequently,an increase in the S.S cost, remarkable surge in traveled distance (Total Distance-Figure 2.8,Scenario III), the fuel cost, CO2 emissions, and traffic congestion. The second and third scenariosexamine the impacts of variability in âGenderâ and âAge Groupâ on the proposed last-mile deliverymodel, implying that demographic attributes play a comparably minor role in comparison to theâIncomeâ. The impacts of age group demographics are relatively more considerable than âGenderâ.Similar to âIncomeâ, the shift from males to females and from age group [18-24] to [30-40] results inthe higher S.S cost owing to the reduced availability of crowd-shippers. Although the compensationcost of crowd-shippers decreases as they serve a smaller number of customers, the T.C increases dueto the inclusion of the opportunity cost of unfulfilled orders, re-delivery expenses, and hyper-localdriver reimbursement fee. A higher delivery success rate implies that fewer hyper-local drivers arerequired to meet unfulfilled customer demand, leading to reduced traffic congestion and an improvedurban mobility.65Baseline Scenario I Scenario II Scenario III635064006450Total Network CostsTotal Network CostsBaseline Scenario I Scenario II Scenario III595060006050Expected ValueExpected ValueBaseline Scenario I Scenario II Scenario III416041804200CVaR CostCVaR CostBaseline Scenario I Scenario II Scenario III17801800182018401860First StageFirst StageBaseline Scenario I Scenario II Scenario III590592594596Second StageSecond StageBaseline Scenario I Scenario II Scenario III4800482048404860Third StageThird StageBaseline Scenario I Scenario II Scenario III400040204040Total DistancesTotal DistanceFigure 2.8: The Impacts of Selected Features on the Overall Performance of Last-Mile DeliveryNetwork (T.C , CVaR, E.V , T.D , F.S , S.S , and T.S)As illustrated in Figure 2.8, Scenario I demonstrates a decrease in the T.C , CVaR cost, E.V ,T.D , F.S cost, S.S cost, and T.S cost as the delivery success rate increases. The consistentinvolvement of individuals in the last-mile delivery network contributes to this improved deliverysuccess rate and reduces the frequency of delayed deliveries. A decrease in the CVaR cost indicatesa lower risk level stemming from the uncertainty and dynamic nature of the last-mile deliveryenvironment. Analyzing the impacts of key features on delivery success rate by decision-makersfacilitates the development of a more robust and reliable delivery schedule. This effort enhancescost management, reduces cost overruns, mitigates unpredictable delivery challenges, and ultimately66reduces the impact of uncertainties on last-mile delivery operations. Furthermore, these threescenarios demonstrate the importance of understanding and considering demographic factors inoptimizing last-mile delivery for courier companies. Each scenario highlights different aspects ofthe system affected by variations in âIncomeâ, âGenderâ, and âAge groupâ. The results highlight thepotential to establish more efficient and eco-friendly delivery networks through effective managementof crowd-shippers in alignment with demographic characteristics.2.8.3 Hyper-Local Drivers Reimbursement PolicyHyper-local drivers receive the reimbursement fee to cover their travel expenses, which is cal-culated based on the travel time, traffic volume, fuel costs, and distance. This section aims todetermine the optimal reimbursement fee policy and investigate its impacts on the overall perfor-mance of the proposed last-mile delivery business model (i.e., the T.C, E.V, CVaR cost, F.S cost,S.S cost, and T.S cost). Figure 2.9 demonstrates the sensitivity analysis performed on thefjdj,fjdâ²j,andfjcâ²ijk.Overall, positive correlations exist between thefjdjand the T.C, E.V, CVaR cost, F.S cost,and S.S cost. It implies the intricate correlation between the reimbursement fee of hyper-localdrivers and the financial fluctuations of last-mile delivery system. The correlation suggests thatthe incentive for hyper-local drivers carries a cost, potentially due to the higher reimbursement feeresulting from their increased engagement. The increase in thefjdjalso aligns with a rise in theCVaR cost. The CVaR measure represents the delivery services financial risk. The rise in theCVaR cost indicates that the reimbursement fee of hyper-local drivers becomes more impactfulregarding the cost of postponement. This demonstrates that higher participation rate of hyper-local drivers results in a higher level of uncertainty and potential fluctuations in costs. The rise inthe F.S cost can be attributed to the additional financial resources to facilitate the engagement ofhyper-local drivers. As thefjdjincreases from 0.2 to 0.5, the T.C, E.V, CVaR cost, and S.S costincrease by 14%, 11%, 21%, and 18%, respectively. The different percentages indicate the variouscost metrics react to fluctuations in thefjdj. The CVaR cost demonstrates the highest sensitivity toalternations infjdjamong financial metrics, due to the highest rise (21%). When the reimbursementfee of hyper-local drivers is the same with the penalty cost for postponing (fjdj= 1), the T.C, E.V,CVaR cost, and the S.S cost decrease by approximately 2%, 2.9%, 2.6%, and 3.7%, respectively.This implies that an unreasonable reimbursement fee results in a higher risk of unfulfilled onlineorders, a reduced overall performance of the proposed last-mile delivery network, and loss of market67share.The variation in the F.S cost remain relatively consistent over different ratios, verifying thatthe F.S cost is not significantly affected byfjdj(i.e., with a maximum change of 9% asfjdjincreasesfrom 0.2 to 1). Although the F.S cost increases due to the increased participation of hyper-localdrivers, overall, it remains stable. The S.S cost doubles whenfjdjincreases from 0.2 to 1. Thisincrease is evidently attributed to the delivery postponing cost, which create the primary part ofthe S.S cost. It implies that a significant proportion of the S.S cost is associated with the costincurred when the postponed orders need to be re-scheduled for delivery. However, there exists anegative correlation betweenfjdjand the T.S cost. The T.S cost rises by 4% asfjdjincreases from0.2 to 0.25, followed by a significant drop of 77% when the reimbursement fee for hyper-local driversis equal to the penalty cost of postponing. The T.S cost experiences meaningful variations by aminor change in the ratio. This indicates the dynamic nature of the delivery network, includingfactors such as dynamic online orders, and the impacts of hyper-local driversâ behavior on deliveryschedules.0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)4100042000430004400045000460004700048000ValuesT.CT.C0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)3000031000320003300034000ValuesE.VE.V0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)1550016000165001700017500180001850019000ValuesCVaRCVaR0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)2900300031003200330034003500ValuesF.SF.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)110001150012000125001300013500ValuesS.SS.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Postponing costs)150002000025000300003500040000ValuesT.ST.SFigure 2.9: Sensitivity Analysis on Hyper-Local Drivers Reimbursement Policy (fjdj)As illustrated in Figure 2.10, negative correlations exist between thefjdâ²jand the T.C, E.V, andCVaR cost. The observed trend of the defined metrics when thefjdâ²jchanges can be attributed68to some fundamental elements such as the availability of crowd-shippers, traffic congestion, andweather conditions. Asfjdâ²jincreases from 0.2 to 1, a significant reduction is observed: 20% in T.C ,28% in E.V , and 20% in CVaR cost. The reduction in T.C indicates a notable drop when anincreased volume of orders is assigned to hyper-local drivers. Similarly, the drop in E.V and CVaRcost highlights that the delivery network is more robust to perturbations, effectively addressing thepotential impacts of an uncertain and dynamic environment.Furthermore, decreasing trends are observed in the F.S cost and the S.S cost asfjdâ²jincreasesfrom 0.2 to 1. This implies that if the reimbursement fee for hyper-local drivers is considerablyless than the penalty cost for order cancellation, fewer hyper-local drivers are willing to participatein the delivery services. This results in higher unfulfilled demand costs imposed on the S.S cost.Despite the decreasing trend in the S.S cost, which drops by approximately 57% asfjdâ²jchangesfrom 0.2 to 0.5, there is a 25% increase when the ratio changes to 1. This means that increasing thereimbursement fee of hyper-local drivers does not necessarily reduce the S.S cost, implying thatthe optimal ratio needs to be accurately adjusted to minimize the T.S cost. It is noteworthy tohighlight that there is a negative correlation between the T.S cost and the S.S cost. As thefjdâ²jincreases from 0.2 to 0.5, the T.S cost noticeably increases due to the higher reimbursement fee,which attracts more hyper-local drivers for the delivery services. This rise aligns with a remarkabledecrease in the S.S cost since a smaller portion of deliveries are executed by crowd-shippers.690.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)400004200044000460004800050000ValuesT.CT.C0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)270002800029000300003100032000330003400035000ValuesE.VE.V0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)1600017000180001900020000ValuesCVaRCVaR0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)5001000150020002500300035004000ValuesF.SF.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)600080001000012000140001600018000ValuesS.SS.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to not Serving Customers)4000500060007000800090001000011000ValuesT.ST.SFigure 2.10: Sensitivity Analysis on Hyper-Local Drivers Reimbursement Policy (fjdâ²j)Figure 2.11 analyzes thefjcâ²ijkto determine the optimal reimbursement policy for hyper-localdrivers and its impacts on the overall performance of the proposed last-mile delivery model. There isa consistent incremental trend in the T.C, E.V, andCVaR cost by 23%, 21%, and 9%, respectively,whenfjcâ²ijkincreases from 0.2 to 1. This indicates that variations in the ratio have a similar impacton the T.C and E.V, while the CVaR experiences a gradual decrease. The higher reimbursementfee compared to the compensation for crowd-shippers gives rise to cost-saving.The F.S cost remains relatively stable across most of the ratios (0.2, 0.25, 0.35, 0.5), indicatingthat it is not significantly impacted by changes in thefjcâ²ijk. However, it remarkably increaseswhenfjcâ²ijkincreases from 0.5 to 1. Furthermore, if the reimbursement fee for hyper-local drivers isequivalent to the compensation for crowd-shippers, and the delivery success rate is low, there will bea high number of declined orders and an increase in the penalty cost of postponing (S.S). The S.Scost demonstrates a distinct pattern; it experiences a 3.3% increase asfjcâ²ijkshifts from 0.2 to 0.25,followed by a 1.3% decrease asfjcâ²ijkchanges from 0.25 to 0.35. This means that the reimbursementfee is not highly effective in motivating hyper-local drivers, given that crowd-shippers are capableof managing the orders. The acceptance rate of delivery by hyper-local drivers also is associatedwith the traffic congestion, weather conditions, and their availability. While the overall trend in the70T.C is upward, except for the shift fromfjcâ²ijk= 0.35 to 0.5, which relates to an increased cost ofthe S.S at a ratio 0.5.0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)380004000042000440004600048000ValuesT.CT.C0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)260002700028000290003000031000320003300034000ValuesE.VE.V0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)1500016000170001800019000ValuesCVaRCVaR0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)5001000150020002500300035004000ValuesF.SF.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)72507500775080008250850087509000ValuesS.SS.S0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Ratio (Occasional Drivers Reimburse Fee to Crowd-shippers Delivery Fee)90001000011000120001300014000ValuesT.ST.SFigure 2.11: Sensitivity Analysis on Hyper-local Drivers Reimbursement Policy (fjcâ²ijk)In summary, such analyses offers managerial insights, implying that a high reimbursement feedoes not necessarily contribute to improved performance in the last-mile delivery business model.As a result, it is crucial to thoroughly determine the equilibrium between these financial factors toestablish an optimal reimbursement policy, which aligns with objectives and resources of the couriercompany.2.9 SummaryIn response to the surge in e-commerce and the growing demand for same-day deliveries, adopt-ing new last-mile delivery policies is essential. This study proposed a platform to optimize last-miledelivery schedules in urban areas by utilizing flexible and cost-effective mobile depots and crowd-shipping. It also emphasized the importance of hyper-local drivers contributing to high-qualityservice, especially considering urban traffic conditions. The success rate of delivery is highly corre-lated with the uncertain availability of crowd-shippers incorporated into the multi-stage stochastic71dynamic risk-averse model (CVaR). Various scenarios with different sizes were generated usingthe case study (City of Toronto). The delivery success rate was calculated through a deep learn-ing model that extracted features from the SET . The most crucial features were determined bycreating an ensemble model. The risk-averse model was compared with the risk-neutral model tovalidate the performance of the risk-averse model in high-risk scenarios. On average, the risk-aversemodel incurred about a 2% higher cost compared to the risk-neutral model. This extra cost enabledthe risk-averse model to effectively manage high-risk scenarios, leading to substantial cost savings.The quality of stochastic solutions was investigated using two measures, EVPI and VSS , demon-strating that stochastic solutions outperformed deterministic ones on average by 9.85% due to theabsence of complete and accurate information in the deterministic model. Sensitivity analyses ofrisk parameters (λ and Ï) demonstrated that, in high-risk scenarios, the risk-averse model can offermore same-day deliveries to hyper-local drivers to assure agile, collaborative, and flexible deliveryoptions. Increasing values of risk parameters resulted in conservative routing and allocation policies,enabling time and resource reservation to manage unpredictable delays.Due to the dynamic nature of online orders, Markov decision process model and ORDAOmethodology were integrated to the stochastic offline orders when dynamic online order were placedduring the working day. The performance of the proposed ORDAO was validated by comparingwith IMAS . The proposed ORDAO generated delivery tours to meet the same number of ordersin almost 11% less delivery time compared to the IMAS . In addition, the IMAS incorporateddynamic online orders into a pre-scheduled set of stochastic offline orders, while the proposedORDAO dealt with online orders by dynamically rescheduling the offline stochastic orders at eachdecision point. Two scenarios (scenario I: mobile depot and crowd-shippers, scenario II: mobiledepot, crowd-shippers, and hyper-local drivers) were considered to compare the performance ofnovel policies. The total delivery time and distance in the second scenario were decreased by12%, leading to lower CO2 emissions and reduced traffic congestion. In order to find the optimalreimbursement fee policy, three ratios were defined (fjdj,fjdâ²j, andfjcâ²ijk). The increase in thefjdjalignedwith a surge in the CVaR cost indicating that the reimbursement fee of hyper-local drivers becamemore significant compared to the cost of postponing. This demonstrated that higher participationrate of hyper-local drivers introduces a higher level of uncertainty and potential fluctuations in costs.Asfjdâ²jincreases, a remarkable reduction was observed in the T.C , E.V , and CVaR cost when anincreased volume of orders were assigned to hyper-local drivers with a reasonable reimbursement fee.There was a consistent incremental trend in the T.C , E.V , and CVaR cost whenfjcâ²ijkincreased.72In this chapter, the concept of resiliency in last-mile delivery is addressed through the develop-ment of an IDSS . Resiliency, in this context, refers to the ability of the last-mile delivery systemto sustain operational efficiency despite uncertainties such as fluctuating traffic conditions, adverseweather, dynamic crowd-shipper availability, and demand variability. To ensure a robust and adap-tive delivery network, the proposed IDSS integrates four key modules: a risk-averse multi-stagestochastic dynamic model, an IMAS model, a SET-EDI predictive analytics module, and a hy-brid ORDAO decision-making framework. Each of these modules contributes to enhancing theresilience of the last-mile delivery system by proactively mitigating risks and dynamically adaptingto unforeseen disruptions.The IMAS simulation model (Module I) plays a critical role in fostering resiliency by simulatingreal-time traffic and weather conditions. By integrating historical and real-time data, the model al-lows for proactive routing adjustments, reducing the likelihood of delivery failures due to congestionor adverse weather. This ensures that the system can respond dynamically to unexpected delays,maintaining high service levels. Furthermore, the incorporation of hyper-local drivers enhancesflexibility by leveraging local resources to address service disruptions, ensuring that deliveries arecompleted efficiently despite environmental uncertainties.Resiliency is further reinforced through the SET-EDI module (Module II), which predictscrowd-shipper availability using deep learning models. By identifying key socio-economic and de-mographic factors that influence participation in last-mile delivery, the model ensures an optimizedallocation of resources. This predictive capability minimizes the risk of delivery delays by main-taining a reliable supply of crowd-shippers, especially during peak demand periods. The ability toanticipate fluctuations in workforce availability enables the system to preemptively adjust staffinglevels and delivery schedules, enhancing the overall robustness of the network.The risk-averse multi-stage stochastic dynamic model (Module III) is specifically designed tomanage uncertainties by incorporating CVaR risk factor. It enhance resiliency by allowing the sys-tem to preemptively plan for disruptions while maintaining flexibility in real-time decision-making.The modelâs capability to optimize delivery plans under uncertainty ensures that supply chaindisruptions, such as unexpected surges in demand or reduced driver availability, do not lead tosignificant service delays.Finally, ORDAO (Module IV) provides an advanced hybrid decision-making framework thatdynamically refines initial delivery policies using RL. This module enables the system to con-tinuously adapt to changing conditions by learning from past disruptions and refining its decision-73making strategies over time. The integration of RL allows for real-time policy adjustments based onstochastic parameters, ensuring that the delivery system can self-correct and optimize performanceeven under highly uncertain conditions. By combining the robustness of stochastic optimizationwith the adaptability of RL, ORDAO ensures that delivery operations remain resilient to externaldisruptions.Resiliency within this framework is measured through a set of performance metrics that assessthe systemâs ability to maintain efficient and reliable service. Key metrics include the deliverysuccess rate, which evaluates the proportion of successfully completed deliveries despite disruptions,and the average delivery delay, which quantifies deviations from planned delivery times. Thesemetrics collectively provide a comprehensive evaluation of the systemâs resilience, ensuring that theproposed IDSS can effectively handle real-world delivery challenges.Through the integration of these modules, the IDSS fosters a highly resilient last-mile deliverysystem capable of anticipating, adapting to, and recovering from disruptions. The combinationof simulation-based forecasting, predictive analytics, stochastic optimization, and reinforcementlearning provides a robust, adaptive, and scalable framework for last-mile logistics, ensuring thatdeliveries remain reliable and efficient even in the face of uncertainty.In the context of the last-mile delivery system, the decision-maker refers to the individual orentity responsible for making decisions regarding the optimization of the delivery network. This in-cludes decisions related to resource allocation (e.g., assigning crowd-shippers or hyper-local drivers),scheduling (e.g., delivery time slots), routing (e.g., optimal delivery paths), and handling uncertain-ties (e.g., weather or traffic disruptions). The decision-maker is typically modeled as an automatedsystem within the IDSS that interacts with the various modules (e.g., risk-averse multi-stagestochastic model, IMAS , SET-EDI , and ORDAO) to make informed decisions based on real-time and predicted data. Therefore, the decision-maker could be a logistics manager or dispatcherwho interacts with the system and finalizes decisions. This individual or system would use the out-puts from the various models (e.g., crowd-shipper availability, delivery time estimates, and weatherforecasts) to make real-time or strategic decisions regarding the allocation of resources and routeplanning. For example, in a situation of heavy traffic or weather disruptions, the decision-makermay decide to reroute deliveries or assign more crowd-shippers to maintain service levels accordingto the output of the IDSS .The data used in this chapter, which supports the development of the interactive decision supportsystem for last-mile delivery, faces several limitations. First, there is a lack of high-resolution, real-74time data across all components of the delivery ecosystem. While the model integrates real-timeweather, traffic, and order patterns, access to such data in continuous and granular formats can berestricted or costly. Second, the availability and reliability of behavioral data, such as demographicinformation, income levels, and crowd-shipper/hyper-local driver participation rates, are often basedon surveys, small-scale experiments, or approximations. These are prone to sampling biases and maynot reflect the full diversity or dynamics of urban populations. In particular, behavioral intention(e.g., willingness to accept orders) may differ significantly from actual behavior, which introducesmodeling uncertainty. Third, data sparsity is an issue in modeling newer or emerging systems suchas mobile depots or flexible delivery modes. Since historical data may not exist or be rich enough forlearning purposes, the ensemble and deep learning modules must rely on simulated or augmenteddata to fill the gaps. This can affect the generalizability of the trained models.The design of the IDSS for last-mile delivery relies on a variety of data sources that areinterrelated, both directly and indirectly. A key correlation exists between demographic char-acteristicsâsuch as educational level, income, and perceived reliabilityâand the availability ofcrowd-shippers and hyper-local drivers. Another significant correlation lies between compensationor reimbursement fees and hyper-local drivers participation rates. Environmental conditions alsointroduce meaningful correlations. Real-time weather and traffic patterns are closely linked withtravel times and influence the reliability of delivery operations. Additionally, there is a strongoperational correlation between order characteristics (e.g., location and timing) and mobile depotplacement decisions. Lastly, there exists a dynamic feedback correlation between policy adjustmentsand system behavior.This study points to various promising directions for future research. These include the opti-mization of mobile depot routing, developing compensation fee policies to minimize postponementcosts or order cancellation costs arising from crowd-shipper unavailability. Additionally, exploringnovel strategies such as incorporating smart lockers to enhance the delivery process, can be anavenue for further investigation.75Chapter 3Intelligent decision support system forglobal dynamic supply chain logisticsresiliency in manufacturing sector3.1 IntroductionThe global economy is experiencing significant disruptions, impacting global supply chain strate-gies across all industries. In recent decades, businesses have faced increasing pressure to reorganizetheir operations, rethink sourcing and manufacturing strategies, and reassess demand fulfillment.The factors driving this transformation include typical elements such as market volatility, varyingcosts, and technological disruptions [63]. The complexity and diversity of global supply chains makethem vulnerable to a variety of logistical, natural, geopolitical, and industrial disruptions that cantemporarily restrict sourcing [64]. Such disruptions occur for reasons beyond the firmâs control, andtheir frequency cannot be easily managed; however, effective supply chain management practicescan mitigate the negative consequences of such interruptions. For example, a more resilient supplychain may be able to recover more quickly from a disruption, returning to its normal full operationalcapacity sooner than a less resilient one [65].Over the past decade, supply chain disruptions including supplier bankruptcies, natural andman-made disasters, labor strikes, and public health crises, have posed serious concerns to firms[66]. The latest global supply chain disruption (e.g., the COVID-19 pandemic) resulted in bothsupply and demand shocks across a wide spectrum of industries [153]. In July 2021, Pipeline Foods,a Minnesota organic food company filed for bankruptcy due to the reduced customer orders duringthe COVID-19 pandemic. Many farms were severely impacted by this bankruptcy. Apart from theirclaims on delivered grain (i.e., delivered grain to Pipeline Foods and owed payment or compensationfor it), they were unable to sell undelivered grain that had been contracted to Pipeline Foods to other76buyers [154]. Another noticeable case is Hanjin Shipping, a top 10 global container carrier, whichfiled for bankruptcy in September 2016 due to declining freight rates caused by reduced demand.The global supply chains have been affected since many of Hanjinâs container ships were deniedports access. Major U.S. retailers, including J.C. Penney and Walmart, responded by divertingtheir container shipments to alternative suppliers. The cost of shipping a 40ft container from Chinato the US surged by up to 50% in a day [155]. Supply chains with long-term supplier relationshiprecover quickly from disruptions [156]. Source diversification is another recommendation to managedisruptions effectively, instead of relying on single sourcing [157]. For example, Aisin, the onlysupplier of brake valves for Toyota, lost revenue estimated at billions of US dollars following a firein one of its plants in 1997 [158]. A good illustration is Nokia, adopting a multiple-sourcing strategyfollowing the fire at Philipsâ Albuquerque plant in the United States [159].The resilience of a firm is highly depend on the firmâs sourcing strategy (e.g., multi-sourcingand contingent sourcing) [160]. The impact of supplier diversification in dealing with disruptionsis analyzed considering hedging strategies (i.e., multiple sourcing, long-term contract, componentsubstitution, and consignment inventory). In the staticâdynamic type of uncertainty, the setups aredecided in the initial period (period 0) for the entire horizon, whereas the production, purchase,and inventory decisions are chosen at each period after the uncertain parameters have been realized.The decision-making process in staticâdynamic environment gives rise to a multi-stage stochasticproblem with Markovian parameters, typically modeled using a scenario tree [161]. In this studyI develop PSDDiP approach to with the complexities of dynamic uncertainty in global supplychains. This method allows for the optimization of decisions over time, enhancing a firmâs resilienceby effectively managing risks and adapting to changing conditions. Through PSDDiP , firms canbetter manage disruptions and sustain operations in challenging environments. The stochasticdual dynamic integer programming (PSDDiP) algorithm is developed to deal with the large-scalemulti-stage stochastic models with Markovian parameters. This algorithm is advantageous overthe scenario tree approach due to the following reasons. First, the stagewise decomposition inPSDDiP mitigates the exponential growth of the number of scenario paths, provided that theprobability distributions of the different decision stages are independent. As a result, PSDDiPconsiders only S â² scenarios per stage. Second, for any realization of the Markovian parameters thecost-to-go approximations remain valid. As new information emerges, PSDDiP updates quantitiesquickly, since it only needs to solve the sub-problem of the corresponding stage [162]. In this study,a global supply chain and the potential global strategies are examined. More specifically, the77following research questions are investigated: i) What strategies are most effective in enhancing theresilience of global supply chains in the face of diverse disruptions? ii) What factors influence thedecision between multi-sourcing and single sourcing in global supply chains, affecting resilience andoperational efficiency? iii) How can global supply chain networks adapt to dynamic uncertainties?iv) How do various global supply chain agents determine their contract terms?The rest of this investigation is arranged as follows: the most relevant studies are reviewedin Section 3.2, and Section 3.3 describes the problem. The mathematical model formulation isformulated in Section 3.4. Section 3.5 describes solution approach. The numerical experiment andresiliency analysis are investigated in Section 3.6 by presenting a case study and respective scenarios.Finally, the managerial implications and conclusions are given in Sections 3.7 and 3.8.3.2 BackgroundThis section is divided to four main streams, i) supply chain resiliency, ii) sourcing strategies(multi-sourcing vs single sourcing), iii) long term contract, and iv) stochastic dual dynamic integerprogramming.3.2.1 Supply Chain ResiliencyThere is an extant literature investigating and highlighting various aspects of risk managementwithin supply chains [163]. The disruption impacts are primarily examined by identifying key factorsto minimize their devastating effects [164]. In recent years, [165] examined how disruption impactspropagate in a simplified supply chain (i.e., assembly network), considering that only a single nodecan be disrupted. [166] introduced a novel approach that employs the TTR factor, assessed throughthe REI , to quantify the financial implications of disruptions across the entire supply chain. Inaddition, [167] proposed the TTS factor (e.g., implemented in the Cisco), defined as the maximumduration the entire supply chain can function without being adversely affected by the disruptionâsripple effects. [168] studied the implementation of supply chain monitoring software in companiessuch as Eaton and UTC to proactively identify signs of potential supplier instability, enabling themto implement preemptive safeguards in a timely manner. [163] integrated probabilistic assessmentof disruption risks into the REI factor to assess supply chain resiliency by evaluating the worst-case conditional value at risk associated with total lost sales during disruptions. Furthermore, [169]defined metrics such as net present value of profit loss, time to recovery, and recovery level to78evaluate supply chain resilience.3.2.2 Multi-Sourcing StrategyDiversification, in which an organization simultaneously procures from multiple suppliers, is acritical sourcing strategy to mitigate disruption risks. For example, [170] and [171] focused on dualsourcing strategy (i.e., procuring supplies from two suppliers) in single period models. A good illus-tration is [172]âs study, introducing the notion of ârecoveryâ and providing case-based evidence onthe effectiveness of disruption management strategies such as multi-sourcing and long-term contract.In the context of transportation procurement planning, it can be referred to [173]âs study, investi-gating a supplier portfolio selection problem considering delivery time uncertainties. [174] examinedmulti-sourcing strategy, focusing on how suppliers set wholesale prices and buyers decide on orderquantities. Moreover, sourcing strategies (e.g., dual sourcing and contingent sourcing) were studiedby [175], focusing on two scenarios, sourcing from an unreliable supplier (i.e., long transportationlead time and is prone to in-transit yield loss) or reliable supplier (i.e., short lead time with noyield loss). Similarly, [65] examined the the capability of a supply chain to recover after a sourcingdisruptions, focusing on the supply chain strategies such as multi-sourcing and long-term contract.In the following year, [176] analyzed dual sourcing strategy for a retailer under disruption risks,adjusting retail pricing upon delivery. Additionally, the souring strategies under disruption riskswere investigated by [165] within a three-tier supply chain. Although multi-sourcing strategies havebeen studied, there is a gap in understanding how these approaches can be effectively integratedand adapted to dynamic and complex supply chain environments. Furthermore, while research hasexplored sourcing from multiple suppliers, additional studies are needed to examine how varioussourcing strategies interact with uncertainty and recovery mechanisms across different contexts.3.2.3 Long-Term ContractsSupply chain contracts have been proposed as a coordination mechanism, providing incentiveswithin the supply chain [177]. Therefore, long-term contracts have improved supply chain perfor-mance, resulting in resiliency, cost saving, quality improvements, and higher profitability [178]. Inthis regard, [179] focused on the comparison of two types contracts (i.e., IBAs and TBAs). Inthe IBAs contracts, partners are bound together in a contractual agreement without a specifiedend date, while in TBAs, they are able to terminate contractual arrangement as needed. Similarly,[180] investigated the strategic decisions between short-term and long-term contracts within a de-79centralized three-echelon supply chain, employing a dynamic game theory approach. In addition,[181] explored how supply chain contracts and delegations can be utilized to incentivize a supplier toenhance its reliability. The contract terms and their impacts on sourcing decisions were analyzed by[170] within a three-tier supply chain (i.e., manufacturer, tier 1 suppliers, and tier 2 suppliers) underdisruption risks. For example, one of the contract terms under disruption risks is âflexibility frac-tionâ, examined by [182]. This term involves suppliers offering contract terms that include flexiblesupply terms, such as wholesale pricing and a minimum delivery fraction. Similarly, [177] analyzedtwo types of contract terms under the latter timing scenario. In the first examined contract term(long-term contracts), the business contractual agreement is extended over an extended period, andin the second contract term (penalty contracts), the supplier is penalized for insufficient capacity. Anew contract structure was introduced by [183] focusing on coordinating the three-echelon agricul-ture supply chain under stochastic demand. Despite extensive research on various contract types,there is a gap in exploring hybrid or novel contract structures that could better address dynamicuncertainties. Additionally, integrating flexibility with reliability and applying findings to diversesupply chain configurations remain underexplored.3.2.4 Parallel Stochastic Dual Dynamic Integer ProgrammingThere exist various sources of uncertainty in supply chain networks, such as fluctuations in de-mand, cost variability, shortage, lead times, and capacity. [184] explored the supply disruptions anddemand fluctuations occurred during the COVID-19 pandemic, while [185] focused on the macroe-conomic interplay between supply shocks and demand shortages during the pandemic. There havebeen various approaches to address stochastic models, including progressive hedging (PH) [186],scenario-based mathematical programming [187], [188], heuristics [189], and branch & bound [190].[191] introduced a methodology to generate cutting planes for multi-stage stochastic mixed-integerlinear programming models. This approach combines valid inequalities derived from the determinis-tic version of the problem. The SDDP algorithm has been widely applied approach in various areas,such as hydrothermal energy operations planning [192, 193], the control of microgrids [194], pastoraldairy farms [195], portfolio optimization [196]. More recently, [197] developed an accelerated versionof the SDDP algorithm, known as the stochastic dual dynamic integer programming SDDiP al-gorithm, capable of solving multi-stage stochastic mixed-integer linear programming models. A keycontribution in their study was the integration of the Lagrangian cuts (i.e., a new class of cuttingplanes) that meet the KPI , including validity, tightness, and finiteness, thus guaranteeing the algo-80rithmâs convergence to optimality. [198] focused on the statistical properties and convergence of theSDDP method, assuming stagewise independence of data process. They developed a framework togenerate random samples from the original distribution to support their analysis. In the followingyear, the SDDP approach was utilized by [199] to approximate the recourse functions.According to the reviewed literature, the dynamic aspects of supply chain networks under dis-ruption and their subsequent recovery processes have remained under explored. Research on supplychains resiliency primarily has focused on conceptual frameworks and outlined the various phases ofa resilient risk management model. Although systemic risk has been extensively studied in financeliterature, research on systemic risk within supply chain networks has remained relatively limited.However, systemic risk in supply chains is economically significant, given that the gross output ofthe manufacturing industry is more than the finance and insurance industry (i.g., in the UnitedStates, $5,712 billion compared to $2,408 billion in 2016, according to the U.S. Department of Com-merce) [175]. Considering dynamic uncertainties and potential supplier disruptions, global supplychains must be designed and planned to effectively navigate and mitigate uncertainties during dis-ruptions [200]. Therefore, developing resilient global supply strategies is crucial. As the literatureshows, there is no study comprehensively addressing the resilience of a global supply chain (i.e.,multi-region, multi-supplier, multi-component, multi-product, and multi-period stochastic-dynamicsupply chain network) under stochastic-dynamic uncertain nature of the environment (Markovianparameters) considering hedging strategies (i.e., multiple sourcing, long-term contract, componentsubstitution, and consignment inventory) to improve the resiliency. A new variant of the SDDiPapproach is proposed to solve large-scale multi-stage stochastic-dynamic problems. The proposedextension relies on two main ideas, the use of a partial decomposition of the scenario tree and theexploitation of existing knowledge on the polyhedral structure of the stochastic-dynamic global sup-ply chain. To the best of our knowledge, this study represents the first exploration of this extensionwithin the context of the SDDiP algorithm. A multi-threading approach is utilized to parallelizethe solution of each stageâs of the multi-stage stochastic model, potentially enhancing the overallcomputational efficiency by utilizing multiple CPU cores.3.2.5 Aims and NoveltyIn this chapter the main aim is to design an IDSS for global SC logistics resiliency in man-ufacturing sector considering hedging strategies such as multi-sourcing, long-term contract, andconsignment inventory. The above research gap in resilience global SC operations opens several av-81enues for investigation. The first research gap lies in the lack of an integrated approach to managingorder scheduling, production planning, and inventory management within global SC . Traditionally,these areas have been studied in isolation, leading to inefficiencies and missed opportunities foroptimization. In a global supply chain, these functions are highly interdependent, and decisions inone area can significantly impact the others. For example, production planning without consideringorder scheduling for bills of materials can lead to delays, increased costs, and inventory imbalances.Another key research gap is the insufficient exploration of the dynamic nature of global SC andthe role of hedging policies in enhancing resilience. Global SC s are subject to frequent disruptionsand uncertainties, such as fluctuating demand, supply shortages, and geopolitical risks. Existingstudies often overlook the need for adaptive strategies that can respond to these dynamic changes.This research fills this gap by investigating the impact of hedging policies, such as multiple sourc-ing, consignment inventory, and long-term contracts, on global SC resilience. The development oflarge-scale multi-stage stochastic dynamic models represents another significant research gap. Manyexisting models for global SC operations are static and fail to capture the complexities and uncer-tainties inherent in real-world scenarios. Moreover, the scalability of these models is often limited,making them impractical for large and complex SC s. This study contributes to this area by de-veloping and implementing a large-scale multi-stage stochastic dynamic model that can handle thecomplexity and uncertainty of global supply chains. This model not only captures the dynamic na-ture of SC operations but also provides a scalable solution that can be applied to large networks.Finally, there is a gap in the development of efficient solution approaches for solving large-scalestochastic dynamic models. Traditional solution approaches can be computationally intensive andtime-consuming, limiting their applicability in real-world scenarios. This challenge is addressed byintroducing a novel solution approach, the parallel SDDiP . To further enhance the efficiency ofthis method, four types of cuts, including Benders optimality cut (BOC ), SWLDC , and MIRcuts, to accelerate the solution process. This contribution not only improves the computationalefficiency of solving large-scale models but also makes it feasible to apply these models to real-worldglobal supply chains, thereby bridging a crucial gap in the literature.The main contributions of this chapter as follows:â A multi-stage stochastic dynamic programming model is developed for the proposed globalsupply chain incorporating order scheduling for bills of materials, production planning, andinventory management.â The incorporation of the hedging policies into the proposed multi-stage stochastic-dynamic82model is accompanied by an investigation of the supply chain resilience.â A discount rate model is presented to find the most appropriate discount rate consideringsupplierâs limited working capital, supplierâs external risk factors, and direct financing.â A parallel accelerated SDDiP algorithm (SDDiP-MIR) is proposed to solve large-scalestochastic dynamic multi-stage model, and compared with the basic version of SDDiP andaccelerated version, SDDiP-SWDC .3.3 Problem StatementResilience, which is referred to as the ability to recover quickly and effectively from a disruption,is a key and complex aspect in supply chain risk management [11]. In this study, a stochastic-dynamic global supply chain (i.e., multi-region, multi-supplier, multi-component, multi-product,and multi-period) is investigated, including three stages. The first stage deals with the strategicdecision-making process (i.e., the purchase of raw materials from supplier(s) ir in region(s) r withor without discount). The tactical decisions in the second stage are related to renting a container inperiod t to carry the raw materials from region r to supplier i, and determining the volume shippedfrom area r in period t. The final stage focuses on operational decisions, specifically addressingproduction planning throughout the planning horizon T . In another words, the decisions relatedto the quantity of produced product p during period t, inventory of raw material q in the initialwarehouse at the end of period t, the used volume of second warehouse at the end of period t,quantity of leased volume over the capacity of the first and second warehouse in period t, overtime,and shortage are made in the third stage. In this context, the manufacturers place their orders(raw materials), waiting for the supplier notification regarding their eligibility for discounts. Then,the model arranges the shipment of the purchased raw materials, considering their eligibility fordiscount, by renting container to deliver them to the respective manufacturer. The initial inventoryof the first warehouse is updated, and the production process starts. In case of insufficient capacityof first and second warehouse, the model needs to decide on leasing volume over the capacity offirst and second warehouse. At the end of each period t, the shortage of each product type Gpt andovertime C â²t will be specified.The first, second, and third stage decisions include investigating a wide range of decisions relatedto the geographic supplier selection, discount, renting, shipment, manufacturing, inventory, over-time, and shortage, posing a significant challenge. Renting, shipment, manufacturing, inventory,83overtime, and shortage decisions are affected by stochastic-dynamic changes and require sequentialdecision-making in a stochastic-dynamic environment. There exists a strong correlation betweenthe integrated hedging policies (i.e., multiple sourcing, long-term contract, consignment inventory,component substitution) and resilience in the face of disruptions in the global supply chain. Inte-grated hedging policies incentivize supply chain stakeholders to implement strategies that ensurecontinuous flow of goods and services across borders, even in the face of disruptions such as naturaldisasters, geopolitical tensions, pandemics, or economic shocks. This includes integrating flexibil-ity and agility into supply chain networks, diversifying sourcing and manufacturing locations, andimplementing robust contingency plans to adapt to unexpected events. Ultimately, the goal is tominimize vulnerabilities and enhance the supply chainâs resilience to recover from disruptions, en-suring business continuity and minimizing impacts on global trade and commerce. Figures 3.1 and3.2 provide a better understanding about the problem statement and the proposed DSS .Figure 3.1: Sequential Decision-Making for Resilient Stochastic-Dynamic Global Supply Chains:Strategic Supplier Selection, Tactical Renting and Shipment, and Operational Manufacturing andInventory Management84Figure 3.2: The Proposed Decision Support System for Global Supply Chain Logistics in Manufac-turing Sector3.4 Mathematical FormulationThis study addresses the procurement strategies for raw materials, production planning, and in-ventory management strategies in materials and products warehouses within a global supply chain,simultaneously. The purpose of this study is the decision on single sourcing or multi-sourcing, deter-mine the optimal volume of procuring raw materials, logistical planning, and production planningover the planning horizon. This problem is characterized as a multi-region, multi-supplier, multi-component, multi-product, and multi-period stochastic-dynamic problem. There is a time intervalbetween placing order and delivering raw materials, varied by the supplierâs geographic location.Therefore the global supply chain network is formulated as follows:85Table 3.1: NomenclatureSets & ParametersIr Set of suppliers based in different zones rR Set of areas including suppliersP Set of manufactured productsQ Set of bill of materialsT Set of time periodsr Index of areas including suppliers r â {1, 2, ...,R}t Index of time periods t â {1, 2, ...,T }p Index of manufactured products p â {1, 2, ...,P}q Index of bill of material q â {1, 2, ...,Q}ir Index of suppliers in zone r ir â {1, 2, ...,Ir}siq Unit purchase price of material q from supplier iθi Discount ratio offered by supplier ipri Minimum purchase for applying the unit cost discount from supplier i ($)Ca The capacity of containervfq Volume per unit of material qvlp volume per unit of product pcrer Rental cost of a container in the area rcin Cost of inventory ($)li Time between ordering and receiving the bill of materials from supplier iifoq Initial inventory level of material q stored in the first warehouseidop Initial inventory level of product p in the second warehousecif First warehouse capacityci1 Second warehouse capacityaâ²pq The quantity of material q required to produce one unit of product pbâ²p Production time required to manufacture one unit of product pmaxtime Maximum operational hours of the factory per periodmaxb Maximum purchase amount eligible for a discount in each period ($)dpt Demand for product p in period tc1 Additional cost of warehouse rental for storing the bill of materials ($)c2 Cost of renting additional warehouse space for manufactured products ($)c3 Overtime labour cost ($)c4 The cost of public transportation ($)c5 Shortage cost (indemnification fee) ($)86Decision variablesXuiqt The purchased material q from supplier i in period t (discount)Xliqt The purchased material q from supplier i in period tYpt The manufactured product p in period tIDFqt The inventory level of material q in the warehouse 1 in period tIDLt The volume used in the warehouse 2 in period tAt The leased volume for raw material in period tBt The leased volume for final products in period tC â²t Overtime hours worked in period tHrt The freight volume transported from area r using in period tGpt The amount of shortage of product p in each period tZ â²it Binary variable, 1 if the discount from supplier i is applied in period tWrt Binary variable, 1 if a container is rented in t for shipment from area rMin Z =âiâIâqâQâtâTsiq âXuiqt +âiâIâqâQâtâT(1â θi)siq âXliqt +ârâRâtâTcrer âWrt+âqâQâpâPâtâTcin â vfq â IDFqt +âtâTcin â IDLt +âtâTc1 âAt +âtâTc2 âBt+âtâTc3 â Ct +âtâTârâRc4 âHrt +âtâTâpâPc5 âGpt(3.1)Subject to:pri â Z â²it â¤âqâQsiq âXliqt â¤ maxb â Z â²it âi â I , t â T (3.2)âqâQâiâIvfq â (Xuiqt +Xliqt) â¤ ca âWrt +Hrt ât â T , r â R (3.3)IDFqt = ifoq +âiâI(Xuiqtâli +Xliqtâli)ââpâPaâ²pq â Ypt ât â T , q â Q, t = 1, tâ li â¥ 0 (3.4)IDFqt = IDFqtâ1 +âiâI(Xuiqtâli +Xliqtâli)ââpâPaâ²pq â Ypt ât â T , q â Q, t â¥ 1, tâ li â¥ 0(3.5)âqâQvfq â IDFqt â¤ cif +At ât â T (3.6)idop +âtâ²â¤tYptâ² ââtâ²â¤tdptâ² +Gpt â¥ 0 ât â T , p âP (3.7)87IDLt =âpâPvlp â idop +âpâPvlp â Ypt ââpâPvlp â dpt ât = 1, (3.8)IDLt = IDLtâ1 +âpâPvlp â Ypt ââpâPvlp â dpt ât â¥ 1, (3.9)IDLt â¤ ci1 +Bt ât â T (3.10)âpâPbâ²p â Ypt â¤ maxtime+ C â²t ât â T (3.11)Xuiqt, Xliqt â Z+ âi â I , q â Q, t â T (3.12)Ypt â Z+ âp âP, t â T (3.13)IDFqt â Z+ âq â Q, t â T (3.14)IDLt, At, Bt â Z+ ât â T (3.15)Hrt â Z+ ât â T , r â T (3.16)Wrt â [0, 1] ât â T , r â T (3.17)Z â²it â [0, 1] ât â T , i â I (3.18)The objective function, Equation (3.1), minimizes the total costs, including the procurementcost of raw materials, considering their eligibility for discounts), logistical cost, inventory manage-ment cost, shortage cost, overtime labour cost, and lost sale opportunity cost. Constraint (3.2)checks the buyerâs eligibility for discounts and controls it. Constraint (3.3) manages the logistics ofraw materials from various geographic regions. Constraints (3.4) and (3.5) apply inventory manage-ment strategies in the first warehouse. Constraint (3.6) defines the first warehouseâs capacity, andexplains that exceeding this capacity with overstocked raw materials incurs higher inventory costs.Constraint (3.7) deals with inventory of the produced products in second warehouse. Constraints(3.8) to (3.10) define the second warehouseâs capacity, and explains that exceeding this capacitywith overstocked produced products incurs higher inventory costs. Constraint (3.11) indicates thatthe production of one unit of product p requires a specific time, and the total production timein period t must not exceed the regular working hours, while any overtime incurred will result inovertime cost. Constraints (3.12) to (3.16) are continuous variables. Constraints (3.17) and (3.18)are binary variables.883.4.1 Hedging PoliciesHedging strategies in supply chain management include risk management strategies to mitigatedisruptions, such as demand fluctuations, supply disruptions, or price volatility.3.4.1.1 Multiple SourcingThe model incorporates the multi-sourcing policy by integrating the associated cost and capacityconstraint.âqâQsiqXLDiqt â¤ dc âi â I , t â T (3.19)Constraint (3.19) is the multi-sourcing capacity constraint, where XLDiqt and dc show thequantity of material q procured from supplier i in period t considering their eligibility for discountand multi-sourcing capacity, respectively. It should be noted that the multi-sourcing cost (dscsâ²) isincluded in the total network cost.3.4.1.2 Long-Term ContractLong-term contract policy is integrated into the developed model for the global supply chainnetwork, considering long-term contract cost and maximum capacity.âqâQLTCiqt â¤ cct âi â I , t â T (3.20)âqâQLTCiqt = 0 âi â I , t â T , if t â¤ cod (3.21)Constraint (3.20) denotes the capacity constraint, where LTCiqt and cct define the quantity ofmaterials supply commit to procure under long-term contract and contractâs capacity, respectively.Constraint (3.21) assures that the long-term contracts are valid for the specified contract dura-tion, where cod denotes the contract duration. Therefore, the material procurement and inventorycapacity constraints are modified as follow:89priZâ²it â¤âqâQsiq(XLiqt +XLDiqt + LTCiqt) âi â I , t â T (3.22)âqâQsiq(XLiqt +XLDiqt + LTCiqt) â¤ Z â²itmaxb âi â I , t â T (3.23)âqâQvfq(XLiqt +XLDiqt + LTCiqt) â¤WitCa+Hit âi â I , t â T (3.24)3.4.1.3 Consignment InventoryThis section explains the adoption of consignment inventory policy into the developed model forthe global supply chain network.Ciqt â¤ Z â²itbigM âi â I , t â T , q â Q (3.25)Ciqt â¤ (1â Z â²it)Cmax âi â I , t â T , q â Q (3.26)Ciqt â¥ minCiqZ â²it âi â I , t â T , q â Q (3.27)Constraint (??) guarantees that the combined production and consignment inventory fulfill thedemand. Constraints (3.26) and (3.27) denote the consignment inventory constraints, where Ciqt,Cmax, and minCiq show the consignment inventory, maximum capacity of consignment inventory,and minimum consignment inventory levels, respectively.The adjusted objective function following the integration of hedging policies is given as follows:Min Z =âiâIâqâQâtâTsiq âXuiqt +âiâIâqâQâtâT(1â θi)siq âXliqt +ârâRâtâTcrer âWrt+âqâQâpâPâtâTcin â vfq â IDFqt +âtâTcin â IDLt +âtâTc1 âAt +âtâTc2 âBt+âtâTc3 â Ct +âtâTârâRc4 âHrt +âtâTâpâPc5 âGpt+âqâQâiâIâtâT(XLDiqtsiqdsc+ LTCiqt) +âqâQâiâIâtâTLTCiqtcc+âqâQâiâIâtâTCiqtc6(3.28)Where dsc, cc, and c6 denote multi-sourcing cost, long-term contract cost, and consignment90inventory cost, respectively.The proposed multi-region, multi-supplier, multi-component, multi-product, and multi-periodglobal supply chain network, incorporating hedging policies is formulated as a multi-stage stochastic-dynamic model. The purchase price, demand, the maximum permissible purchase limit to be eligiblefor the discount, initial inventory of the material q in the primary warehouse, initial inventory ofproduct p in the secondary warehouse, the number of required material q to produce a unit of productp, and long-term contract capacity have stochastic-dynamic nature. These uncertain parametersare represented by the set of scenarios (S â²), where each scenario sâ² has a probability of pâ²sâ² . Thefirst stage decisions, denoted by Z â²it, Wrt and Hrt denote the eligibility for the discount, leasing acontainer to transport purchased materials to the manufacturerâs location, and the volume shippedfrom supplier i at region r to manufacturer, respectively. Such deterministic decisions are made priorto the scenario realization. The subsequent stage decisions, represented by Xuiqt, Xliqt, Ypt, IDFqt,IDLt, At, Bt, and Câ²t, Gpt are made after scenario realization, demonstrating the purchased quantitywith and without discount, inventory level at first and second warehouses, leased volume, overtime,and shortage, respectively. The problem is formulated as a multi-stage stochastic programmingmodel including three main stages, i) sourcing decisions, ii) logistical decisions, and iii) productionplanning decisions. The general form of the multi-stage stochastic programming [201] is given asfollows:Min Z =F (W,H) + Esâ²[Q(Xu,Xl, Sâ²) + Es1[Qâ²(B,C,G, Sâ²)]](3.29)The first stage is formulated as follows:Min F (W,H) =ârâRâtâTcrer âWrt +âtâTârâRc4 âHrt (3.30)The formulation of stages t2 to the last stage T is formulated as follows:91Min Esâ²[Q(Xu,Xl, Sâ²) + Esâ²[Qâ²(B,C,G, Sâ²)]]=E[âiâIâqâQâtâTsiq âXuiqt +âiâIâqâQâtâT(1â θi)siq âXliqt+âqâQâpâPâtâTcin â vfq â IDFqt +âtâTcin â IDLt +âtâTc1 âAt+âqâQâiâIâtâT(XLDiqtsiqdsc+ LTCiqt) +âqâQâiâIâtâTLTCiqtcc+âqâQâiâIâtâTCiqtc6 + E[âtâTc2 âBt +âtâTc3 â C â²t +âtâTâpâPc5 âGpt]]3.5 Solution Approach: The Proposed Parallel Stochastic DualDynamic Integer ProgrammingMulti-stage stochastic programs have always been challenging to solve due to the numerouspossible outcomes resulting from the realization of random processes over time. The SDDiP ap-proach is one of the efficient solution approaches for convex multi-stage stochastic programmingproblems [162]. The SDDiP algorithm solves the multi-stage stochastic by using dynamic pro-gramming recursion, sampling from the scenario tree and iteratively improving a convex piecewisepolyhedral lower approximation of the expected cost-to-go function at each node. The convergencecriteria lies in achieving a certain level of tightness in the lower approximation of the value func-tions through cuts [197]. SDDiP assumes stage-wise independence of probability distributionsto effectively manage the exponential growth in the number of states. Based on this assumption,the complete set of scenarios represents a symmetric scenario tree, with each node representing arealization of the Markovian parameters, and each path is a specific scenario [202]. Since the treeis symmetric, all the stage tâs nodes have branches toward the same scenario set S1(t+1) followingthe Markovian parameters realization in stage t+1. Additionally, the branchesâ probability leadingthe same sample are identical, thereby, representing a stochastic process with a sample S1(t) foreach period t â T . Consequently, the multi-stage stochastic programming models are decomposedper stage in SDDiP . Given the decisions made (i.e., xâ²1,2,...,t) in stages 1 to t â 1 and the Marko-vian parameters realization of in stages 1 to t (sâ²1,2,...,t), the stage tâs sub-problem is formulated toto find the decisions, optimizing the stage tâs cost and the cost-to-go Ït+1(sâ²1,2,...,t;xâ²1,2,...,t). Thiscost-to-go function approximates the expected costs from stage t+1 to T , considering the decisions92made xâ²1,...,t from stage 1 to t and Markovian parametersâ realization (sâ²1,...,sâ²) in Stages 1 to sâ². Thecost-to-go function depends only on the sâ²t and is independent of the entire historical data process[203]. The SDDiP iteratively forms an outer approximation of cost-to-go functions, since they areundefined at the beginning of the process [198]. In each iteration of SDDiP , a forward pass gener-ates a feasible solution, and a backward pass adds information about the cost-to-go functions (i.e.,the cuts are generated). In other words, the procedure for generating a cut is a two-step process,including forward and backward passes. The forward and backward processes are described below.3.5.1 Forward PassThe forward pass simulates the use of the current policy for a set of scenarios ζ re-sampled fromS â² at each iteration. For each scenario ζ â² â ζ, the sub-problems are solved starting from staget = 1 until stage t = T . Each decision stage corresponds to the arrival of new information on theMarkovian parameters. More precisely, the first stage corresponds to the initial state, where noinformation on the Markovian parameters is available, and it decides the decisions focusing on thestrategic purchase of raw materials with or without discount from a supplier i in region r or frommultiple suppliers i1, i2, ...,I in regions r1, r2, ...,R. Similarly, the stage t = {2, ...,T } correspondsto the beginning of period t, where the Markovian parameters in period t â 1 are known, andit decides the shipment of raw materials from suppliers to manufacturers by renting containers.Finally, the last stage deals with the production, inventory, overtime, and shortage decisions.3.5.1.1 First Stage ModelThe first stage decisions are made prior to the realization of Markovian parameters in periodt = 1. It is important to highlight that the developed first stage model includes a variable Ï2,specifying the lower bound of the cost-to-go. The cost-to-go function (Ï2) is defined by a set ofhyper planes (Φ2) built iteratively to improve the approximation of the Ï2. The first stage problem(t = 1) is formulated as follows:93MinârâRât=1crer âWr1 +ât=1ârâRc4 âHr1+E[âiâIâqâQât=1siq âXuiq1 +âiâIâqâQât=1(1â θi)siq âXliq1+âqâQâpâPât=1cin â vfq â IDFq1 +âtâTcin â IDL1 +âtâTc1 âA1+âqâQâiâIât=1(XLDiq1siqdsc+ LTCiq1) +âqâQâiâIât=1LTCiq1cc+âqâQâiâIât=1Ciq1c6 + E[ât=1c2 âB1 +ât=1c3 â C â²1]]+ Ï2(3.31)Subject to:Ï2 â¥ Ïhâ²2 (Wr1, Hr1, Xuiq1, Xliq1, IDFq1, IDL1, A1, B1, LTCiq1, XLDiq1, Ciq1, C â²1) âhâ² â Φ2(3.32)Constraints (3.2)â (3.4), (3.6), (3.8), (3.15)â (3.21)Constraint (3.32) approximate the lower bound for the cost-to-go function.3.5.1.2 Middle Stages ModelIn stage t â {2, ...,T â 1}, the realization of the Markovian parameters enables to find theoptimal values of Xuiqt, Xliqt, Ypt, IDFqt, IDLt, At, Bt at the end of period t â 1 in scenario sâ².The sub-problem of stages t â {2, ...,T â 1} is formulated as follows:Min E[âiâIâqâQâtâTsiq âXuiqt +âiâIâqâQâtâT(1â θi)siq âXliqt+âqâQâpâPâtâTcin â vfq â IDFqt +âtâTcin â IDLt +âtâTc1 âAt+âqâQâiâIâtâT(XLDiqtsiqdsc+ LTCiqt) +âqâQâiâIâtâTLTCiqtcc+âqâQâiâIâtâTCiqtc6 + E[âtâTc2 âBt +âtâTc3 â C â²t +âtâTâpâPc5 âGpt]]+ Ït+1(3.33)Subject to:Ït+1 â¥ Ïhâ²t+1(Xuiqt, Xliqt, IDFqt, IDLt, At, Bt, LTCiqt, XLDiqt, Ciqt, C â²t, Gpt) âhâ² â Φt+1 (3.34)94Constraints (3.2)â (3.7), (3.9), (3.10), (3.15)â (3.21)Constraint (3.38) approximate the lower bound for the cost-to-go function.3.5.1.3 Last Stage ModelThe subproblem of the last stage (T ) is given below, where the decision variables include theC â²t, IDLt, IDFqt, and Gpt in period t for scenario sâ²:Min E[âqâQâpâPât=Tcin â vfq â IDFqt +âtâTcin â IDLt+E[ât=Tc2 âBt +ât=Tc3 â C â²t +ât=TâpâPc5 âGpt]] (3.35)Subject to:Constraints (3.4), (3.6), (3.7)â (3.10)3.5.2 Backward PassThe outer approximation of the cost-to-go Ït+1(sâ²1,...,t, xâ²1,...,t), is defined by a set of hyper planes,which is initially empty and iteratively generated in the backward pass. The backward pass solvesthe sub-problem of each stage t (from t = T to t = 2) for all scenarios sâ² in Sâ²t, given the decisionsmade in the previous stages, to compute the cost-to-go associated with the scenarios in the respectivestage (Sâ²t). The SDDiP adds the generated cut using the duality of the sub-problem in stage t(i.e., Benders optimality cuts) to the sub-problem of stage t â 1 to improve the approximation ofthe cost-to-go in stage tâ 1.3.5.2.1 Cut Families: Multi-Cut SDDiPTo improve the approximation of the cost-to-go function in stage t â 1, SDDiP adds a cutinferred from the dual of the stage t sub-problems to the sub-problem of stage tâ 1.3.5.2.1.1 Benders Optimality Cut The Benders optimality cut generated by the first stage(t = 0) dual sub-problem is as follows:95âsâ²âS â²Î»1sâ²(pâ²sâ²cif) +âsâ²âS â²Î»2sâ²(âpâPpâ²sâ²vlpsâ²idopsâ² +âpâPâtâTpâ²sâ²vlpsâ²dptsâ²) +âsâ²âS â²Î»3sâ²(pâ²sâ²dscsâ²) +âsâ²âS â²Î»4sâ²(âtâTpâ²sâ²ccsâ²t)(3.36)Where Î»1sâ² , Î»2sâ² , Î»3sâ² , and Î»4sâ² are dual variables. The cuts generated from sub-problems in stagest = 1, ...,T â 1 are as follows:âsâ²âS â²Î»5sâ²(âqâQpâ²sâ²ifoqsâ²) +âsâ²âS â²Î»6sâ²(cif) +âsâ²âS â²Î»7sâ²(âpâPpâ²sâ²idopsâ² +âtâTâpâPâsâ²âS â²pâ²sâ²dptsâ²)ââsâ²âS â²Î»8sâ²(âpâPâtâTpâ²sâ²vlpsâ²dptsâ²) +âsâ²âS â²Î»9sâ²(ci1) +âsâ²âS â²Î»10sâ² (pâ²sâ²dscsâ²) +âsâ²âS â²Î»11sâ² (âtâTpâ²sâ²ccâ²sâ²t)(3.37)Where Î»5sâ² , Î»6sâ² , Î»7sâ² , Î»8sâ² , Î»9sâ² , Î»10sâ² , and Î»11sâ² are dual variables. Finally, the cuts generated fromsub-problem in stage t = T are as follows:Î»12sâ² (âsâ²âS â²âpâPvlpsâ²idopsâ² +âsâ²âS â²âpâPâtâTpâ²sâ²vlpsâ²dptsâ²)â Î»13sâ² (âsâ²âS â²âpâPâtâTpâ²sâ²vlpsâ²dptsâ²)+Î»14sâ² (ci1) + Î»15sâ² (âqâQâsâ²âS â²pâ²sâ²ifoqsâ²) + Î»16sâ² (cif) + Î»17sâ² (âpâPâsâ²âS â²idopsâ²)(3.38)Where Î»12sâ² , Î»13sâ² , Î»14sâ² , Î»15sâ² , Î»16sâ² , and Î»17sâ² are dual variables.3.5.2.1.2 Stage-Wise Lagrangean Dual Cuts Lagrangean relaxation produces bounds onthe optimal objective value of mixed-integer programming models, resulting in integer feasible solu-tions, which provides intervals bracketing the optimal value of the original problem [204]. In globalsupply chain models, when incorporating discounts into the model, the Lagrangean dual cut en-hances the modelâs adaptability to varying discount opportunities, facilitating strategic procurementplanning and potentially reducing overall procurement costs. In addition, the developed modelâsflexibility in its assessment of transportation options enhances by employing Lagrangian dual cuts torelax constraints associated with public transportation utilization. This flexibility reflects the real-world environment, where suppliers choose between various transportation options based on factorsincluding cost-effectiveness, capacity constraints, and time efficiency. In multi-stage stochastic pro-96gramming, Lagrangean decomposition relies on decomposing the constraints linking the consecutivestages (i.e., state equations) [205]. Î¶tsâ²tis defined as the Lagrangean multiplier associated with theconstraints linking the consecutive stages. Therefore, the SWLDC are formulated as follows:Min Z =F (W,H) + Esâ²[Q(Xu,Xl, Sâ²) + Es1[Qâ²(B,C,G, Sâ²)]]+âsâ²âS â²âiâIÎ¶tsâ²t(Î³i) (3.39)Where γi is the difference between the right-hand side and the matrices comprising decisionvariables and their associated coefficients for the linking constraint i between consecutive stages.3.5.2.1.3 Mixed-Integer Rounding Cuts The MIR inequalities are derived from a singlemixed-integer constraint [206], and represent a broader application of Chvatalâs integer roundinginequality to the mixed-integer models. Simple MIR cuts, developed to generate strong validinequalities, have been highly effective computationally for many mixed-integer models [207]. Insupply chain management strategies, manufacturers often negotiate discounts with suppliers basedon factors such as minimum purchase limit, contract terms, and ordering frequency. Therefore, inthis study, MIR cuts are integrated into the SSDiP to address the complexities in the multi-stagestochastic model, arising from the discount and logistics aspects of the global supply chain. TheMIR cuts are integrated into the model to check the manufacturerâs eligibility for discount, sincethese discounts can significantly impact procurement costs and overall profitability. TheMIR cutsensure integrality in the decision-making process regarding discount applications, thereby optimizingthe utilization of discount opportunities in the multi-stage stochastic model. In logistical terms,it examines container leasing to transit raw materials to the manufacturers. The decision-makingprocess regarding leasing public transportation depends on factors such as shipment volume, transittime, associated cost, and availability of services. The MIR cuts are generated as follows:97âpâPâqâQpâ²sâ²aâ²pqsâ²Yptsâ² âï£®ï£° 11â(âqâQ pâ²sâ²ifoqsâ² âââqâQ pâ²sâ²ifoqsâ²â)ï£¹ï£»ï£«ï£­âqâQ(pâ²sâ²IDFqtsâ² â pâ²sâ²Xliqtsâ² + pâ²sâ²Xuiqtsâ²)ï£¶ï£¸ â¤ï£¯ï£¯ï£¯ï£°âqâQpâ²sâ²ifoqsâ²ï£ºï£ºï£ºï£» â t â T , sâ² â S â²pâ²sâ²Yptsâ² â[11â (pâ²sâ²dptsâ² â idopsâ² â âpâ²sâ²dptsâ² â idopsâ²â)] (Gptsâ²)â¤ âpâ²sâ²dptsâ² â idopsâ²â â t â T , sâ² â S â²âpâPpâ²sâ²vlpsâ²Yptsâ² âï£®ï£° 11â(âpâP pâ²sâ²vlpsâ²dptsâ² âââpâP pâ²sâ²vlpsâ²dptsâ²â)ï£¹ï£»(pâ²sâ²IDLtsâ² â pâ²sâ²IDLtâ1sâ²) â¤ï£¯ï£¯ï£¯ï£°âpâPpâ²sâ²vlpsâ²dptsâ²ï£ºï£ºï£ºï£» â t â T , sâ² â S â²(3.40)3.5.3 Parallelization in Large-Scale Multi-Stage Stochastic ModelsThis section integrates the parallelization into the proposed SSDiP for the developed multi-stage stochastic model to enhance computational efficiency. In Benders decomposition for multi-stage stochastic models, parallelizing the sequential iterations significantly reduces the computationtime [208]. Parallelization employs available CPU cores to solve independent stages of multi-stagestochastic models, simultaneously [209]. In another words, each separate thread has to deal withone specific stage of the stochastic optimization problem, resulting in simultaneous execution ofstage-specific optimization operations. The simultaneous execution enables efficient CPU resourceutilization and reduces computational time. In multi-stage stochastic models, paralleliztion canbe implemented on both scenario and node [210]. In early iterations, the parallelization by nodestrategy outperforms the parallelization by scenario strategy, due to the poorer quality of valuefunction approximations at this stage [203]. Therefore, In each iteration, the parallelization-by-scenario strategy provides a poor approximation for the value function because it generates multiplecuts. In contrast, the parallelization-by-node strategy results in a much better approximation thanthe scenario strategy, as it generates a single cut, demonstrating desirable CPU scalability properties[210].In this study, the-parallelization-by-node-strategy is applied to the proposed SDDiP algorithmto solve the developed multi-stage stochastic model for the global supply chain network. In par-98allelization, the multi-stage model corresponding to a specific stage is solved by a thread amonga set of created multiple threads. Simultaneous execution allows concurrent progression throughvarious stages, with each thread independently optimizing its respective stage. In addition, the si-multaneous execution of backward pass is also possible, resulting in the generation cuts by multiplethreads and applying for various stages, concurrently. Each stageâs cuts are generated by a threadbased on its corresponding stageâs stochastic model, resulting in relaxation bounds improvement.Simultaneous execution of multiple threads in the backward pass improves efficiency and scalability,resulting in refined solutions and more tighter bounds. The convergence and termination criteriain the parallelized version of SDDiP are the same as in the case without parallelization, but arecoordinated across the set of multiple created threads. The progress and convergence status inshared among threads, leading to global convergence. Algorithm 2 shows the pseudocode of theproposed parallelized SDDiP algorithm.99Algorithm 2 Parallelized Accelerated Stochastic Dual Dynamic Integer Programming AlgorithmInputs : LB â ââ,UB â +â,iâ² â 1,initial approximation {Ïiâ²t (Â·)}t=1,...,T ,predefined threshold ϵOutputs: LB, UBwhile UB â LB > ϵ doSample M scenarios S â²iâ²= {sâ²k1 , . . . , sâ²kT }k=1,...,MForward Step:k = 1, . . . ,M â· Parallelize over scenariosfor t = 1, . . . , T doSolve forward problem P iâ²t (Zâ²iâ²ktâ1, Ïiâ²t , sâ²kt )Collect solution (Xuiâ²kiqt , Xliâ²kiqt , Yiâ²kpt , IDFiâ²kqt , IDLiâ²kt , Aiâ²kt , Biâ²kt , Câ²tiâ²k , Giâ²kpt )enduk âât=1,...,T ft(Xuiâ²kiqt , Xliâ²kiqt , Y iâ²kpt , IDF iâ²kqt , IDLiâ²kt , Aiâ²kt , Biâ²kt , Câ²tiâ²k , Giâ²kpt , sâ²kt )Statistical Upper Bound Update:µËâ 1MâMk=1 uk ÏË2 â 1Mâ1âMk=1(uk â µË)2 UB â µË+ zα/2 ÏËâMBackward Step:for t = T, . . . , 2 dok = 1, . . . ,M â· Parallelize over scenarios j = 1, . . . , Nt â· Parallelize over NtSolve a relaxation of the updated problem P iâ²t (Zâ²iâ²ktâ1, Ïiâ²+1t , sâ²jt )Add cuts (3.40), (3.39), (3.38) to Ïiâ²+1tâ1 to get Ïiâ²+1tâ1endLower Bound Update:Solve P iâ²1 (Z¯â²0, Ïiâ²+11 )Set LB to the optimal valueiâ² â iâ² + 1end3.6 Numerical ExperimentIn this section, a set of instances is generated based on different sizes (i.e., small, medium, andlarge-size) to validate the performance of the proposed SDDiP in dealing with high-risk scenarios.The IS method is used to generate scenarios for the multi-stage stochastic model.1003.6.1 Advance Scenario Sampling: Importance SamplingThe IS method is a variance reduction technique that can produce an estimate of recoursefunction (P) which has lower variance and lower sampling error compared to Monte carlo. Differentprobability distributions are employed to reduce the variance by generating samples in regions,contributing the most to the P [211]. In IS , the lower-variance approximations are estimatedusing an importance sampling distribution gâ² compared to the original sampling distribution f â²[212]. The recourse function can be formulated as follows:Ï(XËu, XËl, BË, CË, GË) = Efâ²sâ²[Q(XËu, XËl, Sâ²) + Es1[Qâ²(BË, CË, GË, Sâ²)]]= (3.41)Egâ²sâ²[Q(XËu, XËl, Sâ²) + Es1[Qâ²(BË, CË, GË, Sâ²)]µ(Sâ²)]Where Efâ², Egâ², and function µ : Î â R demonstrate expectations with respect to the dis-tributions f â² and gâ² and the likelihood function, respectively. µ(Sâ²) = fâ²(sâ²)gâ²(sâ²) shows the likelihoodfunction, demonstrating the likelihood of each sample. The likelihood function controls the biasincurred due to sampling from gâ² instead of f â². The proper of the likelihood function µ over thesupport of f â² (i.e., gâ²(sâ²) > 0 at all values of sâ² where f â²(sâ²) > 0) in IS distribution gâ² is the keyrequirement [213]. After the careful selection of the suitable IS distribution (gâ²), a set of N â² i.i.d.samples sâ²1, sâ²2, ...,S â²N â² are generated and an IS estimate of the recourse function is constructed asbelow:ÏËIS(XËu, XËl, BË, CË, GË) =1N â²N â²âjâ²=1Q(XËu, XËl, Sâ²jâ²) + Es1[Qâ²(BË, CË, GË, Sâ²jâ²)]µ(Sâ²jâ²) (3.42)Where jâ² is the counter of scenario. Variance reduction is a key factor in evaluating the suitabilityof the generated sample from gâ². In IS , gâ² is able to generate samples from the regions that contributethe most to the value of the recourse function at a fixed point, establishing it as the most effectivescenario generation technique in stochastic programming. Therefore, sampling from the followingequation (Equation 3.43) minimizes the variance of an IS estimate [212]:101gâ²â(sâ²) =â£â£â£âN â²jâ²=1Q(XËu, XËl, Sâ²jâ²) + Es1[Qâ²(BË, CË, GË, Sâ²jâ²)]â£â£â£Efâ²sâ²[â£â£â£Q(XËu, XËl, Sâ²) + Es1[Qâ²(BË, CË, GË, Sâ²)]µ(Sâ²)â£â£â£]fâ²(sâ²) (3.43)The IS distribution gâ²â provides estimate with minimum variance that are superior to thoseproduced by any other distribution. Each sampleâs likelihood is calculated by the following equation(Equation 3.44) [211]:µâ(sâ²) =Efâ²sâ²[â£â£Q(Xu,Xl, Sâ²) + Es1[Qâ²(B,C,G, Sâ²)]µ(Sâ²)â£â£]â£â£â£âN â²jâ²=1Q(Xu,Xl, Sâ²jâ²) + Es1[Qâ²(B,C,G, Sâ²jâ²)]â£â£â£ (3.44)Algorithm 3 shows the pseudocode of the IS .Algorithm 3 Importance Sampling AlgorithmInputs : Original distribution f â²,Importance sampling distribution gâ²,Number of samples N â²Outputs: Estimate of recourse function ÏËISInitialize ÏËIS â 0for jâ² = 1 to N â² doGenerate sample Sâ²jâ² from distribution gâ²Calculate likelihood ratio µ(Sâ²jâ²) =f â²(Sâ²jâ² )gâ²(Sâ²jâ² )Compute Q(XËu, XËl, Sâ²jâ²)Compute Es1[Qâ²(BË, CË, GË, Sâ²jâ²)]Update ÏËIS â ÏËIS + (Q(XËu, XËl, Sâ²jâ²) + Es1[Qâ²(BË, CË, GË, Sâ²jâ²)i¯gr]) · µ(Sâ²jâ²)endÏËIS â ÏËISNâ²return ÏËISTable 3.2 evaluates the performance of the proposed SDDiP-MIR by comparing it withSDDiP-SWLDC and SDDiP . The instance sizes vary based on the number of supplier I , theproduct type P, bills of material Q, planning horizon T , and different scenario sample sizes S â².102The performance metrics include C.T in seconds, LB , and UB . These metrics provide insightsinto the efficiency and effectiveness of each model under different scenarios.103Table 3.2: Numerical Experiments ResultsNo Instance Size SDDiP SDDiP-SWLDC SDDiP-MIRI P Q T S â² C.T(s) LB UB C.T(s) LB UB C.T(s) LB UB1 2 1 2 4 2 0.23 113 164 0.42 96 142 0.13 102 1152 20 1 2 4 2 0.40 1,495 1,990 0.69 1,118 1,362 0.32 1,101 1,2003 100 1 2 4 2 81 2,946 3,892 284 2,198 2,396 77 2,123 2,2854 100 100 2 4 2 90 5,738 7,477 88 5,875 6,921 81 5,723 6,2245 100 100 100 4 2 139 5,843 6,686 151 5,719 6,669 117 5,668 6,1726 2 1 100 4 2 88 131 236 79 124 158 73 60 757 2 100 2 4 2 42 172 345 42 153 211 41 128 1478 2 1 2 100 2 162 114 152 145 118 139 120 108 1169 2 1 2 4 100 71 162 189 175 130 161 37 153 16410 2 1 2 4 200 117 122 220 150 179 218 104 102 11011 50 50 50 5 50 242 3,680 5,680 242 3,920 4570 157 3,713 4,17412 50 50 50 5 100 484 3,878 5,294 338 3,559 4,693 356 3,618 4,02813 50 50 50 10 50 910 3,754 4,322 1,080 3,700 3,980 1,071 3,639 3,804104According to the Table 3.2, for small size instances (e.g., Instance 1), SDDiP and its variantsexhibit relatively low computational times. As the instance size increases (e.g., Instances 11-13),the computational time significantly rises, demonstrating the increased complexity of large-sizeinstances. This demonstrates the sensitivity of the sample size (i.e., the number of scenarios). If thenumber of scenarios is too small, the approximation of the stochastic process becomes inaccurate.Conversely, if the number of scenarios is too large, it hinders the convergence of the SDDiPalgorithm and its accelerated versions. In fact, the sample size should depend on the planninghorizon length (T ). For short planning horizons, a higher number of scenarios per stage leads tothe best solution, whereas for longer planning horizon, a smaller number of scenarios per stage resultsin the best solution (see Instances 9 and 12 - 14% and 13% gap, respectively). A simple adaptationof SDDiP is not efficient for the developed multi-stage stochastic model with an optimality gapof 25%. The binary setup variables in the first stage sub-problem significantly slow down theconvergence of SDDiP because the optimality gap is 25% when the setups are not fixed. The multi-cut version SDDiP improves the convergence because adding SWLDC enhances the lower bound(i.e., average gap is 15% which shows 10% improvement in comparison to the SDDiP). SDDiPneeds more iterations to reach the SDDiP-SWLDC âs gap, resulting in higher computational time.This verifies that SWLDC speeds up the convergence.SDDiP-MIR generally denotes more faster computation execution compared to SDDiP-SWLDC and SDDiP , particularly in larg-size instances, verifying its efficiency in dealing withcomplex supply chain scenarios. The lower computational times of SDDiP-MIR for large-sizeinstances suggest that it can be implemented in dynamic and complex supply chains to facilitatetimely decision-making, which is crucial for maintaining the flow of goods and services.SDDiP-MIR consistently achieves small gap between lower and upper bounds (7%), suggestinga tighter solution range. The performance of the SDDiP-MIR depends mainly on the S â² andT . The higher number of scenarios results in higher optimality gap (see Instances 9 and 10), andthe longer time horizon leads to smaller optimality gap (see Instances 11 and 13). The small gapbetween lower and upper bounds achieved by SDDiP-MIR indicates more precise and potentiallycost-effective decision-making. This helps in minimizing logistics, warehousing, and production cost,ensuring better resource utilization and cost savings. Additionally, the integrated hedging policiesinto SDDiP-MIR enhance much more supply chain resilience by diversifying risks and buildingflexibility in comparison to the SDDiP-SWLDC and SDDiP . Finally, retaining the averagescenario path improves significantly the lower bound, but after a sufficient number of iterations, the105variant of SDDiP without high number of scenarios reaches the same lower bound as the defaultversion.3.6.2 Resiliency AnalysisIn todayâs globalized world, global supply chains are highly vulnerable to disruptions stemmedfrom political unrest, natural disasters, and the COVID-19 pandemic. Political unrest in key re-gions often disrupts trade routes, leading to delays, increased costs, and sometimes the shutdown offacilities. Furthermore, trade disputes, sanctions, or civil conflicts can all contribute to market un-certainty, affecting the raw materialsâ procurement. Natural disasters such as bushfires, hurricanes,and floods can cause extensive damage to infrastructure, disrupting transportation routes, and man-ufacturing plants. Such disruptions magnifies the importance of global supply chain managementstrategies to mitigate their impacts. For example, the COVID-19 pandemic shows the importanceof multiple sourcing in dealing with disruption. Production processes and logistics were disruptedduring the pandemic due to lockdowns, travel restrictions, and social distancing measures, resultingin shortages of essential goods, supplier unavailability, and inaccessible transportation routes. Inthis section, a sensitivity analysis is conducted on Appleâs iPhone case study (Figure 3.3) to demon-strate the resilience of the developed model and hedging policies in dealing with disruption. Theplanning horizon spans a year, four quarters, (i.e., t1, t2, t3, and t4). The analysis assumes that theinternational supplier offers a lower initial per unit cost but is less reliable (i.e., higher risk of disrup-tion), while the domestic supplier offers a higher per unit cost but greater reliability. The setting upcontract cost with international and domestic suppliers are set at 40 and 100, respectively [214]. Inaddition, iPhones is considered as the type of product, and the unit purchasing cost from domesticand international suppliers are considered 1 and 4, respectively, [215]. The time interval betweenordering and receiving materials from suppliers is calculated based on service and transportationtimes. The multiple sourcing cost follows the equation si2q = si1q +âs where âs, i2, and i1 showthe percentage rise in the sourcing cost (0, 10, 20), sourcing cost of the second and first suppliers,respectively [214]. The discount rate is modeled based on the [216]âs discount rate model, and theminimum purchase quantities range between 200,000 and 300,000. The volume of a unit of materialq is between 8 and 10, while the volume of a unit of product p is between 1 and 4, considering 0.5as the inventory holding cost and 10 as the shortage cost. The cost of renting a container is basedon the capacity of a Boeing 747 flight, which can carry 150,000 iPhones at a cost of 242,000 [217].The capacity of a container to carry iPhones is considered to be 36,000, similar to a single trailer.106Public logistical costs are based on the Boeing 747 flight capacity and cost, as well as the capacityof a single trailer. The initial inventory of material q ranges between 10 and 80 units, while theinitial inventory of product p ranges between 35 and 60 units. Four units of material q are requiredto produce one unit of product p, with a demand for 231,000 units of product p in each period. Theproduction time for one unit of product p is 17 hours [218]. The capacities of the first and secondwarehouses are between 35,000 and 160,000 units. The maximum working time of the factory ineach period is 15,000 hours, corresponding to a three month period with eight hour working daily,considering o.85 overtime labour cost [219]. The maximum quantity eligible for a discount in eachpurchasing period is defined, and the leasing costs for warehouse space to store both bill of materialsand manufactured products are 10% higher than the current inventory costs. Three scenarios aredesigned including baseline scenario (Scenario I), scenario II (i.e., supplierâs unavailability due todisruptions such as political unrest or pandemic), and scenario III (i.e., transportation route in thesupply chain network becomes unavailable due to disruption such as natural disaster, wildfire orflood).Figure 3.3: The Illustrative Case Study3.6.3 Scenario I: Baseline ScenarioAs demonstrated in Table 3.3, in the baseline, the sourcing journey begins by sourcing 66,000units component q1 from Sunnyvale in the first and second quarters of the year, following by thepurchase of 56,000, 75000, and 75,000 of second component q2 from Taiwan at regular price (withoutdiscount). Due to the initial inventory of the first component, no purchases are made without107a discount. In the first quarter, only 9,000 units of this component were bought from Taiwan,which met the production demand. Switzerland is the sourcing destination to source 83,000 unitscomponent q3 in the second quarter of the year. Subsequently, Taiwan provides 23,000 units ofsecond component q2 in the initial quarter of the year with almost 30% discount. The domesticsupplier, Fujan covers 20,000 units of the forth component q4 each in second and third quartersof planning horizon. The procurement of the third and forth components, q3 and q4, in the thirdquarter of the year is outsourced to Singapore and Germany with the amount of 14,000 and 16,000,respectively.108Table 3.3: Summary of the Scenario I (Baseline) ResultsI R Supplier Type Assembly Center Q Xuiqt-Xliqt T θiSunnyvale North America International Beijing q1 66,000 T1 0%Taiwan AsiaInternational Beijing q2 56,000 T2 0%International Beijing q2 75,000 T3 0%International Beijing q2 75,000 T4 0%International Beijing q2 23,000 T1 30%Fujan AsiaDomestic Beijing q4 20,000 T2 0%Domestic Beijing q4 20,000 T3 0%Domestic Beijing q4 20,000 T4 0%Domestic Beijing q4 20,000 T1 0%Singapore Asia International Beijing q3 14,000 T3 0%Germany Europe International Beijing q4 16,000 T3 0%Switzerland Europe International Beijing q3 83,000 T2 0%CB L:1,489,620 P:1,595 O:1,581,797 I:576 M:397,497 S:208,110 V:620109The KPIs is defined based on the total cost of the network (CB), including logistical cost (L),production cost (P), overtime labour cost (O), inventory cost (I), multi-sourcing cost (M), lost saleopportunity cost (S), and saving due to discount (V).3.6.4 Scenario II: Supplier UnavailabilityIn the second scenario (i.e., supplier unavailability), the domestic supplier (Fujan), internationalsuppliers (Sunnyvale and Taiwan) become unavailable due to disruption. According to the obtainedresults (Table 3.4), Germany ships 18,000 and 5,000 of the component q4 in the second and thirdquarters of the year without any discount, respectively. The demand for the first and second com-ponent q1 and q2 is met by transshipping 49,000 and 88,000 units from Taiwan without consideringdiscount. Thailand supplies 63,000 and 39,000 components of q1 in the initial phase of planning hori-zon, followed by supplying 31,000 units of component q4 in the second quarter of year. Switzerlandis responsible for supplying 16,000 components of q3 in the third quarter of the planning horizon,when Singapore is supplying 14,000 units of this component in the same quarter of the planninghorizon. Domestic supplier, Beijing, supports procuring the third component q3 in the initial andthird quarters of the year with the amount of 16,000 and 14,000, respectively. Finally, 12,500 unitsof the third and forth components (q3 and q4) are shipped from Philippines to production center inthe first and second quarters of the year. The total network cost increases 26% in comparison to thebaseline scenario. While the baseline scenario had no shortages, this scenario incurs a shortage costof 317,732 and the inventory holding cost increases 0.13%. Since the domestic supplier Fujan andinternational suppliers Sunnyvale and Taiwan cover significant amount of Components q1, q2, q3,and q4, the model sources these components in this scenario from other suppliers that increases thesourcing cost significantly (29%). Saving due to the discount, and overtime labour cost decreases39%, 30%, respectively. The inventory holding cost experiences a slight increase of 0.13 percent,while the purchase cost rises significantly by 28%.110Table 3.4: Summary of the Scenario II ResultsI R Supplier Type Assembly Center Q Xliqt-Xuiqt T θiSunnyvale North America International Beijing q1 Disrupted T1 0%Taiwan AsiaInternational Beijing q2 56,000 T2 0%International Beijing q2 Disrupted T3 0%International Beijing q2 Disrupted T4 0%International Beijing q2 88,000 T1 30%International Beijing q1 49,000 T1 0%Fujan AsiaDomestic Beijing q4 Disrupted T2 0%Domestic Beijing q4 20,000 T3 0%Domestic Beijing q4 20,000 T4 0%Domestic Beijing q4 20,000 T1 0%Singapore Asia International Beijing q3 14,000 T3 0%Germany EuropeInternational Beijing q4 18,000 T2 0%International Beijing q4 5,000 T3 0%Switzerland EuropeInternational Beijing q3 Disrupted T2 0%International Beijing q3 16,000 T3 0%Thailand AsiaInternational Beijing q1 63,000 T1 0%International Beijing q1 39,000 T2 0%International Beijing q4 31,000 T2 0%Singapore Asia International Beijing q3 14,000 T3 0%Beijng AsiaDomestic Beijing q3 16,000 T1 0%Domestic Beijing q3 14,000 T3 0%Philippines AsiaInternational Beijing q3 12,500 T1 0%International Beijing q4 12,500 T2 0%1113.6.5 Scenario III: Delays in Sourcing the Productâs ComponentsIn the third scenario (i.e., delays in sourcing the productâs components), due to the delay inprocuring the component q1 in the third quarter of the year, the model changes its Sunnyvaleâsupplier to Thailand with the amount of 52,000 and 51,000 units in the second and third quarterof the year (see Table 3.5). The shipment of the second component q2 from, in the initial phaseof planning horizon, is disrupted due to the delay. However, there is no disruption in sourcing thesecond component q2 in the second and third quarters of the year (i.e., 75,000 units each).112Table 3.5: Summary of the scenario III resultsI R Supplier Type Assembly Center Q Xliqt-Xuiqt T θiSunnyvale North America International Beijing q1 Disrupted T1 0%Taiwan AsiaInternational Beijing q2 Disrupted T2 30%International Beijing q2 50,000 T2 0%International Beijing q2 75,000 T3 0%Fujan AsiaDomestic Beijing q4 20,000 T2 0%Domestic Beijing q4 20,000 T3 0%Domestic Beijing q4 20,000 T4 0%Domestic Beijing q4 20,000 T1 0%Singapore Asia International Beijing q3 14,000 T3 0%Germany Europe International Beijing q4 16,000 T3 0%Switzerland EuropeInternational Beijing q3 Disrupted T2 0%International Beijing q3 22,000 T2 0%International Beijing q3 83,000 T3 0%Thailand AsiaInternational Beijing q1 52,000 T2 0%International Beijing q1 51,000 T3 0%113Switzerland can only ship 22,000 units of the third component q3 in the second quarter of theyear, compared to 83,000 units in the baseline scenario. However, there is no disruption in procuringq3 in the third quarter of the planning horizon, with the full amount of 83,000 units available. In thisscenario, the shipment of 15,000 units of second component q2 and 27,000 units of third componentq3 from Thailand are disrupted due to delay. The rest of the sourcing process is the same as the firstscenario, and there is no purchase with discount in this scenario. The total costs for production,sourcing, transportation, and overtime labor increase by 15%, 8%, 38%, and 0.07%, respectively,compared to the baseline scenario. While inventory holding costs, savings due to the discount, andpurchase costs decrease by 48%, 38%, and 42%, respectively.3.7 Managerial Implications: Discount Rate ModelAccording to the contract, the supplier offers a unit price s, and the buyer determines herordering quantity qâ². Therefore, the final price follows s = dâ1(qâ²), where d denotes the demand.The manufacturer has limited working capital M â², therefore given the unit manufacturing cost uâ²,the manufacturer can only manufacture up to M/uâ² units without additional financing. Moreover,the supplier is subject to external risks, meaning that whatever she produces may be disruptedwith a probability probability pâ² or delivered with probability pËâ² = 1 â pâ². The buyer may offerdirect financing to the supplier to facilitate production process. Specifically, the buyer can enablethe supplier to request a prepayment up to LËâ² from his final invoice prior to the commencement ofproduction. This subjects to an interest rate râ², resulting in a discount rate Ï â² = eârâ² [171].In this section, five scenarios are considered to investigate the impacts of the discount rate onthe supplying process (Figure 3.4). The investigated case study serves as the baseline scenario.In the second, third, fourth, and fifth scenarios, the discount rate is decreased by 25%, decreasedby 50%, increased by 25%, and increased by 50%, respectively. In the baseline scenario, Taiwansupplies 10,000 and 23,000 units of the first and second components (q1 and q2) with a 30% discount.Germany offers up to a 60% discount for 16,000 units of the third component (q3), while Malaysia isresponsible for procuring 5,000 units of the fourth component (q4) with a 30% discount. This setupestablishes a benchmark for sourcing strategies with existing discount rates, providing a referencepoint for evaluating the impact of changes in discount rates.When the discount rate is decreased by 50% for all suppliers, Taiwan still supplies the samequantity of the first and second components. The total cost of the network decreases slightly by1140.1%, while logistical and inventory holding costs drop by 26% and 27%, respectively. There areno shortages, and overtime labor costs remain unchanged. However, savings due to the discountdecrease by 26%, and purchase costs increase by 23%. This scenario indicates that significantreductions in discount rates have minimal impact on total costs but substantially reduce logisticsand inventory holding costs. Consequently, higher discount rates lead to increased logistics andholding costs, highlighting the need for efficient inventory management to maximize these savings.The sensitivity of total costs to discount rates emphasizes the importance of balancing discountrates and purchase volumes to optimize costs.In this scenario, the discount rate is decreased by 25%. Taiwanese and Swedish suppliers offer30% and 10% discounts, respectively, for procuring the first, second, and fourth components. Thetotal cost, inventory holding cost, savings due to the discount, and purchase cost experience negligi-ble changes, with no impact on logistics and overtime labor costs. This stability suggests a resilientsupply chain capable of maintaining cost efficiency despite reduced discounts. Thus, manufactur-ers should prioritize relationships with flexible and reliable suppliers to maintain consistent termsand focus on optimizing internal processes to handle fluctuations in supplier terms. The ability tomaintain stable costs despite varying discounts indicates effective operational efficiency.115T1 T2 T3 T4TaiwanBaseline 10000 (q1)Baseline 23000 (q2)Decrease 50% 10000 (q1)Decrease 50% 23000 (q2)Decrease 25% 10000 (q1)Decrease 25% 23000 (q2)Increase 25% 33000 (q2)Increase 50% 33000 (q1)GermanyBaseline 16000 (q3)Decrease 50% 16000 (q3)Decrease 25% 16000 (q3)Increase 25% 16000 (q3)Increase 50% 16000 (q3)MalaysiaBaseline 5000 (q4)Decrease 50% 5000 (q4)Decrease 25% 5000 (q4)Increase 25% 5000 (q4)Increase 50% 5000 (q4)PhilippinesBaseline 16000 (q4)Decrease 50% 16000 (q4)Decrease 25% 16000 (q4)Increase 25% 16000 (q4)Increase 50% 16000 (q4)T1 T2 T3 T4South KoreaBaselineDecrease 50%Decrease 25%Increase 25%Increase 50% (q2)FujanBaselineDecrease 50%Decrease 25%Increase 25%Increase 50% (q1)BeijingBaselineDecrease 50%Decrease 25%Increase 25%Increase 50% (q2)SwedenBaselineDecrease 50%Decrease 25%Increase 25%Increase 50%Figure 3.4: Gantt Charts Comparing Baseline and Scenario Estimates in Multiple RegionsWhen the discount rate is increased by 25%, Taiwan procures 33,000 units of the second compo-nent, while Singapore and South Korea cover the procurement of the third and fourth components(Figure 3.5). There is no significant change in total cost, logistics cost, and overtime labor cost,but inventory holding cost, savings due to discount, and purchase cost increase by 18%, 13%, and3%, respectively. This scenario highlights the need for efficient inventory management practices tobalance the benefits of higher discounts with increased holding costs. The slight increase in purchase116cost suggests that the benefits of increased discounts outweigh additional expenses.Finally, when the discount rate is increased by 50% in comparison to the baseline scenario,Fujan ships 33,000 units of the first component q1 in the first quarter of the planning horizon. Inthe following quarter of the year, another domestic supplier, Beijing, provides 23,000 units of thesecond component q2. Then, Philippines is responsible to procure 16,000 units component q4 inthe third quarter of the year, when South Korea and Malaysia are procuring each 11,000 units ofsecond and third components (q2 and q3). In this scenario, the total inventory holding cost, pur-chase cost, and saving due to discount increase by 4%, 14%, and 17%, respectively. A significantincrease in discount rates leads to substantial rises in inventory holding costs, necessitating carefulmanagement of inventory levels to balance discount benefits and holding costs. The increased sav-ings due to higher discounts highlight the potential for significant cost reductions through strategicprocurement. Manufacturers should prioritize securing high discount rates while effectively manag-ing inventory levels and fostering robust supplier relationships to optimize procurement and achievecost savings.Baseline Decrease 50% Decrease 25% Increase 25% Increase 50%02,0004,0006,0008,00010,00012,00010,0009,5009,80010,50011,0008,000 7,800 7,9008,100 8,2006,000 5,800 5,9006,100 6,2005,000 4,800 4,9005,100 5,2003,000 2,900 2,950 3,050 3,100Cost($)Total Cost Logistics Cost Inventory Cost Production Cost Overtime CostFigure 3.5: Comparison of Costs Across Different Scenarios3.8 SummaryThis chapter proposed a framework to optimize a resilient global supply chain by proposing aparallelized SDDiP approach. Multiple challenges were addressed concurrently, including order117scheduling for bill of materials, production planning, and inventory management across warehouses(i.e., materials and finished products). Due to the dynamic nature of the global supply chain (e.g.,demand fluctuations, disruptions, and lead time), a multi-stage stochastic model was developedfor the stochastic-dynamic supply chain network. A diverse set of multi-stage stochastic integerprogramming models was explored, incorporating real-world factors (e.g., discount). These modelsinvolved variables (binary and continuous) that share information between stages, resulting in morecomplexity of the multi-stage stochastic models. Consequently, an accelerated parallel SDDiPalgorithm was proposed, incorporating the parallelization scheme and utilizing the binary natureof the state variables. The proposed parallel node strategy for the accelerated SDDiP , performedbetter at each iteration than basic form of the SDDP and presented desirable CPU scalabilityproperties. Therefore, various scenarios with different sizes were generated using the case study toevaluate the performance of the proposed accelerated SDDiP . The results showed that SDDiP-MIR outperformed SDDiP-SWLDC and SDDiP , particularly in large-size instances, with fastercomputational times and a smaller optimality gap of 7%. In the resiliency analysis, the baselinescenario demonstrated a a supply chain operating efficiently with minimal costs. In Scenario II,which involved supplier unavailability, the total network cost increased by 26% due to significantsourcing and shortage costs. Scenario III, which simulated delays in sourcing components, ledto increased production, transportation, and overtime labor costs. The study on discount ratevariations indicated minimal impact on total costs but significant changes in logistics and inventoryholding costs. Higher discount rates increased holding costs, highlighting the importance of efficientinventory management.The future of global supply chain and sourcing policies will be characterized by increased re-liance on advanced technologies and data-driven approaches. Dynamic pricing and real-time dataanalytics, will become integral, enabling companies to respond quickly to market fluctuations andoptimize revenues. Supply chains will be more resilient by adopting blockchain to enhance visibilityand traceability. Sustainable sourcing will gain prominence, driven by consumer demand and regu-latory pressures. In addition, it would also be interesting to see the computation time improvementif the Lagrangian dual problem is solved by a more advanced methods, such as bundle method.118Chapter 4Intelligent decision support system forhealthcare sector logistics resiliency:timing the vaccine flow4.1 IntroductionThe rise and spread of illnesses such as the flu, COVID-19, and Ebola have put peopleâs healthand lives at risk. Annually, 5â15% of the global population has been infected with the flu, resultingin 3â5 million severe cases and 290,000-650,000 deaths [68]. The drastic impact of the COVID-19pandemic has also dramatically affected healthcare systems, economies, and various industries allover the globe. More than 775 million COVID-19 cases have been confirmed globally, and themortality rate has been more than 7 million until April 2024 [68]. Owing to the seriousness andintensity of this infectious disease, the WHO and some pharmaceutical companies have been look-ing for ways to curb the widespread of this pandemic. While many healthcare researchers andscientists have focused on the development of efficient vaccines for this infectious disease, supplychain practitioners have focused on assuring the delivery of vaccines to health centers [69]. Vaccinemanufacturing and distribution are vital steps in mass immunization that require proper planningand performance owing to the high demand [70]. Moreover, ensuring equitable vaccine distributionand administration across various situations necessitates creating a resilient SCN that can with-stand fluctuations in critical input factors such as infectious spread and demand [220]. One keyelement for ensuring equitable access to vaccination is deploying mobile PHUs that can be as-signed to various locations at different times to meet vaccination demand and enhance accessibility[221, 222]. The vaccine supply chain can also assure a constant and uninterrupted supply of vaccinesfrom production centers to demand points [223]. The structured and coherent vaccine logistics andsupply chain planning are decisive and influential for the success of the vaccination program. Oth-119erwise, countless valuable doses will be wasted, and the vaccine program will interrupted, imposingsignificant economic and human losses [224]. A shortage of vaccines resulting from the failure of thevaccine logistics and supply chains can create more complicated conditions. Therefore, consolidatedand well-connected logistics and supply chain infrastructures are essential to maintaining the highamount of vaccine availability [225]. Controlling disease outbreaks (e.g., the Flu every year duringcold months) by vaccination is a challenging optimization problem in terms of location-allocationof vaccines to PHUs. The epidemic vaccine resources are limited and insufficient in most cir-cumstances (i.e., especially in the early phases of virus dispersion). Therefore, policymakers andhealthcare providers should determine the most effective policies to allocate and distribute vaccinesstrategically to the optimal locations to control infectious diseases effectively [226]. Critical inputfactors, such as vaccination demand, significantly affect the overall configuration of the vaccinationnetwork. The demand for vaccination is uncertain and constantly changing as it depends on var-ious factors, such as the spread rate of the disease in each region, making it essential to addressdemand uncertainty when designing a vaccine SCN . Various optimization approaches dealing withuncertainty, such as stochastic programming and RO , are used to handle uncertainty. However,the problem with these conventional methods is that they do not fully utilize the available data.The growth and advancement of technology, increased access to data across different fields, haveled to the emergence of data-driven optimization approaches. These methods extract useful in-formation from available data using machine learning algorithms or statistical methods, which arethen fed to the optimization model to make data-driven decisions [227â229]. This research aimsto present a data-driven DSS containing a data-based and model-based framework for designingan efficient vaccine distribution network. The proposed data-based framework is developed to dealwith parameter uncertainty using DDRO , data generation, and prediction algorithms. Given thesignificant role of the vaccine supply chain in epidemic outbreaks, investigating such uncertaintiesenables policymakers and healthcare providers to handle future crises (e.g., disease outbreaks) moreeffectively. The model-based framework also aims to determine the optimal configuration of thevaccine SCN and the vaccine flow among different entities. The proposed DSS aims to providea dynamic vaccine distribution plan and update the location and number of PHUs accordinglyto meet the uncertain vaccination demand and ensure an equitable vaccine distribution network.The overall structure of this research is as follows: Section 4.2 reviews the relevant literature anddiscusses research gaps and contributions of this research. Section 4.3 defines the problem state-ment and the overall procedure of the proposed DSS . Sections 4.4 and 4.5 describe the proposed120data-based and model-based frameworks, respectively. Section 4.6 provides a numerical analysisto demonstrate the capability of the proposed DSS . Finally, Section 4.7 discusses the concludingremarks and outlines future research directions.4.2 BackgroundIn this section, a literature review of the vaccine supply chain and machine learning-basedapproaches to deal with uncertainty are presented, and then the literature gaps are identified.4.2.1 Vaccine Supply ChainThe reliable distribution of vaccines is vital to implement mass immunization programs. Thedesign and optimization of vaccine distribution networks were investigated by [230â232], and the col-laboration in the emergency supply chain during disasters was studied by [233, 234].[235] modeled aplanning distribution network for the first time to maximize childrenâs immunization considering thecapacity limitation of the distribution network. [236] developed the susceptible-infected-recoveredmodel to ensure an adequate supply of vaccines during disasters. [237] examined the challenge ofcontrolling infectious disease outbreaks by introducing a novel epidemic-logistics integer program-ming model.Equitable access to vaccination ensures all individuals receive the necessary protection againstinfectious diseases and preventing epidemics. [238] proposed an equity constraint to ensure fairdistribution among different population subgroups. [239] examined equitable vaccine distributionduring the COVID-19 pandemic by developing a MILP model for the location-inventory prob-lem. [240] also proposed equity constraints to prioritize healthcare providers, first responders, andthe elderly for the equitable distribution of influenza vaccines in developing countries. In anotherresearch, [241] proposed a model for optimal influenza vaccine distribution in a heterogeneous pop-ulation, incorporating an equity constraint to ensure fair vaccine allocation among subgroups. Thenumerical results indicate the importance of fairness in public health decisions. [242] presented atwo-phase optimization approach for designing an efficient vaccine SCN . The first phase priori-tizes population groups for vaccination using a multiple-attribute decision-making technique, whilethe second phase employs a mathematical model to optimize the location of distribution centers,inventory policies, and routing decisions to minimize total costs. In terms of equity and diver-sity, the availability of mobile health units can also improve the accessibility of different groups121of people to vaccines. [243] introduced a robust bi-level optimization model, considering mobilevaccination centers, for the influenza vaccine distribution that addresses both the risk of mortalitydue to untimely vaccine supply and the risk of distribution inequality. [222] developed a robustmulti-objective model for a resilient vaccine SCN , allocating mobile and fixed injection centers tominimize costs, maximize route reliability, and reduce unmet demand. The model shows improvedstability over fuzzy probability models. [221] developed a multi-objective mathematical model andincorporated vaccine efficacy and value-added benefits to design a sustainable vaccine supply chainthat integrates both permanent and mobile vaccination centers, considering demand substitutionand vaccine perishability during a pandemic outbreak.Addressing uncertainty in the vaccine supply chain also ensures consistent availability, preventsshortages, and efficiently allocates resources. [244] proposed an MILP model to design a robustvaccine SCN under uncertainties in demand, cost, and vaccine perishability. They highlightedthat the robust model outperforms the deterministic model in terms of reliability and performance.[245] proposed a mathematical framework to coordinate the influenza vaccine supply chain underuncertainties, addressing both the uncertain production rate of the manufacturer and the uncertaindemand of the social planner with a two-ordering procurement strategy to improve efficiency. [246]also presented a multi-agent decision-making model for the stochastic optimization of vaccines andtesting kits allocation during the COVID-19 pandemic. They designed a test allocation policythat outperformed other allocation policies when information is scares. [220] proposed an MILPmodel for designing a sustainable SCN for the COVID-19 vaccine distribution. They consideredthe economic, environmental, and social aspects of the SCN and developed a DDRO approach todeal with uncertain demand. [42] presented a multi-objective model designed to create a sustainableand resilient SCN, specifically applied to the influenza vaccine supply chain. Using robust fuzzyoptimization and multi-choice goal programming, the model integrates capacity redundancy, leadtime ratio, and customer de-service level to proactively plan for disruptions. [12] introduced a two-stage decision support framework for designing resilient vaccine SCN . The framework integrates ahybrid multi-criteria decision-making approach and a robust multi-objective optimization model toenhance supplier selection and order allocation under uncertainty, demonstrating improved stabilityand reliability over existing models.1224.2.2 Employing Machine Learning to Tackle UncertaintyThe main idea of RO is to address the worst-case scenario within the uncertainty set, whichencompasses all possible future realizations of uncertain parameters. Therefore, it must be carefullytuned to avoid suboptimal or infeasible solutions. In conventional RO approaches, uncertainty setsare constructed based on fixed shapes, such as âBoxâ and âPolyhedral.â However, the problem isthat these fixed shapes do not account for the complexity of real-world data, potentially leadingto suboptimal or infeasible solutions. To address this challenge, DDRO approaches have beendeveloped to construct uncertainty sets using available historical data [227, 228].Creating data-driven convex polyhedral uncertainty sets can help mitigate the computationalburden of DDRO approaches. [247] employed PCA and KDE to create data-driven polyhe-dral uncertainty sets. [248] proposed kernel PCA to account to construct tight uncertainty sets fordataset with non-linear correlations. [220] also developed aDDRO model using a polyhedral uncer-tainty set to address parameter uncertainty in vaccine SCN design. They created a scheme wherehyperplanes are generated to cut the polyhedral uncertainty space and reduce over-conservatism asnew data on uncertain parameters are observed. In another research, [229] proposed an efficientapproach using SVC and a WGIK function. The proposed WGIK -based SVC can effectivelycreate data-driven polyhedral uncertainty sets to encompass the available data. [249] employedPCA for the WGIK -based SVC to construct data-driven uncertainty sets for high-dimensionaldata. In case of limited data available, the data-driven uncertainty set may not encompass the truespace of uncertainty. To address this issue, [250] developed the WGIK -based Conservative SVC(WGIK -based CSVC ) to construct data-driven uncertainty sets. WGIK -based CSVC reducesdependency on uncertain data by creating a fuzzy support for areas of higher density. When his-torical data contain multiple clusters and data samples are not labeled, the previously mentionedapproaches may lead to overly conservative solutions. To address this, [251] proposed a data-drivenstochastic RO framework that employs the fuzzy c-means clustering algorithm to cluster and labeldata samples. Following that, an uncertainty set is constructed for each cluster usingWGIK -basedSVC . [252] also developed aOC-DNN approach to create non-convex data-driven uncertainty setsfor high-dimensional and multi-cluster data samples. They also developed an iterative constraintgeneration algorithm to solve resulting adversarial problem. WGIK -based SVC may result inover-conservative solutions for asymmetric data samples. To this end, [253] developed a (SKL-and MKL-based OC-SVM ) to effectively construct compact uncertainty sets for datasets withasymmetric distributions. The number of available data samples and the conservatism degree of the123uncertainty set significantly impact the additional number of variables and constraints in the RCof MKL- and SKL-based OC-SVM approaches. To address this, [254] developed a two-stageclustering algorithm for the MKL- and SKL-based OC-SVM approaches to effectively maintainthe computational tractability of the RC model for different conservatism degrees and number ofavailable data. [255] also developed SKL- and MKL-based Weighted OC-SVM (WOC-SVM)to assign a set weight to historical data to indicate the importance of each data sample for the uncer-tainty set construction. They also proposed two weighting methods to effectively create uncertaintysets that encompass regions of higher density or areas around prediction points.4.2.3 Aim NoveltyIn this chapter the main aim is to design an IDSS for healthcare sector logistics resiliencyfor vaccine distribution considering novel policies such as mobile public health units and inventoryreallocation between stationary and mobile public health units. The contribution of this chapteris twofold: conceptual and methodological. In terms of methodological contribution, this chapterintroduces a novel data-driven DSS that integrates various components, including mathematicalmodels, DDRO , machine learning algorithms, and data generation processes. The developed DSScombines real-time and historical data on uncertain parameters to make real-time and data-informeddecisions.For the VDP problem, only a few historical data points are available at the beginning of thevaccination period. This limited data may not accurately reflect the actual distribution of uncer-tain parameters. Therefore, if data-driven uncertainty sets are constructed using limited data, theDDRO approach may result in infeasible or over-conservative solutions. Moreover, constructingdata-driven uncertainty sets with limited data often yields nearly identical solutions across differentconservatism levels, resulting in inseparable robust solutions. In case of limited data availability,some DDRO approaches exist in the literature. However, these approaches do not take predic-tion values into account. There is also a need to develop a DDRO approach that yields feasibleand non-conservative solutions while enhancing the separability of robust solutions across differentconservatism degrees using data generation process. The data-based framework proposes a novel ap-proach, ADDRO , by integrating SKL- orMKL-basedWOC-SVM , data generation algorithms,and prediction values to learn dynamic uncertainty sets and improve the out-of-sample performancein case of limited data availability. This study pioneers the concept of separability of robust solutionswith different conservatism degrees in cases with limited data availability. Constructing data-driven124uncertainty sets with limited data may yield identical solutions, leading to inseparable outcomeswhere decision-makers cannot distinguish and interpret the conservatism levels of robust solutions.The concept of separability of robust solutions states that robust solutions associated with varyingdegrees of conservatism should be distinct and interpretable by decision-makers, thereby enhancingthe explainability of operations research models. This improvement increases the interpretabilityof robust solutions and fosters trust among decision-makers to rely on robust solutions. Two data-driven algorithms are also developed based on density information and noise to generate new datasamples. The advantage of the proposed algorithms is to employ clustering approaches to clusteravailable data based on their distributional characteristics. Subsequently, KDE is applied to eachcluster to learn its distributional information and generate new data samples. This framework en-hances the capability of the KDE approach to effectively learn the distributional information andgenerate new data samples. Another advantage of the proposed algorithms is that the similaritybetween the generated data samples and real-world data can be adjusted using a single parameter.To ensure that the generated data reflects the actual distribution of uncertain parameters, statisticaldistance measures, the Wasserstein distance and the Cosine similarity, are employed to maintain aminimum statistical distance between generated and real-world data.In the model-based framework, three different optimization models are proposed. A bi-objectiveVDP model is developed to optimize the vaccine distribution network and determine the optimallocations of stationary and mobile PHUs. The first objective of the proposed VDP model aims tominimize the total cost of the vaccine distribution network, while the second objective function aimsto maximize the coverage of PHUs by maximizing the minimum distance among all PHUs. Thisobjective function ensures that all PHUs are distributed across different regions, enhancing theequity and diversity of vaccine distribution and improving accessibility for various groups of peopleto stationary or mobile PHUs. The data-driven uncertainty set constructed from the data-basedframework is fed to the model-based framework. The RC of the VDP model can be developedto determine robust solutions for the VDP problem. However, it results in an increased numberof variables and constraints in the VDP model, forming a more complex model. The uncertaindemand parameters within the VDP model exhibit column-wise uncertainty, meaning that onlyone dimension of the uncertain parameters appears on the RHS of each constraint. Therefore, thevalue of uncertain parameters using the constructed uncertainty set can be determined using aDRCmodel. Therefore, to maintain the tractability of the VDP model, a DRC model is developedto determine the robust values of uncertain demand. The robust values are then fed to the VDP125model to obtain the robust vaccine distribution network. Once the robust vaccination network is es-tablished, mobile and stationary PHUs are deployed, and vaccines are allocated among all PHUsfor administration. Subsequently, the actual vaccination demand at each PHU is revealed throughonline registration and real-time monitoring systems for the period, and the inventory levels andshortages of all PHUs are updated accordingly. In this stage, one assignment model is proposedalong with the DPA algorithm. The DPA algorithm updates the pool of candidate locations formobile PHUs by dynamically removing and adding some candidate locations. Afterward, the as-signment model is employed to allocate surplus inventories to PHUs facing shortages. Additionally,the surplus inventory of mobile PHUs is sent to stationary PHUs as inventory for the next periodto ensure that surplus inventories are kept in appropriate conditions.The applicability of mobile PHUs is explored in the literature to meet the vaccination demandin periods where the demand exceeds the capacity of available stationary PHUs. However, ifa specific region requires mobile PHUs for multiple periods, the location of mobile PHUs mayremain unchanged. In terms of conceptual contribution, I have proposed a new policy to dynamicallychange the location of mobile PHUs. In this research, it is assumed that multiple candidatelocations are available for each region or groups of people to deploy mobile PHUs. Therefore, whena specific region needs mobile PHUs for multiple periods, the location of mobile PHUs shouldchange constantly to improve the equitable access of all groups of people to vaccination centers. Adynamic PHU allocation algorithm is also developed to apply this policy and dynamically updatethe pool of candidate locations for mobile PHUs. When a candidate location has been selected forspecific periods, it is moved from the pool of candidate locations to a discarded set, using the DPAalgorithm. This algorithm guarantees that the locations of mobile PHUs are constantly changing,ensuring that everyone has access to vaccination.4.3 Systematic Decision Support System DesignThis section proposes the data-driven DSS developed in this research for the VDP problem,beginning with a definition of the VDP problem, followed by a detailed explanation of the DSS .4.3.1 Problem DefinitionVaccination for different infectious diseases, such as the Flu or COVID-19, is critical to preventthe spread of infection within the human body, thereby safeguarding the health, well-being, and126longevity of communities [256]. Vaccines are sensitive biological substances that can lose theirpotency if they are not handled in recommended conditions (e.g., temperature range). In addition,there are a variety of factors causing vaccine damage (e.g., expiration before usage, heat damage,and physical damage in transit). Therefore, there is a need to design an efficient SCN for theVDP to receive, store, and transport vaccines in the appropriate condition. Moreover, the demandfor vaccination is highly uncertain and drastically changes over time. For instance, the spread ofthe seasonal flu virus starts every year as the cold seasons (fall and winter) approach. Therefore,there is a need to consider demand uncertainty and its dynamic changing behaviour over time whendesigning SCN for the VDP problem. Consequently, it is crucial to consider uncertain demandover different periods when planning the VDP .In this research, I consider a vaccine SCN consisting of manufacturers, distribution centers,PHUs, and residential regions. In this network, manufacturers produce vaccines and transportthem to distribution centers. The distribution centers then deliver vaccines to PHUs for admin-istration. Finally, people from different regions can access PHUs for vaccination. The actualvaccination demand is determined through online registration or other appointment platforms pro-vided for different groups of people across various regions. Due to the lead time required to transportvaccines from manufacturers to PHUs, the actual vaccination demand cannot be determined be-fore the completion of the vaccine delivery process. The uncertain vaccination demand may varydrastically during different periods and depends on various factors such as spread rates, public an-nouncements, the emergence of new variants, the necessity for booster shots to enhance immunity,and population behavior. Another challenge in addressing the uncertain vaccination demand is thelack of historical data related to vaccination demand at the beginning of the vaccination program.Two types of PHUs are considered: stationary and mobile. Stationary PHUs are located atfixed sites, such as hospitals, and are equipped with specialized storage facilities to ensure vaccinesare kept at the appropriate temperatures. These units serve as the primary sites for vaccine ad-ministration to the public. Mobile PHUs have lower capacities compared to stationary PHUs.However, they are equipped with portable cold storage to maintain vaccine efficacy during transportand at the point of use, enabling wider distribution and accessibility of vaccines to various popula-tion groups. At the beginning of the vaccination program, the optimal locations of manufacturers,distribution centers, and stationary PHUs should be determined. As the vaccination program pro-gresses, the vaccination demand may increase to exceed the total capacity of available stationaryPHUs. Therefore, there is a need to deploy mobile PHUs to meet the uncertain vaccination de-127mand. In this stage, one assignment model is proposed along with the DPA algorithm. The DPAalgorithm updates the pool of candidate locations for mobile PHUs by dynamically removing andadding some candidate locations. Afterward, the assignment model is employed to allocate surplusinventories to PHUs facing shortages. Additionally, the surplus inventory of mobile PHUs is sentto stationary PHUs as inventory for the next period to ensure that surplus inventories are kept inappropriate conditions. The objective of this research is to answer the following questions:I) Which location(s) should be considered for manufacturing, cross-docking facilities, andPHUs?II) Which location(s) should be selected for the establishment of mobile PHUs and when shouldthe location of mobile PHUs be changed?III) What are the required doses of vaccines, considering wastage rates, to PHUs?IV) How can the limited available data be effectively employed to address parameter uncertainty?4.3.2 Systematic Decision Support System Design for Vaccine DistributionPlanningThis section explains the overall procedure of the proposed data-driven DSS for designing theSCN of the VDP problem. It is assumed that a few historical data for vaccination demandare available at the beginning of the vaccination period. As time progresses, more historical dataon vaccination demand is accumulated, facilitating informed decision-making. To provide a dy-namic plan for the VDP problem that captures the complexities of the real-world situation andpromptly responds to changes in vaccination demand, a data-driven DSS has been proposed inthis research. Figure 4.1 illustrates the overall structure of the developed DSS . The proposedDSS consists of data-based and model-based frameworks that work together to make data-drivendecisions for the VDP problem. The data-based framework is proposed to address uncertainty invaccination demand values. Within this framework, a DDRO approach is developed, integratingprediction values with a data augmentation process to tackle demand uncertainty. A detailed ex-planation of this data-based framework is provided in Section 4.4. The result of the data-basedframework, data-driven uncertainty sets, is then fed to the model-based framework. In the firststage of the model-based framework, a DRC model calculates the robust values of uncertain pa-rameters. Following that, a VDP model determines the optimal locations for PHUs and the flowof vaccines from manufacturers to PHUs. Subsequently, the actual vaccination demand values arerecorded. This new observation is then incorporated into both the data-based and model-basedframeworks. In the model-based framework, the shortages and surplus inventories of PHUs are128updated. Ultimately, surplus inventories are allocated to those PHUs experiencing shortages tosatisfy vaccination demands. In the data-based framework, the new data enriches the existing his-torical data, and prediction results and data-driven uncertainty sets are updated for forthcomingperiods.Figure 4.1: The Overall Procedure of the Proposed Data-Driven DSS for the VDP Problem4.4 Data-Based FrameworkThe vaccination demand in each region over different periods is uncertain in the VDP problem.In addition, a few, if any, historical data related to uncertain vaccination demand are available atthe beginning of the vaccination program. However, more historical demand data is consistentlycollected as the vaccination program progresses. One solution to deal with uncertain demand wouldbe to use conventional optimization under uncertainty approaches, such as RO . Nonetheless, thesemethods could lead to over-conservative solutions since the demand for vaccination is constantlychanging over different periods. Another solution is to use DDRO approaches to deal with param-eter uncertainty. However, the challenge with these methods is that sufficient data is unavailableto construct data-driven uncertainty sets that accurately encompass the actual distribution of un-certain parameters. Predicting future realizations of uncertain parameters using machine learningalgorithms could also be an effective approach to address parameter uncertainty. The main problem129with this approach is that enough data samples related to uncertain parameters should be avail-able. However, a few, if any, data samples are available for this type of problem. Therefore, theprediction results are not reliable. Consequently, to address the challenges posed by each approach,a hybrid data-based framework is developed in this section. The overall framework of the developedalgorithm is shown in Figure 4.2. As shown in Figure 4.2, in periods where data is insufficient, theconventional RO approach is employed to deal with uncertainty. However, when the vaccinationprogram continues over several periods or sufficient data is available, the framework switches to itsdata-based component, leveraging historical data to cope with uncertainty.Figure 4.2: The Overall Procedure of the Data-based FrameworkThe proposed data-based framework contains three phases. At the first phase, possible futurerealization is predicted using machine learning or statistical algorithms, such as LR, LSTM neuralnetworks, or ARIMA models. At the second Phase, additional data samples are generated toenrich the dataset. Various methods can be employed to generate new data samples, includingadding noise to existing data and using KDE . However, when generating new data samples, there130should be a minimum statistical distance between the real-world and generated data samples. Thisis because the limited available data may not reflect the actual distribution of uncertain parameters,resulting in poor out-of-sample performance. Therefore, a minimum statistical distance is neededto ensure that the data-driven uncertainty sets cover all areas that may contain future realization ofuncertain parameters. Additionally, having more data helps prevent significant variations in robustsolutions with varying conservatism degrees. Furthermore, possessing a larger dataset improves theseparability and range of robust solutions by avoiding significant deviations. Once the potentialfuture outcomes are predicted and the dataset is enriched through data generation techniques,the data-driven uncertainty sets are constructed using the SKL- or MKL-based WOC -SVMapproach in the third phase. The primary reason for using this approach is its ability to constructuncertainty sets encompassing all areas around the predicted point using a lower fraction of datacoverage. This allows for a lower conservatism degree in constructing the uncertainty set, avoidingover-conservative solutions. Additionally, the uncertainty set yield from theWOC-SVM approachencompasses all regions surrounding the predicted points, ensuring the feasibility of robust solutions.Within the developed framework, three different regularization parameters should be tunedto align with the volume of available data. The first regularization parameter is the number ofgenerated data samples. The number of generated data samples must be large enough to ensure theactual distribution of uncertain parameters is encompassed within the data-driven uncertainty set.Therefore, in situations where limited data is available, more data should be generated. The needfor generating additional data diminishes over time as more real-world data becomes available. Onceenough real-world data is collected, generating new data samples becomes unnecessary. The secondregularization parameter is the similarity index that calculates the statistical distance between thereal-world and generated data. Different statistical measurements can be employed for this purpose.However, the Wasserstein distance is the index commonly used in distributionally RO approaches[257]. The Wasserstein distance is used to construct a Wasserstein ball in the space of probabilitydistributions and to hedge against the worst-case distribution within this Wasserstein ball [258].Similarly, in this framework, the Wasserstein distance is used to tune the data generation process,therefore, the generated data maintains a minimum statistical distance from existing data. Thisapproach prevents overfitting and enhances the out-of-sample performance of the resulting data-driven uncertainty set [257, 258]. The third regularization parameter, denoted as v, representsthe conservatism degree in the SKL-based WOC-SVM approach. Specifically, it indicates thefraction of data coverage for the uncertainty set construction. For the data generation process, two131different algorithms have been developed. Section 4.4.1 explains the proposed algorithms and thedata generation phase of the data-based framework. The explanation of theWOC-SVM approachand theMSC algorithm, the third phase of the data-based framework, for constructing data-drivenuncertainty sets to cover areas around the predicted point is also provided below.4.4.1 Data Generation ProcessAs mentioned earlier, when limited data is available, generating artificial data can improve theout-of-sample performance of the data-driven solutions. In this section, two different data generationprocesses are proposed to augment the empirical data. The first approach is to give noise to empiricaldata. The second approach, DRI, incorporates distributional information of different clusters forthe data generation process. In the following, a brief description of each approach is provided.4.4.1.1 Noise Range Random Injection AlgorithmThe overall procedure of this approach is provided by Algorithm 4. One key input of thisalgorithm is parameter NN which is the number of nearest neighbors. In this method, the first stepinvolves calculating the average distance of the NN nearest neighbors for each of the existing datasamples. Afterward, each data samples are given a noise using a uniform distribution concerningthe calculated average to generate new data samples. In Algorithm 4 it is guaranteed that allartificial data samples are positive, reflecting the inherently positive characteristic of uncertaindemand. This algorithmâs primary advantage lies in its ability to determine a specific noise rangefor each individual data sample. Therefore, it generates new data samples through a randomizedprocess, ensuring that the augmented data retains the characteristics of the original dataset whileintroducing controlled variability.132Algorithm 4 Noise Range Random Injection AlgorithmInputs : Dataset O = {ui, âi = 1, . . . , N},NN = number of nearest neighbors,NG = number of new dataOutputs: New dataset containing real-world and generated data samples (NO)δi â Average distance of NN close neighbors of data sample ui, for i = 1, . . . , NCreate an empty dataset Gfor i to NG doj â i mod N New data (ND) â uj +Uniform(âÎ´i, δi) for dim in ND doif dim < 0 thendim â dim +Î´iendendGâ Gâª NDendNew dataset (NO) â G âªOreturn New dataset (NO)4.4.1.2 Density-based Random Injection AlgorithmThe overall procedure of this approach is detailed in Algorithm 5. Initially, data samples areclustered using the K-means clustering algorithm. Subsequently, the KDE approach is employedto learn the distributional information of each cluster. Afterward, new data samples are generatedbased on the learned KDE for each cluster. Clustering data samples is an effective method forimproving the data generation process through KDE , as each cluster may exhibit unique distribu-tional characteristics [259]. KDE is a commonly used approach for generating new data samples[260]. In comparison to other standard sampling techniques, KDE provides a more natural andless prone to overfitting way of generating new instances from existing data [260]. In the KDEapproach, the density of each data sample is calculated using Equation (4.1):fË(u) =1NNâi=1kh (u, ui) (4.1)133The value of fË(u) is estimated by calculating the average distance from u to all available datasamples {ui, âi = 1, . . . , N}. In Equation 4.1, kh is defined as the kernel function, and hË is thebandwidth parameter. A variety of kernel functions are available for KDE, such as exponential,tophat, linear, and cosine. Nonetheless, the Gaussian function stands out as the most widely usedkernel function, as shown in Equation (4.2) [247]:kh (u, ui) =1â2ÏhËexp(â(uâ ui)22hË2)(4.2)Where hË is a bandwidth parameter that regulates the smoothness of the estimated densityfunction. Parameter n also represents the dimension of input data. The estimated density functioncan then be used for generating new data samples. The main advantage of this algorithm is itsability to incorporate actual distributional information of different clusters, each exhibiting uniquedensity characteristics. By applying KDE to each cluster individually, DRI algorithm ensuresthat the density variations within the data are accurately captured and represented.134Algorithm 5 Density-based Random Injection AlgorithmInputs : Dataset O = {ui, âi = 1, . . . , N},Bandwidth parameter hË,Number of new data NGOutputs: New dataset containing real-world and generated data samples (NO)Cluster Dataset O into C clusters using K-means Clustering algorithmConsider each cluster as a unique dataset Uc = {uj , âj = 1, . . . , Nc}for each cluster c = 1, . . . , C doCreate an empty dataset Gc NGc â NcN ÃNGApply Kernel density estimation approach to fit dataset UcGenerate NGc data samples based on the learned density function and store in Gcfor data dË in Gc doif dË contains any negative value thenGenerate new data sample based on the learned density function and replace dËendendendNew dataset (NO) â O âªGc âc = 1, . . . , Creturn New dataset (NO)4.4.1.3 SKL- and MKL-based WOC-SVMThis section delves into the DDRO approach for creating data-driven uncertainty sets. OC-SVM algorithm is primarily employed in anomaly detection [261]. Its core concept revolves aroundestimating a support for the distribution of unlabeled data. [253] developed the SKL- and MKL-based OC-SVM algorithm by combining the OC-SVM algorithm with multiple kernel settings.The SKL- and MKL-based OC-SVM create compact data-driven uncertainty sets that resultin tractable RC models. [255] further developed the MKL- and SKL-based OC-SVM to con-sider a set of weights {wi | âi = 1, . . . , N}. The WOC-SVM approach leverages supplementaryinformation, such as density information or prediction results, to construct adjustable uncertaintysets. To be more specific, a set of weights is assigned to dataset O = {ui | âi = 1, . . . , N} toindicate the importance of each data sample being encompassed by the uncertainty set. When135prediction points are available, the weight of each data sample can be determined by its inversedistance to the predicted point. The key parameter affecting the construction of the uncertainty setis the regularization parameter v, which controls the fraction of outliers. Specifically, approximately(1 â v) Ã 100% of data samples are covered by the uncertainty set [253]. The dual formulation ofthe SKL-based WOC-SVM model is as follows:minNâi=1Nâj=1Î±iÎ±jK(ui, uj)s.t. 0 â¤ αi â¤ ÏiNv, âi = 1, . . . , NNâi=1Î±i = 1 (4.3)In dual formulation (4.3), Ïi also specifies the weights of data samples. The weight of eachdata samples indicates the importance of each data sample to be covered by the uncertainty set.The weight Ïi assigned to each data sample indicates the significance of that data sample in beingencompassed by the uncertainty set [255]. In other words, these weights can be viewed as indicatorsof the probability of each data sample occurring in the future. Dual variable αi also is dual variablethat determines the type of each data sample for the uncertainty set construction. The optimalvalue of dual variable αi divides data samples into three groups. Data samples not included in theuncertainty set, either on the boundary or outside of it, are called SVs. Those that lie exactly onthe boundary are called BSVs. Finally, all those samples that are encompassed by the uncertaintyset are called IDs [249, 253]. In order to determine set of SVs, BSVs, and IDs, Equations (4.4)to (4.6) are used.SV = {i | αi > 0, âi = 1, . . . , N} (4.4)BSV = {i | 0 < αi < ÏiNv,âi = 1, . . . , N} (4.5)ID = {i | αi = 0, âi = 1, . . . , N} (4.6)In dual formulation (5.36), K(., .) denotes the kernel matrix and is constructed using a directsum of all basis kernel matrices {Km(., .)}, as shown in (4.7):136K(ui, uj) =Mâm=1Ïm Â·Km(ui, uj) (4.7)The direction vector qm and dispersion factor Cm distinguish each basis kernel function from theothers. The dispersion degree Cm of dataset O along with each direction vector qm is determinedusing Equation (4.8):Cm = maxiâ{1,...,N}{qTmui}â miniâ{1,...,N}{qTmui},âm = 1, . . . ,M (4.8)In Equation (4.8), Maxϵi determines the ϵ-upper quantile of the set {}. If the parameter K issufficiently large, kernel functions become positive-definite [253]. The value of parameter K is alsodefined by Equation 4.9:K = maxm=1,...,MSmCm , Sm = maxi,j=1,...,N{qTm(ui â uj)},âm = 1, . . . ,M (4.9)In the context of MKL, it is necessary to create a large number of direction vectors, evenlydistributed in the data space, to make sure that the appropriate direction vectors are also takeninto account [253]. Upon solving the MKL version of the dual Model (4.3), the optimal value ofkernel weights is also specified. The kernel matrices with Ïm > 0 contribute to the uncertainty setconstruction and are called SKs. However, in the SKL-based WOC-SVM approach, first thecovariance of dataset O is calculated. Afterwards, the eigenvectors of the covariance matrix areconsidered as direction vectors. Finally, the uncertainty set U is formulated by Equation (4.10):UO ={ui â SV |âÎ±iâmâSKqTm(ui â uj)Cm Â·K â¤ 1â Ï}(4.10)Where Ï is computed by Equation (4.11):Ï =1|BSV|âjâBSVâiâSVâmâSKÏm Â·Km(ui, uj) (4.11)1374.4.1.4 Weight Parameter SettingIn this study, the distance-based approach proposed by [255] is employed to weight data sam-ples. Having prediction results, the weight of each data sample can be specified as the inverse ofits distance to the predicted point. Employing the inverse Euclidean distance enables data pointssurrounding the predicted point to acquire larger weights compared to other data points. Conse-quently, the algorithm tends to shift the uncertainty toward predicted points. The inverse distanceof each data sample can be obtained using Equation (4.12):dËi =1â¥Gâ uiâ¥2 + ϵ ,âi = 1, . . . , N (4.12)In Equation (4.12), G stands for the goal point. The goal point is considered as the predictedpoint. Moreover, e is a small value to avoid undefined fractions when the prediction point is equalto a data sample. Further, ϵ is a small value that prevents the fraction from being undefined whenthe prediction point coincides with a data point. The impact of the inverse distance dËi on theuncertainty set construction can be tuned using Equation 4.13:dËi = Ï · di â dmaxi + 1â bdmaxi â dmini, Ï = 2 · bdmaxi â dminidmaxi â dmini(4.13)In Equation (4.13), dmaxi and dmini refer to the maximum and minimum inverse distances amongall available data samples. dËi is also the inverse distance of data sample i that lies in the range[1 â b, 1 + b], where b â [0, 1). The larger the value of parameter b, the bigger the effect of weightparameters on the uncertainty set construction will be. The aim is to completely cover the areasaround the predicted point. Therefore, the value of b is considered equal to 0.99 [255]. Finally, inorder to make sure that the regularization parameter lies within the range (0, 1), Equation (4.14)is used to specify the final weight of each data sample:Ïi =di ÃNâNi=1 di, âi = 1, . . . , N (4.14)When the uncertainty set U(O) is constructed, the robust counterpart (RC) of uncertain pa-rameters can be formulated. Consider the following mathematical formulation:138MinxCT · x (4.15)aT · x â¤ b,âa â U(O) (4.16)The vector c represents the coefficients of variables in the objective function, x denotes thevector of decision variables, and a refers to the uncertain matrix of coefficients on the left-hand side(LHS) of the model, which is defined within the uncertainty set U(O). By incorporating the dualvariables µ and λ, the RC of Constraint (4.16) can be expressed as Constraints (4.21):âiâSVâmâSK(µim â λim) · qTm · (ui)cm · l + η · (1â Ï) â¤ b (4.17)âiâSVâmâSK(µim â λim) · qmcm · l = x (4.18)µim + λim = η · αi · Ïm âi â SV,âm â SK (4.19)µim, λim â¥ 0 âi â SV, âm â SK (4.20)η â¥ 0 (4.21)Utilizing the WOC-SVM approach, when accounting for inverse distance weights, could leadto inadequate coverage of regions surrounding the predicted point. This is more likely to happenwhen the predicted point is situated in areas of low density. Consequently, [255] developed anMSCalgorithm that ensures the coverage of areas around the predicted point. The overall procedure oftheMSC algorithm is provided in Algorithm 6. The main idea behind theMSC algorithm is thatthe regularization parameter v is set to a small value, such as 0.05. Subsequently, the SKL-basedWOC-SVM approach is applied to the dataset at each stage. Afterward, SVs are detected anddiscarded from the dataset. This process continues until the number of remaining data samples isclose to the desired number of covered data. Afterward, the regularization parameter v is set toa small value, such as 0.01, to cover all the remaining datasets. At the final stage of the MSCalgorithm, both SKL- andMKL-based WOC-SVM approaches can be used. For symmetric andasymmetric datasets, it is recommended to use SKL- and MKL-based OC-SVM approaches,respectively [253].139Algorithm 6 Multi-Stage Clustering AlgorithmInputs : Dataset O,predicted point G,regularization parameter v,fraction of data coverage (1â γ)Outputs: Value of dual variables αiN â Number of data samples in dataset ONumber of Remaining Data (RD)â (1â Î³)ÃNwhile N > RD+ ϵ doCalculate wi using Equation (4.14)Calculate the covariance matrix of dataset OConsider eigenvectors of the covariance matrix as direction vectors qmCalculate basis kernel matrices Km using Equation (4.7)Set coefficient of basis kernel matrices as 1MCalculate the final kernel matrix using Equation (4.6)Solve the SKL-based WOC-SVM Model (4.3)Determine SVs using Equation (4.4)Discard SVs from dataset OUpdate N â Number of remaining data samples in dataset Oendv â 0.01wi â 1,âi = 1, . . . , NCalculate the covariance matrix of dataset OConsider eigenvectors of the covariance matrix as direction vectors qmCalculate basis kernel matrices Km using Equation (4.7)Set coefficient of basis kernel matrices as 1MCalculate the final kernel matrix using Equation (4.6)Solve the SKL-based WOC-SVM Model (4.3)return Value of dual variables αi4.5 Model-Based FrameworkThis section explains the proposed model-based framework for the VDP problem. Figure 4.3shows the procedure of the proposed model-based framework. At the beginning of the planningperiod, although only a few historical data points are available, there is still a need to make somestrategic decisions for the SCN vaccine. Therefore, a robustVDP model is solved to determine theoptimal location of stationary PHUs and distribution facilities. For the forthcoming periods, thevaccine demand of different regions or groups of people is determined using the proposed data-based140framework explained in Section 4.4. Once the data-driven uncertainty sets for uncertain demandparameters are constructed, the robust values of the uncertain parameters are specified using theDRC model. The RC values of uncertain demand are then fed into theVDP model. Subsequently,the deterministic VDP model is solved to identify the optimal locations for different PHUs andthe optimal flow of vaccines between each entity. Consequently, the mobile PHUs are placed atselected locations, and vaccines are transported from manufacturers to PHUs.Figure 4.3: The Overall Procedure of the Model-based FrameworkOnce the location of mobile PHUs is determined, the set that specifies the number of timeseach candidate location has been selected for establishing mobile PHUs is updated. Subsequently,a threshold is defined to determine the maximum number of selections permitted for each loca-tion for placing mobile PHUs. This threshold will be employed to identify and exclude locationsthat surpass the set limit from the pool of candidate locations for the subsequent period. There-fore, the model-based framework ensures a balanced distribution of mobile PHUs, preventingover-concentration in certain areas while under-serving others. This method facilitates a dynamicallocation system that enhances overall healthcare accessibility and reduces disparities by ensuringequitable distribution of critical health services. Subsequently, the actual demand for vaccinationsduring period T is revealed. As a result, the actual shortage and inventory level of each PHU are141updated. Following this, surplus inventories are allocated to those PHUs experiencing shortages,utilizing an assignment model. The primary objective of this reallocation is to minimize overallcosts and reduce the total shortage through the planning horizon. The overall explanations of theRC , VDP , and assignment models are provided in the following. DPA algorithm in the thirdphase of the model-based algorithm is also developed to update the Set RD . Set RD is the set thatspecifies the locations that are discarded from the pool of candidate locations for placing mobilePHUs. The overall explanation of the DPA algorithm is also as follows.4.5.1 Developed Robust Counterpart ModelThis section provides the DRC model for determining the RC value of the uncertain demand.As shown in Figure 4.3, when a data-driven uncertainty set is constructed, the DRC model shouldbe solved to deterministic robust values of uncertain demand. The uncertain demand parameter(Dht) is the right-hand side of Constraint (4.26), known as column-wise uncertainty. In the contextof column-wise uncertainty, only one dimension of uncertain parameters appears in each constraint[254, 262]. As a result, the worst-case scenario of each dimension within the uncertainty set isconsidered the RC value of uncertain parameters. Therefore, the RC values can be calculatedusing a simple DRC model. Afterward, the RC values will be fed into the VDP model, and themodel will be solved to obtain robust solutions. For this purpose, the Model (4.22) must be solvedfor every period (t â T ) and for every region (h â H) to obtain the RC value of the uncertainparameter Dht.minxËhDËmax¬Dh â UO h â HDh · avh â¤ D (4.22)In Model (4.22), an auxiliary variable, avh, is introduced. The value of this decision variable isfixed at 1 for the region whose robust values are being calculated and at 0 for other regions. Theobjective function of the Model (4.22) determines the RC value of uncertain demands for eachregion.The RC for the Model (4.22) is formulated as the DRC Model (4.23) and is referred to asthe DRC model. The definition of auxiliary variables and parameters of the DRC Model (4.23)is provided in 4.4.1.3.142minwiDËâiâSVâmâSK(µim â λim) · qTm(ui)cm · l + η · (1â Ï) â¤ DËâiâSVâmâSK(µim â λim) · qmcm · l = xËh âh â Hµim + λim = η · αi · Ïm (4.23)4.5.2 Vaccine Distribution Planning ModelIn this section an MILP model for the VDP problem is proposed to design a multi-echelonVSCN . Table 4.1 indicates the indices, parameters, and variables employed in the proposed model.143Table 4.1: List of Sets, Indices, Parameters, and Decision VariablesIndices & SetsP Set of vaccine manufacturers (p â P )L Set of potential locations for distribution centers (DSs) (d â L)R Set of potential locations for PHUs (r, râ² â R)RS Set of stationary PHUs (rs â RS) (RS â R)RM Set of mobile PHUs (rm â RM) (RM â R)RD Set of discarded locations for mobile PHUs (rd â RD) (RD â R)H Set of residential regions (h â H)T Set of time periods (t â T )ParametersAp Capacity of manufacturer pBd Capacity of DC dCr Capacity of PHU rFpd Shipping lead time between manufacturer p and DC dGdr Shipping lead time between DC d and PHU rIrh Shipping lead time between PHU r and region hKdr Maximum time allowed for transportation between DC d and PHU rLrh Maximum time allowed for transportation between PHU r and region hMd Vaccine waste in DC dvwr Vaccine waste in PHU rDht Demand for vaccine at region h in period tDSrrâ² Distance between candidate location r and râ² for placing PHUsTP pdt Transportation cost per unit between manufacturer p and DC d in period tTMdrt Per unit transportation cost between DC d and PHU r in period tTRrht Transportation cost per unit between PHU r and region h in period tip Fixed cost of agreement with manufacturer pjd Fixed cost of agreement with DC dkr Fixed cost of agreement with PHU rYht Penalty cost associated with shortage of vaccine at region h in period tBM A sufficiently large numberNU Maximum number of available mobile PHUs144Decision VariablesQpdt Doses of vaccine transported from manufacturer p to DC d in period tEdrt Doses of vaccine transported from DC d to PHU r in period tSrht Doses of vaccine assigned from PHU r to region h in period tUht Number of unfulfilled demands at region h in period tVp 1, if a manufacturer is selected at location p, 0, otherwiseWd 1, if a DC is selected at location d, 0, otherwiseXr 1, if a PHU is selected at location r, 0, otherwiseMD Minimum distance between selected PHUsMin z1 =âpâdâtTPpdt Â·Qpdt +âdârâtTMdrt · Edrt +ârâhâtTRrht · Srht+âhâtYht · Uht +âpip · Vp +âdjd Â·Wd +ârkr Â·Xr (4.24)Max z2 =MD (4.25)Subject to:ârSrht + Uht â¥ Dht, âh â H, t â T (4.26)ârEdrt â¤ 1âMD Â·Qpdt, âd â L, t â T (4.27)âhSrht â¤ 1â Vd Â·Wd · Edrt, âr â R, t â T (4.28)âdQpdt â¤ Ap · Vp, âp â P, t â T (4.29)ârEdrt â¤ Bd Â·Wd, âd â L, t â T (4.30)âhSrht â¤ Cr Â·Xr, âr â R, t â T (4.31)Qpdt = 0 if Fpd â¥ Jpd, âp â P, d â L, t â T (4.32)Edrt = 0 if Gdr â¥ Kdr, âd â L, r â R, t â T (4.33)145Srht = 0 if Irh â¥ Lrh, âr â R, h â H, t â T (4.34)Xr = 1, âr â RS (4.35)Xr = 0, âr â RD (4.36)ârâRMXr â¤ NU (4.37)MD â¤âr,râ²âRDSrrâ² Â·Xr Â·Xrâ² +BM · (1âXr Â·Xrâ²), âr, râ² â R (4.38)Vp,Wd, Xr â {0, 1}, âr â R, d â L, p â P (4.39)Qpdt, Edrt, Srht, Uht â¥ 0, âp â P, d â L, r â R, h â H, t â T (4.40)The objective function (4.24) is defined to minimize the fixed costs (i.e., costs of agreementwith third parties) and variable costs (i.e., transportation costs between facilities, shortage costsof vaccine). The objective function (4.25) aims to maximize the distance between all PHUs,facilitating a balanced and equitable distribution of vaccines. Constraint (4.26) represents doses ofvaccine assigned from PHUs to different regions and groups of people and the amount of unfulfilleddemand. Constraints (4.27) and (4.28) are related to doses of vaccine wasted in DCs and PHUs.Constraints (4.29), (4.30), and (4.31) indicate the maximum capacity of province repositories, DCs,and PHUs, respectively. Constraints (4.32), (4.33), and (4.34) ensure that the shipping lead timebetween two facilities is less than the maximum time allowed. As previously stated, theVDP modelis solved at the start of the VDP period, leading to the selection of stationary PHUs. Duringsubsequent periods, these stationary PHUs (RS set) remain continuously open for vaccination.Constraint (4.35) states that stationary PHUs remain open continuously for vaccinations. Thereis also a set of locations (RD) discarded from candidate locations for placing mobile PHUs.This set is empty at the beginning of the vaccination period. However, this set will be updatedover time. Constraint (4.36) indicates that candidate locations outlined in set RD should not beselected for placing mobile PHUs. Constraint (4.37) determines the maximum number of availablemobile PHUs. Constraint (4.38) calculates the minimum distance between all selected PHUs.Constraints (4.39) and (4.40) are related to binary and non-negative decision variables, respectively.4.5.2.1 LineralizationConstraints (4.38) calculate the minimum distance among all selected PHUs. In these con-straints, two binary decision variables, Xr and Xrâ² , are multiplied, resulting in a nonlinear mathe-146matical model. Therefore, there is a need to linearize Constraints (4.38) to maintain the computa-tional tractability of the proposed mathematical model. To achieve this, a binary decision variable,Yrrâ² , is introduced, which is valued at 1 if both PHUs r and râ² are selected; otherwise, it is valuedat 0. As a result, Constraints (4.38) are replaced with Constraints (4.41) to (4.43) to linearize theproposed mathematical model.Xr +Xrâ² â¤ Yrrâ² + 1, âr, râ² â R (4.41)Xr +Xrâ² â¥ 2 · Yrrâ² , âr, râ² â R (4.42)MD â¤âr,râ²âRDSrrâ² · Yrrâ² +BM · (1â Yrrâ²), âr, râ² â R (4.43)Constraints (4.41) and (4.42) are used to determine the value of the binary decision variableYrrâ² . Constraints (4.43) also calculate the minimum distance among all selected PHUs using thebinary decision variable Yrrâ² .4.5.2.2 Distance-Based ApproachThe proposed VDP model contains two conflicting objective functions. The first objectivefunction aims to minimize the total costs, including the transportation costs of the VDP network.Consequently, the model tends to select locations close to each other to minimize transportationexpenses. On the other hand, the second objective function aims to maximize the distance amongall PHUs to ensure equitable access for different groups of people to vaccination centers. The firstobjective function accounts for the traveling costs of different groups of people to PHUs. However,set H represents the centroid of each region or group of people. Therefore, the second objectivefunction is necessary to maximize the distances among all PHUs, ensuring that individuals fromdifferent parts of regions have equitable access to vaccination centers.The issue with the second objective function is that if it is the sole criterion for optimizingthe VDP network, the model will result in selecting at most one candidate location. This isbecause if only one location is selected, the value of the decision variable MD would be equal toBM . If the value of BM is greater than or equal to the maximum distance among all PHUs,the second objective function will achieve its possible maximum value. To address this challengeand consider both objective functions when designing the vaccine distribution network, a distance-based algorithm is developed to solve the proposed VDP model. The distance method is commonly147used to find optimal solutions for multi-objective optimization models [263, 264]. Equation (4.44)demonstrates how the distance method combines various objective functions, each with differentscales and values, into a single objective function. Here, zâi and Ïi represent the best solutions anddistance metrics associated with each objective function.Z =(âiÏi Â·(zi â zâizâi)Ï) 1Ï, âi = 1, 2, . . . ,â (4.44)Therefore, to implement the distance approach, there is a need to obtain the optimal value ofeach objective function. Then, Equation (4.44) is used to calculate the final objective function ofthe VDP model. The VDP model will first be used to determine the best solution for the firstobjective function zâ1 and the optimal location and number of required PHUs. The model will thenbe solved using the second objective function. If the second objective function is used for designingthe vaccine distribution network, the optimal value of the objective function would be equal to BMif BM is set to be equal to or greater than the maximum distance among all PHUs. In such acase, there is no need to solve the model for the second objective function, and zâ2 will be set to thevalue of BM .4.5.3 Assignment ModelThis section proposes the assignment model, which aims to reallocate surplus inventories toPHUs experiencing shortages after the actual demand in each region has been revealed. Table 4.2indicates the indices, parameters, and variables employed in the proposed model.Min z1 =ârârâ²dvrrâ² · dsrrâ² +ârnur · SCr (4.45)Subject to:ârâ²dvrrâ² â¤ Invr, âr â Râ (4.46)ârdvrrâ² â¤ LSrâ² â nurâ² , ârâ² â Râ (4.47)dvrrâ² â¥ 0, nur â¥ 0, âr, râ² â Râ (4.48)The objective function (4.45) aims to minimize the total costs, which include both transportationand shortage costs. Constraints (4.46) state that the total number of vaccines transported from PHU148Table 4.2: List of Sets, Indices, Parameters, and Decision VariablesIndicesRâ Set of selected PHUs (r, râ² â Râ)ParametersInvr Inventory of PHU rLSr Shortage of PHU rSCr Shortage cost in PHU rdËsrrâ² Transportation cost for one unit of vaccine from PHU r to PHU râ²Decision Variablesdvrrâ² Doses of vaccine transported from PHU r to PHU râ²nur Number of unfulfilled vaccination demands at PHU rr must not exceed the number available at that PHU . Constraints (4.47) calculate the number ofunfulfilled vaccinations for every PHU râ². Constraints (4.48) specify that the domain of the decisionvariable must be non-negative integers.4.5.4 Update Candidate LocationsThe value of the threshold and the number of times a specific location is discarded from candidatelocations also depends on the size and number of available candidate locations for placing mobilePHUs. In cases where the number of available candidate locations for mobile PHUs is limited, thethreshold and Set RD should be updated carefully to ensure that enough mobile PHUs are availableto meet the vaccination demand. To achieve this, the overall procedure proposed in Algorithm 7 isemployed. As shown in Algorithm 7, there are two variables, NSr and NDr, that determine thenumber of periods a specific location is selected for placing PHUs and discarded from the poolof candidate locations, respectively. Additionally, an empty set, named RD , is created to containlocations discarded from the pool of the candidate locations. For every period, the ED is calculatedusing the proposedDRC model. Furthermore, the ACA of all PHUs, except for those in Set RD ,is calculated. If ED exceeds AC , some PHUs are moved from RD to RM to ensure that thevaccination demand is met. Upon solving the VDP model, the optimal value of the binary decisionvariable Xr will be determined. Subsequently, the decision variables NSr and NDr, along withSet RD , are updated. This algorithm ensures that there are always enough candidate locations to149meet the vaccination demand while appropriately updating Set RD .Algorithm 7 Dynamic PHU AllocationInputs : Candidate locations for placing mobile PHUs (RM),Time-Periods,ThresholdOutputs: Set RD, NSr, and NDr values for every periodNSr â 0, NDr â 0, âr, and RD = {}for each t in Time-Periods doSolve DRC model to calculate the expected vaccination demand as EDCalculate the total available capacity of all PHUs except those in RD and ACif ED > AC thenCalculate the number of needed mobile PHUs NP = EDâACCaprExclude NP PHUs from RD to meet the customersâ demandendSolve VDP model and determine the optimal value of Xrfor each r in RM doif Xr = 1 thenNSr â NSr + 1endif NSr > Threshold thenRD â RD âª {r} NDr â NDr + 1endif NDr > Threshold thenNSr â 0 RD â RD {r}endendendreturn Set RD, NSr, and NDr values for every period4.6 Numerical ExperimentsIn this section, the numerical experiments of the proposed DSS for the VDP problem areprovided. First, the applicability of the proposed data-based framework is proposed. Thereafter,the capability of the proposed model-based framework in tandem with the data-based frameworkwill be provided. Both data-based and model-based frameworks are coded in Python to createdata-driven uncertainty sets and to solve optimization models. An AMD Ryzen 5 7530U computerwith a 2.0 GHz CPU and 16.0 GB RAM is used to perform numerical analysis.1504.6.1 Supporting Data of Case StudyThis section provides the historical data and the case study used to evaluate the proposed DSSfor the VDP problem. A real-world case study is investigated in Toronto, Canada, using real-worldlocations to evaluate the proposed DSS âs performance. For this purpose, access to vaccination datafor each region of Toronto is needed. However, since regional demand data is not available, theoverall vaccination data from two countries, Canada and the USA, are used for further evaluation.Figure 4.4 shows the weekly vaccination demands of the two countries.Figure 4.4: Weekly Vaccination Demand of Canada and the USATo assess the overall performance of the proposed DSS , a network of candidate locations forboth stationary and mobile PHUs was generated in a section of Toronto that includes six FEDs.Additionally, two candidate suppliers and distributors are considered for this network. The vacci-nation demands of first three regions in Toronto are considered to follow the vaccination demandtrend of Canada, while the remaining regions align with that of the USA. The weekly vaccinationdemands are divided by the total population of each country and then multiplied by the populationof the intended region to determine the vaccination demand of different regions. To calculate thedistance and transportation time between different points of the vaccination network, the VeRoVizpackage [265] is used with the option of âfastest route.â Figure 4.5 shows the candidate locationsfor stationary PHUs (RS â 1, 2, . . . , 12) and mobile PHUs (RM â 12, 13, . . . , 25) as well as de-mand density points of FEDs (h â 1, 2, . . . , 6). The capacity of stationary and mobile PHUs isconsidered 6000 and 3000 doses per week, respectively.151Figure 4.5: Candidate Locations for Establishing Stationary and Mobile PHUs4.6.2 Numerical Analysis of the Data-Based FrameworkIn this section, the capability of the proposed data-based framework is demonstrated. For thesake of simplicity, the vaccine demand for two different regions of the GTA, as explained in Section4.6.2, for the entire vaccination period is shown in Figure 4.6 in the following.152Figure 4.6: Historical Vaccine Demand of Two Different Regions of GTAEach data sample represents the demand of the two regions for each week, and the samplesare colored according to the time they occurred. In total, there are 110 data samples related touncertain vaccination demand available once vaccination is complete. However, no historical datais available at the beginning of the vaccination period. As time progresses, the historical demandof each region is stored over time and used to address future demand uncertainty. Due to thelack of sufficient data samples, predictions for future demand may not be reliable. As a result, theweighted DDRO approach can be employed to construct data-driven uncertainty sets that coverall areas around the predicted points. This approach allows for a more reliable solution, ensuringthe feasibility of the solution while avoiding over-conservatism. In the following, it is assumed thatonly 50 data samples are available and the prediction for the 51st week is provided. Therefore, theMSC algorithm (Algorithm 6) is employed to construct data-driven uncertainty sets covering allregions around the predicted point. Figure 4.7 shows the constructed uncertainty sets with differentconservatism degrees (from 20% to 80% coverage). As shown in Figure 4.7, there is a sudden changein the uncertainty boundaries when the conservatism degree is decreased from 60% coverage to 40%coverage. The reason for this is the limited number of data samples available, which creates someempty regions without any historical observations. In the space between the uncertainty sets with40% and 60% coverage, there are few historical data samples. Moreover, the data-driven uncertaintysets only cover areas where data samples are available. Consequently, there may not be an accurate153representation of the real distribution of the uncertain parameter based on the limited availabledata. Therefore, the data-driven uncertainty sets may result in poor out-of-sample performance.Consequently, it is necessary to take measures to improve the out-of-sample performance of thedata-based framework.Figure 4.7: Data-Driven Uncertainty Using MSC Algorithm for Limited DataIn this study, data augmentation through data generation methods is proposed to improve theout-of-sample performance of the data-based framework. Two different algorithms are proposed andcompared for generating new data samples. In the DRI algorithm (Algorithm 5), data samplesare segmented into different clusters. Subsequently, KDE is applied independently to each clusterto learn the distributional information of each cluster. Afterward, new data samples are generatedfor each cluster using the KDE approach. For the data shown in Figure 4.6, two clusters areidentified using the K-MEANS algorithm. The bandwidth parameter hË for the KDE algorithm isalso determined using grid search and cross-validation for each cluster. The bandwidth parameterfor clusters is determined as 1610 and 920, respectively. Subsequently, the KDE algorithm isemployed to learn the distributional information. 100 data samples are generated in total usingthe proposed procedure. Figure 4.8a shows the new data samples generated along with real-worlddata. Additionally, the MSC algorithm is employed to create data-driven uncertainty sets withdifferent conservatism degrees. According to Section 4.4, new generated data samples should notbe overfitted to the empirical distribution of the limited available data to improve out-of-sampleperformance. To prove this, new data samples are generated using different values for the bandwidthparameters. Figure 4.8b shows the constructed uncertainty sets for these generated data samples.Adding noise through the NRRI algorithm (Algorithm 4) to existing data is another method for154generating new data samples. For the NRRI algorithm, the value of parameter NN (number ofnearest neighbors) will be predetermined. For each data sample, the average distance to its NNnearest neighbors is calculated. Subsequently, new data samples are generated using a uniformdistribution in the vicinity of available data samples, with an upper and lower bound based on theobtained mean value. Therefore, the only parameter that influences the data generation processis the number of nearest neighbors. Using the proposed process, two datasets containing 100 datasamples are generated using two different values for the NN parameter. Figures 4.8c and 4.8dshow the generated data samples along with the constructed uncertainty sets. Figure 4.8 showsthat generating new data samples improves the overall quality of the constructed uncertainty sets.In addition, the data augmentation process results in covering areas containing data samples aswell as some empty areas that may contain new observations in the future. Compared with Figure4.7, the constructed uncertainty sets become more distinct, encompassing regions with existingdata samples as well as vacant areas that could potentially hold new observations in the future.This enhances the distinctiveness between uncertainty sets of different conservatism degrees. Thecomparisons between Figures 4.8a and 4.8b, as well as Figures 4.8c and 4.8d show that the generateddata samples can overfit the existing data if hË and NN parameters are not carefully tuned. Thismay result in the same problem as the original method outlined in Figure 4.7.155(a) KDE with hË1 = 1610 and hË2 = 920 (b) KDE with hË1 = 900 and hË2 = 200(c) NRRI with NN = 10 (d) NRRI with NN = 2Figure 4.8: Data-Driven Uncertainty Sets using the MSC Algorithm with New Generated DataSamplesTo ensure that the generated data samples do not overfit the existing data, two similaritymeasures are suggested in this research: the Wasserstein distance and the Cosine similarity. Thegreater the Wasserstein distance or the smaller the value of the Cosine similarity method, the largerthe statistical distance between the two datasets. Table 4.3 shows the values of these two measuresfor the generated data samples. As shown in Table 4.3, the DRI algorithm with bandwidthparameters (900, 200) and the NRRI algorithm with NN = 2 overfit the data samples. To preventoverfitting, the hyperparameters should be adjusted accordingly to maintain a minimum statisticaldistance from the existing data. When limited data is available, a key question arises: how manydata samples should be generated to ensure the feasibility of the optimal solution? To examinethe impact of the number of generated data samples on the overall performance of the DDROapproach, a sensitivity analysis is conducted. The results of this experiment are available in Section4.6.2.1.156Table 4.3: Similarity Measurements for the Generated Data SamplesApproach Hyperparameter Wasserstein distance Cosine similarityDRI 1610, 920 313.5 0.62DRI 900, 200 131.1 0.82NRRI 10 237.14 0.65NRRI 2 117.9 0.804.6.2.1 How Many Data Samples Should be Generated?When limited data is available, one key question is how many data samples should be generatedto ensure the feasibility of the optimal solution. To answer this question, 25 to 200 new data samplesare generated to analyze how the size of the generated data samples impacts the optimal value of thedata-based framework. For generating new data samples, it is assumed that only 50 data samplesare available. Four different methodologies are employed for the generation process. The first twomethodologies are the DRI and NRRI algorithms (Algorithms 4 and 5). Two different values oftheir hyperparameters are used and compared for these approaches. The âmultivariate Gaussianâand âmultivariate VineCopulaâ methods, constituting the third and fourth methodologies, are fittedto the available data [266]. Afterward, the generated data samples are merged with the existingones, and the SKL-basedWOC-SVM approach is employed to construct data-driven uncertaintysets. The demand value for each region is then determined by identifying the worst-case scenariowithin each dimension. In this analysis, the demand values from two distinct regions are utilized,as shown in Figures 4.4 and 4.6. Figure 4.9 shows the total demand of these two different regionsfor each generated dataset.Figure 4.9 demonstrates that constructing data-driven uncertainty sets only with existing datacan lead to an inaccurate representation of the actual distribution of limited data and poor out-of-sample performance. Figure 4.9 demonstrates sudden fluctuations in demand values when onlyexisting data is utilized for constructing uncertainty sets. As the size of the data samples increases,the sudden variations in demand values, like those from v = 0.55 to v = 0.6, become less obvious.However, datasets generated using NRII and DRI algorithms with imprecise hyperparameters(NN = 2andhË = 900, 200) encounter the same challenge as the main dataset, attributable to thehigh similarity between the existing and generated datasets. Nevertheless, with careful tuningof hyperparameters to ensure a specific statistical distance between the generated and existing157datasets, improvements in both the out-of-sample performance and the separability of the finalsolution can be achieved. Figure 4.9 indicates that demand values from generated datasets aremore conservative than those from existing data, which enhances the out-of-sample performanceof the robust solution. Additionally, as the dataset size increases, there are no sudden shifts indemand values, which enhances the separability of robust solutions. This means a broader range ofdiverse values can be achieved by adjusting the conservatism degree. The results show that despitevariations in uncertainty sets arising from different data generation processes, the DRI algorithmwith hË = (1620, 900), NRRI with NN = 10, and Multivariate VineCopula enhance the out-of-sample performance. In addition, these methods effectively improve both performance and solutionseparability regardless of the uncertainty set differences. The Multivariate Gaussian approach hasresulted in a less conservative solution compared to the original dataset for some conservatismdegrees. However, this approach has smoothed the sudden change in demand values for differentconservatism degrees. The Multivariate Gaussian approach yields less conservative solutions forsome conservatism degrees compared to the original dataset. However, it smoothness the variationsin demand values across different conservatism degrees.158(a) NRRI, NN = 2 (b) NRRI, NN = 10(c) DRI 900 (d) DRI 1600(e) Multivariate Gaussian (f) Multivariate VineCopulaFigure 4.9: Impact of Generated Dataset Size on Uncertainty Set Construction and Final DemandValues1594.6.3 Numerical Analysis of the Model-Based DSSIn this section, the performance of the proposedDSS for theVDP problem is investigated usingthe data and case study described in Section 4.6.1. As mentioned, the data-based framework is firstemployed to create data-driven uncertainty sets. Afterward, the created uncertainty sets are fedinto the model-based framework to determine the optimal configuration of the vaccine distributionnetwork and the optimal flow between different entities. In the data-based framework, it is assumedthat only five historical demand data points are available at the beginning of the planning horizon(from periods T=1 to T=5). Therefore, these data points are fed into the data-based framework.The possible future realization of demand parameters is determined using a prediction algorithm.Subsequently, 200 new data samples are generated using theNRRI algorithm with NN = 5. Havingenriched the existing data, theMSC algorithm creates a data-driven uncertainty set that covers allareas around the predicted point for period T=6. For the following period (T=7), the actual demandvalue from period T=6 is revealed and added to the existing historical data. Consequently, the data-based framework utilizes the updated data to refine the predicted point and the uncertainty set.This process continues until the vaccination program is completed. In the following, the applicabilityof the proposed DSS system to handle periods with shortage caused by prediction values will beinvestigated. For this purpose, 6 different scenarios are considered. The explanation of each scenariois provided in the following.4.6.3.1 Overview of Scenarios and Approaches for ComparisonThis section explains the generated scenarios to demonstrate the capability of the proposeddata-driven DSS . The first scenario involves using the predicted values directly as values for theuncertain demand parameters while discarding the DDRO process. For the prediction, a linearregression model is employed along with rolling mean and historical demand as input featuresto forecast the vaccination demand for the next week. To be more specific, different amountsof historical data are tested as input features to calculate the rolling mean. Using the past fivehistorical vaccination demands as input features of the machine learning algorithm outperformedother values, achieving an RMSE of 289.2. For the second scenario, the prediction step of the data-based framework is discarded, and the prediction point is set to be at the center of the dataset.The approach of integration of DDRO and data generation process is called ADDRO where theprediction step of the data-based framework is discarded. Furthermore, the ADDRO approach isemployed to construct data-driven uncertainty sets. These two scenarios are designed to determine160the importance of the prediction and ADDRO steps within the data-based framework. The thirdscenario employs the data-based framework (ADDRO + Prediction) to create the data-drivenuncertainty set for the demand parameter. For this scenario, 100 new data are generated using theNRRI algorithm with NN = 5. Furthermore, the coverage of the data-driven uncertainty set is setto 10%. Scenario 4 is the same as the third, with the coverage of the data-driven uncertainty setsset to 30%. Scenario 5 is also the same as the third scenario, but 30 new data points are generatedusing the data augmentation process.Prediction points are a good estimation of the uncertain parameters. The concept of the AD-DRO component of the data-based framework is to ensure the feasibility of the prediction values.However, not all the prediction values are lower than the actual demand. When prediction valuesare less than the actual demand, the ADDRO component can improve the feasibility of the opti-mal solution by adding a margin to the prediction values. On the other hand, when the predictionpoint is higher than the actual demand, the ADDRO component increases the prediction value,resulting in higher operational costs and vaccine waste. Therefore, there is no need to always relyon ADDRO to make robust predictions. The challenge is that it is unknown whether the predictedvalue will be lower or higher than the actual value. To tackle this challenge, one can use a machinelearning algorithm that predicts whether the prediction values will be lower or higher than theactual value. In time series data, this can be addressed by adding more features to the dataset. Forexample, in the vaccination program, especially for COVID-19, this could include incorporating thetrend of increasing or decreasing demand for each vaccination dose. One alternative idea is to set athreshold on the prediction results. If the prediction value for period T-1 is lower than the actualdemand, the ADDRO component will be employed to create robust predictions for the upcomingperiods. On the other hand, if the prediction values of the previous periods are higher than theactual demand, the prediction results can be used as the values of demand parameters. This processis also considered as Scenario 6 to assess the impact of this revision process on the performance ofthe data-based framework. The overall procedure of Scenario 6 is also displayed in Figure 4.10.161Figure 4.10: The Overall Procedure of the Proposed Scenario 6 (Actual Demand)Table 4.4 represents the numerical results of this experiment for two different regions in Toronto.Region 1 is considered to follow the demand trend of Canada, while Region 2 follows that of the USA.The column âPSsâ displays the percentage of periods in which the estimated demand values are lowerthan the actual values. The âMean and SDâ column in Table 4.4 displays the mean and standarddeviation of robust predicted values compared to actual demand. The column âImprovement overPredictionâ specifies the percentage reduction in periods facing shortage for all scenarios comparedto Scenario 1 (prediction values).162Table 4.4: Summary of Scenarios, Region Performance, and ImprovementScenarios Region PSs Mean and SD Improvement over predictionScenario 1 1 44.5% â8.5± 538.7 -Scenario 2 1 27.2% â1286± 2765 17.2%Scenario 3 1 11% â547± 669 34.5%Scenario 4 1 6.3% â1107± 837 38.2%Scenario 5 1 24.5% â379± 742 20.0%Scenario 6 1 21.8% â391± 584 22.7%Scenario 1 2 40.9% â9± 328 -Scenario 2 2 13.6% â1461± 1432 27.2%Scenario 3 2 15.4% â190± 146 25.5%Scenario 4 2 9% â576± 347 31.8%Scenario 5 2 25.4% â103± 135 15.5%Scenario 6 2 24.5% â111± 141 16.4%PSs: Percentage of periods with shortage. SD: Standard Deviation. heightFigure 4.11 also shows the detailed values of different scenarios for the first region. Specifically,Figure 4.11a shows the computational results for Scenarios 1 to 3. The prediction values (Scenario1) have resulted in an accurate estimation of the vaccination demand compared to the ADDROapproach. However, these values have led to a shortage in vaccination for 46.6% of all periods.In contrast, using the ADDRO approach and neglecting the prediction values (Scenario 2) willresult in poor out-of-sample performance, leading to over-conservative or infeasible solutions forthe VDP program. To tackle the challenges posed by scenarios 1 and 2, the data-based framework(ADDRO + Prediction) approach is developed to create a data-driven uncertainty set that coversall areas around the predicted point (Scenario 3). This scenario has improved the final demandestimations, resulting in shortage for only 10.5% of all the periods, which is 36.1% lower comparedto the prediction results. In this experiment, only 10% of the data around the predicted points arecovered by the data-driven uncertainty set. Figure 4.11b illustrates the impact of data coverage onthe uncertainty set within the proposed data-based framework. The results show that increasingthe coverage percentage from 10% to 30% results in a decrease in the percentage of periods facingshortage, from 10.5% to 6.6%. This demonstrates that as the coverage of the uncertainty setincreases, the number of periods with shortage also decreases at the expense of higher operational163costs.Figure 4.11c displays the impact of the number of generated data samples on the overall per-formance of the proposed data-based framework. The results indicate that generating 30 new datasamples appears insufficient for the initial periods, resulting in a 15.2% increase (25.7% in total) inperiods facing shortage compared to Scenario 1. However, as the vaccination program progressesand more actual data are incorporated into the data-based framework, fewer new data samples needto be generated. This is demonstrated by the converging demand values in scenarios 3 (200 newdata samples) and 5 (30 new data samples) from periods 70 to 110. Finally, Figure 4.11d revealsthat Scenario 6 enhances the capability of the data-based framework by removing the ADDROprocess for some prediction points whose values are more than the actual demand values. Thisscenario has reduced the number of transported vaccines by 5.5% while increasing the number ofinfeasible solutions by 12.3% compared to the third scenario (23.8% lower than prediction values).164(a) Comparison of Scenarios 1, 2, and 3(b) Comparison of Scenarios 3 and 4(c) Comparison of Scenarios 3 and 4(d) Comparison of Scenarios 3 and 6Figure 4.11: Comparison of Data-based Framework Compared to Different Approaches1654.6.4 Determining the Optimal Location of Stationary PHUsAs mentioned earlier, little to no historical data is available at the beginning of the vaccinationprogram. Additionally, the location of stationary PHUs must be determined before the vaccinationprogram begins. Therefore, a conventional optimization under uncertainty approach should beemployed to cope with parameter uncertainty in the data-based framework. When T=0 and thevaccination program has not started, the robust VDP model is used to select the optimal numberand location of PHUs. In this phase, only stationary PHUs and their candidate locations areconsidered for the vaccination program, while candidate locations for mobile PHUs are discarded.In this experiment, an RO approach with a box uncertainty set is used to deal with uncertaintyassumed to vary within a range of 1% to 4% of the total population in each region. Consequently,the maximum vaccination demand is assumed to be up to 4% of the total population for eachregion. Therefore, the vaccination demand is equal to 4% of the total population of each period ineach region. Moreover, since the VDP model is a bi-objective optimization model, the distance-based approach is used to deal with these conflicting objectives and calculate the optimal andnon-dominated solutions of the VDP model. However, one key parameter that highly affects theresult of the distance-based approach is BM parameter (a big number), which should be tunedcarefully. If the value of BM is set to a large number, the proposed distance-based algorithmwill result in a solution where no PHUs are selected. On the other hand, if the value of BMis set to a small number, it results in the incorrect calculation of the minimum distance amongall PHUs. Additionally, the second objective function will not be considered when configuringPHUs. To assess the impact of parameter BM on the optimal configuration of the VDP network,five different scenarios are taken into account. For the first scenario, a large number, 1,000,000, isassigned to BM. Conversely, a small number, 100, is assigned to BM for the second scenario. ForScenarios 3, 4, and 5, the minimum, mean, and maximum distances among all PHUs, respectively,are assigned to BM.As shown in Table 4.5, assigning a large number to the BM parameter will result in an infeasiblesolution where only 1 PHU is selected, and the vaccine shortage is very high at 21,133 doses. On theother hand, if a small value is assigned to the BM parameter, the weights of the objective functionsdo not affect the optimal value of the proposed model, discarding the second objective function asits value is always equal to 100. Using the minimum distance among all PHUs has resulted in thesame solution as the second scenario. If the mean of all distances among all PHUs is selected forthe value of parameter BM, two different networks are obtained through the optimization model.166This shows an improvement in considering the effect of both objective functions when designingthe VDP network. Using the maximum distance among all PHUs tends to cover a wide rangeof optimal solutions for different values of objective weights. This scenario has resulted in threedifferent networks. This shows that considering the maximum distance for the value of parameterBM allows for the exploration of diverse spatial configurations by conducting a trade-off betweencoverage and cost-effectiveness in the configuration of VDP networks.167Table 4.5: The Effect of BM Parameter on the Optimal Solution of the VDP ModelNo. BM w1 w2 Selected PHUs Z1 Z2 Uiq1 1,000,000 0.9 0.1 11 3,264,546 1,000,000 21,1332 1,000,000 0.5 0.5 11 3,264,546 1,000,000 21,1333 1,000,000 0.1 0.9 11 3,264,546 1,000,000 21,1334 100 0.9 0.1 2, 5, 7, 9, 11 480,527 100 05 100 0.5 0.5 2, 5, 7, 9, 11 480,527 100 06 100 0.1 0.9 2, 5, 7, 9, 11 480,527 100 07 Min: 2411 0.9 0.1 2, 5, 7, 9, 11 480,527 2,411 08 Min: 2411 0.5 0.5 2, 5, 7, 9, 11 480,527 2,411 09 Min: 2411 0.1 0.9 2, 5, 7, 9, 11 480,527 2,411 010 Mean: 6508 0.9 0.1 2, 5, 7, 9, 11 480,527 3,166 011 Mean: 6508 0.5 0.5 1, 5, 7, 9, 10 493,866 5,188 012 Mean: 6508 0.1 0.9 1, 5, 7, 9, 10 493,866 5,188 013 Max: 14435 0.9 0.1 2, 5, 7, 9, 11 480,527 3,166 014 Max: 14435 0.5 0.5 1, 5, 7, 9, 10 493,866 5,188 015 Max: 14435 0.1 0.9 2, 7 2,482,985 14,139 15,133168Figure 4.12 shows the selected locations for stationary PHUs in Scenario 5 (maximum value)with three different weighting values for objective functions. As shown in Figure 4.12, if a higherweight is assigned to objective D.1 (Z1) compared to objective D.2 (Z2), the model selects thelocations that minimize the total costs of the VDP phase, discarding the second objective functionthat maximizes the distance among selected PHUs. This results in the selection of PHUs thatare close to both regions and distributors. Scenarios 10 to 15 reveal that as the weight of the secondobjective function increases, the value of the second objective function increases as well. Therefore,the VDP model tends to select locations that are farther apart from each other, ensuring equitableaccess for different groups of people to PHUs. In an extreme scenario where the second objectivefunction is weighted as 0.9, only two PHUs far from each other are selected to maximize the secondobjective function. However, this results in a shortage of 21,133 doses of vaccines. The weightassigned to each objective function depends on the preferences of the decision-maker. However,in cases such as vaccine distribution networks, ensuring equitable access to PHUs is at least asimportant as minimizing the total costs of the vaccination network. Therefore, an equal weight of 0.5is assigned to both objective functions for the subsequent experiments. The location of stationaryPHUs for vaccination should be determined before the beginning of the vaccination program.169(a) (w1, w2) = (0.9, 0.1) (b) (w1, w2) = (0.5, 0.5)(c) (w1, w2) = (0.1, 0.9)Figure 4.12: Selected Locations for Stationary PHUsBased on the results of Table 4.5 and Figure 4.12, considering an equal weight of 0.5 for bothobjective functions and maximum distances among all PHUs for the parameter BM will result inthe selection of PHUs 1, 5, 7, 9, and 10. Therefore, when the vaccination program starts, thesePHUs will be available for all upcoming periods. When demand exceeds the total capacity of thesePHUs, mobile PHUs will be allocated to candidate locations to ensure that sufficient vaccinationservices are provided and, the populationâs needs are met efficiently and equitably across all regions.To ensure equitable access to vaccination for all demographic groups, especially during periods ofhigh demand, two measures are considered. The first measure employs the second objective functionof the VDP model, which maximizes the minimum distance between all selected PHUs to ensurewidespread availability. The second measure involves setting a threshold for the number of times aspecific location can be selected for mobile PHU placement. For instance, if the threshold is equalto 2, any candidate PHU location selected at least twice in previous periods will be transferredfrom Set RM to Set RD , thereby excluding it from the pool of potential locations for future170mobile PHU placements. These two measures ensure that the selected PHUs are accessibleduring vaccination programs for different groups of people by distributing PHUs across differentregions and constantly changing the locations of mobile PHUs.4.6.5 Managing the Optimal Location of Mobile PHUsTo demonstrate the applicability of the proposed DSS for selecting mobile PHUs during dif-ferent periods of the vaccination program, the case study explained in Section 4.6.1 is considered.The third scenario described in Table 4.4 is also used to construct the data-driven uncertainty setsof the proposed data-based framework. Furthermore, the data-driven uncertainty set is fed into themodel-based framework to determine the candidate locations for mobile PHUs. This process isconducted for the entire vaccination program (i.e., 110 weeks). For this experiment, the thresholdfor mobile PHUs is set to 1, meaning that if a mobile PHU is selected for period 1, it cannot beselected for subsequent period. Additionally, Algorithm 7 is employed to update the set RD . Figure4.13 shows the optimal locations of mobile PHUs during four different weeks of the vaccinationprogram: weeks 20, 27, 28, and 29. As shown in Figure 4.13, the location and number of mobilePHUs are constantly changing. The number of mobile PHUs depends on the required numberof vaccines to meet the vaccination demand. For instance, the vaccination demand increases fromweek 20 to week 29. Consequently, the number of mobile PHUs increases from 4 to 8 to meet therising demand. The locations of the mobile PHUs also change due to the two measures explainedearlier. This results in a dynamic vaccination network design adaptable to changes in key inputparameters, such as vaccination demand.171(a) T = 20 (b) T = 27(c) T = 28 (d) T = 29Figure 4.13: Selected Locations for Stationary and Mobile PHUs for Different Time PeriodsIn the following, the performance of the data-based framework is compared with the predic-tion results for managing inventory and reducing shortages, using Scenario 3 in Table 4.4 for thiscomparison. Figure 4.14 compares the overall inventory and the number of PHUs between thepredicted values and the proposed data-based framework. As shown in Figure 4.14a, the proposeddata-based framework results in a lower shortage compared to the predicted values, although itleads to excess inventory in some periods and the selection of more PHUs. However, this excessinventory is used as the initial inventory of PHUs for subsequent periods, so it does not result invaccine waste. Moreover, the proposed data-based framework has resulted in placing more mobilePHUs. Figure 4.14b also shows the number of selected PHUs for both scenarios. The resultsdemonstrate the adaptability of the proposed DSS when facing increasing demand, which leads tothe selection of more mobile PHUs to ensure that vaccination demand is met. One of the mainadvantages of the proposed model-based framework is the availability of mobile PHUs when facingincreasing demand. The impact of the availability of mobile PHUs is compared with the case whereno mobile PHU is available. Figure 4.15 shows the overall shortage for both scenarios. As shown172in Figure 4.15, when mobile PHUs are available, the overall shortage in the proposed vaccinationnetwork decreases by 80%. This demonstrates the importance of having mobile PHUs that canquickly adapt to changing demands and effectively reduce shortages.(a) Inventory and Shortage(b) Number of Selected PHUsFigure 4.14: The Impact of the Proposed Data-based Framework on the Vaccination NetworkCompared to Predicted Values173Figure 4.15: Impact of Mobile PHUs on the Overall PerformanceOnce the actual demand is revealed, the actual inventory and shortage of all PHUs are de-termined. In this case, the model-based framework aims to minimize the shortage by reallocatingexcess inventory to PHUs that are experiencing shortages, using the assignment model. Therefore,this step of the proposed model-based framework is also of significant importance as it reduces theshortage as much as possible. Figure 4.16 shows the impact of this step in reducing the shortage inall regions. The results show that the reallocation of excess inventories reduces the overall shortageby 52%.Figure 4.16: Impact of Assignment on the Overall PerformanceIn general, the proposed data-driven model in this chapter presents a comprehensive and highlyrelevant approach to addressing the challenges of vaccine distribution during the COVID-19 pan-174demic. One of the key strengths of the model is its real-time adaptability. In terms of outcomes,the model delivers impressive results. The case study conducted in Toronto demonstrated an 80%reduction in vaccine shortages and a 60% increase in coverage compared to existing approaches.These results underline the effectiveness of the model in improving vaccine distribution. Addition-ally, the model ensures that vaccine access is equitable, which is a critical concern in any large-scalepublic health initiative. The fair access across different residential regions ensures that no group isleft behind in the distribution process, making the model an important tool for addressing dispar-ities in healthcare access. The conceptual contribution of the model is significant. The proposedpolicy for maximizing coverage, along with the reallocation strategy for surplus inventory, offers aforward-thinking approach to vaccine distribution. These strategies not only address the immediateneeds of the pandemic but also provide a framework that can be adapted for future large-scaledistribution efforts in uncertain environments.4.7 SummaryAn efficient vaccine distribution plan ensures widespread immunization coverage and reducesoverall shortage to enhance public health outcomes. The primary challenge in this problem is de-termining the optimal locations for stationary and mobile PHUs and dynamically adjusting thelocations of mobile PHUs to improve equitable access to vaccination for different groups. Addition-ally, managing the flow of vaccines among various entities to meet uncertain vaccination demandand reduce shortages in the context of limited available data presents another significant challenge.To address these challenges and provide a dynamic vaccine distribution plan and configuration, thisresearch has proposed a novel data-driven DSS . In the case of limited data availability, predictionresults may not be accurate, and DDRO approaches may yield inaccurate or over-conservative uncer-tainty sets. These challenges arise because the limited available data may not accurately reflect theactual distribution of uncertain parameters. To address these challenges, a data-based frameworkhas been developed as a component of the DSS. This framework synergizes various approaches,such as machine learning algorithms, data-driven optimization, and data generation, to mitigatetheir drawbacks and enhance overall effectiveness in managing uncertainty. The developed DSShas been implemented on a real-world case study, Toronto, Canada. The numerical results indicatethat the proposed data-based framework can effectively reduce the number of periods with shortageby 33% and 16% compared to prediction results and DDRO approaches. The resulting data-driven175uncertainty set from the data-based framework is then fed into the model-based framework. Thismodel-based framework optimizes the vaccine distribution network, with mobile PHUs being a keycomponent. Numerical results indicate that incorporating mobile PHUs has reduced vaccinationshortages of the case study by up to 80% compared to other approaches. Additionally, the resultsreveal that the proposed DPA enables dynamic location selection for mobile PHUs across differentperiods, thereby enhancing equitable access to vaccination centers for diverse population groups.Once the actual vaccination demand is revealed, the assignment model within the model-basedframework reallocates surplus inventories to PHUs experiencing shortages. Numerical analysisshows that this reassignment of surplus inventories has reduced shortages by up to 52%.For further development, it is essential to consider the distinct characteristics of various vaccines,including factors such as storage requirements, shelf life, distribution channels, and efficacy rates.Additionally, addressing uncertainty in key input parameters, such as vaccine waste rate, can beconsidered another future research direction. The proposed data-based framework can also beemployed to address uncertainty in various problems with similar characteristics, such as limitedavailable data. Consequently, another future research direction would be to focus on implementingthis data-based framework to manage uncertainty across different problems.176Chapter 5Intelligent decision support system forhealthcare sector logistics resiliency:harmonizing sustainability for maskdistribution and recycling5.1 IntroductionOutbreaks (e.g., SARS and the COVID-19 outbreak) have caused unprecedented challenges forsupply chains, particularly in the healthcare sector, over the past few years [267]. SC networkshave become increasingly critical due to the urgent need for a variety of medical supplies (e.g.,face masks) [268]. PPE have been recommended by health organizations as a control measure anda precaution against the spread of the COVID-19 outbreak [269]. One preventive measure is theuse of face masks, which helps reduce the prevalence of respiratory viral diseases, including theCOVID-19 outbreak. [270]. Using a face mask has become obligatory in internal public areas tostop the massive number of deaths. Since humans have been severely impacted by the COVID-19outbreak due to its severity, scientists focused their investigation onto human health. However, thetransmission of the COVID-19 outbreak and its repercussions on behavior changes, exhibited bythe entire human population, have a significant impact on the environment worldwide [271]. Withthe increasing demand for masks and their limited availability, it is crucial for decision-makers tofocus on efficient production, supply chain management, distribution, and inventory control [272].The efficiency of the supply chain is influenced by decisions regarding the locations of productioncenters, distribution, collection, and disposal of masks. The number and placement of these centers,as well as the quantity of masks stored at each site, directly impact supply chain costs and, moreimportantly, individual health [273]. For example, during the COVID-19 outbreak, Shanghai-GM-177Wuling halted car production and shifted to mask production due to the decreased demand forvehicles and the increased demand for masks [274].Global sustainability concepts are becoming mainstream through the principles of greenness, cir-cularity, and bioeconomy [275]. The motivation behind investigating the challenges of distributinggoods in short supply during a pandemic lies in the critical need to address logistical complexitiesand ensure efficient supply chain management in times of crisis. Pandemics, such as the COVID-19outbreak, severely disrupt global supply chains, leading to shortages of essential goods like med-ical supplies, including face masks. These disruptions highlight the urgency of developing robustdistribution strategies that can swiftly respond to fluctuating demands, logistical bottlenecks, andsupply chain vulnerabilities. Our study aims to elucidate these challenges, offering insights intoeffective distribution planning and recycling strategies under uncertain and dynamic conditions,thereby contributing to the resilience and sustainability of supply chain operations during globalhealth crises. The COVID-19 pandemic has made the sustainable development of supply chainnetworks even more essential [226]. According to the mandatory face mask policies, a new envi-ronmental problem has arisen [276]. One mask weighs approximately four grams [277], with NorthAmericaâs population using one mask daily, nearly 7,765 tons of plastic are generated in one year.Although the current situation will not last for ever, the amount of plastic waste, accumulatedin every country, is considerable [278]. Nowadays, the importance of environmental criteria hasheightened the need for effective and efficient waste management and recycling, particularly of facemasks. Properly managing these processes can minimize environmental pollution and reduce supplychain costs. Additionally, promoting reusable face masks, potentially provided for free as part ofmarketing strategies, can further support these goals [279]. Since it is likely that the COVID-19outbreak will continue for some time, approximately 89 million medical masks is estimated to beneeded in the United States [280]. This estimation for the UK is around 24.37 billion annually [281].The WHO ordered approximately a 40 percent rise in PPE (e.g., face masks) production duringthe early months of 2020 [282]. EOU and EOL masks may have an impact on the environment inthe same way of other discarded plastics [283]. For the purpose of preventing plastic contaminationon account of the face masks usage at the time of the COVID-19 outbreak, several options havebeen put forward: (i) the utilization of alternative materials, (ii) the production of reusable masks,and (iii) the usage of biodegradable materials which decompose naturally [276]. In the midst ofthe COVID-19 outbreak, the production of solid waste has been much higher than usual [284].China produced roughly 14.8 million face masks daily as of February 2020 and as of April 2020 the178Japaneseâs monthly face maskâs consumption has been almost 600 million [285]. CLSCN providesan opportunity for recycling of such waste and contributes to reduce plastic contamination.Overall, the importance of mask usage as a preventive health measure during the pandemic isrecognized. Therefore, ensuring sufficient supply, efficient production, and effective distribution bygovernments is crucial. Additionally, the growing demand makes mask production economicallyattractive for production managers [286]. Moreover, it is crucial to consider timely disposal andproper treatment methods due to the environmental and health risks associated with mask waste.This study aims to address all the previously mentioned issues and explore the potential for recyclingCOVID-19 related masks within a closed-loop supply chain, focusing on sustainable development.Therefore, this study seeks to investigate PPE supply chain challenges including the fulfillmentof consumers demand and the recycling of discarded masks. A MILPM is developed to design asustainable network (i.e., CLSCN ). The presented model optimizes the total networkâs costs andenvironmental influence of the face mask CLSCN and maximizes the social factors (i.e., customerssatisfaction and service level). A set of solution approaches (i.e., SAA, SD, and a novel GTCalgorithm is developed for the large-scale problem. Large-size stochastic optimization problem refersto optimization problems characterized by a high dimensionality, involving numerous variables andconstraints. Silhouette analysis is performed to validate the functionality of the proposed GTCalgorithm with regards to clustering accuracy and CPU time (computational time).5.1.1 Aims and NoveltyIn this chapter the main aim is to design an IDSS for healthcare sector logistics resiliency formask distribution and recycling. In real-world problems, there are always uncertainties in the pa-rameters which can either be stochastic or erroneous due to the lack of information [220, 287]. Someoptimization techniques (e.g., robust optimization, stochastic programming) are necessary to be de-veloped due to the uncertainty type of parameters. Stochastic programming models the randomvariability by estimating the probability distribution (e.g., recovery rates of return products). Insome cases, the imprecise parameters may deviate within a deterministic set, while the computationof their distributional information may be challenging. In resilient systems, robust optimization canfind the best solution. Consequently, in order to cope with uncertainty, some integrated solutionapproaches (e.g., robust-stochastic models) can be developed. Resilient systems typically refer tosystems or processes that have been designed or optimized to minimize the impact of uncertainty.As the COVID-19 outbreak is likely to persist for a long time, sustainability aspects (i.e., economic179benefits, environmental conservation, and societal responsibility) must be considered in PPE sup-ply chain network design [220]. Environmental conservation, in the context of PPE supply chainnetwork design during the COVID-19 outbreak, refers to practices and strategies aimed at minimiz-ing negative impacts on the environment. Socaietal responsibility entails ensuring equitable accessto PPE , particularly for vulnerable populations and healthcare workers in underserved areas, thuspromoting public health and reducing. In this investigation, the purpose is to design and opti-mize a resilient and sustainable mask CLSCN by developing a robust-stochastic multi-objectivemixed-integer linear programming model. The purpose of this study is to develop and optimize aclosed-loop supply chain for recycling COVID-19 masks, focusing on sustainability. We justify ourapproach by integrating multiple objective functions to minimize costs, environmental impact, andmaximize social benefits such as customer satisfaction and service levels. A CLSCN integratesrecycling or reuse of products and materials back into the supply chain. It aims to minimize waste,enhance resource efficiency, and reduce environmental impact by reprocessing materials for newproduction cycles rather than disposal. This approach supports sustainable practices and promotescircular economy principles. When operational decisions are modeled by robust-stochastic modelsfor different scenarios, the modelâs size considerably increases. The SAA algorithm is integratedinto the SD algorithm SAA-SD to tackle large-scale instances. Each sample problem in SAA is arobust-stochastic model. Although there are fewer scenarios in comparison with the main problem,directly resolving the problem is still challenging. The GTC approach is proposed to solve theproblems with numerous scenarios (i.e., accelerating SAA-SD algorithm).In the SAA approach, achieving precise estimation requires a large number of scenarios, whichin turn increases computational time. Therefore, employing a clustering algorithm can effectivelyreduce model complexity while maintaining an adequate sample size. Traditional clustering algo-rithms are unsuitable for data that are not convex, and they are quite sensitive to the outliers andcan be easily drawn to the local optimal [288]. These strengths and weaknesses were the motivationto propose the GTC algorithm, to cover the weakness of traditional algorithms. The principal su-periority of the developedGTC is to cluster data point in a high dimensional feature space, analyzenoise data and separate overlapping clusters. Furthermore, there is no need to pre-define the re-quired number of clusters in the initial phase. Clustering analysis has been developed for large-scaledata analysis. In this study, the Silhouette analysis is applied for assessing cluster performance andaccuracy.The rest of this investigation is arranged as follows: the most relevant studies are reviewed180in Section 5.2, and Section 5.3 describes the problem. The mathematical model formulation isformulated in Section 5.4. Sections 5.5 and 5.6 describe solution approach and the validity ofthe presented model, respectively. The multi-objective mathematical model is formulated and itsapplication is investigated in Section 5.7. Finally, the managerial implications and conclusions aregiven in Sections 5.8 and 5.9.5.2 Research BackgroundIn this section, an extensive literature review of the PPE supply chain network design andlarge-scale exact methods are presented, and then the literature gaps are identified.5.2.1 PPE Supply Chain Network DesignThis section reviews key studies related to the supply chain of medical items. It examines re-search focused on optimizing logistics, ensuring supply chain resilience, and enhancing efficiencyin the distribution of critical medical supplies. [289] proposed a resilient-sustainable model fordeveloping a pharmaceutical distribution and production supply chain under uncertainty. Theyemployed possibilistic-stochastic programming to address parameter uncertainties effectively. [290]developed a medical equipment supply chain network in Iran, addressing uncertainties throughpossibilistic programming. Their model aimed to minimize supply chain costs effectively. [291] fo-cused on decision-making and coordination within a dual-channel supply chain network influencedby low-carbon preferences and channel substitution. They developed centralized and decentralizeddecision-making models for a supply chain network comprising one manufacturer and one retailer.[292] designed a supply chain network model for distributing medical equipment during crisis sce-narios. Their approach involved formulating a multi-objective mathematical model to minimizedistribution and production costs while maximizing the fulfillment of demand. [293] introduced amodel for determining the optimal locations of medical equipment distribution centers and allocat-ing equipment to medical centers. Their primary goal was to maximize patient satisfaction in thecontext of limited resources, illustrated through a case study in Brazil. [294] designed a medicinesupply chain involving manufacturers, distributors, hospitals, and patients. They proposed a multi-period model to optimize the flow of medicines and medical equipment transfers across variouscenters. They focused on the main operations (i.e., suitable identifying, collecting, separating, dis-infecting), and other tasks related to the face mask waste generated in the COVID-19 outbreakâs181period. At the COVID-19 outbreakâs period and post COVID-19 outbreak, [295] discussed the chal-lenges, opportunities and the importance of medical waste management (e.g., gloves, face masks).[296] provided an estimation about the optimum number of maskâs disposal facilities in Asia duringthe COVID-19 outbreakâs period, as well as how many face masks were used during the pandemic.[297] studied schemes required for recycling of the waste generated by plastic in the COVID-19outbreakâs period. They highlighted the lack of appropriate procedures in current systems to dealwith the increasing use of plastic. A pharmaceutical SSCN was designed considering uncertainty ofdemand, goodsâ perishability, and mobility of facilities by [298]. [299] developed a direct and reversemedicine supply chain model considering biological risks. In the direct supply chain, they focusedon locating warehouses and distribution centers, while in the reverse supply chain, they addressedthe placement of medical waste disposal centers. The primary objectives of their model were tomaximize the difference between revenues and costs and to minimize the time distance betweenclinics and sterilization facilities. They applied their model to a case study in Tehran, Iran.Priority has been given to the economic aspects in CLSCN design. However, recently, there hasbeen an increase in interest in improving the sustainability indicators due to the consumers environ-mental and social awareness [287]. [296] conducted an estimation of the number of face masks andmask disposal centers needed during the COVID-19 outbreak. The study surveyed hospitals, maskmanufacturers, and landfills across Asia. Key parameters included population size and an estimatedcommunity mask acceptance rate of 80%. The research ultimately provided estimates for the num-ber of masks required and the number of disposal centers needed across 54 Asian countries. [300]investigated the reduction of plastic and paper waste during the COVID-19 pandemic. Their studyexamined how the pandemic affected plastic waste and environmental pollutants, such as carbondioxide. Using a case study of hospitals, landfills, and households, they found that although vehicleemissions decreased during the pandemic, plastic waste surged dramatically. This increase led toa greater number of landfills and created more jobs in waste management. [301] concentrated ona SSCN during the COVID-19 outbreak. They proposed a model enabling pharmaceutical prod-ucts distribution under perishability limitations. Owing to the NP-hard nature of the developedmathematical model, hybrid meta-heuristic algorithms were utilized to resolve large-size instances.[302] proposed a SSCN considering the COVID-19âs circumstance. They considered digitization,agility, and localization characteristics in SSCN. A pharmaceutical SSCN considering uncertaintywas developed by [289]. Possibilistic-stochastic programming was applied to overcome parametersâuncertainty. Their main contribution was establishing production facilities by built-in technological182levels considering inter-modal freight service transport. The developed model was resolved by theuse of the Pareto-based lower-bound method to implement the real-world case study. Similarly, apharmaceutical SSCN was developed by [303] at the COVID-19 pandemic era. Hybrid algorithmsand parameter tuning were developed to solve the problem by the response surface method. [304]explored the management of hospital waste disposal through a reverse supply chain model. Theydeveloped a multi-period, multi-item stochastic framework with three main goals, lowering trans-portation expenses, minimizing the costs associated with inventory holding and the establishmentof disposal centers, and reducing the volume of stored hospital waste. Utilizing fuzzy goal program-ming, they effectively solved the model. In the same year, [305] developed a simulation-optimizationmodel for distributing medicines and medical equipment across a bi-level supply chain network thatincludes hospitals and pharmacies. Two stochastic models were introduced to address differentaspects of the distribution process. The first model focused on managing the expiration dates ofmedicines and maintaining a high level of patient service, while the second model concentratedon inventory control and the allocation of medical equipment to hospitals. Using the ϵ-constraintapproach to solve these models, the study achieved a 16% reduction in overall supply chain costs.[306] presented a cost-efficient and reliable multi-modal SC network design model for biomassdelivery to biofuel plants, addressing the challenges posed by the seasonal nature of biomass supplyand the impacts of natural disasters. Utilizing an accelerated Benders decomposition algorithmand a hybrid rolling horizon algorithm, the model demonstrated significant cost advantages underdisaster scenarios compared to traditional models, highlighting its value in dynamic and resilientSC management. [307] introduced a two-stage stochastic programming model for designing andmanaging a biomass co-firing multi-modal SC network under feedstock supply uncertainty, incorpo-rating congestion effects. By linearizing the model and employing a nested decomposition algorithmwith various heuristics, the study demonstrates the ability to solve large-scale problems efficiently,revealing that accounting for congestion costs results in higher delivery costs and fewer selected hubswith higher capacities. [308] introduced a bi-objective stochastic optimization model to address theissue of multi-commodity rebalancing and multi-modal transportation in humanitarian logistics,particularly before and during large-scale disasters where road disruptions can make some reliefcenters inaccessible. The model, linearized and solved using an adaptive augmented ϵ-constraintmethod, generates Pareto-optimal solutions. A case study of an emergency event demonstrates themodelâs decision-making effectiveness, and sensitivity analysis provides insights into the trade-offsbetween maximizing fairness and minimizing total transportation time.1835.2.2 Large-Scale Optimization Under UncertaintyUncertainty analysis is of great importance in strategic decision-making process. In SSCNdesign under uncertainty, as the number of scenarios increases, there is a need for efficient approaches(e.g., SAA method) to solve large-scale optimization [309]. A heuristic approach was integratedinto the SAA algorithm by [310] for the inventory routing problem with uncertain parameters (i.e.,stochastic inventory routing problem). [311] employed SAA method to investigate three types ofrouting problems with uncertain parameters. Similarly, [312] and [313] applied SAA method forthe routing and transportation planning problems, respectively. [314] adopted the SAA algorithmfor the stochastic dial-a-ride problem on a multigraph considering user satisfaction. [315] developeda heuristic algorithm to accelerate the stochastic shift design problem. They concluded that theSAA algorithm outperforms the similar approaches in terms of cost. Although the SAA algorithmwas capable of handling stochastic mathematical models, it became unable to perform efficiently asthe number of samples grows exponentially. Therefore, [316] proposed SD algorithm to handle thecomplexity of large-scale stochastic mathematical models.The SD algorithm can be integrated into the SAA algorithm to explore the candidate solutions(i.e., solutions for sub-problems). Then, the SD algorithm restricts the feasible solution region andcloses the lower bound and upper bound (duality gap) to improve the SAA algorithm [317]. The SDalgorithm was applied by [318] for the multi-stage stochastic programming mathematical models.[319] employed the SD algorithm for the two-stage stochastic vehicle routing problem consideringtime window constraints. [320] solved risk-averse multi-stage stochastic programming using the SDalgorithm. [321] accelerated the SD algorithm for the mean-risk stochastic mathematical model byrelaxing non-anticipativity constraints. [322] incorporated an accelerated multi-objective two-phasealgorithm into the SAA-SD algorithm to handle multi-objective, multi-modal cargo distributionproblem. Table 5.1 summarizes the related studies.[288] provided a precise examination of various clustering algorithms and classified them basedon different factors. Two possible clustering categories can be referred to: (i) clustering based on thepartition (e.g., K-means, K-medians) and (ii) clustering based on the hierarchy (e.g., Chameleon).The main advantage of the first category is high computing efficiency and low time complexity.However, non-convex data cannot be handled by such algorithms [323]. Furthermore, sensitivity tothe outliers is their main feature and can be easily stuck to the local optimum [324]. Therefore,the clustering output is dependent on the pre-determined number of clusters. The second categoryof algorithms are relatively high in scalability and suitable for datasets with arbitrary shape and184attribute types [324]. However, the main weaknesses of such algorithms are determining the requirednumber of clusters and high computational time complexity.185Table 5.1: The Most Relevant Research ReviewsStudies Mathematical Model Application Sustainability Solution Approach Case StudyEconomicEnvironmentalSocial ML Exact[325] SO-Stochastic Programming ... ... ... ... ... ...[326] SO-Certain Battery ... ... ... Outer Approximation[327] MO-Certain Energy ... ... ... ...[289] MO-Fuzzy Programming Pharmaceutical ... ...[298] MO-Robust Optimization Pharmaceutical ... ... ...[285] SO-Certain Vaccine ... ... ... ... ...[328] SO-Uncertain Manufacturing ... ... ... ... ...[302] ... Pharmaceutical ... ... ... ... ... ...[303] MO-Certain Pharmaceutical ... ... ...[329] SO-Stochastic Programming ... ... ... ... ... ...[294] MO-Certain Pharmaceutical ... ... ...[330] SO-Certain Construction ... ... ... ...[263] MO-Robust Optimization Mask ... ...[331] SO-Fuzzy Programming Automobile ... ... ... ... ...[332] MO-Robust optimization Pharmaceutical ... Game TheoryCurrent study MO-Robust-Stochastic Mask GTC SAA & SDSO= Single Objective MO=Multi-Objective ML= Machine Leraning186The COVID-19 pandemic highlighted the critical need for resilient supply chain networks ca-pable of adapting to unforeseen disruptions. Research in the healthcare sector has extensivelyexamined supply chain networks, particularly in pharmaceutical supply chains and the challengesof vaccine distribution through location-allocation strategies. This investigation prioritizes sustain-able practices, focusing on managing contagious waste such as face masks to minimize environmentalpollution and address significant health risks. The primary objective is to develop a CLSCN thatis both sustainable and resilient, facilitating the production, distribution, and recycling of reusableface masks during outbreaks such as the COVID-19.A key contribution of this study lies in the development of a machine learning approach toaccelerate the SAA algorithm. This approach enhances the SAAâs efficiency in handling large-scale real-world cases, optimizing distribution strategies using diverse transportation modes withinstrict time constraints. Moreover, integrating a SD algorithm within the accelerated SAA frame-work further enhances computational efficiency while maximizing societal responsibilities. Theseadvancements not only improve operational efficiency but also reinforce sustainability efforts byminimizing environmental impact and promoting responsible resource management in healthcaresupply chains.5.3 Problem StatementThe extensive global use of PPE during the COVID-19 pandemic has highlighted significantchallenges, including inefficient face mask distribution and the accumulation of EOU and EOLface masks. The initial shortage of PPE in early 2020 highlighted the critical need for sustainableand resilient CLSCN s globally [333, 334]. In the developed CLSCN, the factory f producesproducts and sends to warehouse w for distribution purpose. Then, the products are distributedfrom distribution centers (warehouses) w to the population zones c. In the backward flow, theEoU products are collected from population areas c and send to recycling centers i. The recycledproducts are then forwarded to the factory f for re-production purpose. Strategic and tacticaldecisions inCLSCN configuration are essential. At the strategic level, decisions involve determiningoptimal locations for production (Yf ), if product is produced in factory f (Wâ²pâ²f ), optimal locationof warehousing w (Y â²w), if the product is stored in warehouse w (W â²â²pâ²w), optimal location of collection& recycling centers (Y â²â²i ), if product is recycled in recycling centre i (Wâ²â²â²pâ²i). While the operationaldecisions are related to the optimal flow of products between echelons, Xpâ²fwt, Xâ²pâ²wct, Xâ²â²pâ²cit, and187X â²â²â²pâ²ift.A multi-objective MILP is proposed for a multi-echelon, sustainable CLSCN design in theCity of Toronto. As shown in Figure 5.1, Toronto is divided into 21 zones and should receivethe appropriate amount of face masks in an equitable manner. Considering the high demandfor masks in the City of Toronto, achieving the optimal decisions in terms of facility selection (i.e.,agreement with potential service providers) and the optimal flow of face masks is critical in uncertainsituations. Additionally, each optimal plan has some criteria that gives rise to making the optimaldecision difficult. There are several ways to categorize these criteria, such as cost, time-frame, andenvironmental impact (e.g., the amount of produced waste such as EOU masks) and social factors(e.g., customer satisfaction). It should be noted that, the distribution of PPE, specifically facemasks in this study, refers to the logistics involved in transporting masks from central distributioncenters to local pharmacies or other designated points of sale (c) where individuals can purchasethem.Figure 5.1: Municipal District of the Case StudyFigure 5.2 illustrates the link between a multi-modal distribution network and sustainableCLSCN.188Figure 5.2: Simplified Illustration of the Sustainable Mask Distribution PlanningAs illustrated in Figure 5.2, the multi-modal transportation system inherently ties the trans-portation and distribution networks together. An example of a transportation network is shown inthe bottom layer, while an example of a sustainable CLSCN is depicted in the top layer. Figure5.2 demonstrates two layers, including: (i) The bottom layer, the transportation network, illus-trates the system through which products are transported using various modes, such as trucks,trains, ships, and planes. This network is a fundamental part of the supply chain, facilitating thephysical movement of products from manufacturers to distributors, retailers, and ultimately to endconsumers. (ii) The top layer, sustainable CLSCN, represents a sustainable CLSCN designedto minimize waste and promote sustainability by efficiently managing the return and recycling ofproducts and materials. This layer demonstrates the environmentally conscious aspect of the supplychain, focusing on reducing environmental impact, reusing materials, and recycling products at theend of their life cycle.In the context of a CLSCN, there are typically two layers, bottom layer and top layer. The bot-tom layer manages the physical movement of products from manufacturing facilities to distribution189centers, retailers, and ultimately to consumers. It ensures that products are transported efficientlyand in compliance with delivery schedules. The layer focuses on sustainability and resource effi-ciency. It includes processes for recycling, reusing, or safely disposing of products at the end oftheir life cycle. By integrating a multi-modal transportation system, the CLSCN can optimizethe movement of products within the closed-loop system. This optimization reduces transporta-tion costs, minimizes environmental impact (such as emissions from transportation), and ensurestimely delivery of products to recycling or recovery facilities. The multi-modal system facilitatesthe efficient movement of products throughout the supply chain, ensuring that they reach their des-tinations promptly and in optimal condition. This efficiency is crucial for maintaining supply chainresilience and meeting customer demand effectively, especially during fluctuating market conditionsor disruptions.Figure 5.3 depicts the proposed decision support (DS) platform for the sustainable CLSCN.The proposed system develops an adaptable (flexible) and a correlative (interactive) tool to handleforward and reverse flows (i.e., recycling phase), simultaneously. The DS platform is designed asan integrated (distributed) platform consisting of a system for collecting customersâ orders and adatabase to record them. The database is employed to serve the fleet administrator to plan thefulfillment of customer demand. The retailers (customers) orders are registered via the designedplatform and recorded in the database. Finding the solution is primarily handled by the computationengine to deal with CLSCN problems. A GTC-SD algorithm (i.e., integrated GTC algorithm toSAA-SD algorithm) is applied in this engine to implement the optimization for large-scale cases,which is introduced in Section 5.5. Two phases are involved in the proposed mathematical modelin computational engine for facility selection and scheduling, respectively. In preparation for theexecution of the courier service, customersâ orders are transferred from the database, and then anoptimal distribution plan is scheduled to fulfill the market demand. When the first and secondphases are implemented, the EOLs or EOU s (e.g., recycling and reusing phases) are handled bythe mathematical model. The DS platform is designed to manage the complexities of the maskCLSCN efficiently and consists of two main components: (i) Order collection: Within the proposedDS platform, a system is embedded for collecting customer orders. To assist fleet administratorsin fulfilling customer demand, a database is employed to record and store these orders. The DSplatform includes a computation engine that utilizes a GTC-SD algorithm to optimize large-scalesupply chain scenarios. (ii) Scheduling: the DS platform schedules an optimal distribution plan forefficient product delivery to customers. Furthermore, it employs the optimization model to handle190EOL products or EOU products, ensuring their sustainable recycling and reuse.Figure 5.3: The Architecture of the Proposed DSS Platform for the Sustainable CLSCNThe major objectives of this investigation are organized to deal with the following challenges(questions):â How a resilient, sustainable, and well-founded face mask supply chain network can be de-signed (i.e., first stage decisions)? Which potential location(s) should be selected for theproduction, warehousing, and collection & recycling centers (i.e., agreements with differentpotential service providers)?â How an optimal plan can be provided for the face maskâs distribution considering environmen-tal and social factors (i.e., when and how much face masks should be delivered to customerszones) (i.e., second stage decisions)?â How many EOU s (e.g., face masks) products (second stage decisions) can be collected for191recycling?â When is the latest face masks delivery time (time window limitations) to maximize the totalcustomer service level and minimize the potential risks?â How does the model response to customer demand under operational and disruption risks?5.4 Mathematical FormulationOver the preceding few decades, climate change has been a global issue which goes beyond theoperations of a single company. Furthermore, the economic and social aspects (i.e., the economicrefers to the production transportation, warehousing, and distribution costs, while, social aspectsrefer to the customersâ demand fulfillment rate) need to be considered to design a sustainableCLSCN. Therefore, three objectives are optimized in this investigation (i.e., the total networkâscosts, the total emissions footprints, and the customer service level). However, there are differentapproaches to investigate environmental challenges in Canada (e.g., the implementation of a carbontax system or government subsidy for green technology development) [287]. In this regard,first thetotal networkâs costs is considered as a primary objective, that traditionally, is the most importantobjective in CLSCN s. The mathematical modelâs notation (i.e., indices, sets, parameters, anddecision variables) is briefed in Table 5.2 to formulate the sustainableCLSCN model. TheCLSCNmodelâs assumptions are as follows:â The number of potential facilities and their locations (e.g., factories, warehouses, and collection& recycling centers) for making agreement are not pre-determined.â The customer demand and processing time are considered uncertain.â The distribution network is multi-modal (e.g., rail, road).â At least a specified amount of products (specified percentage of customer demand) is shippedto collection & recycling center for recycling.â At least a specified amount of products (specified percentage of recycled products at collection& recycling center) is shipped to factory for reusing.â The capacity of the third-party(s) (i.e., production facility, storing facility, and collection &recycling facility) are certain.â The focus on developing a CLSCN is not to replace existing supply chain networks but toadapt and optimize them to effectively respond to the unique challenges and requirements192posed by pandemics and similar unforeseen disruptions in order to maintain essential servicesand mitigate risks to public health and the environment.Table 5.2: Nomenclature: Indices & Sets, Parameters, and Decision VariablesIndices & SetsC Set of retailersF Set of potential plantsI Set of potential collection & recycling centersPâ² Set of productsT Set of transportation modesW Set of potential warehousesc Index of retailers c â {1, 2, ...,C}f Index of potential plants f â {1, 2, ...,F}i Index of potential collection & recycling centers i â {1, 2, ..., I}pâ² Index of different types of products pâ² â {1, 2, ...,Pâ²}t Index of transportation options t â {1, 2, ...,T}w Index of potential warehouses w â {1, 2, ...,W}Parametersafw Distance between plant f and warehouse waâ²wc Distance between warehouse w and retailer caâ²â²ci Distance between retailer c and collection & recycling center iaâ²â²â²if Distance between collection & recycling center i and plant fet Cost of option t for a unit distance between facilitiesgpâ²c Demand c of product pâ²pfpâ² Production time of product pâ² at plant fpâ²â²ipâ² Processing time for collecting and recycling product pâ² at center iq Minimum percentage of product, transferring to center iqâ² Minimum percentage of product, transferring to plant frwpâ² Processing time for handling product pâ² at warehouse wsfpâ² Time for producing product pâ² at plant fsâ²wpâ² Time for handling product pâ² at warehouse wsâ²â²ipâ² Time for collecting and recycling product pâ² at collection & recycling center ivfpâ² Cost of production for product pâ² at plant fvâ²wpâ² Cost of warehousing for product pâ² at warehouse wvâ²â²ipâ² Cost of collecting and recycling for product pâ² at center i193αf Maximum production and re-manufacturing capacity of plant fβw The warehouseâs maximum capacity wγi The collection & recycling centerâs maximum capacity iδt Emissions by transportation option t due to transportation between facilitiesκf Emissions by plant f due to manufacturingζw Emissions by warehouse w due to handlingηi Emissions by collection & recycling center i due to collection and recyclingµf Emissions by plant f due to re-manufacturingÏf Total available time for producing products at plant fÏ â²w Total available time for handling products at warehouse wÏ â²â²i Total available time for collecting and recycling at collection & recycling center ieλwt Service levelVariablesW â²pâ²f Binary variable, 1 if product pâ² is produced at plant f , otherwise 0W â²â²pâ²w Binary variable, 1 if product pâ² is stored at warehouse w, otherwise 0W â²â²â²pâ²i Binary variable, 1 if product pâ² is recycled at center i, otherwise 0Xpâ²fwt Flow of product pâ² shipping from plant f to warehouse wX â²pâ²wct Flow of product pâ² shipping from warehouse w to retailer cX â²â²pâ²cit Flow of product pâ² shipping from retailer c to collection & recycling center iX â²â²â²pâ²ift Flow of product pâ² shipping from collection & recycling center i to plant fYf Binary variable, 1 if the plant f is selected to make agreement, otherwise 0Y â²w Binary variable, 1 if the warehouse w is selected, otherwise 0Y â²â²i Binary variable, 1 if the collection & recycling center i is selected, otherwise 0Ztfw Binary variable, 1 if the vehicle t moves from plant f to warehouse w, otherwise 0Z â²twc Binary variable, 1 if the vehicle t moves from warehouse w to retailer c, otherwise 0Z â²â²tci Binary variable, 1 if the vehicle t moves from retailer c to center i, otherwise 0Z â²â²â²tif Binary variable, 1 if the vehicle t moves from center i to plant f , otherwise 0The presented model is formulated as an MILP as follows:Min z1 =âfâFâwâWâtâTâpâ²âPâ²Xpâ²fwtet +âwâWâcâCâtâTâpâ²âPâ²X â²pâ²wctet+âcâCâiâIâtâTâpâ²âPâ²X â²â²pâ²citet +âiâIâfâFâtâTâpâ²âPâ²X â²â²â²pâ²iftet+âfâFâpâ²âPâ²âwâWâtâTvfpâ²Xpâ²fwt +âwâWâcâCâtâTâpâ²âPâ²vâ²wpâ²Xâ²pâ²wct194+âiâIâcâCâtâTâpâ²âPâ²vâ²â²ipâ²Xâ²â²pâ²cit +âiâIâfâFâtâTâpâ²âPâ²vfpâ²Xâ²â²â²pâ²ift (5.1)Subject to: âpâ²âPâ²âwâWâtâTXpâ²fwt â¤ αfYf âf â F (5.2)âpâ²âPâ²âfâFâtâTXpâ²fwt â¤ βwY â²w âw âW (5.3)âpâ²âPâ²âcâCâtâTX â²pâ²wct â¤âpâ²âPâ²âfâFâtâTXpâ²fwt âw âW (5.4)âpâ²âPâ²âtâTâcâCX â²â²pâ²cit â¤ Y â²â²i γi âi â I (5.5)âpâ²âPâ²âtâTâwâWX â²pâ²wct â¥âpâ²âPâ²gpâ²c âc â C (5.6)âpâ²âPâ²âtâTâiâIX â²â²pâ²cit â¥âpâ²âPâ²gpâ²cq âc â C (5.7)âpâ²âPâ²âtâTâfâFX â²â²â²pâ²ift â¥âpâ²âPâ²âcâCâtâTX â²â²pâ²citqâ² âi â I (5.8)âpâ²âPâ²âtâTâiâIX â²â²â²pâ²ift â¤ αfYf âf â F (5.9)âpâ²âPâ²âwâWâtâTpfpâ²Xpâ²fwt +âpâ²âPâ²sfpâ²Wpâ²f â¤ Ïf âf â F (5.10)âpâ²âPâ²âcâCâtâTrwpâ²Xâ²pâ²wct +âpâ²âPâ²sâ²wpâ²Wâ²pâ²w â¤ Ï â²w âw âW (5.11)âpâ²âPâ²âfâFâtâTpâ²â²ipâ²Xâ²â²â²pâ²ift +âpâ²âPâ²sâ²â²ipâ²Wâ²â²pâ²i â¤ Ï â²â²i âi â I (5.12)W â²pâ²f â¤ Yf âpâ² â Pâ², f â F (5.13)W â²â²pâ²w â¤ Y â²w âpâ² â Pâ², w âW (5.14)W â²â²â²pâ²i â¤ Y â²â²i âpâ² â Pâ², i â I (5.15)W â²pâ²f â [0, 1] âf â F, pâ² â Pâ² (5.16)W â²â²pâ²w â [0, 1] âw âW, pâ² â Pâ² (5.17)W â²â²â²pâ²i â [0, 1] âi â I, pâ² â Pâ² (5.18)Xpâ²fwt â Z+ âf â F, pâ² â Pâ², w âW, t â T (5.19)195X â²pâ²wct â Z+ âc â C, pâ² â Pâ², w âW, t â T (5.20)X â²â²pâ²cit â Z+ âc â C, pâ² â Pâ², i â I, t â T (5.21)X â²â²â²pâ²ift â Z+ âf â F, pâ² â Pâ², i â I, t â T (5.22)Yf â [0, 1] âf â F (5.23)Y â²w â [0, 1] âw âW (5.24)Y â²â²i â [0, 1] âi â I (5.25)Ztfw â [0, 1] âw âW, f â F, t â T (5.26)Z â²twc â [0, 1] âw âW, c â C, t â T (5.27)Z â²â²tci â [0, 1] âc â C, t â T, i â I (5.28)Z â²â²â²tif â [0, 1] âf â F, t â T, i â I (5.29)The Equation (5.1) (objective function) optimizes the total networkâs costs which includes thetotal operational costs (i.e., production, warehousing, collecting and recycling) and the total trans-portationâs costs. Constraint (5.2) describes that the total produced products at plant f that flowsfrom plant f to warehouse w by transportation mode t is less than or equal to the capacity of plant f .Similarly, constraint (5.3) explains that the number of products shipped from plant f to warehousew by transportation mode t need to be less than or equal to the warehouse wâs maximum capacity.Constraint (5.4) balances the total products delivered to retailer c from warehouse w should equalwith the total entered products to warehouse w by transportation option t. Constraint (5.5) is asso-ciated with the collection centers capacity. The total EOLs or EOU s which are flowed to collection& recycling center i by transportation option t need to be less than or equal to the capacity of thecollection & recycling center i. Constraint (5.6) describes that the total demand of each retailer cmust be fulfilled. Constraint (5.7) ensures that collected products (i.e., EOU s or EOLs) are shippedfrom retailer c to collection & recycling center i for recycling. Constraint (5.8) ensures that the flowto transfer at least a minimum percentage of flowed products from collection & recycling center i toplant f for reusing. Constraint (5.9) is related to re-producing capacity of plant f . The total flowedproducts from collection & recycling center i to plant f by transportation option t should be lessthan or equal to the re-producing capacity of plant f . Constraints (5.10)-(5.12) are incorporatedwith the processing time limitations. Constraint (5.10) guarantees that the total production timeat plant f is not exceed the total available time for production. Constraint (5.11) ensures that thehandling time at warehouse w is less than or equal to the pre-defined warehousing time. Constraint196(5.12) assures that the total processing time for collecting and recycling is less than or equal to thetotal available time for collecting and recycling. Constraints (5.13)-(5.15) explain that the products(e.g., new produced products, EOLs, EOU s) are not flowed between facilities unless the facilitieshave been selected (i.e., agreement with potential service providers). Constraints (5.19)-(5.22) arenon-negative continuous decision variables and constraints (5.16)-(5.18), (5.23)-(5.29) are binaryvariables.5.4.1 Robust CounterpartThe robust optimization method is a well-known approach to reach the best solution amongstdata-uncertainty-immunize solution [335, 336]. The proposed model is extended to investigatedifferent probability-based scenarios. Given Sâ scenarios, the scenario vector can be shown Sâ =[Sâ1 , Sâ2 , ..., Sân] as follows:âsââSâpâsâ = 1 (5.30)Where pâsâ shows the probability of occurrence related to each scenario [337]. The robust coun-terpart formulation of the main problem is given as follows:Min z(x) =âsââSâpâsâQâsâ + uâ âsââSâpâsâ(Qâsâ â pâsâQâsâ + 2Î¸sâ) + rââsââSâpâsâÏsâ (5.31)Subject to:AâsâX + Ïsâ = Bâsâ âsâ â Sâ (5.32)Qâsâ â pâsâQâsâ + Î¸sâ â¥ 0 âsâ â Sâ (5.33)Where, râ balances the modelâs robustness with solution robustness, and uâ is the risk associatedwith deviation from the mean, Qâsâ shows the objective function value of deterministic model underscenario sâ, Î¸sâ is added for linearization, and Ïsâ indicates the penalty for model infeasibilityunder scenario sâ. Constraint (5.32) ensures that the penalty is applied in case of unmet demand orviolated time window. Constraint (5.33) ensures the linearity of the objective function. Generally,the robust counterpartâs objective function is formulated based on the Equation (5.70). Constraint(5.33) is added for linearization of the robust counterpart objective function. Equations (5.1) to(5.29) are modified to incorporated the uncertainty and penalize the fluctuations.1975.4.2 Robustness CheckingThe modelâs robustness and the generated solutions are assessed using the model variation test[338â340]. In this regard, [341] defined four main phases for the robustness checking. The first phaseis defined as the development of the baseline model (i.e., deterministic equivalent). The second phasedeals with the relaxation of the assumptions and generating the robust model I and robust modelII. Finally, the comparison between the generated models (i.e., relaxed assumptions) and baselinemodel (i.e., deterministic model) validates the robustness of the model and generated solutions.According to the given assumptions, the uncertainty of parameters (i.e., demand, operational andtravel time) are incorporated in the robust model (i.e., assumption two). The assumptions one,three, four, and five are already relaxed to make the model more adaptable with the reality. Asthe capacity of third-parties is considered as certain in this study (i.e., last assumption), the robustcounterpart of its model is investigated. rË, uË, Î¸Ësâ , and Î»Ësâ define the weight assigned to varianceof the solution, the weight placed on the model infeasibility penalty, variable for linearizing thefunction, and the modelâs infeasibility under scenario sâ, respectively. Table 5.3 summarizes theresults for different sample sizes and compares the baseline model with robust model I and robustmodel II based on the total networks costs and computational time. If the obtained solution is nearto optimal and feasible for all scenarios, it can be considered as robust [342, 343]. Three possiblescenarios (i.e., low, moderate, and high) are considered for uncertain parameters (i.e., demand,capacity) based on the literature [344].198Table 5.3: Robustness CheckingDeterministic Robust I Robust IINo F W C I S OF C.T(s) OF C.T(s) OF C.T(s)1 3 2 6 1 3 169.50 0.04 102.00 0.02 185.20 0.082 9 4 100 2 3 1,680.00 12 1,625.10 7 2,196.80 13 15 7 300 4 3 4,883.09 37 4,724.20 30 4,783.62 704 15 7 500 4 3 9,149.00 59 8,048.20 42 6,628.26 1605 25 7 500 4 3 8,939.00 64 7,884.20 62 6,637.55 2666 25 12 500 4 3 8,800.90 79 8,010.50 81 6,987.02 1,0197 25 12 500 8 3 8,916.00 84 8,052.00 88 6,978.02 1,142C.T: Computational Time OF: Objective Function199According to the Table 5.3, robust models consider different scenarios (best, neutral, and worst-case scenarios) under uncertainty, whereas the deterministic model does not deal with any param-etersâ fluctuations. The average of differences between the deterministic model and Robust I andthe deterministic model and Robust II are about 12 and 20 percent, respectively. Both averages arereasonable as the sample size increases. This means that the total violations of robust constraintsare not significant when there is uncertainty and perturbations in the system (i.e., even in the worstcase scenarios). The robust models are obligated to handle the uncertain parameters (i.e., avoidingunmet demand and operating based on available capacity) when the parameter uË is set to a largeamount, otherwise a large penalty cost is imposed on models. Therefore, the robust models performwell since there is no noticeable rise in values of their objective functions. The solution variance iscontrolled by parameter rË and if it is set to a large value it shows that, the decision-maker preferto focus on the total networkâs costs and providing high-level customersâ services rather than thevariability. The total networkâs costs will increase significantly by increasing the rË. In addition, thetrade-off between robustness of the models and the robustness of the solutions are handled by rË.The obtained results prove the ability of the developed model and its robust counterparts in dealingwith uncertainties. Decision-makers set imprecise parameters in an economically justifiable way tohandle uncertainty in real-world instances. According to the computational time, it is expectedthat the problem described in this study deals with a considerable amount of data to generate morerobust models. Indeed, this imposes challenges concerning the complexity of the approaches (i.e.,algorithms) and their functionality in real time. The computational time of the models rise byincreasing the size of the samples, however, they show different behaviour. In another words, forsmall size instances, Robust I outperforms the deterministic and Robust II, however, for the largesize instances, outperforms the other models. The deterministic model and the robust counterpartI have almost the same computational time, while, there is a sharp spike in computational time ofthe model robust II for the large-size samples.5.5 Solution ApproachThis section aims to provide a brief explanation about the proposed solution approach. TheSAA-SD approach is applied to deal with large-size samples [311]. Also, the GTC algorithm isproposed to incorporate into the SD algorithm [318] to accelerate the large-scale robust-stochasticmodel. Then, a common method namely ϵ-constraint [345] is adopted to solve the multi-objective200optimization model. The ϵ-constraint method is a computational approach used to generate aPareto frontier by solving a series of single-objective problems. Each problem is derived by treatingone of the objectives as the primary objective and converting the other objectives into constraintswith specified bounds (epsilon values). Generally, given the complexity and scale of the problem,a hybrid solution methodology is developed combining SAA and SD methods. This hybrid ap-proach, referred to as SAA-SD, effectively balances the computational load and ensures convergenceto high-quality solutions within a reasonable time frame. The rationale for incorporating the GTCalgorithm is to further enhance the efficiency of the SAA-SD method. Clustering helps in reducingthe problem size by grouping similar scenarios, thereby simplifying the problem without compro-mising the accuracy of the solution. By clustering scenarios based on their characteristics andcomputational time, a more structured and efficient optimization process can be achieved, whichis crucial for handling large-scale stochastic optimization problems. The generation of scenarios iscritical for capturing the uncertainty inherent in real-world problems, especially during a pandemic.Scenarios are generated to represent various possible future states of the system, considering factorssuch as demand fluctuations, supply disruptions, and logistical constraints. This comprehensivescenario generation enables robust decision-making and helps in designing resilient supply chainscapable of adapting to unforeseen changes.5.5.1 Sample Average ApproximationThe SAA approach has a position in dealing with stochastic and robust-stochastic models toprovide solutions with high quality and obtain statistical bounds [346]. In the SAA approach,the expected value of problem is estimated based on the value of the sampling problem [317]. Thesampling process is repeated intermittently to reach enough information about the solution [347]. Inall replication, sample of size M is generated by the random vector realization [317]. Consequently,the robust-stochastic modelâs approximation is as follows:Min Zx =âiâIzixi +1MMâm=1Z â²(x, Ïm) (5.34)Subject to:201âpâ²âPâ²âwâWâtâTXpâ²fwtsâ â¤ αfYf âf â F sâ â Sâ (5.35)âpâ²âPâ²âfâFâtâTXpâ²fwtsâ â¤ βwY â²w âw âW sâ â Sâ (5.36)âpâ²âPâ²âcâCâtâTX â²pâ²wctsâ â¤âpâ²âPâ²âfâFâtâTXpâ²fwtsâ âw âW sâ â Sâ (5.37)âpâ²âPâ²âtâTâcâCX â²â²pâ²citsâ â¤ Y â²â²i γi âi â I sâ â Sâ (5.38)âpâ²âPâ²âtâTâwâWX â²pâ²wctsâ â¥âpâ²âPâ²gpâ²csâ âc â C sâ â Sâ (5.39)âpâ²âPâ²âtâTâiâIX â²â²pâ²citsâ â¥âpâ²âPâ²gpâ²csâqsâ âc â C sâ â Sâ (5.40)âpâ²âPâ²âtâTâfâFX â²â²â²pâ²iftsâ â¥âpâ²âPâ²âcâCâtâTX â²â²pâ²citsâqâ²sâ âi â I sâ â Sâ (5.41)âpâ²âPâ²âtâTâiâIX â²â²â²pâ²iftsâ â¤ αfYf âf â F sâ â Sâ (5.42)âpâ²âPâ²âwâWâtâTpfpâ²sâXpâ²fwtsâ +âpâ²âPâ²sfpâ²sâWpâ²fsâ â¤ Ïf âf â F sâ â Sâ (5.43)âpâ²âPâ²âcâCâtâTrwpâ²sâXâ²pâ²wctsâ +âpâ²âPâ²sâ²wpâ²sâWâ²pâ²wsâ â¤ Ï â²w âw âW sâ â Sâ (5.44)âpâ²âPâ²âfâFâtâTpâ²â²ipâ²sâXâ²â²â²pâ²iftsâ +âpâ²âPâ²sâ²â²ipâ²sâWâ²â²pâ²isâ â¤ Ï â²â²i âi â I sâ â Sâ (5.45)W â²pâ²fsâ â¤ Yf âpâ² â Pâ², f â F sâ â SâW â²â²pâ²wsâ â¤ Y â²w âpâ² â Pâ², w âW sâ â Sâ (5.46)W â²â²â²pâ²isâ â¤ Y â²â²i âpâ² â Pâ², i â I sâ â Sâ (5.47)W â²pâ²fsâ â [0, 1] âf â F, pâ² â Pâ² sâ â Sâ (5.48)W â²â²pâ²wsâ â [0, 1] âw âW, pâ² â Pâ² sâ â Sâ (5.49)W â²â²â²pâ²isâ â [0, 1] âi â I, pâ² â Pâ² sâ â Sâ (5.50)Xpâ²fwtsâ â Z+ âf â F, pâ² â Pâ², w âW, t â T sâ â Sâ (5.51)X â²pâ²wctsâ â Z+ âc â C, pâ² â Pâ², w âW, t â T sâ â Sâ (5.52)X â²â²pâ²citsâ â Z+ âc â C, pâ² â Pâ², i â I, t â T sâ â Sâ (5.53)X â²â²â²pâ²iftsâ â Z+ âf â F, pâ² â Pâ², i â I, t â T sâ â Sâ (5.54)Yf â [0, 1] âf â F (5.55)Y â²w â [0, 1] âw âW (5.56)202Y â²â²i â [0, 1] âi â I (5.57)Ztfwsâ â [0, 1] âw âW, f â F, t â T sâ â Sâ (5.58)Z â²twcsâ â [0, 1] âw âW, c â C, t â T sâ â Sâ (5.59)Z â²â²tcisâ â [0, 1] âc â C, t â T, i â I sâ â Sâ (5.60)Z â²â²â²tifsâ â [0, 1] âf â F, t â T, i â I sâ â Sâ (5.61)Where, zixi shows the deterministic part of the objective function (i.e., the facilities allocationand making agreement with potential service providers). Moreover, M demonstrates the samplesize and Z â²(x, Ïm) explains the expected value of uncertain objective function. Algorithm 8 demon-strates the major stages of the SAA algorithm as follows: the required number of samples (M andMâ²) and the required number of SAA replications (N) should be set. Both accuracy and compu-tational difficulty must be considered in interpreting these parameters. Then, for N replications,the SAA problem is solved by generating sample of M scenarios. Let Xn and an represent theoptimal solutions and the optimal objective values of the sample problems, respectively. In theSAA algorithm, the lower and upper bounds are calculated to assess the quality of the solutions.The statistical bounds for aâ of the robust-stochastic model is determined by anâs value. Here,the real problem is the scenario-based model, which encompasses all potential scenarios. Finally, afeasible solution (X¯) and the lowest objective value between N replications should be selected. Theupper bound (ZX¯) of the original model is estimated by another sample size of Mâ² by solving theequation in the algorithm. The SAA problems tend to have a larger sample size Mâ² than M. Theoptimality gap can be calculated using the given equation of Algorithm 8.203Algorithm 8 Sample Average ApproximationInputs : M: Number of scenarios,Mâ²: Number of scenarios,N: Number of replications,λ%: Pre-defined accepted GapOutputs: Optimal objective value a, Updated Lower bound α¯, Gap Î´Lâ ââ U â +âwhile δ â¤ λ% dofor mâ 1 to M doMin z(x) =âiâI Zixi +1MâmâM zâ²(x, Ï)endLâ α¯ = 1NânâN anfor mâ² â 1 to Mâ² doU â Z1Mâ²(x¯) = 1(Mâ²â1)Mâ²âmâ²âMâ²(f(x, Ïmâ²)â zâ²(x¯,Ïmâ² )Mâ²)2endÎ´ â Z1mâ²(x¯)â α¯mendreturn Optimal objective value a, Updated Lower bound α¯, Gap δGenerally, the SAA algorithm initializes key parameters such as the number of scenarios (M),replications (N), accepted gap (λ%), and bounds (lower (L) and upper (U)). It iterates until thegap between upper and lower bounds meets the accepted threshold. During each iteration, for eachscenario m â M, the algorithm minimizes the approximated objective function by summing andaveraging costs across entities. The lower bound is updated using averages of optimal objectivevalues from replications, while upper bound is adjusted to reflect objective function variabilityacross secondary scenarios mâ² â Mâ². Recalculation of gap determines if the stopping criterionis satisfied. This approach enhances accuracy, ensures convergence, and efficiently handles large-scale stochastic problems. SAA improves objective function estimation by averaging scenarios andreplications, capturing problem stochasticity effectively. Iterative bound updates drive convergencetowards near-optimal solutions within the predefined gap, critical for computationally challengingproblems. Tested on real-world data, this method manages supply chains resiliently, including underdisruption conditions, demonstrating practical applicability.5.5.2 Graph Theory-Based Clustering AlgorithmParameters values (i.e., defining the process of decision-making) are continuously fluctuated bydifferent sources and levels of uncertainty [348]. In this regard, different scenarios are generated to204investigate the impact of uncertainty (i.e., operational and disruption risks) on the CLSCN design[348]. The SAA approach is a method of handling problems with a large number of scenarios.Although the adoption of SAA helps decrease the number of scenarios, it is still difficult to solvelarge-size instances.Clustering is a crucial step in the process of managing and reducing the complexity of large-scale stochastic optimization problems. By grouping similar scenarios together, clustering cansignificantly reduce the computational burden and improve the efficiency of solution algorithms.Traditional clustering methods, however, face challenges when dealing with high-dimensional dataand overlapping clusters, which are common in real-world supply chain problems.In this respect, the GTC approach is developed and integrated into the SD algorithm to solvethe problems with numerous scenarios. The GTC algorithm employs graph theory to identify andcluster data points in a high-dimensional feature space, making it particularly suitable for complex,high-dimensional datasets with noise and overlapping clusters.Accordingly, the GTC algorithm is proposed to cover the weaknesses of traditional algorithms.The principal superiority of the presented GTC algorithm, in comparison with existing similarapproaches, lies in its ability to:â Cluster Data Points in High-Dimensional Feature Space: The GTC algorithm can handlehigh-dimensional data effectively, making it suitable for complex problems like CLSCN de-sign.â Analyze Noise Data: It can distinguish between meaningful data and noise, improving thequality of clustering results.â Separate Overlapping Clusters: Unlike many traditional algorithms, GTC can accuratelyidentify and separate overlapping clusters.â Eliminate the Need for Pre-Defined Number of Clusters: The GTC algorithm dynamicallydetermines the optimal number of clusters during the clustering process.While the computational time complexity of the GTC algorithm is negligibly higher thantraditional methods in large-scale sample sizes due to the extensive iterations required for high-dimensional data, the clustering results are more precise. This improved accuracy is critical fordeveloping robust and efficient solutions in the context of stochastic optimization and supply chaindesign, where the quality of the clustering can directly impact the performance of the overall model.The proposed GTC algorithm introduces novelty by integrating graph theory principles into sce-nario clustering within stochastic optimization. By modeling scenarios as nodes connected by edges205representing similarity metrics (e.g., computational time and objective function values), the pro-posed approach facilitates a structured and efficient clustering process. Unlike other clusteringmethods, it considers both scenario similarities and relationships based on occurrence probabili-ties and penalty costs. This dual focus ensures more robust groupings of scenarios with similaroperational impacts, enhancing decision-making effectiveness.According to the Algorithm 9, the major stages of the developed methodology are as follows:(i) a set of scenarios {s1, s2, ...,Sn} is generated and Equation (5.62) is calculated, (ii) for eachscenario s â S (si, i is the counter of scenario), probability is estimated using Equation (5.63) andthe computational time is calculated. Then, a minimizer xâsi for each scenario s â S is estimatedaccording the Equation (5.64), (iii) the penalty cost is calculated for scenario si considering scenariosiâ² based on Equation (5.65). This means that scenario si is expected to occur, while scenario siâ²happens instead. Then, each scenario based on its features is clustered in a special cluster, (iv)the first measure is compared between two scenarios. If â(si, siâ²) is less than pre-defined threshold,then their computational time is compared. If they are close in terms of computational time, theyare assigned in a same cluster, otherwise, the algorithm iterates. There is a checking step in ourdeveloped algorithm. After the clustering, the average of each cluster is calculated in line withthe objective functionâs expected value and computational time. Then, the difference between eachscenario and the average of its cluster is calculated. If there is no significant difference betweenthem, the scenario is assigned to the right cluster. Otherwise, the scenarioâs features (i.e., theobjective functionâs value and computational time) are compared by the average of other clustersand then the scenario is assigned to the closest cluster.P â² =Nâsi=1psiÏsi (5.62)Ï =Nâs=1hsi(x, s)ps (5.63)β(xsi , hsi) â¥ Î²(xâsi , hsi) âs â S (5.64)â(si, siâ²) = Î²(xâsi , hsi)â Î²(xâsiâ² , hsiâ² ) âs â S (5.65)206Algorithm 9 Graph Theory-Based Clustering AlgorithmInputs : Number of scenarios S,Scenario counter I,Cluster counter K,Pre-defined tolerance for objective values ϵOutputs: Clusters of scenariosSâ SIâ IKâ Kâ(si, siâ²)ObjsÏµC.T (s)M â 0Ïâ 0µâ 0µâ² â 0nkwhile K Ì¸= â dofor iâ 1 to S doÏââNs=1 hsi(x, s)ps M â β(xsi , hsi) â(si, siâ²)â Î²(xâsi , hsi)â Î²(xâsiâ² , hsiâ² )endif â(si, siâ²) > ϵ thensi â si+1endelseif C.Tsi â C.Tsiâ² < Ïµâ² thenk â si k â siâ²endendendreturn Clusters of scenariosGenerally, Algorithm 9 presents a methodical approach to scenario clustering within our de-veloped methodology. First, a set of scenarios sâ1, sâ2, ..., sân, is generated, and Equation (5.62) iscomputed to establish foundational parameters. Each scenario sâ â Sâ undergoes probability es-timation using Equation (5.63), alongside its computational time C.Tsâi (i.e., i is the counter ofscenario) and determination of the minimizer xâsâi using Equation (5.64). Following this, penaltycosts are computed for scenario sâi , considering its deviation from scenario sâiâ² based on the Equa-207tion (5.65). This step quantifies the repercussions of scenario deviations on clustering decisions.Utilizing graph theory principles, scenarios are clustered based on similarities in objective functionvalues and computational times. If the difference â(sâi , sâiâ²) in optimal objective values falls belowa predefined threshold, their computational times are compared. Scenarios with close operationalimplications are grouped into clusters iteratively. After clustering, the average objective functionvalue and computational time for each cluster are computed. Each scenario is then assigned tothe cluster where its deviations from the cluster averages are minimized, ensuring clusters accu-rately reflect operational similarities and enhancing decision-making within stochastic optimizationframeworks.In this section, a comparative examination is conducted to compare the developed GTC algo-rithm with the state of the arts (i.e., main machine learning clustering algorithms) (i.e., K-means,DBSCAN, GM, BIRCH, AP,MS) to justify the functionality and effectiveness of the proposedmethodology. Figure 5.4 compares the above mentioned algorithms graphically. Figure 5.6 demon-strates the parameter tuning for Kmeans and DBSCAN. The clustering algorithmsâ comparisondepends on some factors (i.e., size of the dataset, number of generated clusters, type of dataset,accuracy). The major scheme behind the proposedGTC algorithm is to accelerate the SD method(i.e., exact decomposition algorithm) in order to speed up the convergence rate of the presentedalgorithm. In our application, the algorithms DBSCAN (Figure 5.4 (b)), BIRCH (Figure 5.4(d)), and MS (Figure 5.4 (f)) are not able to distinguish clusters precisely. The K-means (Figure5.4 (a)) and GM (Figure 5.4 (c)) reached comparable outputs and the identification of the bestalgorithm between these two methods is challenging. Although K-means algorithm is widely usedat scenario clustering applications, it may lead to converging to un-optimal values. In addition, itmay not result in global optimum for the large-size instances that is not computationally expen-sive. Moreover, there must be a pre-determined number of clusters in the data sets. Although thenumber of pre-defined clusters can be adjusted by elbow curve (i.e., see Figure 5.6 (a)), it onlycalculates the global characteristics [349]. Consequently, the defined number of clusters by elbowmethodology is not accurate and the computational time of the K-means algorithm grows signifi-cantly by increasing the number of scenarios. There are some subjective elements to determine theoptimal number of clusters, and it is largely influenced by the methods of measuring similarity andpartitioning parameters [350]. In addition, considering Figures 5.6 (b) and 5.4(b), DBSCAN isnot able to generate the accurate number of required clusters in terms of sorted observation andK-NN distance in noisy environment. This implies that the parameters of sorted observation and208K-NN distance should be set separately for all evaluationâs parameters. DBSCAN algorithm doesnot distinguish clusters precisely since it is not able to generate the clustersâ centroids as the outputin each iteration. GM and K-means outperform other algorithms since they are able to generatefour clusters, while DBSCAN, BIRCH, and MS are not capable of exhibiting any discerniblepatterns, and AP generates eight overlapping clusters. The main superiority of the proposed GTCalgorithm (Figure (5.5)) is to generate clusters without the predefined number of clusters. One ofthe common behaviours of investigated clustering algorithms is that they are sensitive to outliers(Figure 5.4 (a)) and the noise data (Figures 5.4(a), (b), (c), (d), (e), (f)) which results in overlappingclusters (See Figure 5.4 (e)).2094.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time((a)) K-means4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time-10((b)) DBSCAN4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time((c)) GM4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time((d)) BIRCH4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time((e)) AP4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational Time((f)) MSFigure 5.4: Graph Theory-Based Clustering Algorithm Comparison with Six Top Machine LearningClustering Algorithms2104.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0Objective Value2.02.53.03.54.04.5Computational TimeFigure 5.5: Graph Theory-Based Clustering Algorithm1 2 3 4 5 6Number of clusters51015202530Within Clusters Sum of Squares((a)) K-means0 20 40 60 80 100 120 140Sorted observations (4th NN)2.02.53.03.54.0k-NN distance((b)) DBSCANFigure 5.6: Parameter Tuning for the k-means and DBSCANBriefly, the clustering results presented in this study aim to provide a thorough comparativeanalysis of the proposedGTC algorithm against several state-of-the-art machine learning clusteringmethods, including K-means, DBSCAN, GM, BIRCH, AP, and MS. This study evaluatesthese algorithms across various factors such as dataset size, number of clusters generated, datasettype, and overall accuracy. Notably, the findings indicate that while some algorithms such asK-means and GM perform comparably in generating distinct clusters, they can converge to sub-optimal solutions and require a predefined number of clusters, which may limit their applicabilityto large-scale scenarios. Conversely, algorithms such as DBSCAN, BIRCH, and MS exhibitchallenges in accurately distinguishing clusters, particularly in noisy environments or datasets with211complex structures. Specifically, theGTC algorithm demonstrates significant advantages over thesemethods by autonomously determining cluster numbers and effectively handling noise and outliers.Despite other machine learning clustering algorithms, GTC employs graph theory principles toenhance cluster separation without the need for predefined cluster numbers, thereby improvingthe accuracy and robustness of clustering outcomes. This capability is crucial for applicationswhere data characteristics are dynamic or unknown a priori. Moreover, the comparative analysishighlights that while other algorithms may struggle with noise sensitivity or the complexity ofdataset structures, GTC consistently generates well-defined clusters without overlap, contributingto clearer decision-making and more reliable insights in various real-world scenarios. The efficacyof GTC in overcoming these challenges highlights its potential as a robust tool for complex dataclustering tasks.All in all, machine learning algorithms perform in different ways to identify clusters. Accordingly,initialization has a significant impact on generating accurate clusters, which are not overlapped orsensitive to outliers, to avoid reaching local optima. The comparison between six main algorithms(e.g., K-means, DBSCAN, GM, BIRCH, AP, MS) demonstrates that GTC with three outputclusters (Figure (5.5)) outperforms other clustering algorithms.5.5.2.1 The Graph Theory-based Clustering Algorithm Performance Measurement(Silhouette Analysis)As mentioned previously, the performance of clustering algorithms is different in terms of qualityand computational time. There are some approaches to evaluate clustering algorithms, such as,Davies-Bouldin evaluation [351], Dunn evaluation [352], Silhouette analysis [353]. The Silhouetteanalysis calculates the membership of data points by calculating the mean distance between themin a cluster. Then, the selected data points distance is compared with other data points distancesbetween clusters [353]. The Silhouette score is calculated as follows:1) The data points distance from all other data points within the same cluster is calculated,which is known as the measure of mean intera-cluster distance (α).2) The distance between a data point and other data points in the next-closest cluster is calcu-lated. The mean nearest cluster distance (i.e., β) is estimated, and then the Silhouette score, Sâ, isevaluated by Equation (5.66) for each sample.212Sâ = (Î²âÎ±)(Max{Î±, β}) (5.66)Scores are indexed from -1 to 1. Score 1 demonstrates that clusters are well-separated, andScore 0 indicates the overlap among clusters. A negative score implies that samples are groupedincorrectly. In this study, the Silhouette score for the GTC algorithm is estimated approximately0.73. This validates that the obtained clusters are grouped precisely.The performance of the clustering algorithms is impacted by datasets [354]. A measure of valid-ity (i.e., accuracy, Silluhote score, objective value, and computational time) supports the optimalnumber of clusters [355]. Figures 5.7 and 5.8 compare the validity measures of the proposed GTCwith six investigated algorithms for 25 generated scenarios for different sample sizes. Furthermore,the clustering algorithms are evaluated based on the accuracy as well. The obtained values close to1 indicates desirable clustering algorithm in terms of accuracy. However, the obtained value close to1 for the objective function (errors) and computational time demonstrates undesirable performance.As the sample size increases, all clustering algorithms are degraded in terms of accuracy and Sill-houtte score. Similarly, DBSCAN, BIRCH, and MS are deteriorated as the number of clustersincreases (See Figure 5.7 (b), (d), (e), (f)). However, K-means (Figure 5.7 (a)) and GM (Figure5.7 (c)) show more stable patterns as the sample size increases. GM has the highest accuracy andlowest computational time for different samples. It turns out that low complexity and executiontime are largely determined by parameter estimation and iteration requirements. Although, GMdenotes the reasonable accuracy with the low computational time, its scalability degrades as thenumber of samples increases. K-means and the elbow approach have less accuracy and more linearscalability in the same number of iterations. As a result of the initial clustering centers, K-meansalgorithm converges to divergent values. Figure 5.8 denotes that GTC has the highest accuracyand Sillhoutte score and lowest objective function (errors) and computational time for the generatedsamples. Furthermore, GTC demonstrates the stable manner owing to its capability in diagnosingthe noise data.213((a)) K-means ((b)) DBSCAN((c)) GM ((d)) BIRCH((e)) AP ((f)) MSFigure 5.7: Sensitivity Analysis214Figure 5.8: Sensitivity Analysis for the Proposed Graph Theory-Based Clustering Algorithm5.5.3 Accelerated Scenario Decomposition[316] proposed the SD algorithm to solve robust-stochastic and stochastic models. Although,in SAA method, the problem has less scenarios in comparison with the main problem, it is stillchallenging to deal with the approximated version of original model. In the SD method, thesolutions in scenario sub-problems are explored as candidate solutions for the problem. Then,the solutions are cut after evaluation in terms of objective function and solutions. This leads tosignificant improvement in the lower bound and the duality gap [319]. A novel GTC-SD algorithmis proposed to handle the group of scenarios rather than all scenarios. The main stages of thedeveloped GTC-SD algorithm are described in Algorithm 10 as follows: (i) setting the lower andupper bounds to ââ and +â, respectively, (ii) the lower-bounding problem is solved. The lowerbound can be estimated in the algorithm. Then, for each feasible solution, the lower-boundingproblem is solved. If the estimated lower and upper bounds have negligible gap, the algorithmterminates. Otherwise, it iterates until reaches stopping criteria.215Algorithm 10 Accelerated Scenario DecompositionInputs : Number of scenarios M,Upper bound U ,Lower bound L,Set of solutions S,Best solution found yâOutputs: Optimal solution yâMâ MU â +âLâ ââSâ â yâ â 0riyiwhile U > L dofor iâ 1 to M doSolve Min fi(y) =âkâK fkYk + P (Y, θi)ri â Optimal objective function valueyi â Optimal value of variablesendLââiâM 1MriSËâ âªMi=1yiSâ S âª SËfor y â SË doSolve β ââkâK fkYk + 1MâmâM P (Y, θm)if U > β thenU â Î²yâ â yendendendreturn yâ5.6 Numerical ExperimentA set of instances is generated based on different sizes (i.e., small-size, middle-size, and large-size) to verify the applicability and efficiency of the presented algorithm. The main features of thepresented model, affecting the problem complexity (e.g., the number of facilities and scenarios),are considered to generate samples. According to Table 5.4, CPLEX and SAA-SD reach optimal216solutions with the same computational time (see Samples 1, 2, and 3). The SAA-SD and theGTC-SD have the same computational time for Samples 1 and 2 as well. As the sample size increases, theexact method (i.e., CPLEX) is only capable of solving small-size instances. Accordingly, the CPLEXand the SAA-SD algorithms result the same solutions in the small-size samples. The SAA-SDand GTC-SD are able to handle large-scale samples in a reasonable time. As the complexity ofthe problem increases, the GTC-SD demonstrates better performance in terms of computationaltime compared to SAA-SD. It is worth noting that SAA-SD, GTC-SD, and CPLEX obtain thesame solutions with negligible difference.217Table 5.4: Graph Theory-Based Clustering Algorithm ValidationNo F W C I S CPLEX SAA & SD GTC-SDOF C.T(s) OF C.T(s) OF C.T(s)1 3 2 6 1 3 554.440 0 560.397 0 554.909 02 3 2 12 1 3 1,679.292 0 1,679.344 0 1,674.680 03 14 4 50 3 3 4,029.712 0 4,038.052 0 4,029.342 04 14 4 100 3 3 7,807.573 2 7,876.999 2 7,807.342 05 18 6 300 5 3 â â 51,297,232 4 51,297.158 36 18 6 1000 5 3 â â 169,359.436 30 169,359.104 237 18 6 2000 5 3 â â 335,347.726 105 335,347.495 918 18 6 2500 5 3 â â 431,401.804 215 431,401.819 1799 18 6 3000 5 3 â â 528,702.995 490 528,703.001 43910 25 6 3000 5 3 â â 591,205.715 551 591,205.364 50311 25 16 3000 5 3 â â 690,552.011 685 690,551.928 619218In todayâs competitive markets, manufacturing companies are motivated to adopt differentstrategies to achieve competitive advantages and higher customer service level. These strategicdecisions deal with determining the optimum number of facilities and optimum product flow amongfacilities. In this study, the impacts of the number of facilities and their locations on the configura-tion of supply chain network is investigated. As expected, the number of customer zones and theirlocations have significant impacts on the total networkâs costs and networkâs design topology. Asthe number of customers increases by 65 percent, the total networkâs costs experiences a sharp risenearly 67 percent. This rise stems from higher operational costs and transportation costs due tothe larger size of the network. A warehouse, as a market terminal, is responsible for distributingproducts in a way that matches customers orders with producers capacity. Despite their significantrole in CLSCN, they have less impacts on the total networkâs cost. Accordingly, as the numberof potential warehouses increases by 65 percent, the total networkâs cost increases by 14 percent.Furthermore, as the number of factories decreases by 30 percent, the total networkâs cost reducesby 10 percent.5.7 An Extension of Multi Objective OptimizationIn SSCN design, the economic benefits, environmental conservation, and social impacts of theproduct flow (e.g., raw material extraction, production, storage, and delivery) should be considered,simultaneously [287, 356]. It is important to enhance the customer service level, while minimizingenvironmental issues (e.g., energy consumption and waste production) [357]. Environmental con-siderations and social factors are investigated by proposing a multi-objective mathematical modelas follows:Min z(x) = (z1(x), z2(x), ..., zn(x)) (5.67)Subject to:c(x) â¤ 0 (5.68)Where c(x) defines the model constraints. The presented mathematical model encompassesthree main objectives in which the total CLSCN cost is minimized. The second objective (5.69)minimizes the total emissions of production, handling, re-manufacturing, collecting & recycling, and219transportation. The third objective (5.70) maximizes the total customer service level by deliveringthe customer demand on time.Min z2 =âfâFâwâWâtâTZtfwÎ´t +âwâWâcâCâtâTZ â²twcÎ´t +âcâCâiâIâtâTZ â²â²tciÎ´t+âiâIâfâFâtâTZ â²â²â²tifÎ´t +âfâFâpâ²âPâ²W â²pâ²fÎºf +âwâWâpâ²âPâ²W â²â²pâ²wÎ¶w+âiâIâpâ²âPâ²W â²â²â²pâ²iÎ·i +âfâFâpâ²âPâ²W â²pâ²fµf(5.69)Max z3 =âwâWâpâ²âPâ²âcâCâtâTX â²pâ²wcteâÎ»wt(5.70)5.7.1 ϵ-Constraint MethodThe ϵ-constraint method is utilized to solve multi-objective mathematical model. The mostimportant objective function is considered to optimize as the principal objective and the rest ob-jectives are transferred to the constraints and restricted [358]. In this study, the total networkâscost is investigated as the principal objective and the total emissions and customer service level areconsidered as the constraints.Minimize Z1 (5.71)Subject to:Z2 â¤ ϵ1 (5.72)Z3 â¤ ϵ2 (5.73)Equations (5.35) to (5.61) (5.74)Where, Z1, Z2 and Z3 denote the three objectives of the mask CLSCN.5.7.2 Scenario and Computational Time AnalysisIn the era of globalization, the structure of CLSCN s does not remain in its first topology sizeand is affected by many factors (e.g., new partnership and agreement with third parties, changesin customers behavior and demand, environmental awareness and regulations). The large-scaleCLSCN s need to be managed effectively under uncertainty. This emphasizes the importance220of required computational time. The computational time of two exact algorithms SAA-SD andGTC-SD (i.e., integrated GTC with SAA-SD are compared in the multi-objective optimizationmodel). Figure 5.9 (a) compares the various scenarios (the number of possible scenarios) generatedby the SAA-SD and the GTC-SD (i.e., accelerated SAA-SD) while Figure 5.9 (b) visualizesthe computational time of the SAA-SD and the GTC-SD. As expected, the GTC-SD is able tosolve large-scale instances in reasonable time since it deals with less scenario clusters.((a)) Scenario analysis ((b)) Computational timeFigure 5.9: Scenario and Computational Time Analysis5.8 Managerial ImplicationsIn recent decades, CLSCN s have been given a great deal of attentions due to the focus ofcompanies on recovery activities and eco-friendly business structure owing to the mandatory envi-ronmental regulations [287]. This research provides beneficial insights for decision-makers.5.8.1 Case Study: Baseline ScenarioIn the original scenario (i.e., baseline scenario), the multi-objective mathematical model is ap-plied to assess the face mask CLSCN in the COVID-19 era and similar outbreaks. The COVID-19pandemic highlighted significant challenges in the distribution of essential goods, particularly PPEsuch as face masks. During the early stages of the pandemic, there was a global surge in demand forface masks, which led to severe shortages and distribution bottlenecks. This scenario highlighted thecritical need for efficient supply chain management strategies to ensure timely delivery of essentialgoods to mitigate the spread of the virus and protect public health. This situation necessitatedinnovative approaches to optimize distribution networks, manage inventory effectively, and ensure221equitable access to face masks for healthcare workers and the general public. This study focuseson the metropolitan area of Toronto, Canada, which serves as a representative case for analyzingthe distribution challenges during a pandemic. Toronto, being a major urban center with a densepopulation and significant economic activities, faced substantial logistical hurdles in distributingface masks efficiently. A summary of the results (e.g., the selected facilities and the optimal flowof face mask) for different possibilities of market demand and time window is demonstrated inFigure 5.10. The generated plan begins by delivering 1,000 face masks Type 1 from Factory F1 toWarehouse W4 by the road transportation option under the second possibility of market demand(i.e., moderate demand). If the demand is high, the model plans to send 900 unit face masks Type1 from Factory F1 to Warehouse W4 by rail transportation option. Then, 360 and 740 face maskType 1 are delivered from Factory F3 to Warehouse W3 and Warehouse W7 under the possibilityof moderate market demand by the road transportation option, respectively. Factory F4 schedulesto send 890 face masks Type 1 to Warehouse W3 by the road transportation option under thepossibility of moderate market demand. Furthermore, 300 face mask Type 1 from Factory F4 aresent to Warehouse W4 by the rail transportation option. This factory delivers 1,190 face maskType 1 to Warehouse W6 by the rail transportation option when the demand is high. Factory F6only covers Warehouse W6 by sending 620 unit face mask Type 1 by the rail transportation optionwhen the demand is moderate. Then, Warehouse W6 fulfills the demand of customer zones (zones1-21) by different transportation options under different possibilities of market demand . In thebackward flow, EOUs and EOLs are collected and sent to collection & recycling centers for therecycling purpose. Totally, 3,000 face mask Type 1 are collected from retailersâ zones and sent tocollection & recycling centers by the road transportation option under different demandâs scenarios.The Collection & recycling center I1 delivers 1,000 face mask Type 1 to Factory F1, 900 face maskType 1 to Factory F2 and 1,100 face masks to Factory F3 by road transportation option underthe possibilities of low, moderate and high market demand for recycling purpose. Generally, theresults are obtained as follows: The total network costs Z1, emissions Z2, and customer servicelevel Z3 are equal to 9,701.523, 275,113.131, and 4,133.636, respectively. It should be noted thatcustomer service levels are typically measured using various units, depending on the organizationâspolicies. In this study, service levels are determined by the percentage of orders or deliveries fulfilledwithin the specified time window. For example, if a mask delivery is considered on-time when itarrives within a specific time frame, the customer service level can be expressed as the percentageof on-time deliveries.222Figure 5.10: Baseline Scenario ConfigurationIn general, the robust-stochastic optimization model is applied to the setting of the COVID-19pandemic, focusing on the distribution and recycling of face masks within the Toronto metropolitanarea. The model was designed to handle the distribution of goods under uncertainty, consideringvarious market demand scenarios and time windows. The results of the model provide detailedinsights into the optimal flow of face masks and the selection of facilities under different demandscenarios. The model successfully determines the optimal distribution routes and transportationmodes for face masks under different market demand scenarios. For moderate demand, road trans-portation is primarily used, while rail transportation is preferred under high demand to handlelarger volumes efficiently. Factories and warehouses are strategically selected to minimize totalnetwork costs and emissions. For instance, Factory F1 and Warehouse W4 are frequently utilized,indicating their central role in the supply chain network. The model ensures high customer servicelevels by fulfilling orders within specified time windows. This is crucial during a pandemic whentimely delivery of face masks is essential for public health and safety. Despite the urgent need forface masks, the model also considers environmental impact by minimizing total emissions. This bal-anced approach highlights the feasibility of integrating sustainability into emergency supply chainplanning.2235.8.2 Case Study: Scenario I-Resource UnavailabilityThe configuration of supply chains is affected by the most impactful events (e.g., bushfires,strikes, and pandemics) [263, 359]. The recent COVID-19 outbreak is different from previous dis-ease outbreak since it has affected all the nodes (i.e., facilities) and edges (i.e., links), simultaneously[360]. Accordingly, a bunch of products remain stranded around the world due to the COVID-19lock-downs, and blank transshipment due to products stuck. Retailers are not received their prod-ucts on time due to the closure or unavailability of warehouses for delivery. The networkâs flowfaces significant disruptions, giving rise to multiple challenges for supply, transportation, recycling,and producing. Closed borders, restrictions on supply markets, slowed international trade, laborshortage, and physical distances between manufacturing firms are some of these examples [361]. Inthis scenario, it is assumed that Factories F1, F3, and F4 become out of access due to the financialdifficulties, quarantine, lock-downs, and unavailability of transportation options (e.g., truck, train),respectively. Therefore, the proposed model aims to offer contingency plan to cover the unavail-ability of resources in uncertain situations. Factories F2 and F5 are incorporated into the modelto cover the unavailability of Factories F1, F3, and F4. It should be noted that Factory F6 has anotable influence on this scenario since the huge amount of retailers demand is fulfilled by FactoryF6. The lower and upper bounds of the total networkâs cost decrease owing to the unavailabilityof resources. The model can tackle disruption by imposing pressure on Factory F6 to meet thecustomer demand in a robust manner. If Warehouses W3, W4, and W7 become disrupted due to thementioned reasons, Warehouses W2, W5, and W6 are incorporated into the model to balance theCLSCN. In particular, Warehouse W2 is the most active warehouse under this circumstance. Ifcollection & recycling centers confront disruption, the total networkâs cost and emissions increase,while the customers satisfaction level (i.e., customer service level) drops substantially. Table 5.5demonstrates the results of disruption in collection & recycling centers. In this scenario, collection& recycling centers I1, I3, and I7 are taken into account as disrupted resources. In this situation,the proposed model balances the network by incorporating Collection & recycling centers I2, I5,and I6. Although, the model uses alternative collection & recycling centers to satisfy the customerdemand, Collection & recycling center I2 is more active than others due to the lower distance tofactories and customers zones. As indicated in Table 5.5, the total networkâs cost and emissionsincrease about 9 percent and 2 percent, respectively, since the total distance increases from 673 to730 km. However, the social factors (i.e., customer service level) drops by 13 percent. Figure 5.11visualizes the facilities and respective flows under the Scenario I.224Table 5.5: Disruption and Robustness AnalysisNo Scenarios (Si) Z1 Z2 Z3 Total distance (km)1 Baseline 9,701.523 275,113.131 4,133.636 673.852 Disruption (I ) 9,791.528 280,784.197 3,594.000 730.982Figure 5.11: Scenario I (Resource Unavailability) Configuration5.8.3 Case Study: Scenario II-Workforce UnavailabilityIn the earlier stages of the pandemic, different preventive policies (e.g., practicing self-isolatingand physical distancing) were publicized to mitigate spread of viruses. Additional measures reducedthe production capacity of facilities. Accordingly, I investigate Scenario II in which all resources(e.g., workforce) work with 50 percent of their capacity due to the COVID-19 preventive policies.The results demonstrate that the model can provide a robust solution in case of disruption (i.e.,workforce unavailability). Factory F4 has more potential to produce face masks to prevent theunmet demand of customers due to the higher production capacity. Warehouse W5 is the mostactive warehouse when warehouses work with half of their capacities. The market demand for face225mask Type 1 has been unmet for zones C3, C5, C6, C9, C13, and C14. All market demand of facemask Type 2 has been fulfilled. The proposed model is capable to satisfy the demand of face maskType 3 of all customer zones, except C7, C8, and C19. Table 5.6 tabulates the result for betterunderstanding.Table 5.6: Disruption and Robustness AnalysisNo Scenarios (Si) Z1 Z2 Z3 Total distance (km)1 Baseline 9,701.523 275,113.131 4,133.636 673.852 Workforce Unavailability 9,838.507 280,564.159 3,996.340 701.172According to Table 5.6, the total network costs and carbon dioxide footprints degrade by 1.39percent and 1.9 percent, respectively. Furthermore, the customer service level experiences a 3.46percent drop when the network works with half of its resource capacity.5.9 SummaryThis study has investigated the challenges for mask distribution planning and recycling un-der uncertainty in the COVID-19 era. A robust-stochastic optimization model has been appliedto optimize the total networkâs cost and environmental pollution and optimize the total customerservice level. The model has incorporated several producers, warehouses, distribution centers, col-lection & recycling centers, different types of products, and multiple time periods. The large-scaleinstances have been handled using a hybrid SAA-SD approach by introducing a novel algorithm(i.e., GTC-SD). The sensitivity analyses and numerical experiments have validated the feasibilityrobustness and the optimality robustness of the robust-stochastic optimization model. As expected,the total number of customers zones and their locations have significant impacts on the total net-workâs cost and networkâs design topology. As the total number of customers zones has increasedby 20 percent, the total networkâs cost has increased by 20.9 percent due to the larger size of theCLSCN. Despite the significant role of warehouses (i.e., the warehouse is a market terminal andresponsible for distributing products) in the supply chain networks, they have less impacts on thetotal networkâs cost. In other words, the efficiency in the topology of CLSCN (i.e., agreementwith potential service providers) can enhance profit, decrease environmental issues and enhance thecustomer service level. The large-scale supply chain models need to be managed effectively under226uncertainty that emphasizes the importance of required computational time. The sensitivity analy-sis, based on the number of generated scenarios in SAA-SD andGTC-SD algorithms, has verifiedthe applicability and functionality of the developed solution approach in dealing with large-scaleinstances. The proposed model and developed solution approaches have been investigated usinga real-world case in Toronto. Three different schemes (i.e., baseline, resource unavailability andworkforce unavailability) have been considered to demonstrate the performance of the proposedmethodological framework in dealing with operational and disruptions risks. In the case of disrup-tions, the customer service level has degraded by 3.89 percent, and the total networkâs cost andcarbon emissions have increased by 1.39 percent and 1.94 percent, respectively. Furthermore, thecustomer service level has decreased by 4.09 percent, and the total networkâs cost and total carbonemissions have increased by 1.41 percent and 1.98 percent, respectively, when the network workswith half of resources (i.e., operational risks).The proposed model has provided a feasible schedule for distributing the face masks and recy-cling the EOL and EOU by balancing the network flow on available facilities during the resourceand workforce unavailability. Generally, the results demonstrated that the disruption risks hadhigher impacts on the CLSCN than the operational risks. As for future avenues, the adoption ofreinforcement learning algorithms (e.g., predicting market demand) can support decision-makers toenhance the resiliency of supply chain. While machine learning and reinforcement learning tech-niques are commonly suggested, our rationale for their application lies in their potential to enhancesupply chain resilience. For instance, reinforcement learning algorithms can effectively predict mar-ket demand fluctuations, thereby enabling proactive decision-making and adaptive SC strategiesin response to disruptions. This strategic adoption of advanced learning algorithms aligns withindustry trends towards improving SC responsiveness and resilience in dynamic environments.227Chapter 6Conclusions and Future WorkRecommendationsThis dissertation has introduced several main contributions by developing IDSSs for large-scalestochastic dynamic SC s implemented on various case studies (e.g., e-commerce SC , manufacturingSC , and healthcare SC ). The outcomes of this dissertation will open several directions for futureresearch in designing of IDSS .6.1 Summary of Research FindingsChapter Chapter 2 designed an IDSS for SC network resiliency and validated on a case studyin e-commerce sector. Chapter 2 introduced a platform for optimizing last-mile delivery in urbanareas using mobile depots and crowd-shipping in response to rising e-commerce and same-day deliv-ery demands. The platform highlighted the importance of hyper-local drivers for high-quality serviceto deal with urban traffic challenges. The proposed multi-stage stochastic dynamic risk-averse modeldemonstrated improved delivery success rates by accounting for crowd-shippersâ availability, withthe risk-averse model achieving about 2% higher costs but significantly better management of high-risk scenarios, leading to cost savings. Stochastic models outperformed deterministic ones by 9.85%,due to better handling of incomplete information. The proposed approach is incorporated a Markovdecision process model and the ORDAO methodology to address dynamic online orders, showing areduction in delivery time by 11% compared to the IMAS method. Comparing two scenarios, theinclusion of hyper-local drivers reduced total delivery time and distance by 12%, resulting in lowerCO2 emissions and reduced traffic congestion. The analysis of reimbursement fee policies revealedthat higher fees for hyper-local drivers, aligned with increased CVaR costs, improved participationand reduced total costs, demonstrating the impact of optimal reimbursement strategies on efficiencyand cost management.In Chapter 3, the application of the proposed IDSS was investigated on global SC resiliency228in manufacturing sector. Chapter 3 introduced an IDSS for resilience global SC logistics using aparallelized SDDiP approach. The proposed IDSS addressed challenges such as order scheduling,production planning, and inventory management across warehouses by developing a multi-stagestochastic model that accounts for demand fluctuations, disruptions, and lead times. Various multi-stage stochastic integer programming models were explored, incorporating real-world factors suchas discounts, which increased model complexity due to the inter-stage information sharing. Anaccelerated parallel SDDiP algorithm was proposed, showing improved performance and CPUscalability compared to the basic SDDP . The evaluation using different scenarios revealed thatSDDiP-MIR outperformed SDDiP-SWLDC and SDDiP , particularly in large instances, withfaster computation and a smaller optimality gap of 7%. Resiliency analysis showed that supplierunavailability increased costs by 26% due to sourcing and shortage costs, while delays in sourcingcomponents raised production, transportation, and overtime costs. Variations in discount rateshad minimal impact on total costs but significantly affected logistics and inventory holding costs,highlighting the need for effective inventory management.Vaccine distribution in Toronto was investigated in Chapter 4 to validate the performance ofthe proposed IDSS . Chapter 4 investigated efficient resilient vaccine distribution planning whichis crucial for achieving broad immunization coverage and minimizing shortages to improve publichealth. The primary challenge involved determining optimal locations for stationary and mobilePHUs and dynamically adjusting mobile PHU locations to ensure equitable access across variouspopulation groups. Moreover, managing vaccine flow in the face of uncertain demand and limiteddata resulted in additional challenges. This research addressed these challenges by proposing a noveldata-driven IDSS . Given limited data availability, traditionalDDRO approaches produced inaccu-rate and conservative uncertainty sets. The research introduced a data-based framework integratingmachine learning, data-driven optimization, and data generation to better manage uncertainty. Theproposed data-driven DSS was implemented on real-world case study (Toronto). The data-basedframework in DSS reduced shortage periods by 33% and 16% compared to prediction results andDDRO methods. The uncertainty set generated was used in the model-based framework, optimiz-ing the vaccine distribution network with mobile PHUs. This resulted in reduction in vaccinationshortages by up to 80% compared to other methods. Furthermore, the DPA model enhanced eq-uitable access by allowing dynamic location adjustments for mobile PHUs. Reallocating surplusinventories among PHUs reduced shortages by up to 52%.The resilient mask distribution and recycling in Toronto was also examined in Chapter 5 as229the case study to validate the performance of the proposed in this chapter. Chapter 5 addressedmask distribution and recycling challenges under the uncertainty during the pandemic by employinga robust-stochastic optimization model to minimize total network cost, environmental impact, andenhance customer service. The model incorporated multiple producers, warehouses, distributioncenters, and recycling centers across various time periods. A hybrid SAA-SD approach with anovel GTC-SD algorithm was introduced to deal with large-scale instances. Sensitivity analysesand numerical experiments confirmed the modelâs robustness and optimality. Results showed thatincreasing the number of customer zones by 20% raised the network cost by 20.9%, highlighting thesignificant impact of zone locations on network cost and configuration. Although warehouses playeda crucial role, their impact on overall network cost was relatively minor. Efficient network topologyimproved profits, reduced environmental issues, and enhanced service levels. Sensitivity analysis ofscenario generation in the SAA-SD and GTC-SD algorithms demonstrated their effectiveness inmanaging large-scale problems. The proposed model and solution approaches were implemented onreal-world case study (Toronto), considering scenarios such as resource and workforce unavailability.The results demonstrated that disruptions led to a 3.89% decrease in service level, with cost andcarbon emissions increasing by 1.39% and 1.94%, respectively. Operational risks, such as halvingresources, further decreased service levels by 4.09% and increased costs and emissions by 1.41% and1.98%, respectively.6.2 Categorization of Contributions to the KnowledgeAs outlined in Section 1.5.2. this dissertation made several significant contributions to knowl-edge in the field of SC management, DSS , and optimization under uncertainty, particularly inlarge-scale, dynamic, and stochastic environments. These contributions included new insights,methodological entrancements, and practical applications, as categorized below:6.2.1 Advancement of Intelligent Decision Support SystemsThis dissertation developed and demonstrated innovative IDSSs that addressed critical chal-lenges in diverse domains, including e-commerce logistics, manufacturing sectorâs logistics, andhealthcare logistics. Despite traditionalDSSs, which often focus on specific isolated methodologies,this dissertation integrated multiple decision-making tools and methods, such as advanced optimiza-tion, simulation, machine learning, and data-driven techniques into cohesive systems. These IDSSs230provided robust solutions for complex, real-world SC challenges characterized by uncertainty, dy-namic changes, and large-scale operations, enhancing real-time decision-making capabilities for SCmanagers. For example, in Chapter 2, the integration of hyper-local drivers into a last-mile deliverysystem, alongside crowd-shippers, offers several advantages in terms of cost, time, and environ-mental impact. In the first scenario, where only crowd-shippers are used, the total cost is 176.37units, with a delivery distance of 75.61 km. However, in the second scenario, where hyper-localdrivers handle failed deliveries, the total cost rises slightly to 179 units due to reimbursement fees.Despite this, the delivery time and distance are reduced by 12%, and there are fewer issues withCO2 emissions and traffic congestion. The addition of hyper-local drivers improves the ability tomanage failed deliveries, making the system more resilient, especially during high-demand periodslike holidays. Overall, the integration enhances delivery efficiency and addresses challenges likeextreme weather, albeit with a minimal increase in cost.6.2.2 Advancement of Stochastic and Dynamic Modeling in SC ManagementThe dissertation extended the body of knowledge by designing novel stochastic and dynamicoptimization models that explicitly considered risk, uncertainty, and multi-stage decision-making.Multi-Stage stochastic dynamic models implemented for e-commerce, manufacturing, and healthcarecase studies (i.e., last-mile delivery, global SC logistics, and healthcare logistics) accounted forinterdependencies across decision stages, improving responsiveness and adaptability. For example, inChapter 2, the sensitivity analysis conducted on the risk-averse model in last-mile delivery highlightsthe impact of high-risk scenarios, such as traffic congestion and adverse weather, on decision-making,including crowd-shipping, mobile depot locations, and hyper-local drivers. As risk parameters (Ïand λ) increase, decision-makers adopt more conservative policies, relying on hyper-local drivers forsame-day deliveries to avoid delays. This approach results in a 1.3% rise in the expected total costwhen comparing the scenario of Ï = 1 and λ = 0.25 to Ï = 0.25 and λ = 1. In turn, the CVaRvalue decreases by 4.6%. These changes emphasize the trade-off between cost and risk, where ahigher Ï and λ lead to higher total costs but also mitigate potential risks, especially in uncertainenvironments. The analysis underlines the importance of adjusting policies based on risk factorsto ensure reliable and flexible delivery operations, with managerial insights on how to balance costand risk in dynamic environments.2316.2.3 Development of Scalable Solution ApproachesThis dissertation proposed advanced solution methodologies to solve large-scale optimizationproblems efficiently. Chapter 3 developed parallel SDDiP algorithms that improve scalability andcomputational performance, enabling the analysis of larger and more complex instances. It alsocombineed sampling-based approaches such as SAA with decomposition techniques such as SD , andaccelerated version GTC-SD , for robust performance in large-scale cases. Lastly, this dissertationintroduced a novel integration of machine learning and data generation with optimization to improveaccuracy in uncertainty modeling. For example, in Chapter 3 the performance of the proposedSDDiP-MIR is compared with its variants SDDiP-SWLDC and SDDiP , using metrics suchas computational time, lower bound, and upper bound. The performance varies with instance size,planning horizon, and scenario sample size. For small instances, all models show low computationaltimes, but as the instance size increases, the computational time rises significantly, especially withlarger sample sizes. The study shows that sample size affects the accuracy and convergence of thealgorithm, with an optimal number of scenarios depending on the planning horizon: short horizonsbenefit from more scenarios, while long horizons benefit from fewer scenarios. The SDDiP-MIRconsistently outperforms SDDiP and SDDiP-SWLDC in large instances by demonstrating fastercomputation and more efficient decision-making. It achieves a smaller gap (7%) between the lowerand upper bounds, indicating more precise solutions. SDDiP-MIRâs performance improves withthe number of scenarios and decreases with a longer time horizon. The inclusion of hedging policiesfurther strengthens SC resilience by diversifying risks. The study confirms that SDDiP-MIR issuitable for dynamic and complex SC s, optimizing costs, resource utilization, and resilience.6.2.4 Addressing Real-World Challenges in Supply Chain ManagementBy applying the proposed models and frameworks to real-world case studies, this research demon-strated tangible improvements in SC responsiveness, cost-efficiency, sustainability, and time man-agement:â E-commerce: Enhanced last-mile delivery by reducing delivery times, carbon emissions, andtraffic congestion while managing urban traffic challenges with mobile depot, hyper-localdrivers, and crowd-shippers. More specifically, the proposed ORDAO outperforms IMAS inlast-mile delivery by achieving an 11% reduction in travel times, meeting all demand points,and dynamically adapting to real-time online orders through continuous reoptimization. Itsagility and responsiveness to uncertainties make it a more effective solution for last-mile de-232livery challenges, particularly in dynamic and time-sensitive scenarios.â Manufacturing: Improved resilience through hedging strategies, dynamic inventory manage-ment, and insights into supplier reliability and discount rate effects. A specific scenario in-volving delays in sourcing product components increased costs for production, sourcing, trans-portation, and labor by 15%, 8%, 38%, and 0.07%, respectively, emphasizing the importanceof strategic inventory management and supplier collaboration to mitigate financial impacts.Despite these cost increases, the model successfully maintained operations and met demand,demonstrating its adaptability and optimization capabilities under disruptions. This resilienceunderscores the modelâs robustness in managing disruptions and ensuring SC stability.â Healthcare Logistics: Significant reductions in vaccine shortages and improvements in vaccineaccessibility were achieved by dynamically optimizing the locations of mobile PHU s. WhenmobilePHU s are available, the overall shortage in the proposed vaccination network decreasesby 80% in comparison with the scenario that I do not have mobile PHU s, highlighting theirrole in quickly adapting to changing demands. Additionally, reallocating excess inventory toPHU s with shortages reduces the overall shortage by 52%, further optimizing the vaccinationnetwork.â Healthcare Logistics: Proposed a closed-loop SC network for masks, addressing both dis-tribution and recycling challenges, with significant cost, environmental, and service-level im-provements. In a disrupted scenario involving the unavailability of echelons, the proposedmodel responds by integrating alternative facilities to compensate for the disruption of criti-cal resources. While disruptions to warehouses and collection centers lead to increased costs,emissions, and reduced customer satisfaction, the model effectively mitigates these impactsthrough its contingency plan. Specifically, the total networkâs cost and emissions increase by9% and 2%, respectively, while customer service levels decrease by 13%.6.2.5 Some Practical Insights for Decision-MakersThe proposed IDSS provided actionable insights for SC managers and policymakers by demon-strating the effectiveness of real-time data integration, advanced optimization, and robust method-ologies. Key practical insights included:â Guidelines for reimbursement strategies to balance costs and participation in last-mile deliveryoperations (Chapter 2).â Strategies for managing supplier and resource disruptions in global SC s for manufacturing233industry (Chapter 3).â Recommendations for vaccine distribution policies to enhance equity and minimize shortages(Chapter 4).â Frameworks for sustainable and resilient SC designs that consider environmental, economic,and social dimensions (Chapter 5).6.2.6 Impact on Sustainability and ResiliencyBy incorporating the triple bottom line of sustainability (i.e., economic, environmental, andsocial objectives) and addressing disruptions such as pandemics and geopolitical conflicts, thisdissertation contributed to the growing field of sustainable SC management. It demonstrated howto balance efficiency with long-term resilience and adaptability to disruptive events, providing aframework for more sustainable and resilient SC networks.6.3 Limitations and Future Work RecommendationsThis section explains limitations, and I conclude with a number of suggestions for how thisresearch can further be expanded in the future.6.3.1 Possible Extensions for E-commerce Business LogisticsThe availability and quality of crowd-shippersâ availability data might not reflect real-worldcomplexities fully, such as sudden cancellations or delays.In Chapter 2, the study of IDSS design for e-commerce business logistics points to variouspromising directions for future research. These include the optimization of mobile depot routing,developing compensation fee policies to minimize postponement costs or order cancellation costsarising from crowd-shipper unavailability. Additionally, exploring novel strategies such as incorpo-rating smart lockers to enhance the delivery process, can be an avenue for further investigation.6.3.2 Possible Extensions for Resilient Global Supply Chain LogisticsThe effectiveness of the proposed IDSS relies on access to accurate and comprehensive real-world SC data, including demand patterns, supplier lead times, inventory levels, and disruptionscenarios. However, such data may not always be available due to proprietary restrictions, lack ofdetailed records, or inconsistencies in data collection processes across global SC entities.234In Chapter 3, the reliance on advanced technologies and data-driven approaches for the globalSC logistics and sourcing policies can be a possible extension for future research. Dynamic pricingand real-time data analytics, will become crucial, enabling companies to respond quickly to marketfluctuations and optimize revenues. SC s will be more resilient and agile by adopting blockchain toenhance visibility and traceability. Sustainable sourcing will become increasingly important, drivenby consumer demand and regulatory pressures. In addition, it would also be interesting to seethe computation time improvement if the Lagrangian dual problem is solved by a more advancedmethods, such as bundle method or column generation.6.3.3 Possible Extensions for Healthcare Logistics: Vaccine DistributionThe proposed IDSS for vaccine distribution assumes access to detailed datasets, such as popula-tion demographics, healthcare facility capacities, and mobility patterns. In real-world applications,such datasets are often incomplete, outdated, or unavailable precise modeling. Moreover, dataprivacy concerns, particularly in healthcare, may further restrict access to sensitive information.In Chapter 4, for further development in healthcare logistics such as vaccine distribution andplanning, it is essential to consider the distinct characteristics of various vaccines, including factorssuch as storage requirements, shelf life, distribution channels, and efficacy rates. Additionally,addressing uncertainty in key input parameters, such as vaccine waste rate, can be consideredanother future research direction. The proposed data-based framework can also be employed toaddress uncertainty in various problems with similar characteristics, such as limited available data.Consequently, another future research direction would be to focus on implementing this data-basedframework to manage uncertainty across different problems.6.3.4 Possible Extensions for Healthcare logistics: Mask Distribution andRecyclingRegarding the limitation of this case study, the SAA-SD and GTC-SD algorithms rely onpredefined scenario structures, which might not encompass all possible variations in a pandemicsetting.In Chapter 5, the adoption of reinforcement learning algorithms can be considered for futureavenue to support decision-makers in enhancing the resiliency of supply chain. While machinelearning and reinforcement learning techniques are commonly suggested, our rationale for theirapplication lies in their potential to enhance supply chain resilience. 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Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Bichler, Lukas
Milani, Abbas S.
Integrating resiliency in intelligent decision support systems for real-time management of disruptions in large-scale supply chains
Text