Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Larizadeh, Razieh
Master of Applied Science - MASc
University of British Columbia
Developing an efficient production plan requires considering sustainability practices and the dynamic nature of manufacturing environments. This helps minimize waste to align with sustainability goals, enhance operational efficiency for cost savings, and foster resilience to adapt to market dynamics, thereby ensuring viability. To achieve these goals in the plastic industry, exploring opportunities for recycling integration and adaptability to the uncertain nature of key parameters such as market demand and recycling rate is necessary. The reason stems from the fact that fluctuations in time-varying parameters can pose serious challenges to a predetermined static production plan and make it infeasible in the real world. Furthermore, adhering to sustainability practices is essential to mitigate the detrimental effect of plastic pollution on the ecosystem and to conserve valuable natural resources by decreasing the demand for virgin materials. This thesis develops a novel Data-driven Rolling Horizon Planning (DRHP) approach for a sustainable and dynamic production plan in the plastic industry. In this regard, a dynamic Rolling Horizon (RH) planning framework is formulated as a multi-product, multi-period Mixed Integer Linear Programming (MILP) model. This model aims at minimizing total production costs while taking into account the system’s constraints and sustainability considerations. To deal with uncertainty, the RH-based MILP model is coupled with a Long Short-Term Memory (LSTM) model. The LSTM model leverages historical data of market demand and recycling rate to predict future trends in time-varying parameters and consequently improve the efficiency of the production plan. The outperformance of the proposed DRHP approach is demonstrated through an extensive comparison with a robust static counterpart in terms of total production cost and sustainability measures. Results indicate significant reductions, up to 80%, in production costs using the proposed DRHP approach. Furthermore, the effect of various rolling durations is investigated regarding total production cost, backlog, late-order, and inventory level. Findings underscore the potential of utilizing the proposed DRHP approach to mitigate inventory- and late-order-related challenges.
A Novel Data-driven Rolling Horizon Production Planning Approach for the Plastic Industry under the Uncertainty of Demand and Recycling Rate by Razieh Larizadeh B.Sc., Bu-Ali Sina University, 2016 M.Sc., K. N. Toosi University of Technology, 2020 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) July 2024 © Razieh Larizadeh, 2024ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis entitled: A Novel Data-driven Rolling Horizon Production Planning Approach for the Plastic Industry under the Uncertainty of Demand and Recycling Rate submitted by Razieh Larizadeh in partial fulfillment of the requirements of the degree of Master of Applied Science. Dr. Babak Mohamadpour Tosarkani, School of Engineering Supervisor Dr. Qian Chen, School of Engineering Supervisory Committee Member Dr. Amir Ardestani-Jaafari, Faculty of Management Supervisory Committee Member Dr. Mohammad Hossein Zarifi, School of Engineering University Examiner iii Abstract Developing an efficient production plan requires considering sustainability practices and the dynamic nature of manufacturing environments. This helps minimize waste to align with sustainability goals, enhance operational efficiency for cost savings, and foster resilience to adapt to market dynamics, thereby ensuring viability. To achieve these goals in the plastic industry, exploring opportunities for recycling integration and adaptability to the uncertain nature of key parameters such as market demand and recycling rate is necessary. The reason stems from the fact that fluctuations in time-varying parameters can pose serious challenges to a predetermined static production plan and make it infeasible in the real world. Furthermore, adhering to sustainability practices is essential to mitigate the detrimental effect of plastic pollution on the ecosystem and to conserve valuable natural resources by decreasing the demand for virgin materials. This thesis develops a novel Data-driven Rolling Horizon Planning (DRHP) approach for a sustainable and dynamic production plan in the plastic industry. In this regard, a dynamic Rolling Horizon (RH) planning framework is formulated as a multi-product, multi-period Mixed Integer Linear Programming (MILP) model. This model aims at minimizing total production costs while taking into account the system’s constraints and sustainability considerations. To deal with uncertainty, the RH-based MILP model is coupled with a Long Short-Term Memory (LSTM) model. The LSTM model leverages historical data of market demand and recycling rate to predict future trends in time-varying parameters and consequently improve the efficiency of the production plan. The outperformance of the proposed DRHP approach is demonstrated through an extensive comparison with a robust static counterpart in terms of total production cost and sustainability measures. Results indicate significant reductions, up to 80%, in production costs using the proposed DRHP approach. Furthermore, the effect of various rolling durations is investigated regarding total production cost, backlog, late-order, and inventory level. Findings underscore the potential of utilizing the proposed DRHP approach to mitigate inventory- and late-order-related challenges. iv Lay Summary A sustainable and dynamic production plan in the plastic industry ensures addressing plastic waste challenges, and the viability of the plan under time-varying situations. This helps minimize production costs, integrate recycling practices, and adjust to market dynamics. This thesis proposes a Data-driven Rolling Horizon Planning (DRHP) approach, coupling a dynamic Rolling Horizon (RH)-based Mixed Integer Linear Programming (MILP) model with a Long Short-Term Memory (LSTM) model. The RH-based MILP model optimizes the production plan through an adaptive framework with the help of the LSTM model, which predicts the future values of uncertain parameters. This approach minimizes total production costs while considering the system’s constraints, sustainability considerations, and the uncertain nature of the problem. Comparative analysis demonstrates the superiority of the dynamic DRHP approach over a robust static counterpart, highlighting its ability to improve operational efficiency and sustainability measures. Findings indicate the importance of the rolling duration parameter in the DRHP approach, showing that shorter durations enhance production efficiency. Overall, the present thesis aims to underscore the potential of dynamic data-driven approaches for mitigating production planning challenges and improving sustainability under uncertainty. v Preface This thesis, entitled “A Novel Data-driven Rolling Horizon Production Planning Approach for the Plastic Industry under the Uncertainty of Demand and Recycling Rate”, is an original work conducted by Razieh Larizadeh under the supervision of Dr. Babak Mohamadpour Tosarkani at the Industrial & Systems Engineering (ISE) Research Group. To provide this thesis, generative AI was not used for any aspects of the work. To date, the data and results of this thesis have been submitted in the form of a journal paper to the “Expert Systems with Applications”. Furthermore, the following oral/poster presentations have been delivered through this research. • The 59th Annual Canadian Transportation Research Conference, Kelowna, Canada, 12-15 May 2024. • The 2024 PRRC Symposium on the Advancement in Plastic Recycling, University of British Columbia, Kelowna, Canada, 20 February, 2024. • The 2024 MMRI Symposium on Circular Economy, University of British Columbia, Kelowna, Canada, 21 February, 2024. • The 3rd Teach-in on Climate and Justice, University of British Columbia, Kelowna, Canada, March 12, 2024. vi Table of Contents Abstract .......................................................................................................................................... iii Lay Summary ................................................................................................................................. iv Preface............................................................................................................................................. v Table of Contents ........................................................................................................................... vi List of Tables ................................................................................................................................. ix List of Figures ................................................................................................................................. x List of Abbreviations .................................................................................................................... xii Acknowledgments........................................................................................................................ xiii Dedication .................................................................................................................................... xiv 1 Introduction ............................................................................................................................. 1 1.1 Motivation ....................................................................................................................... 1 1.2 Objectives ....................................................................................................................... 8 1.3 Thesis Outline ................................................................................................................. 9 2 Literature Review.................................................................................................................. 10 2.1 RH Planning .................................................................................................................. 10 2.1.1 RH-based Production Planning ............................................................................... 10 2.2 Data-driven Production Planning Optimization............................................................ 12 2.3 Demand Forecasting ..................................................................................................... 13 2.4 Literature Gap ............................................................................................................... 14 3 Problem Statement, Modeling, and Solution Approach ....................................................... 17 vii 3.1 Problem Description ..................................................................................................... 17 3.2 The RH-based Model .................................................................................................... 18 3.3 The Rolling LSTM Model ............................................................................................ 22 3.4 The Proposed DRHP Approach .................................................................................... 25 3.5 Robust Optimization ..................................................................................................... 27 3.5.1 Box Uncertainty Set-based Robust Optimization ................................................... 28 4 Results and Sensitivity Analysis ........................................................................................... 30 4.1 Data and Parameter Setting ........................................................................................... 30 4.2 Forecasting Accuracy Measure ..................................................................................... 32 4.3 Performance Evaluation ................................................................................................ 33 4.3.1 Evaluation of the LSTM Model .............................................................................. 33 4.3.2 Evaluation of the DRHP Approach ......................................................................... 37 4.4 Sensitivity Analysis ...................................................................................................... 42 5 Conclusions and Future Works ............................................................................................. 48 5.1 Thesis Summary............................................................................................................ 48 5.2 Research Contribution .................................................................................................. 49 5.3 Research Limitations .................................................................................................... 50 5.4 Future Research ............................................................................................................ 51 Bibliography ................................................................................................................................. 53 Appendices .................................................................................................................................... 60 Appendix A: The Static Counterpart ........................................................................................ 60 Appendix B: Synthetic Daily Demands .................................................................................... 64 viii Appendix C: Synthetic Daily Recycling Rates ......................................................................... 66 ix List of Tables Table 1. Plastic pollution at each life stage of a plastic product. .................................................... 3 Table 2. A summary of recent studies on production planning and scheduling. .......................... 15 Table 3. Parameter setting for the RH-based MILP model. ......................................................... 32 Table 4. Performance of the rolling LSTM model (RMSE) in predicting recycling rate and market demand based on different scenarios of rolling duration. ............................................................. 34 Table 5. Reduction in ATC (percentage) by adopting the DRHP approach instead of the robust static approach. ............................................................................................................................. 39 Table 6. Amount of raw material (kg) sourced through virgin plastic stream in the robust static approach. ....................................................................................................................................... 40 x List of Figures Fig.1. Global plastics production from 1950 to 2022. .................................................................... 1 Fig.2. Distribution of global plastics production by a) resource and b) application. ...................... 2 Fig.3. Cross-cutting impacts of plastic waste on the environment, wildlife and humans. .............. 4 Fig.4. Different methods of plastic waste treatment. ...................................................................... 6 Fig.5. Plastic recycling: challenges and solutions. ......................................................................... 7 Fig.6. Structure of a) an LSTM unit, and b) the employed LSTM network. ................................ 23 Fig.7. An example of the proposed RH planning framework. ...................................................... 25 Fig.8. Flow of parameters in the kth planning horizon. ................................................................. 26 Fig.9. Three different scenarios for daily market demand. ........................................................... 31 Fig.10. Three different scenarios for daily recycling rate. ............................................................ 31 Fig.11. Accuracy of the rolling LSTM model’s predictions (RMSE) for a) Recycling Rate Scenario 1 (RRS1), b) RRS2, and c) RRS3 in the Horizon era; Purple line: fine-tuned, orange line: non-fine-tuned. ..................................................................................................................................... 35 Fig.12 Accuracy of the rolling LSTM model’s predictions (RMSE) for a) Demand Scenario 1 (DS1), b) DS2, and c) DS3 in the Horizon era; Purple line: fine-tuned, orange line: non-fine-tuned........................................................................................................................................................ 36 Fig.13. Comparison between the DRHP approach and the robust static approach in terms of ATC (thousands) across different instances characterized by: a) DS1-RRS1, b) DS1-RRS2, c) DS1-RRS3, d) DS2-RRS1, e) DS2-RRS2, f) DS2-RRS3, g) DS3-RRS1, h) DS3-RRS2, and i) DS3-RRS3. ............................................................................................................................................ 38 Fig.14. Performance of the DRHP approach in terms of ATC across different instances characterized by: a) DS1-RRS1, b) DS1-RRS2, c) DS1-RRS3, d) DS2-RRS1, e) DS2-RRS2, f) DS2-RRS3, g) DS3-RRS1, h) DS3-RRS2, and i) DS3-RRS3. ..................................................... 41 xi Fig.15. Performance of the DRHP approach in terms of a) backlog (thousands), b) raw material inventory (thousands), c) final product inventory (thousands), and d) late-order (thousands). .... 42 Fig.16. Impact of improving uncertainty handling strategy on ATC (Thousands) in the DRHP approach: a) Average to LSTM and b) LSTM to Exact. .............................................................. 43 Fig.17. Performance of the RH-based model across different rolling durations in terms of backlog........................................................................................................................................................ 44 Fig.18. Performance of the RH-based model across different rolling durations in terms of raw material inventory. ........................................................................................................................ 44 Fig.19. Performance of the RH-based model across different rolling durations in terms of final product inventory. ......................................................................................................................... 45 Fig.20. Performance of the RH-based model across different rolling durations in terms of late-order. ............................................................................................................................................. 45 Fig.21. Impact of rolling duration on a) backlog (thousands), b) raw material inventory (thousands), c) final product inventory (thousands), and d) late-order (thousands) in the DRHP approach. ....................................................................................................................................... 46 Fig.22. Sensitivity analysis on different elements of production cost in terms of ATC (thousands)........................................................................................................................................................ 47 xii List of Abbreviations ANN Artificial Neural Network CNN Convolutional Neural Network DRHP Data Rolling Horizon Planning DRL Deep Reinforcement Learning DS Demand Scenario HDPE High-Density Polyethylene KDE Kernel Density Estimation LDPE Low-Density Polyethylene LSTM Long Short-Term Memory MILP Mixed Integer Linear Programming PET Polyethylene Terephthalate PP Polypropylene PS Polystyrene PSO Particle Swarm Optimization PVC Polyvinyl Chloride RC Robust Counterpart RH Rolling Horizon RMSE Root Mean Squared Error RNN Recurrent Neural Network RRS Recycling Rate Scenario xiii Acknowledgments My sincere gratitude goes to my supervisor, Dr. Babak Mohamadpour Tosarkani, for his invaluable guidance, support, and wisdom throughout my academic journey. His continuous encouragement and insightful feedback have contributed a lot to this thesis. Additionally, I express my appreciation to my committee members, Dr. Amir Ardestani-Jaafari and Dr. Qian Chen, for their informative suggestions and precious insights. I am deeply thankful for the support provided by my colleagues at the Industrial & Systems Engineering (ISE) Research Group, especially Samuel Yousefi, whose support and care have been invaluable to me. My heartfelt appreciation also goes to my dear family and friends for their unwavering presence and encouragement, which have been a source of warmth and strength throughout this chapter of my life. Furthermore, I would like to thank the Syilx Okanagan Nation for the use of their ancestral and unceded territory, the land on which my research was conducted. xiv Dedication In loving memory of my mother, who may have left this world, but her spirit forever lives on within me. 1 1 Introduction This introductory chapter elaborates on the underlying motivations driving the research and the objectives pursued within this thesis. Additionally, an outline of the thesis is provided to offer a preview of the next chapters. 1.1 Motivation The use of plastics has expanded across various industries due to their advantageous properties such as durability, ability to resist erosion, versatility, and affordability (Chen et al., 2021; Joseph et al., 2021; Zhang et al., 2021; Tosarkani et al., 2024). As a result, there has been a significant surge in global plastic production over the past few years. The annual worldwide production of plastics in 2022 (400.3 million metric tons) was reported to be 266 times higher than in 1950 (1.5 million metric tons) (Jaganmohan, 2024), see Figure 1. Fig.1. Global plastics production from 1950 to 2022. Approximately 90% of global plastic production is sourced from fossil-based feedstocks, with packaging representing its primary application at 44% (Plastics – the facts, 2022), see Figure 2. Plastic packaging comes in different forms (e.g., beverage bottles and food containers) to serve different purposes. Common types of plastics utilized in the packaging industry include Polyethylene Terephthalate (PET), High-Density Polyethylene (HDPE), Low-Density 050100150200250300350400PRODUCTION VOLUME IN MILLION METRIC TONESYEAR2 Polyethylene (LDPE), Polypropylene (PP), Polystyrene (PS), and Polyvinyl Chloride (PVC) (Rabnawaz et al., 2017). Fossil-based plastics differ from bio-based plastics in terms of their sources of raw materials and their environmental impacts. (Walker and Rothman, 2020). Bio-based plastics are sourced from renewable materials like plants or algae and are more environmentally friendly than fossil-based plastics. The reason lies in their lower carbon footprint and potential biodegradability. However, concerns about land use and competition with food crops remain. On the other hand, fossil-based plastics, derived from non-renewable resources like petroleum, are criticized for their environmental impact, including greenhouse gas emissions and long-lasting pollution. Fig.2. Distribution of global plastics production by a) resource and b) application. Reducing the industry’s reliance on virgin plastics by replacing recycled plastics can significantly help conserve natural resources (Shen and Worrell, 2024). Table 1 presents an overview of the pollution generated at each phase of a plastic product's lifecycle, from resource extraction to disposal and remediation (Kassotis et al., 2015; Muncke et al., 2020; Jayathilaka et al., 2022; Ramasamy et al., 2022; Fernandez and Trasande, 2024). Adopting recycling practices helps eliminate pollution stemming from resource extraction and polymer production. Moreover, it results in mitigating the environmental impact of the transportation stage, as local collection, recycling, and remanufacturing reduce the transportation phase between virgin plastic suppliers and manufacturers. 90.20%8.30% 1.50%390.7 Mtin 2021Fossil-based plasticsPost-consumerrecycled plasticsBio-based/attributedplasticsa)44%18%8%7%7%4%12%390.7 Mtin 2021PackagingBuilding andConstructionAutomativeElectrical andElectronicsHousehold, Leisureand SportsAgriculture, Farmingand GardeningOthersb) 3 Table 1. Plastic pollution at each life stage of a plastic product. No. Stage Pollution 1 Resource extraction CO2, CH4, fracking water, oil pills, chemicals, fertilizers and pesticides. 2 Polymer production Pellet/nurdle loss, loss of flakes and powder, CO2, CH4, hazardous air pollutants, micro-/nano-plastics pollution, airborne microplastics, monomers and polymers, non-intentionally added substances (e.g., formaldehyde), chemicals, etc. 3 Product manufacturing Micro-/nano-plastics pollution, pellet/nurdle loss, microfibers, general microplastics/paint fragments in wastewater, loss of flakes and powder, monomers and polymers, chemicals, etc. 4 Transportation and trade CO2, micro-/nano-plastics pollution (pellet loss, airborne microplastics, litter, fragmentation), unintentional releases of pellets, flakes and powders, monomers and polymers, chemicals, etc. 5 Commercial, industrial and consumer use Tire dust, paint dust, microfibers, cigarette butts, fishing gear, agricultural plastics, microplastics, littering (e.g. food packaging), monomers and polymers, endocrine-disrupting and other chemicals, etc. 6 Waste management and recycling Microplastics, heavy metals, CO2, CH4, monomers and polymers, chemicals, etc. 7 Removal and remediation Micro-/nano-plastics, monomers and polymers, microfibers, endocrine-disrupting and other chemicals, etc. 4 Transportation Extraction Production 12% Environment and landfills Waste collection Consumer Global warming and climate change Sea level rise and heavy rainfalls Wildfires Rivers, lakes, and oceans Water contamination Entanglement of marine animals Additives leakage Ingested microplastic in marine organisms Soil contamination Incineration 79% 9% Recycling Human life Plants Wildlife Degradation Microplastics Air Wind Underground water contamination Soil quality degradation Absorption Absorption Respiratory diseases Rivers Runoff Food chain Food chain Food chain Microplastics Additives leakage Degradation Fig.3. Cross-cutting impacts of plastic waste on the environment, wildlife and humans. 5 About 9% of plastic waste is recycled, 12% is incinerated, and the rest ends up in landfills and the environment (Geyer et al., 2017; Plastic waste and pollution reduction, 2023). Figure 3 depicts the cross-cutting impacts of plastic waste directed into landfills, waste-to-energy facilities, or the environment. The blue lines represent the physical flow, and the red lines denote the consequential impacts. Discarded plastics in the environment can be blown into rivers or lakes, or go down the storm drain and end up in the oceans (Zero plastic waste, 2021). Marine litters can transfer contaminants, damage marine habitats, impact fisheries, and cause harm to wildlife through ingestion or entanglement (Geyer et al., 2017; Zero plastic waste, 2021; Gondal et al., 2023). Toxic leachate from plastic waste in the surrounding environment and landfills contaminate soil and deteriorate the surrounding land (Geyer et al., 2017; Cao et al., 2023; Gondal et al., 2023; Kibria et al., 2023). Furthermore, ultraviolet light can break down plastic waste into smaller fragments called microplastics, which can persist in the environment for hundreds or thousands of years. Microplastics are ingested by aquatic and terrestrial organisms and can enter the food chain, potentially harming wildlife and humans who consume contaminated foods (de Souza Machado et al., 2018; Evode et al, 2021; Kurniawan et al., 2021). As these microscopic plastic particles disperse into the atmosphere, they exacerbate the greenhouse effect, intensifying global warming (Geyer et al., 2017; Gondal et al., 2023). Additionally, inhalation of airborne microplastics poses serious health risks, such as respiratory diseases and other pulmonary complications (Geyer et al., 2017; Gondal et al., 2023). These all highlight the importance of employing recycling practices to mitigate the harmful impacts of discarded plastic waste. Following the collection, sorting, and cleaning, there are four common standard recycling methods to treat plastic waste: (i) physical recycling, (ii) mechanical recycling, (iii) chemical recycling, and (iv) energy recovery (Faraca et al., 2019; Hahladakis and Lacovidou, 2019; Joseph et al., 2021), see Figure 4. These methods are differentiated based on the technology employed and the output of the recycling process. Among the different recycling methods, mechanical recycling stands out as a well-established and industrially feasible one (Shamsuyeva and Endres, 2021). This method transforms plastic waste into secondary raw materials while maintaining the chemical structure of the original polymer largely intact (Shamsuyeva and Endres, 2021). This process involves various stages, including collection, inspection, segregation, sorting, washing, shredding, and extrusion, which can vary to some extent depending on the plastic type and employed technologies (Joseph 6 et al., 2021). In the mechanical recycling method, material recovery facilities receive collected waste and classify it into distinct types (e.g., PET, HDPE, LDPE, PP, PS, and PVC). These sorted materials are then processed into secondary raw materials such as flakes, pellets, or granules, suitable for manufacturing new products. Fig.4. Different methods of plastic waste treatment. Although environmentally friendly, recycling practices face challenges, both technically and economically, in real-world implementation, see Figure 5. At a strategic level, policymakers can intervene to promote recycling programs and green production. Their initiatives usually include establishing minimum targets for recycled materials, enforcing recycling labels to denote recyclability, and implementing systems that encourage consumer preference for green products made from recycled plastics (Shamsuyeva and Endres, 2021). 7 Fig.5. Plastic recycling: challenges and solutions. Mandatory approaches, incentives, and advisory guidelines should be accompanied by manufacturing management strategies. This helps to justify recycling practices from an economic perspective and to secure the genuine commitment of industrial partners to sustainability. Manufacturing management involves planning, organizing, directing, and controlling resources such as people, materials, equipment, and technology to ensure that customer needs are met on time at the minimum possible production cost (Kumar, 2022). This encompasses various activities such as production scheduling, raw material sourcing, and inventory management (Kumar, 2022). The ultimate goal of manufacturing management is to maximize efficiency, minimize costs, and increase the profitability of the production system (Kumar, 2022). Incorporating recycling practices into production planning necessitates a comprehensive analysis of the system and an examination of challenges and barriers. Depending on factors such as material type, purity, and complexity, as well as recycling technologies, sorting and recycling rates may vary across different facilities (Antonopoulos et al., 2021). Consumption patterns, social awareness, weather conditions, anomalies, events, distance to recycling collection points, and recycling policies are among the other factors influencing the efficiency of recycling programs (Reijonen et al., 2021; Ahmed et al., 2022; Williams and Phillips, 2022). For instance, the plastic waste recycling rate is thirteen times higher when collected separately compared to mixed collection schemes (Plastics – the facts, 2022). In addition to the 8 recycling rate, production plants encounter uncertainty in market demand. Demand fluctuates over time due to various factors such as market trends, consumer preferences, and seasonal variations. Both recycling rate and market demand are potential parameters whose fluctuation can impact predetermined production decisions (e.g., raw material sourcing, production schedules, inventory management, production costs, and sustainability goals). Most previous studies have focused on addressing production planning problems through predetermined static approaches. In a static, also known as offline, approach, it is assumed that the problem's input data are available prior to planning and the entire scheme is preplanned in advance (Furini et al., 2015; Lu et al., 2016; Koskinen et al., 2020). However, employing static approaches to tackle real-world optimization problems is not always feasible, given that accurate and reliable information is usually unavailable for the entire planning scheme beforehand (Lu et al., 2023). Consequently, solutions generated using static approaches, based on the assumption of complete and accurate input data, may significantly deviate from optimality and result in excessive costs (Lu et al., 2016). On the contrary, dynamic approaches take into account the change in input data, recognizing that the information available to decision-makers may evolve over time (Dehghan Shoorkand et al., 2023; Forel and Grunow, 2023). Dynamic approaches incorporate considerations for data uncertainty and are adjusted in accordance with updated real-time information (Lu et al., 2016). Considering the time-varying nature of input data, conventional static models are inefficient for production planning in dynamic real-world production systems. 1.2 Objectives In this thesis, a novel dynamic Data-driven Rolling Horizon Planning (DRHP) approach is developed to optimize production planning in the plastic industry, incorporating recycling opportunities and considering the uncertainty of parameters. In this regard, a novel multi-product, multi-period Rolling Horizon (RH)-based Mixed-Integer Linear Programming (MILP) model is developed for sustainable and dynamic production planning. The aim is to minimize total production costs, including costs of raw material sourcing, recycling activities, production activities, and inventory holding, as well as unfulfilled demand, backlogs, and late-order. The planning of each horizon in this model, involving operational and forecasting periods, is affected 9 by the previous horizon’s predictions, newly updated data, and forecasts for the next horizon’s demand and recycling rate. Therefore, a Long Short-Term Memory (LSTM) model is coupled with the RH-based model to review and update the predictions of time-varying parameters continuously. As rolling duration is a key parameter affecting prediction accuracy and total production costs, a comprehensive analysis is also conducted to investigate its impacts. The performance of the developed DRHP approach is evaluated against its robust static counterpart in terms of total production cost and sustainability considerations. 1.3 Thesis Outline The thesis consists of five chapters and two appendices. Chapter 2 provides a literature review on the applications of RH approaches in time-dependent optimization problems, along with recent studies integrating optimization techniques with Deep Learning models. Additionally, a comparative analysis of recent research in the production planning literature is provided in this chapter to highlight the research gap. Chapter 3 explains the developed RH-based mathematical model and the proposed DRHP approach as well as its robust static counterpart. The performance of the proposed approach is evaluated across different instances and results are discussed in chapter 4. Finally, Chapter 5 summarizes the main findings of the thesis and offers suggestions for future research directions. Appendix A details the developed static MILP model counterpart of the RH-based model. Appendices B and C provide the step-by-step process of generating synthetic historical data of demand and recycling rate. 10 2 Literature Review In this chapter, a comprehensive literature review is conducted to explore various aspects of the thesis, including RH planning, demand forecasting, and data-driven optimization. Furthermore, the research gaps and challenges of the topic are discussed in details. 2.1 RH Planning Today, most optimization problems are formulated over a set of time periods. To tackle optimization problems having a time dimension, RH approaches have been widely used in different areas such as production planning (Clark, 2005; Li and Ierapetritou, 2010; Ziarnetzky et al., 2018; Koskinen et al., 2020; Wu et al., 2020; Torkaman et al., 2022), transportation planning (Furini et al., 2015; Cavagnini et al., 2022; Zaneti et al., 2022; Lu et al., 2023), energy planning (Marquant et al., 2015; Cuisinier et al., 2022; Shalaby et al., 2022; Abedi and Kwon, 2023), and supply chain management (Lu et al., 2016; Fattahi and Govindan, 2022). RH approaches decompose the computationally expensive main problem into smaller ones that can be solved within a reasonable time. Glomb et al. (2022) introduced a framework to apply an RH approach in various large-scale optimization problems with a time dimension. They outlined conditions under which this framework could guarantee the optimality of the generated solutions. In addition to time-dependent problems, RH approaches have been proven beneficial in dynamic and uncertain environments, where conditions may be subject to changes (Ziarnetzky et al., 2018; Fattahi and Govindan, 2022; Shalaby et al., 2022; Abedi and Kwon, 2023; Dehghan Shoorkand et al., 2023; Forel and Grunow, 2023). 2.1.1 RH-based Production Planning Given the dynamic nature of production environments, RH approaches can effectively address multi-period production planning problems. Tolio and Urgo (2007) developed an RH-based model to address the challenges of production planning and outsourcing under uncertainty. They incorporated the uncertain nature of resource needs by formulating the problem within a scenario-based framework. Their proposed RH approach was based on a two-stage stochastic programming method, accounting for multiple uncertain scenarios. The results highlighted the advantages of 11 their proposed model over planning approaches based only on the expected values of uncertain variables. Li and Ierapetritou (2010) leveraged an RH approach to incorporate production capacity information into the integrated production planning and scheduling problem. The findings indicated that a precise capacity model led to near-optimal solutions. This improvement was credited to the planning model's capability to forecast future costs associated with potential backorders when informed by production capacity data. Torkaman et al. (2022) studied the problem of production-routing with price-dependent demand within an outer approximation framework. They solved the primal problem using a non-linear programming solver, but to tackle the mixed integer programing master problem, they developed four different RH-based heuristics. They showed the outperformance of their proposed heuristics in addressing the computationally expensive master problem compared to other algorithms, with minimal or no deviation from the optimal solution. Ziarnetzky et al. (2018) showed the improved performance of a chance-constrained water fab production planning model incorporating demand forecast updates. In this regard, they employed the multiplicative martingale model of forecast evolution. They illustrated the outperformance of the RH-based model in terms of expected service level and profit by effectively considering safety stocks. Forel and Grunow (2023) developed a dynamic stochastic, capacitated lot-sizing methodology adapted to RH planning. They integrated forecast evolution models into lot-sizing formulations, efficiently incorporating cumulative demand distributions using linearization techniques. The authors proved the effectiveness of the proposed method through a large-scale numerical analysis with real-world and synthetic data. The results demonstrated a significant cost reduction compared to traditional deterministic and stochastic methods relying only on demand history. Dehghan Shoorkand et al. (2023) considered data-driven predictive maintenance in a multi-period, multi-product capacitated lot-sizing problem based on an RH approach. They integrated an LSTM model with an RH-based model to dynamically forecast and update the health conditions of machines along with tactical production decisions. The proposed integrated approach was validated on a set of benchmarks, and its outperformance over other solution approaches was shown. In addition to production planning, the integration of data-driven models with RH approaches has attracted attention in other domains. Abedi and Kwon (2023) developed an RH-based optimization model aimed at improving the efficiency of battery energy storage operations. They coupled the RH-based model with an LSTM model to address the 12 uncertainty of demand, price, and solar power generation. The proposed integrated model iteratively forecasted uncertainty and optimized operational decisions. Evaluation against an offline model demonstrated the satisfactory performance of their proposed model. 2.2 Data-driven Production Planning Optimization Data-driven optimization has recently attracted great interest across various industries and academic research. Data-driven optimization approaches widely employ machine learning and other artificial intelligence techniques, often coupled with mathematical optimization models, to optimize processes and systems. Data-driven optimization enables decision-makers to address the challenges of coordinating various elements of an optimization problem in dynamic environments by integrating medium-term planning and short-term scheduling (Ziarnetzky et al., 2018; Hubbs et al., 2020; Santander et al., 2020; Beykal et al., 2022; Lee and Lee, 2022; Vieira et al., 2022; Dehghan Shoorkand et al., 2023). In the field of production planning, Hubbs et al. (2020) proposed a Reinforcement Learning (RL) model to dynamically schedule a single-stage multi-product chemical process. Their study demonstrated the superior performance of the approach compared to conventional scheduling based on a receding horizon MILP model. The authors argued that handling uncertainty through simulation techniques is more advantageous than within a mathematical programming framework. Beykal et al. (2022) developed a data-driven optimization approach for the integrated problem of production planning and scheduling under uncertain demand. They extended a mixed-integer bi-level multi-follower programming, based on the DOMINO algorithm, and conducted stochastic analysis of various product demand scenarios to provide feasible solutions for complex industrial processes. Lee and Lee (2022) employed a Deep Reinforcement Learning (DRL) algorithm (i.e., deep Q-network) to optimize production scheduling. They aimed to ensure a realistic decision-making process considering the complex re-entry characteristic and long lead times in the semiconductor industry. They showed that by a novel state-action-reward formulation, the DRL method outperforms other dispatching rules, offering robust solutions in dynamic manufacturing environments with high uncertainty. Vieira et al. (2022) proposed a recursive optimization-simulation approach to facilitate decision-making for efficient production planning and scheduling in a human-robot collaborative environment. This approach determined plans through a two-level MILP model and iteratively evaluated them by a 13 discrete-event simulation model in order to guarantee capacity-feasible solutions at the scheduling level. The authors reported a significant improvement in operational decisions by implementing the hybrid approach. 2.3 Demand Forecasting Production planners should determine daily production quantity so as to meet market demand at the minimum production costs while meeting system constraints. Market demand is a key parameter in production planning problems, given its potential to significantly impact production scheduling, raw material sourcing, and inventory-related decisions. Given the case study of PET bottles in this thesis, exploring the forecasting models employed to predict urban daily water consumption is beneficial. When dealing with demand forecasting, statistical methods stand out as efficient tools. Du et al. (2020) proposed an auto-regressive integrated moving average model combined with a Markov chain. This thesis showed that the prediction error of their proposed model on the test set can be considerably reduced by using the Markov model for predicting data trends. With the growing application of Artificial Neural Network (ANN)-based methods in predictive analysis, they have emerged as a popular choice for demand forecasting across diverse industries and domains. Farah et al. (2019) employed a feed-forward back-propagation ANN model to forecast water consumption on the campus of Lille University. The results highlighted the acceptable performance of the ANN model on both daily and hourly analyses, including peak values. Benítez et al. (2019) indicated that good prediction accuracy can be heavily challenged by the inclusion of various seasonality patterns. In this regard, they adopted a pattern-similarity method, removing the need for annual seasonality determination and extending the horizon of prediction to 24 hours. Kühnert et al. (2021) reported the outperformance of LSTM models over other conventional methods previously employed. They showed that LSTM models can capture and integrate the effect of seasonality and events on water demand while only requiring a couple of days of training data. To address the inherent uncertainty in water demand, Du et al. (2022) developed a hybrid model that combines LSTM networks with Kernel Density Estimation (KDE). They optimized their proposed model by employing the Particle Swarm Optimization (PSO) algorithm. The 14 authors utilized the hybrid KDE-PSO-LSTM for predicting intervals of urban water demand, incorporating a novel splitting strategy to classify prediction errors into different levels. By optimizing bandwidth parameters and applying a confidence-window shifting method, the model aimed to accurately quantify uncertainties in predictions and facilitate water supply planning. Pu et al. (2023) integrated wavelet multi-resolution analysis into a Convolutional Neural Network (CNN)-LSTM model for short-term water demand forecasting. Their objective was to assist water utilities in reducing energy costs and mitigating unforeseen disruptions. They demonstrated the superior performance of the hybrid wavelet-CNN-LSTM model compared to previously used models in the literature, achieving enhanced accuracy in both single- and multi-step predictions. Iwakin and Moazeni (2024) proposed a probabilistic forecasting method for predicting future water consumption patterns, considering the inherent uncertainties in the system. By leveraging statistical techniques, they developed a conformal prediction-based hybrid demand forecast model, incorporating CNN and bidirectional LSTM. Validation in real-world settings demonstrated the effectiveness of the proposed framework in generating accurate deterministic demand forecasts and reliable adaptive probability estimates. Overall, the literature demonstrates the potential advantages of ANN-based methods for enhancing decision-making and resource management within water distribution systems. 2.4 Literature Gap Table 2 presents a comparative analysis of recent studies addressing production planning problems by highlighting different aspects. A thorough review demonstrates a research gap in the literature concerning dynamic production planning that incorporates sustainability opportunities and considers uncertainty challenges with an analysis of updating strategies. To address this gap, the present thesis develops a dynamic multi-product, multi-period RH-based optimization model tailored for production planning in the plastic industry considering recycling opportunities. To tackle uncertainty, the proposed mathematical model is augmented with an LSTM model to forecast future values of market demand and recycling rate. Additionally, the thesis conducts a sensitivity analysis on rolling duration, a key parameter in RH planning that directly affects updating strategies. 15 Table 2. A summary of recent studies on production planning and scheduling. Authors Industry Mathematical optimization models Multi-period programming Data-driven techniques Sustainability considerations Uncertain environment Dynamic environment Analysis of updating policy Methodology Ziarnetzky et al. (2018) Semiconductor fabrication ✓ ✓ - - ✓ ✓ - Rolling horizon planning Rossit et al. (2019) Cyber-physical production system - - ✓ - ✓ ✓ - Big data techniques Kamal et al. (2019) - ✓ - - ✓ ✓ - - Fuzzy goal programming Hubbs et al. (2020) Chemical production process ✓ ✓ ✓ - ✓ ✓ - Deep reinforcement learning and receding horizon planning Kim et al. (2020) Construction industry - ✓ - - ✓ ✓ - Discrete-time simulation Mohammadi et al. (2020) Furniture manufacturing ✓ - - - - - - Hybrid particle swarm optimization algorithm Morariu et al. (2020) - - ✓ ✓ - ✓ ✓ - Big data and machine learning Rodríguez et al. (2020) Industrial hospital laundry - - ✓ - ✓ ✓ - Fuzzy logic and machine learning Santander et al. (2020) Chemical manufacturing ✓ ✓ - - ✓ ✓ - - Sehovac and Grolinger (2020) Electricity planning - ✓ ✓ ✓ ✓ ✓ - Attention mechanism and long short-term memory Goli et al. (2021) - ✓ - - - ✓ - - A hybrid of genetic algorithm and wale optimization algorithm Guo et al. (2021) - ✓ - - ✓ ✓ - - Stochastic hybrid discrete grey wolf optimizer Villalonga et al. (2021) Cyber-physical production system - - ✓ - ✓ ✓ - Fuzzy logic and machine learning 16 Authors Industry Mathematical optimization models Multi-period programming Data-driven techniques Sustainability considerations Uncertain environment Dynamic environment Analysis of updating policy Methodology Beykal et al. (2022) - ✓ ✓ ✓ - ✓ - - DOMINO algorithm Gahm et al. (2022) Metal processing - - ✓ - ✓ - - Machine learning algorithms Lee and Lee (2022) Semiconductor fabrication ✓ ✓ ✓ - ✓ ✓ - Deep reinforcement learning Vieira et al. (2022) - ✓ ✓ - - ✓ ✓ - Recursive optimization-simulation approach Zhang et al. (2022a) - - ✓ ✓ - ✓ ✓ - Deep reinforcement learning Zhang et al. (2022b) - ✓ - - - - - - Hierarchical multi-strategy genetic algorithm Dehghan Shoorkand et al. (2023) - ✓ ✓ ✓ - ✓ ✓ - Rolling horizon planning Ghaedy-Heidary et al. (2023) Semiconductor manufacturing ✓ - - - ✓ - - Simulation optimization, and genetic algorithm Hameed and Schwung (2023) Injection molding - - ✓ - - ✓ - Tabu search, genetic algorithm, and reinforcement learning Yağmur and Kesen (2023) - ✓ - - ✓ - - - Partial local search and non-dominated sorting genetic algorithm-ii Zhang et al. (2023) - ✓ - - - - - - Improved artificial bee colony algorithm Tosarkani et al. (2024) Plastic industry ✓ ✓ ✓ ✓ ✓ - - Multi-objective data-driven stochastic possibilistic programming Current thesis Plastic industry ✓ ✓ ✓ ✓ ✓ ✓ ✓ Data-driven rolling horizon planning 17 3 Problem Statement, Modeling, and Solution Approach This chapter offers a thorough explanation of the problem. Furthermore, mathematical model and the proposed DRHP approach are presented in details. 3.1 Problem Description In this thesis, production planning is defined as a series of decisions regarding production scheduling, raw material sourcing, and inventory management. Unlike conventional planning, which adheres to predetermined decisions throughout the entire planning scheme, the present thesis introduces a dynamic framework that allows for the integration of updated data to adjust production planning accordingly. In this thesis, demand and recycling rate are considered uncertain parameters whose actual values are gradually revealed over time. Once a raw material order is placed, whether through virgin plastic or a recycling stream, it is considered irrevocable. In a case where a recycling stream is selected, the quantity of the sourced plastic waste is calculated based on the forecasted recycling rate. Upon receiving the order and determining its actual recycling rate, the actual-added raw material is ascertained accordingly. This value is then replaced with its forecasted value and the production plan is updated. The reason is that the raw material inventory level considerably affects total costs and subsequent production decisions. In addition to the recycling rate, forecasted future demand is another determinant influencing the production systems in terms of production scheduling and raw material sourcing. The production plan is updated consistently by evolving the available information on actual market demand. This is due to the fact that market demand can markedly influence the backlog and the inventory level. The accuracy of recycling rate and market demand predictions is crucial, especially considering penalties for raw material late-order, unfulfilled demand, and production capacity constraints. The primary objective of this thesis is to demonstrate the advantages of the proposed dynamic data-driven optimization approach to improve production costs and sustainability considerations. This approach integrates both short- and medium-term decisions without compromising the effectiveness of either. 18 3.2 The RH-based Model RH planning is an adaptive approach that involves updating a plan over time as new information becomes available (Cuisinier et al., 2022; Fattahi and Govindan, 2022; Glomb et al., 2022; Abedi and Kwon, 2023; Dehghan Shoorkand et al., 2023; Forel and Grunow, 2023). The main idea is to break a longer-term planning problem into a series of shorter-term planning horizons and to update the plan as new information becomes available (Tolio and Urgo, 2007; Li and Ierapetritou, 2010). In an RH approach, a plan is initially created for the first horizon, typically covering a short period of time. As the first horizon comes to an end, the plan is adjusted for the next horizon, taking into account the current system status, updated information, and forecasts of the future. This iterative process is repeated for subsequent horizons as well. This approach enables planners to respond quickly to changes in the environment (e.g., unexpected events or changes in market conditions), and to make more accurate and informed decisions. In this thesis, the production planning problem is defined under H horizons. It is assumed that each horizon consists of Θ operational periods and Ξ forecasting periods (Θ ≤ Ξ), each period spanning τ days. The parameters Θ and Ξ are introduced to define the durations of operational and forecasting sets, with the assumption that raw material delivery/preparation takes Θ𝜏 days. At the beginning of each horizon, the actual demands for operational periods (the first Θ𝜏 days) are available, while forecasting periods remain uncertain. The developed production plan of each horizon is mandatory to be implemented within the operational periods, yet it can be further modified for the forecasting periods by moving to the subsequent horizons. Regular raw material orders, whether recycled or virgin plastics, are placed at the beginning of the operational set and are received at the beginning of the forecasting set of the same horizon. The order for the plastic waste stream (if decided) is placed based on a predicted recycling rate, while the actual-added raw material is further revealed based on the actual recycling rate. Raw material late-order aims to compensate for raw material shortage resulting from overestimating the recycling rate in the previous horizon. Late-order is placed and received at the beginning of the operational set in each horizon. By moving to the next horizon (shifting Θ𝜏 days forward), new operational and forecasting sets are defined, and the optimization process is repeated. 19 The developed RH-based MILP model is defined as follows for each realization of the horizon ℎ. Indices: 𝑡 Days; t = (ℎ − 1)Θ𝜏 +1, …., (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏. 𝑝 Type of raw materials/products; 𝑝 = 1, … , 𝑃. Parameters: 𝐷𝑝𝑡ℎ Demand of product p on day t during operational periods of horizon h (unit). 𝐷′𝑝𝑡ℎ Predicted demand of product p on day t during forecasting periods of horizon h (unit). 𝑅𝑅′𝑝ℎ Predicted recycling rate of the plastic waste type p in horizon h (percent). 𝐿𝑝ℎ Actual amount of raw material type p sourced through recycling stream for horizon h (kg). 𝑋𝑝ℎ Actual amount of raw material type p sourced through virgin plastics stream for horizon h (kg). 𝑃𝑐𝑎𝑝𝑝𝑡ℎ Production capacity for product type p on day t in horizon h (unit). 𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ Inventory cost of raw material type p on day t in horizon h ($ per kg). 𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ Inventory cost of final product type p on day t in horizon h ($ per unit). 𝐶𝑑𝑜𝑝ℎ Late-order cost for virgin plastic type p in horizon h ($ per kg). 𝐶𝑝𝑟𝑜𝑝𝑡ℎ Production cost of product type p on day t in horizon h ($ per unit). 𝐶𝑏𝑙𝑝𝑡ℎ Backlog cost of product type p on day t in horizon h ($ per unit). 𝐶𝑣𝑝𝑝ℎ Cost of virgin plastic type p in horizon h ($ per kg). 𝐶𝑤𝑝𝑝ℎ Cost of plastic waste type p in horizon h ($ per kg). 𝐶𝑟𝑝ℎ Cost of recycling plastic waste type p in horizon h ($ per kg). 𝐶𝑐𝑣𝑝ℎ Contract cost for virgin plastic type p in horizon h ($). 𝐶𝑐𝑤𝑝ℎ Contract cost for plastic waste type p in horizon h ($). 𝐼𝑛𝑣𝑟𝑝ℎ Inventory of raw material type p at the beginning of horizon h (kg). 𝐼𝑛𝑣𝑓𝑝ℎ Inventory of final product type p at the beginning of horizon h (unit). 𝛼𝑝 Unitary raw material consumption for product type p (percent). 𝑀 A very large positive number. 20 𝜀 A very small positive number. Decision variables: 𝑘𝑝ℎ Amount of late-order raw material type p in horizon h (kg). 𝑙′𝑝ℎ Amount of raw material type p expected to be sourced through recycling stream for forecasting periods in horizon h (kg). 𝑝𝑞𝑝𝑡ℎ Number of product type p produced on day t in horizon h (unit). 𝑠𝑞𝑝𝑡ℎ Number of product type p sold on day t in horizon h (unit). 𝑖𝑛𝑣𝑟𝑝𝑡ℎ Inventory of raw material type p at the end of day t in horizon h (kg). 𝑖𝑛𝑣𝑓𝑝𝑡ℎ Inventory of final product type p at the end of day t in horizon h (kg). 𝑣′𝑝ℎ Equals 1 if virgin plastic type p contributes to raw material sourcing for forecasting periods in horizon h, otherwise 0. 𝑤′𝑝ℎ Equals 1 if recycling stream contributes to raw material sourcing of product type p for forecasting periods in horizon h, otherwise 0. 𝑥′𝑝ℎ Amount of virgin plastic type p ordered for forecasting periods in horizon h (kg). 𝑦′𝑝ℎ Amount of plastic waste type p ordered for forecasting periods in horizon h (kg). Objective function: 𝑀𝑖𝑛 𝑍ℎ = ∑ (𝐶𝑑𝑜𝑝ℎ. 𝑘𝑝ℎ + 𝐶𝑣𝑝𝑝ℎ. 𝑥′𝑝ℎ+ 𝐶𝑤𝑝𝑝ℎ. 𝑦′𝑝ℎ+ 𝐶𝑟𝑝ℎ . 𝑙′𝑝ℎ+ 𝐶𝑐𝑣𝑝ℎ. 𝑣′𝑝ℎ+ 𝐶𝑐𝑤𝑝ℎ. 𝑤′𝑝ℎ)𝑃𝑝=1+ ∑ ∑(𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ . 𝑖𝑛𝑣𝑟𝑝𝑡ℎ + 𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ . 𝑖𝑛𝑣𝑓𝑝𝑡ℎ + 𝐶𝑝𝑟𝑜𝑝𝑡ℎ . 𝑝𝑞𝑝𝑡ℎ )𝑃𝑝=1(ℎ−1)Θ𝜏+(Θ+Ξ)𝜏𝑡=(ℎ−1)Θ𝜏+1+ ∑ ∑ 𝐶𝑏𝑙𝑝𝑡ℎ . (𝐷𝑝𝑡ℎ − 𝑠𝑞𝑝𝑡ℎ )𝑃𝑝=1(ℎ−1)Θ𝜏+Θ𝜏𝑡=(ℎ−1)Θ𝜏+1+ ∑ ∑ 𝐶𝑏𝑙𝑝𝑡ℎ . (𝐷′𝑝𝑡ℎ − 𝑠𝑞𝑝𝑡ℎ )𝑃𝑝=1(ℎ−1)Θ𝜏+(Θ+Ξ)𝜏𝑡=(ℎ−1)Θ𝜏+Θ𝜏+1 (1) Constraints: 𝑝𝑞𝑝𝑡ℎ ≤ 𝑃𝑐𝑎𝑝𝑝𝑡ℎ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 1, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏}, ∀𝑝 ∈ {1, … , 𝑃} (2) 21 𝑠𝑞𝑝𝑡ℎ ≤ 𝐷𝑝𝑡ℎ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 1, … , (ℎ − 1)Θ𝜏 + Θ𝜏}, ∀𝑝 ∈ {1, … , 𝑃} (3) 𝑠𝑞𝑝𝑡ℎ ≤ 𝐷′𝑝𝑡ℎ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + Θ𝜏 + 1, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏}; ∀𝑝 ∈ {1, … , 𝑃} (4) 𝐼𝑛𝑣𝑟𝑝ℎ + 𝑋𝑝ℎ + 𝐿𝑝ℎ + 𝑘𝑝ℎ − 𝛼𝑝𝑝𝑞𝑝𝑡ℎ = 𝑖𝑛𝑣𝑟𝑝𝑡ℎ 𝑡 = (ℎ − 1)Θ𝜏 + 1; ∀𝑝 ∈ {1, … , 𝑃} (5) 𝑖𝑛𝑣𝑟𝑝(𝑡−1)ℎ − 𝛼𝑝𝑝𝑞𝑝𝑡ℎ = 𝑖𝑛𝑣𝑟𝑝𝑡ℎ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 2, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏} − ((ℎ − 1)Θ𝜏 + Θ𝜏 + 1 ); ∀𝑝 ∈ {1, … , 𝑃} (6) 𝑖𝑛𝑣𝑟𝑝(𝑡−1)ℎ + 𝑥′𝑝ℎ+ 𝑙′𝑝ℎ − 𝛼𝑝𝑝𝑞𝑝𝑡ℎ = 𝑖𝑛𝑣𝑟𝑝𝑡ℎ 𝑡 = (ℎ − 1)Θ𝜏 + Θ𝜏 + 1; ∀𝑝 ∈ {1, … , 𝑃} (7) 𝐼𝑛𝑣𝑓𝑝ℎ + 𝑝𝑞𝑝𝑡ℎ − 𝑠𝑞𝑝𝑡ℎ = 𝑖𝑛𝑣𝑓𝑝𝑡ℎ 𝑡 = (ℎ − 1)Θ𝜏 + 1; ∀𝑝 ∈ {1, … , 𝑃} (8) 𝑖𝑛𝑣𝑓𝑝(𝑡−1)ℎ + 𝑝𝑞𝑝𝑡ℎ − 𝑠𝑞𝑝𝑡ℎ = 𝑖𝑛𝑣𝑓𝑝𝑡ℎ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 2, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏}; ∀𝑝 ∈ {1, … , 𝑃} (9) 𝜀. 𝑣′𝑝ℎ ≤ 𝑥′𝑝ℎ≤ 𝑀. 𝑣′𝑝ℎ ∀𝑝 ∈ {1, … , 𝑃} (10) 𝜀. 𝑤′𝑝ℎ ≤ 𝑦′𝑝ℎ≤ 𝑀. 𝑤′𝑝ℎ ∀𝑝 ∈ {1, … , 𝑃} (11) 𝑅𝑅′𝑝ℎ. 𝑦′𝑝ℎ= 𝑙′𝑝ℎ ∀𝑝 ∈ {1, … , 𝑃} (12) 𝑘𝑝ℎ, 𝑙′𝑝ℎ , 𝑝𝑞𝑝𝑡ℎ , 𝑠𝑞𝑝𝑡ℎ , 𝑖𝑛𝑣𝑟𝑝𝑡ℎ , 𝑖𝑛𝑣𝑓𝑝𝑡ℎ , 𝑥′𝑝ℎ, 𝑦′𝑝ℎ∈ 𝑅+ ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 1, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏}; ∀𝑝 ∈ {1, … , 𝑃} (13) 𝑣′𝑝ℎ, 𝑤′𝑝ℎ ∈ {0,1} ∀𝑡 ∈ {(ℎ − 1)Θ𝜏 + 1, … , (ℎ − 1)Θ𝜏 + (Θ + Ξ)𝜏}; ∀𝑝 ∈ {1, … , 𝑃} (14) In the developed MILP model, Objective (1) minimizes the expected total production cost in horizon h. This is formulated based on costs related to raw material sourcing, recycling activities, production activities, inventory handling, backlog, and late-order. Constraint (2) takes production capacity limits into account. Constraints (3) and (4) consider the impact of market demand on selling quantity. Constraints (5) - (7) track the flow of raw materials inventory throughout the entire horizon h. Constraints (8) and (9) balance the inventory flow of final products. Constraints (10) and (11) determine through which streams raw materials are sourced. Constraint (12) determines the expected amount of raw materials sourced from the recycling stream. Constraints (13) and (14) specify the domain of the decision variables. 22 It is worth mentioning that 𝐿𝑝ℎ , 𝑋𝑝ℎ, 𝐼𝑛𝑣𝑟𝑝ℎ, 𝐼𝑛𝑣𝑓𝑝ℎ are calculated based on the outputs of the previous horizon and recently revealed data where 𝐿𝑝ℎ = 𝑅𝑅𝑝ℎ−1. 𝑦′𝑝ℎ−1, 𝑋𝑝ℎ = 𝑥′𝑝ℎ−1 for 𝑝 ∈{1, … , 𝑃} and 𝐼𝑛𝑣𝑟𝑝ℎ = 𝑖𝑛𝑣𝑟𝑝𝑡ℎ−1, 𝐼𝑛𝑣𝑓𝑝ℎ = 𝑖𝑛𝑣𝑓𝑝𝑡ℎ−1 for 𝑝 ∈ {1, … , 𝑃} and 𝑡 = (ℎ − 2)Θ𝜏 + Θ𝜏. After rolling through all the horizons, the Actual Total Cost (ATC) is calculated for the entire planning scheme as follows: 𝐴𝑇𝐶 ∶= ∑ ∑ (𝐶𝑑𝑜𝑝ℎ . 𝑘𝑝ℎ + 𝐶𝑣𝑝𝑝ℎ . 𝑥′𝑝ℎ+ 𝐶𝑤𝑝𝑝ℎ . 𝑦′𝑝ℎ+ 𝐶𝑟𝑝ℎ . 𝐿𝑝ℎ+1 + 𝐶𝑐𝑣𝑝ℎ. 𝑣′𝑝ℎ𝑃𝑝=1𝐻ℎ=1+ 𝐶𝑐𝑤𝑝ℎ. 𝑤′𝑝ℎ)+ ∑ ∑ (𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ . 𝑖𝑛𝑣𝑟𝑝𝑡ℎ + 𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ . 𝑖𝑛𝑣𝑓𝑝𝑡ℎ + 𝐶𝑝𝑟𝑜𝑝𝑡ℎ . 𝑝𝑞𝑝𝑡ℎ𝑃𝑝=1(ℎ−1)Θ𝜏+Θ𝜏𝑡=(ℎ−1)Θ𝜏+1+ 𝐶𝑏𝑙𝑝𝑡ℎ . (𝐷𝑝𝑡ℎ − 𝑠𝑞𝑝𝑡ℎ )) (15) 3.3 The Rolling LSTM Model In this section, a rolling LSTM model (compatible with the proposed RH-based model) is presented to predict future values of uncertain parameters (i.e., 𝑅𝑅′𝑝ℎ and 𝐷′𝑝𝑡ℎ). LSTM models are a specific category of Recurrent Neural Networks (RNNs) designed to address the vanishing/exploding gradient problem that occurs when modeling long-term dependencies in time-series data. In standard RNNs, gradients can either diminish or escalate significantly during backpropagation through multiple layers, hindering the network's ability to effectively learn long-term relationships within the data. An LSTM model tackles this challenge by introducing a cell state and three different gates at each unit: (i) input gates for adding information to the cell, (ii) forget gates for discarding unnecessary information, and (iii) output gates for selecting and outputting relevant information. The cell state, akin to memory, allows the LSTM model to retain and manipulate information over extended sequences, effectively capturing temporal dependencies and enabling accurate predictions. LSTM models are advantageous in predicting water consumption profiles, as understanding long-term patterns, seasonal variations, and behavioral trends is crucial for accurate demand forecasting. 23 The ability of LSTM models to effectively handle long-term dependencies makes them favorable for solving intricate time-series prediction tasks. They are beneficial to model complex nonlinear relationships and derive insightful patterns from sequential observations. Figure 6 illustrates the classic representation of an LSTM cell and the structure of the LSTM network used in this thesis. The notations in Fig.6.a) are explained by the following equations: 𝑓𝑡 = 𝜎(𝑊𝑓𝑥𝑡 + 𝑈𝑓ℎ𝑡−1 + 𝑏𝑓) (16) 𝑖𝑡 = 𝜎(𝑊𝑖𝑥𝑡 + 𝑈𝑖ℎ𝑡−1 + 𝑏𝑖) (17) ?̃?𝑡 = 𝑡𝑎𝑛ℎ(𝑊𝑐𝑥𝑡 + 𝑈𝑐ℎ𝑡−1 + 𝑏𝑐) (18) 𝑜𝑡 = 𝜎(𝑊𝑜𝑥𝑡 + 𝑈𝑜ℎ𝑡−1 + 𝑏𝑜) (19) 𝑐𝑡 = 𝑓𝑡⨂𝑐𝑡−1 + 𝑖𝑡⨂?̃?𝑡 (20) ℎ𝑡 = 𝑜𝑡⨂tanh (𝑐𝑡) (21) where ℎ𝑡−1 represents the previous hidden state and 𝑥𝑡 denotes the current time step’s input. In the presented cell state, 𝑓𝑡, 𝑖𝑡, 𝑜𝑡 correspond to the forget gate, input gate, and output gate, respectively. ?̃?𝑡 represents the candidate memory cell used for updating the cell state. 𝑐𝑡 is the current cell state, 𝑐𝑡−1 is the previous cell state, and ℎ𝑡 represents the current hidden state. The weighted matrices a) b) Fig.6. Structure of a) an LSTM unit, and b) the employed LSTM network. 24 are denoted by 𝑊𝑓, 𝑊𝑖, 𝑊𝑐, 𝑊𝑜 and 𝑈𝑓, 𝑈𝑖, 𝑈𝑐, 𝑈𝑜 while 𝑏𝑓, 𝑏𝑖, 𝑏𝑐, 𝑏𝑜 represent bias terms. All these parameters are trainable. The symbol ⊗ signifies the Hadamard product; 𝜎 denotes the sigmoid function, and tanh represents the Hyperbolic Tangent function. Algorithm 1 outlines the rolling LSTM model employed in this thesis. Algorithm 1: Proposed Rolling LSTM Model Inputs: Historical data, train-test ratio, 𝜏 and Θ. Step 1: Normalize data; 𝑥𝑖 =𝑥𝑖−𝑥𝑚𝑖𝑛𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛 Step2: Determine rolling duration = Θ𝜏 Step 3: Create sequential data for 𝑖 = 0, 1, 2, … , |𝐻𝑖𝑠𝑡𝑜𝑟𝑖𝑐𝑎𝑙 𝑑𝑎𝑡𝑎| − 2Θ𝜏 do 𝑖_𝑡ℎ observation: 𝑋𝑖 ← (𝑥𝑖+1, … , 𝑥𝑖+Θ𝜏) 𝑖_𝑡ℎ label: 𝑌𝑖 ← (𝑥𝑖+Θ𝜏+1, … . , 𝑥𝑖+2Θ𝜏) return 𝑋𝑖 and 𝑌𝑖 end for Step 4: Shuffle sequential data Step 5: Split sequential data into train and test sets based on the train-test ratio 𝑀 ⟵ {(𝑋𝑖, 𝑌𝑖); ∀𝑖 ∈ 𝑡𝑟𝑎𝑖𝑛 𝑠𝑒𝑡} 𝑁 ⟵ {(𝑋𝑖, 𝑌𝑖); ∀𝑖 ∈ 𝑡𝑒𝑠𝑡 𝑠𝑒𝑡} Step 6: Model = sequential () Step 7: Model.add (LSTM (units)) Step 8: Model.add (Dense (Θ𝜏)) Step 9: Model.compile (Loss = RMSE, Optimizer = ADAM) Step 10: For epoch = 1, 2, …, do Model.fit (𝑋𝑀, 𝑌𝑀, epochs) Return Model End for Step 11: Model.predict (𝑋𝑀) Step 12: Model.predict (𝑋𝑁) Step 13: Report RMSE values for train and test sets Step 14: Add new Θ𝜏 days of data as 𝑋′𝑖 Step 15: 𝑌′𝑖 = Model.predict (𝑋′𝑖) Outputs: Trained LSTM model and predictions. 25 3.4 The Proposed DRHP Approach In this approach, the planning scheme is divided into multiple horizons. Each horizon consists of Θ operational periods and Ξ forecasting periods, with each period spanning τ days. Figure 7 presents an RH planning framework with one operational period and Ξ forecasting periods. The developed MILP model optimizes production planning over each horizon. The resulting plan is mandatory to be implemented within the operational periods, yet it can be modified for the forecasting periods. Upon finishing one set of operational periods, a new horizon is defined, and the optimization step is repeated. Fig.7. An example of the proposed RH planning framework. Once a horizon is rolled (i.e., when its operational set ends), the production plan is updated based on the newly revealed market demand and recycling rate, as well as the system’s current status including the inventory level and the quantity of received raw materials, see Figure 8. 26 Fig.8. Flow of parameters in the kth planning horizon. Algorithm 2 is the detailed representation of the developed DRHP approach, where ℎ𝑜 and ℎ𝑓 denote the operational set and the forecasting set of the horizon ℎ, respectively. Algorithm 2: Proposed DRHP Approach Inputs: RH-based model and its parameters, trained rolling LSTM model, 𝜏, Θ, and Ξ. Step 1: Determine 𝐻 = ⌊𝑇ΘΞ⌋ − 1 Step 2: For p ∈ P Train the LSTM model on both historical demand and recycling rate based on Θ𝜏 end for Step 3: Let ℎ = 1 Step 4: For p ∈ P Update 𝐷𝑝𝑡ℎ𝑜 ∀𝑡∈ 𝑡ℎ𝑜 Fine tune the LSTM model (if needed) and forecast 𝑅𝑅′𝑝ℎ𝑓 Set recycling rate on 𝑅𝑅′𝑝ℎ𝑓 for t ∈ 𝑡ℎ𝑜 Set demand on 𝐷𝑝𝑡ℎ𝑖𝑜 end for 27 for t ∈ 𝑡ℎ𝑓 Fine tune the LSTM model (if needed) and forecast 𝐷′𝑝𝑡ℎ𝑓 Set demand on 𝐷′𝑝𝑡ℎ𝑓 end for end for Step 5: Solve the RH-based model for horizon h Step 6: Return decision variables and production cost related to horizon ℎ Step 7: Let ℎ = ℎ + 1 Step 8: While ℎ ≤ H Update 𝑅𝑅𝑝(ℎ−1)𝑓 Calculate 𝐿𝑝ℎ using 𝑅𝑅𝑝(ℎ−1)𝑓 Calculate 𝐼𝑛𝑣𝑟𝑝ℎ, 𝐼𝑛𝑣𝑓𝑝ℎ, and 𝑋𝑝ℎ using 𝑖𝑛𝑣𝑟𝑝(ℎ−1)𝑜, 𝑖𝑛𝑣𝑓𝑝(ℎ−1)𝑜 , and 𝑥𝑝(ℎ−1)𝑜 Go back to Step 4 end while Outputs: Developed production plan and corresponding ATC. 3.5 Robust Optimization To evaluate the performance of the proposed DRHP approach, a static MILP counterpart is developed for the defined production planning problem (refer to Appendix A for details). To tackle the uncertainty of demand and recycling rate in the static approach, the box uncertainty set-based robust optimization is adopted. Robust optimization is particularly beneficial when accurately estimating the probability distribution of uncertain parameters is challenging or when decision-makers adopt a risk-averse strategy (Ben-Tal and Nemirovski, 1999; Bertsimas et al., 2004; Kisomi et al., 2016; Mohseni and Pishvaee, 2020; Tosarkani and Amin, 2020; Goerigk and Kurtz, 2023). In this approach, only the maximum and minimum possible values of uncertain parameters are required to model uncertainty. Simply put, variation in a parameter is represented as an uncertainty set that comprises a range of possible scenarios without explicitly defining a probability distribution. The objective is to offer a solution that performs well across all scenarios in the uncertainty set, ensuring robustness against fluctuations in uncertain parameters. The primary advantage of an uncertainty-based robust optimization approach is its ability to create a solution that is less sensitive to specific realizations 28 of uncertain parameters within their uncertainty sets. This provides a degree of feasibility assurance when confronting unforeseen situations. Over the last years, several uncertainty sets (e.g., box uncertainty set, ellipsoidal uncertainty set, polyhedral uncertainty set, box and ellipsoidal uncertainty set, box and polyhedral uncertainty set, ellipsoidal and polyhedral uncertainty set) and their robust counterpart formulation are introduced and discussed in the literature (Ben-Tal and Nemirovski, 1999; Bertsimas et al., 2004; Mohseni and Pishvaee, 2020), aiming to investigate their weaknesses and strengths in different optimization problems under uncertainty. 3.5.1 Box Uncertainty Set-based Robust Optimization To address the uncertainty of the developed static counterpart model, consider the following linear optimization model: 𝑀𝑖𝑛 {∑ ?̃?𝑗𝑥𝑗𝑗 | ∑ ?̃?𝑖𝑗𝑥𝑗 − ?̃?𝑖 ≤ 0 ∀𝑖𝑗 } (22) In this model, ?̃?𝑖, ?̃?𝑖𝑗 and ?̃?𝑖 represent uncertain parameters as follows: ?̃?𝑗 = 𝑐𝑗 + 𝜌𝑗?̂?𝑗, ∀𝑗 ∈ 𝐽𝑖 (23) ?̃?𝑖𝑗 = 𝑎𝑖𝑗 + 𝜌′𝑖𝑗?̂?𝑖𝑗, ∀𝑗 ∈ 𝐽𝑖 (24) ?̃?𝑖 = 𝑏𝑖 + 𝜌′′𝑖?̂?𝑖 (25) Where 𝑐𝑖, 𝑎𝑖𝑗, and 𝑏𝑗 denote the nominal values of the uncertain parameters, while ?̂?𝑖, ?̂?𝑖𝑗, and ?̂?𝑗 represent the scales of uncertainty. The Robust Counterpart (RC) of the previous model is formulated as follow: 𝑀𝑖𝑛 {∑ 𝑐𝑗𝑥𝑗𝑗 + [max𝜌∈𝑈{∑ 𝜌𝑗 ?̂?𝑗𝑥𝑗𝐽𝑖 }] |−𝑏𝑖 + ∑ 𝑎𝑖𝑗𝑥𝑗 + [max𝜌∈𝑈{−𝜌′′𝑖?̂?𝑖 + ∑ 𝜌′𝑖𝑗?̂?𝑖𝑗𝑥𝑗𝐽𝑖 }] ≤ 0𝑗 ∀𝑖} (26) In this formulation, 𝜌𝑗 , 𝜌′𝑖𝑗 , and 𝜌"𝑖 are random variables symmetrically distributed in the interval [-1,1]. To ensure the model feasibility, an uncertainty set U is defined for any 𝜌. A robust solution is characterized by its ability to remain feasible across all potential scenarios in the uncertainty set. 29 This thesis adopts the box uncertainty approach as described by Li et al. (2011), where the uncertainty set is defined based on the ∞-norm of the random variable ρ, incorporating the adjustable parameter Ψ to control the size of the uncertainty set. 𝑈𝑏𝑜𝑥 = {𝜌|‖𝜌‖∞ ≤ Ψ} = {𝜌| |𝜌𝑗| ≤ Ψ , ∀𝑗 ∈ 𝐽𝑖} (27) Using the box uncertainty set, the RC is reformulated as the following expression: 𝑀𝑖𝑛 {∑ 𝑐𝑗𝑥𝑗𝑗 + Ψ[∑ (?̂?𝑗|𝑥𝑗)𝐽𝑖 ]|−𝑏𝑖 + ∑ 𝑎𝑖𝑗𝑥𝑗 + Ψ[∑ (?̂?𝑖𝑗|𝑥𝑗)𝑗∈𝐽𝑖 + ?̂?𝑖] ≤ 0𝑗 ∀𝑖} (28) The adoption of the box uncertainty set ensures maximum protection against uncertainty, albeit at the expense of high costs for robustness in practical applications. This uncertainty set imposes stricter constraints compared to the original linear programming, as it enables all uncertain parameters to take their worst values at the same time. The conservatism of the box uncertainty set is evident in its capacity to account for the rare occurrence of the worst possible combination of uncertain parameters at the same time. 30 4 Results and Sensitivity Analysis In this chapter, the performance of the proposed DRHP approach is evaluated across a set of instances in terms of different criteria such as inventories, backlog, late-order, and ATC. 4.1 Data and Parameter Setting The scarcity of real-world data has been a daunting challenge in numerous scientific studies. Although efforts have been made to provide public datasets, the availability of reliable data is constrained by factors such as data accessibility, scale, and privacy (Zhang et al., 2018). To address this challenge, generating synthetic datasets is a promising solution, allowing researchers to develop innovative data-driven models and evaluate them. Synthetic data features are categorized into two distinct statistical components: level and pattern. The level component encompasses key statistical attributes such as mean, scale, and variance, while the pattern component captures the underlying trend in the data (Zhang et al., 2018). A survey conducted by Jones et al. (2007) investigated drinking water consumption in British Columbia, Canada, revealing an average daily intake of 1.0 liter per capita. Notably, 23% of respondents relied on bottled water as their primary drinking water source, accounting for at least 75% of their daily intake. With the reported population of British Columbia at 5,437,722 as of April 1, 2023, it can be perceived that 1,250,676 individuals rely on bottled water as the main source of daily intake. Having that said, at least 938,007 liters of daily water intake are supplied through bottled water. Assuming each bottle holds 0.5 liters, the average daily demand for bottled water totals around 1,900,000 units. With an assumption of a market share of 1.5%, the average demand for a specific manufacturing plant is 28,500 bottles per day. To synthesize historical data, the pattern in daily demand is generated similar to studies in the literature (Wong et al., 2010; Farah et al., 2019; Du et al., 2020; Nasser et al., 2020). Figure 9 illustrates three synthetic scenarios for daily bottle demand over 365 days with the same average but different variations and patterns. 31 Fig.9. Three different scenarios for daily market demand. Antonopoulos et al. (2021) analyzed recycling activities in a number of different facilities and reported sorting rate ranging from 45% to 97% and recycling rate from 63% to 95%, which vary depending on the efficiency of the recycling process. Figure 10 demonstrates three synthetic scenarios for daily recycling rate over a year, with trends imitated based on studies by Ahmed et al. (2022) and Williams and Phillips (2022). With the assumption of access to the first 180 days of historical data on demand and recycling rate, the goal is to develop a production plan for the upcoming 185 days, known as the Horizon era. Table 3 represents the parameter setting for the RH-based MILP model. Henceforth, it is assumed that 𝛩 = 𝛯 = 𝑃 = 1 indicating rolling duration is equal to Θ𝜏 = 1 × 𝜏 = 𝜏. Different scenarios of τ, i.e., {2, 4, 6, …, 22} are investigated to evaluate the impact of rolling duration on forecasting accuracy and ATC. Fig.10. Three different scenarios for daily recycling rate. 010,00020,00030,00040,00050,00060,00070,00080,0001 32 60 91 121 152 182 213 244 274 305 335Daily DemandDayScenario 1 Scenario 2 Scenario 30.30.40.50.60.70.80.911 32 60 91 121 152 182 213 244 274 305 335Recycling RateDayScenario 1 Scenario 2 Scenario 332 To evaluate the role of the LSTM model in managing uncertainty in the proposed DRHP approach, its impact is benchmarked against two alternatives. The first alternative involves eliminating the uncertainty assumption and using the exact actual values of uncertain parameters. The second one relies on the average values of uncertain parameters (derived from historical data) as predictions of their future values. Table 3. Parameter setting for the RH-based MILP model. Parameters Value Initial raw material inventory (𝐼𝑛𝑣𝑟𝑝ℎ; ℎ = 0) 0 Initial final product inventory (𝐼𝑛𝑣𝑓 𝑝ℎ; ℎ = 0) 0 Initial virgin raw material supply (𝑋𝑝ℎ; ℎ = 0) 0 Initial recycled raw material supply (𝐿𝑝ℎ ; ℎ = 0) 0 Daily production capacity (𝑃𝑐𝑎𝑝𝑝𝑡ℎ ) 30,000 Unitary raw material inventory cost (𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ ) 1 Unitary final product inventory cost (𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ ) 0.1 Raw material late-order cost (𝐶𝑑𝑜𝑝ℎ) 8 Unitary production cost (𝐶𝑝𝑟𝑜𝑝𝑡ℎ ) 0.3 Unitary backlog cost (𝐶𝑏𝑙𝑝𝑡ℎ ) 3 Virgin plastic cost (𝐶𝑣𝑝𝑝ℎ) 4 Plastic waste cost (𝐶𝑤𝑝𝑝ℎ) 1 Virgin plastic’s contract cost (𝐶𝑐𝑣𝑝ℎ) 300 Plastic waste’s contract cost (𝐶𝑐𝑤𝑝ℎ) 100 Recycling cost (𝐶𝑟𝑝ℎ) 2 4.2 Forecasting Accuracy Measure Various measures can be used to evaluate the performance of time-series forecasting models, each assessing the outputs in terms of specific criteria. In this thesis, the performance of the LSTM model is evaluated using Root Mean Squared Error (RMSE), a metric that measures the average magnitude of the errors between predicted values and actual values. Lower RMSE values indicate a better fit of the model to the data, while higher values imply a greater deviation between actual data and their predictions. This measure is calculated using Eq. 29, where 𝑌𝑖 and ?̂?𝑖 are the actual and forecasted values of the 𝑖th observation, respectively. The number of total observations is denoted by n. 33 𝑅𝑀𝑆𝐸 = √∑ (𝑌𝑖 − ?̂?𝑖)2𝑛𝑖=1𝑛 (29) RMSE is scale-dependent, indicating that this measure is presented in the same unit as the data. Therefore, using normalized data is preferred for a more understandable interpretation of the results. Additionally, it is important to take into account that RMSE is sensitive to outliers. This implies that significant errors in a few data points can greatly influence the RMSE value. 4.3 Performance Evaluation In this section, the performance of the proposed DRHP approach is explored across multiple instances characterized by different scenarios of demand, recycling rate, and rolling duration. 4.3.1 Evaluation of the LSTM Model The proposed rolling LSTM model is trained using the first 180 days of normalized historical data. Table 4 demonstrates the RMSE values for various scenarios of market demand and recycling rate under different rolling durations. For normalized data, a favorable range of RMSE is close to zero, indicating close alignment between the model's predictions and actual values. The rolling LSTM model exhibits satisfactory performance for both demand and recycling rate, with RMSEs less than 0.2 in most cases. However, forecasting accuracy declines as the rolling duration increases. The impact of rolling duration on other performance criteria is investigated in the next sections. 34 Table 4. Performance of the rolling LSTM model (RMSE) in predicting recycling rate and market demand based on different scenarios of rolling duration. Train Test Train Test RR-S1 RR-S2 RR-S3 RR-S1 RR-S2 RR-S3 D S1 D S2 D S3 D S1 D S2 D S3 Rolling Duration 2 0.1881 0.1418 0.1766 0.1857 0.1084 0.1549 0.1127 0.1310 0.0633 0.1065 0.1431 0.0641 4 0.2022 0.1692 0.1778 0.2255 0.1797 0.2100 0.1096 0.1304 0.0640 0.1088 0.1295 0.0588 6 0.2096 0.1516 0.1696 0.2163 0.1994 0.1657 0.0992 0.1196 0.0821 0.1061 0.1269 0.0792 8 0.2165 0.1514 0.1688 0.2114 0.1763 0.1626 0.0992 0.1200 0.0928 0.0991 0.1236 0.0907 10 0.2177 0.1534 0.1705 0.2202 0.1581 0.1592 0.1011 0.1192 0.1062 0.0998 0.1206 0.1010 12 0.2171 0.1632 0.1700 0.2233 0.1711 0.1677 0.1003 0.1185 0.1191 0.1019 0.1206 0.1107 14 0.2194 0.1607 0.1690 0.2312 0.1702 0.1787 0.0989 0.1187 0.1522 0.1068 0.1208 0.1409 16 0.2164 0.1609 0.1822 0.2334 0.1539 0.1784 0.0963 0.1203 0.1360 0.1016 0.1181 0.1207 18 0.2175 0.1575 0.1748 0.2379 0.1409 0.1812 0.0942 0.1183 0.1515 0.1009 0.1197 0.1325 20 0.2197 0.1427 0.1654 0.2375 0.1282 0.1798 0.0941 0.1186 0.1390 0.1021 0.1175 0.1620 22 0.2392 0.1421 0.1685 0.2639 0.1329 0.1883 0.0948 0.1167 0.1424 0.1020 0.1194 0.1639 Figures 11 and 12 depict the performance of the trained rolling LSTM model over the Horizon era. Results indicate that the LSTM model trained with smaller values of 𝜏 maintains its superior performance in the Horizon era as well. The results are reported in terms of both a fine-tuned and a non-fine-tuned LSTM model. In the context of LSTM models, fine-tuning refers to additional training on a new dataset after pretraining on a general dataset. Fine-tuning involves training the model for a few more epochs with a reduced learning rate on the new dataset, enabling the model to adapt its learned features to new data. This is particularly advantageous when available data for the target task is limited. According to Figures 11 and 12, fine-tuning does not affect the RMSE score for recycling rate predictions, but it enhances demand forecasting accuracy. Henceforth, in this thesis, when referring to the LSTM model, it implicitly means a model that has undergone fine-tuning. 35 Fig.11. Accuracy of the rolling LSTM model’s predictions (RMSE) for a) Recycling Rate Scenario 1 (RRS1), b) RRS2, and c) RRS3 in the Horizon era; Purple line: fine-tuned, orange line: non-fine-tuned. b) c) a) 36 Fig.12 Accuracy of the rolling LSTM model’s predictions (RMSE) for a) Demand Scenario 1 (DS1), b) DS2, and c) DS3 in the Horizon era; Purple line: fine-tuned, orange line: non-fine-tuned. b) c) a) 37 4.3.2 Evaluation of the DRHP Approach Performance of the DRHP approach is compared to its robust static counterpart across nine different instances characterized by various combinations of demand and recycling rate scenarios, see Figure 13. Setting future demand at the maximum of its historical data (𝐷′ = 𝐷′𝑚𝑎𝑥) and future recycling rate at the minimum of its historical data (𝑅′ = 𝑅′𝑚𝑖𝑛) results in the worst-case scenario in terms of the expected total production cost (Appendix A, Eq. 30). However, determination of the worst-case scenario in terms of ATC (Appendix A, Eq. 45) is not straightforward. The reason is that ATC depends not only on historical data but also on future values of uncertain parameters. In this regard, all four potential worst-case scenarios (by setting demand and recycling rate at their historical extremes) are examined. The results show the superiority of the DRHP approach over its robust static counterpart, particularly in cases characterized by DS2 and DS3, as evidenced by a significant reduction in ATC. However, when dealing with DS1, the comparison between the two approaches becomes nuanced, depending on the rolling duration. Moreover, the results demonstrate that in the robust static counterpart, ATC remains relatively unaffected by increasing rolling duration. On the contrary, in the DRHP approach, ATC significantly differs across various values of τ, indicating that smaller values of rolling duration lead to better performance of the DRHP approach. This implies the significance of efficient raw material sourcing as the rolling duration to some extent depends on the efficiency of raw material delivery/preparation. According to Table 5, the DRHP approach surpasses its robust static counterpart by reducing ATC up to 65% and 80% in instances characterized by DS2 and DS3, respectively. In cases characterized by DS1, the DRHP approach loses superiority for rolling durations exceeding four days. This happens only when the worst-case scenario in the robust static approach is defined by setting future demand at the maximum value of the historical data. 38 Fig.13. Comparison between the DRHP approach and the robust static approach in terms of ATC (thousands) across different instances characterized by: a) DS1-RRS1, b) DS1-RRS2, c) DS1-RRS3, d) DS2-RRS1, e) DS2-RRS2, f) DS2-RRS3, g) DS3-RRS1, h) DS3-RRS2, and i) DS3-RRS3. 02,0004,0006,0008,00010,00012,00014,00016,00018,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsa)02,0004,0006,0008,00010,00012,00014,00016,00018,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsb)DRHP-LSTMStatic (D'min-RR'min)Static (D'min-RR'max)Static (D'max-RR'min)Static (D'max-RR'max)02,0004,0006,0008,00010,00012,00014,00016,00018,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsc)01,0002,0003,0004,0005,0006,0007,0008,0009,00010,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsd)01,0002,0003,0004,0005,0006,0007,0008,0009,00010,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandse)01,0002,0003,0004,0005,0006,0007,0008,0009,00010,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsf)02,0004,0006,0008,00010,00012,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsg)02,0004,0006,0008,00010,00012,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22h)02,0004,0006,0008,00010,00012,000𝜏=2𝜏=4𝜏=6𝜏=8𝜏=10𝜏=12𝜏=14𝜏=16𝜏=18𝜏=20𝜏=22Thousandsi)39 Table 5. Reduction in ATC (percentage) by adopting the DRHP approach instead of the robust static approach. Instance Worst-Case Scenario Raw Material Preparation Efficiency/Rolling Duration 2 4 6 8 10 12 14 16 18 20 22 DS1-RRS1 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 56.18 51.49 45.89 42.77 37.47 30.59 30.09 24.14 21.14 14.42 9.57 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 13.45 5.30 -4.05 -8.53 -16.88 -28.11 -27.70 -37.40 -41.87 -51.99 -58.90 DS1-RRS2 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 57.97 53.81 49.39 46.14 40.61 36.52 32.14 27.09 24.66 20.06 15.76 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 16.75 9.62 2.47 -2.34 -11.19 -17.35 -24.14 -32.23 -35.73 -42.14 -48.18 DS1-RRS3 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 57.65 53.49 48.90 45.68 40.33 36.06 32.81 27.71 24.62 19.54 15.77 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 14.83 7.63 0.08 -4.69 -13.29 -19.79 -24.54 -32.82 -37.52 -44.84 -49.95 DS2-RRS1 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 59.83 54.74 50.17 44.61 40.47 34.24 27.95 24.73 18.14 10.67 7.73 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 64.76 60.19 56.08 51.12 47.42 41.81 36.21 33.39 27.66 21.11 18.19 DS2-RRS2 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 56.89 51.93 46.29 40.54 35.85 29.09 23.75 18.98 13.83 8.16 2.89 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 65.65 61.532 56.83 52.04 48.13 42.43 37.86 33.81 29.51 24.77 20.00 DS2-RRS3 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 57.81 52.58 47.18 41.72 36.93 30.96 25.80 21.32 16.64 9.29 3.92 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 64.84 60.37 55.73 51.04 46.93 41.76 37.24 33.36 29.37 23.13 18.20 DS3-RRS1 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 74.18 69.92 63.40 59.43 54.05 47.69 48.75 40.73 38.32 28.42 24.07 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 79.94 76.47 71.22 67.92 63.49 58.23 58.95 52.37 50.27 42.07 38.32 DS3-RRS2 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 73.04 68.73 61.55 56.83 51.391 45.25 42.82 35.25 33.74 26.86 20.99 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 80.77 77.52 72.15 68.52 64.32 59.57 57.53 51.65 50.26 44.81 40.11 DS3-RRS3 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑎𝑥 73.33 69.142 62.13 57.56 52.31 46.12 44.44 37.59 36.00 27.92 22.75 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 80.23 76.97 71.56 67.93 63.76 58.84 57.35 51.86 50.40 43.89 39.63 To comprehensively evaluate the performance of the two approaches, an assessment of sustainability performance is also conducted, see Table 6. Results highlight a key difference in raw material sourcing strategies opted by the two approaches. The DRHP approach demonstrates a commitment to sustainability by prioritizing recycled plastics over virgin plastics. In contrast, the robust static counterpart in some cases relies on virgin plastic, which goes against sustainability considerations. This implies that the DRHP approach is a more environmentally favorable option when compared with its robust static counterpart. 40 Table 6. Amount of raw material (kg) sourced through virgin plastic stream in the robust static approach. Instance Worst-Case Scenario Raw Material Preparation Efficiency 2 6 10 14 18 22 DS1 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑖𝑛 116,168 113,629 111,090 108,550 106,011 103,472 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 549,000 537,000 525,000 513,000 501,000 499,000 DS2 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑖𝑛 475,049 464,666 454,282 443,898 433,515 423,131 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 549,000 537,000 525,000 513,000 501,000 499,000 DS3 𝐷’𝑚𝑖𝑛 − 𝑅𝑅’𝑚𝑖𝑛 454,407 444,474 434,542 424,610 414,677 404,745 𝐷’𝑚𝑎𝑥 − 𝑅𝑅’𝑚𝑖𝑛 549,000 537,000 525,000 513,000 501,000 499,000 The significance of employing a forecasting model for managing uncertainty in the DRHP approach is depicted in Figure 14. The role of the LSTM model is benchmarked against two alternatives: (i) the average of historical data, and (ii) knowing the exact future values of uncertain parameters. Across different instances, the proposed DRHP approach achieves performance closely resembling that of the RH-based model knowing exact future values of uncertain parameters. The DRHP approach substantially outperforms the RH-based model relying on the average of historical data. This emphasizes the importance of coupling the RH-based model with an accurate forecasting model in order to manage uncertainty challenges. 41 -7,000-6,000-5,000-4,000-3,000-2,000-1,00001,0002,00002,0004,0006,0008,00010,00012,00014,0002 4 6 810121416182022f)-7,000-6,000-5,000-4,000-3,000-2,000-1,00001,0002,00002,0004,0006,0008,00010,00012,00014,0002 4 6 810121416182022e) Fig.14. Performance of the DRHP approach in terms of ATC across different instances characterized by: a) DS1-RRS1, b) DS1-RRS2, c) DS1-RRS3, d) DS2-RRS1, e) DS2-RRS2, f) DS2-RRS3, g) DS3-RRS1, h) DS3-RRS2, and i) DS3-RRS3. When addressing optimization problems, determining the primary cost drivers is beneficial for informed decision-making. Figure 15 depicts the performance of the DRHP approach in terms of backlog, raw material inventory, final product inventory, and late-order. By leveraging the LSTM model, the RH-based model results in inventory and late-order levels similar to those obtained with exact data. However, backlog remains constant across different strategies of uncertainty handling. This observation suggests that in cases where production plants struggle with -600-400-20002004006008001,0001,2001,40002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022 ATC Reduction (Thousands)ATC (Thousands)Rollong Duration (Day)a)-600-400-200020040060002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022b)LSTM to AverageLSTM to ExactExactAverageLSTM-500-400-300-200-100010020030040050002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022c)-6,000-5,000-4,000-3,000-2,000-1,00001,0002,00002,0004,0006,0008,00010,00012,00014,0002 4 6 810121416182022ATC Reduction (Thousands)ATC (Thousands)Rolling Duration (Day)d)-10,000-8,000-6,000-4,000-2,00002,0004,00002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022ATC Reduction (Thousands)ATC (Thousands)Rolling Duration (Day)g)-10,000-8,000-6,000-4,000-2,00002,00002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022h)-10,000-8,000-6,000-4,000-2,00002,00002,0004,0006,0008,00010,00012,00014,00016,0002 4 6 810121416182022i)42 inefficiencies related to inventory or late-order management, the proposed DRHP approach holds promise. Note that the data presented in Figure 15 is based on the average results of the different nine instances explained earlier. Fig.15. Performance of the DRHP approach in terms of a) backlog (thousands), b) raw material inventory (thousands), c) final product inventory (thousands), and d) late-order (thousands). 4.4 Sensitivity Analysis Sensitivity analysis aims to evaluate how changes in input parameters or assumptions of a problem can affect the outputs. This offers decision-makers insight into the robustness and reliability of their approach. In this regard, an analysis is conducted in this section to explore the sensitivity of the DRHP approach to the rolling duration. Figure 16 demonstrates the sensitivity of ATC to rolling duration and forecasting accuracy. It can be seen that improving the accuracy of the forecasting model (whether from average to LSTM or LSTM to exact) holds greater significance when dealing with longer rolling durations. This 43 observation suggests that in cases where setting rolling duration on small values is not feasible, adopting the proposed DRHP model is highly advisable. Fig.16. Impact of improving uncertainty handling strategy on ATC (Thousands) in the DRHP approach: a) Average to LSTM and b) LSTM to Exact. Figures 17 - 20 show the influence of different values of rolling duration on the backlog, raw material inventory, final product inventory, and late-order, respectively. Summarized in Figure 21, an increase in rolling duration imposes the most negative impact on raw material inventory, followed by late-order and final product inventory. However, no significant effect is observed on the backlog level. This implies that the increase of ATC at large values of rolling duration stemmed from an increase in inventory and late-order levels, not backlog. DS1, RRS1DS1, RRS2DS1, RRS3DS2, RRS1DS2, RRS2DS2, RRS3DS3, RRS1DS3, RRS2DS3, RRS3ATC Reductiona) τ=22τ=20τ=18τ=16τ=14τ=12τ=10τ=8τ=6τ=4τ=2DS1, RRS1DS1, RRS2DS1, RRS3DS2, RRS1DS2, RRS2DS2, RRS3DS3, RRS1DS3, RRS2DS3, RRS3ATC Reductionb) τ=22τ=20τ=18τ=16τ=14τ=12τ=10τ=8τ=6τ=4τ=244 Fig.17. Performance of the RH-based model across different rolling durations in terms of backlog. Fig.18. Performance of the RH-based model across different rolling durations in terms of raw material inventory. 45 Fig.19. Performance of the RH-based model across different rolling durations in terms of final product inventory. Fig.20. Performance of the RH-based model across different rolling durations in terms of late-order. 46 Fig.21. Impact of rolling duration on a) backlog (thousands), b) raw material inventory (thousands), c) final product inventory (thousands), and d) late-order (thousands) in the DRHP approach. Cost-related parameters play a major role in production planning decision-making. These parameters have a significant impact on the overall profitability and economic viability of a production plan. The developed RH-based model comprises a wide range of cost-related components, including raw material sourcing, production, recycling, backlog and late-order, and inventory management. Sensitivity analysis on cost-related parameters provides insights into the robustness of the proposed DRHP approach, enabling the identification of critical components and their potential risks. In this regard, an analysis is conducted to examine the impact of various values of inventory costs (𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ , 𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ ), penalty costs (𝐶𝑏𝑙𝑝𝑡ℎ , 𝐶𝑑𝑜𝑝ℎ), and raw material sourcing costs (𝐶𝑣𝑝𝑝ℎ, 𝐶𝑟𝑝ℎ) on ATC, see Figure 22. Results indicate that penalty costs lead to increase of production costs at higher values as the DRHP approach does not address delays. However, 47 increasing inventory and raw material sourcing costs have only a marginal influence on ATC, implying that the proposed approach can adjust the plan to prevent a drastic increase in total production cost. Note that the data in Figures 21 and 22 is based on the average results of the nine different instances explained earlier. Fig.22. Sensitivity analysis on different elements of production cost in terms of ATC (thousands). 48 5 Conclusions and Future Works This chapter provides an overview of the problem at hand and the developed solution approach. Additionally, a summary of the main findings and contributions of the thesis is offered. Research limitations and potential research directions are also outlined at the end of this chapter. 5.1 Thesis Summary Developing an efficient production plan in the plastic industry not only requires embracing recycling practices but also demands considering the dynamic nature of key parameters. To achieve this, the current thesis develops a dynamic DRHP approach for sustainable production aiming to incorporate recycling practices, fulfill market demand at the minimum possible production cost, and consider the uncertainty of market demand and recycling rate. This approach couples a novel RH-based mathematical model with a rolling LSTM model. The RH-based production planning is formulated as a multi-product, multi-period MILP model, incorporating various production-related components. This model assists decision-makers in selecting raw material sourcing stream (i.e., virgin or recycled), production scheduling, inventory management, and backlog and late-order handling. The rolling LSTM model continuously monitors and adjusts the predictions for future demand and recycling rate, consequently assisting in modifying the production plan as horizons progress. After each horizon roll, the entire system is re-assessed, and the production plan is updated based on the current status of the system, recently revealed data, and forecasting of future trends in uncertain parameters. The accuracy of future forecasting is a determinant in this approach, impacting ongoing and future horizon planning. To evaluate the performance of the proposed DRHP approach, it is benchmarked against a robust static MILP counterpart model to investigate the impact of dynamic planning on the problem at hand. Findings demonstrate the superiority of the developed DRHP approach over the robust static counterpart from both economic and environmental points of view. Moreover, findings underscore the significance of the rolling duration parameter on the DRHP approach’s performance, by affecting both the RH-based model’s and the LSTM model’s outcomes. Results illustrate that total production cost substantially escalates as the rolling duration increases. This implies that by 49 improving the raw material preparation efficiency and consequently shortening the rolling duration, the performance of the DRHP approach significantly improves. Furthermore, findings indicate that increment in total production cost in long rolling durations mainly stems from backlog level. The proposed DRHP approach significantly mitigates inventory- and late-order-related costs, while the backlog does not change as significantly. Results show that improving the LSTM forecasting accuracy significantly improves the RH-based model’s outcome. This improvement is more substantial when dealing with a longer rolling duration. This highlights that applying a data-driven technique is crucial specifically when the rolling duration is set on longer durations. Aligning with previous results, sensitivity analysis indicates that penalty costs (𝐶𝑏𝑙𝑝𝑡ℎ , 𝐶𝑑𝑜𝑝ℎ) are the most influential cost components affecting ATC. However, the approach effectively confronts increment costs related to inventory (𝐶𝑖𝑛𝑣𝑟𝑝𝑡ℎ , 𝐶𝑖𝑛𝑣𝑓𝑝𝑡ℎ ) and raw material sourcing (𝐶𝑣𝑝𝑝ℎ, 𝐶𝑟𝑝ℎ), showing the robustness of the approach when dealing with inventory and raw material sourcing challenges. 5.2 Research Contribution The proposed DRHP approach holds promise for an efficient and sustainable framework for production planning within dynamic and uncertain environments. The primary contributions of this thesis are outlined as follows: • Development of a data-driven optimization framework for production planning in the plastic industry: This thesis integrates an RH-based MILP model with a rolling LSTM model, collaborating interactively based on a shared parameter known as rolling duration. • Demonstration of superior performance of the dynamic data-driven approach over a conventional conservative robust static approach: This superiority is demonstrated in terms of both total production cost and sustainability performance. • Emphasis on sustainable development in production planning by incorporating recycling opportunities: To the best of our knowledge, there is a lack of research focusing on production planning in the plastic industry that incorporates plastic waste recycling streams as an alternative to virgin plastics. 50 • Consideration of the dynamic and uncertain nature of parameters: To ensure the feasibility of solutions in the real world, the RH-based model is augmented with predictive capabilities. • Investigation into the impact of raw material preparation efficiency on total production cost: This is accomplished by analyzing the rolling duration parameter, which is impacted by the efficiency of the raw material recycling/preparation process. • Analysis of the primary areas of improvement in production planning: The findings of the thesis highlight that the developed DRHP approach significantly reduces costs related to inventory and late-order. This indicates the effectiveness of the developed approach in managing raw material and final product inventory levels, as well as mitigating shortages in raw materials through informed decision-making. 5.3 Research Limitations Although the research conducted in this thesis makes significant contributions to the field of sustainable production planning, it is crucial to acknowledge its barriers and limitations. This provides valuable insights into the scope of the research, thereby improving the understanding of its findings. Some potential barriers and limitations of the present thesis are as follows: • The main challenge encountered in this research is the scarcity of real-world data. Acquiring such data is difficult due to privacy concerns, as industries are often reluctant to disclose classified information. Despite the efforts to synthesize reliable data using available real information and consider various scenarios for more robust conclusions, there remains a need for improvement through the collection of 100% real data. Using real-world data helps in confronting and addressing any potential flaws that may exist in the developed models, thus enhancing their performance. • Similar to any research study in the field of mathematical optimization, the MILP models formulated in this thesis are based on a number of simplifying assumptions. These assumptions may mitigate the complexities of real-world production systems but are necessary to facilitate modeling, enhance the tractability, and simplify the analysis of the results. For instance, the developed mathematical models in this thesis assume a fixed 51 rolling duration parameter over the entire planning scheme. Furthermore, cost components are considered certain parameters disregarding the different sources of uncertainties that may exist in practice. • Like many other research, this study faces challenges in collaborating with industry partners and identifying other domains of improvement. Although the problem addressed in this thesis is completely defined according to the literature, collaborating with industrial partners results in acquiring a more comprehensive understanding of real-world challenges and developing more practical solutions. Without access to authentic industrial information, researchers are forced to rely on the conventional definition of the problem, often resulting in findings that may not comprehensively address real-world challenges. 5.4 Future Research Given the findings and limitations discussed in this chapter, there are several paths for future exploration, offering promising directions for further advancement in the field. • Evaluating the DRHP approach using real data of market demand and recycling rate. By analyzing real-world data, the effectiveness of the DRHP approach in handling practical scenarios can be accurately assessed, ensuring its applicability beyond theoretical frameworks. • Exploring the impact of other sources of uncertainty (e.g., cost parameters or production capacity) on the problem and its outcomes. By incorporating various sources of uncertainty, the model can better mimic the complexities of real-world dynamics, providing more insightful and reliable results. • Benchmarking the DRHP approach against other robust optimization models to further investigate its strengths and weaknesses across different situations of the problem and different scenarios of uncertain parameters. • Performing sensitivity analysis on other parameters of the RH-based model. By systematically varying parameters and observing their effects on results, decision-makers can make informed adjustments, optimizing decisions to align with desired objectives and constraints. 52 • Incorporating other components of the supply chain management problem into the RH-based MILP model ensures holistic solution consistency. By considering factors such as suppliers, distribution centers, and retail stores, the model can provide comprehensive and feasible solutions that address the entire network's needs and constraints. • Tailoring the proposed RH-based model to the production environment of other industries (e.g., paper industry) as sustainability is a common goal across various domains. • Extending the present single-objective MILP model into a multi-objective model and developing a multi-objective solution approach to more specifically follow environmental and social aspects of sustainability. • Utilizing DRL techniques to optimize updating strategy by learning from historical data and real-time information. It helps in dynamically adjusting rolling duration to minimize total production cost and enhance the system’s efficiency. 53 Bibliography Abdelmegid, M. A., González, V. A., O’Sullivan, M., Walker, C. G., Poshdar, M., & Alarcón, L. F. (2023). Exploring the links between simulation modelling and construction production planning and control: a case study on the last planner system. Production Planning & Control, 34(5), 459-476. Abedi, S., & Kwon, S. (2023). Rolling-horizon optimization integrated with recurrent neural network-driven forecasting for residential battery energy storage operations. International Journal of Electrical Power & Energy Systems, 145, 108589. Addis, B., Carello, G., Grosso, A., & Tànfani, E. (2016). Operating room scheduling and rescheduling: a rolling horizon approach. Flexible Services and Manufacturing Journal, 28(1-2), 206-232. Ahmed, A. K. A., Ibraheem, A. M., & Abd-Ellah, M. K. (2022). Forecasting of municipal solid waste multi-classification by using time-series deep learning depending on the living standard. Results in Engineering, 16, 100655. Antonopoulos, I., Faraca, G., & Tonini, D. (2021). Recycling of post-consumer plastic packaging waste in the EU: Recovery rates, material flows, and barriers. Waste Management, 126, 694-705. Benítez, R., Ortiz-Caraballo, C., Preciado, J. C., Conejero, J. M., Sánchez Figueroa, F., & Rubio-Largo, A. (2019). A short-term data based water consumption prediction approach. Energies, 12(12), 2359. Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations research letters, 25(1), 1-13. Bertsimas, D., Pachamanova, D., & Sim, M. (2004). Robust linear optimization under general norms. Operations Research Letters, 32(6), 510-516. Beykal, B., Avraamidou, S., & Pistikopoulos, E. N. (2022). Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty. Computers & chemical engineering, 156, 107551. Cao, X., Liang, Y., Jiang, J., Mo, A., & He, D. (2023). Organic additives in agricultural plastics and their impacts on soil ecosystems: compared with conventional and biodegradable plastics. TrAC Trends in Analytical Chemistry, 117212. Cavagnini, R., Bertazzi, L., & Maggioni, F. (2022). A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment. European Journal of Operational Research, 301(3), 912-922. Chen, Hui Ling, Tapan Kumar Nath, Siewhui Chong, Vernon Foo, Chris Gibbins, and Alex M. Lechner. "The plastic waste problem in Malaysia: management, recycling and disposal of local and global plastic waste." SN Applied Sciences 3 (2021): 1-15. Clark, A. R. (2005). Rolling horizon heuristics for production planning and set-up scheduling with backlogs and error-prone demand forecasts. Production Planning & Control, 16(1), 81-97. 54 Cuisinier, É., Lemaire, P., Penz, B., Ruby, A., & Bourasseau, C. (2022). New rolling horizon optimization approaches to balance short-term and long-term decisions: An application to energy planning. Energy, 245, 122773. de Souza Machado, A. A., Kloas, W., Zarfl, C., Hempel, S., & Rillig, M. C. (2018). Microplastics as an emerging threat to terrestrial ecosystems. Global change biology, 24(4), 1405-1416. Dehghan Shoorkand, H., Nourelfath, M., & Hajji, A. (2023). A deep learning approach for integrated production planning and predictive maintenance. International Journal of Production Research, 1-20. Du, B., Huang, S., Guo, J., Tang, H., Wang, L., & Zhou, S. (2022). Interval forecasting for urban water demand using PSO optimized KDE distribution and LSTM neural networks. Applied Soft Computing, 122, 108875. Du, H., Zhao, Z., & Xue, H. (2020). ARIMA-M: A new model for daily water consumption prediction based on the autoregressive integrated moving average model and the markov chain error correction. Water, 12(3), 760. Evode, N., Qamar, S. A., Bilal, M., Barceló, D., & Iqbal, H. M. (2021). Plastic waste and its management strategies for environmental sustainability. Case Studies in Chemical and Environmental Engineering, 4, 100142. Farah, E., Abdallah, A., & Shahrour, I. (2019). Prediction of water consumption using Artificial Neural Networks modelling (ANN). In MATEC Web of Conferences (Vol. 295, p. 01004). EDP Sciences. Faraca, G., Martinez-Sanchez, V., & Astrup, T. F. (2019). Environmental life cycle cost assessment: Recycling of hard plastic waste collected at Danish recycling centres. Resources, Conservation and Recycling, 143, 299-309. Fattahi, M., & Govindan, K. (2022). Data‐driven rolling horizon approach for dynamic design of supply chain distribution networks under disruption and demand uncertainty. Decision Sciences, 53(1), 150-180. Fernandez, M. O., & Trasande, L. (2024). The Global Plastics Treaty: An Endocrinologist's Assessment. Journal of the Endocrine Society, 8(1), bvad141. Forel, A., & Grunow, M. (2023). Dynamic stochastic lot sizing with forecast evolution in rolling‐horizon planning. Production and Operations Management, 32(2), 449-468. Furini, F., Kidd, M. P., Persiani, C. A., & Toth, P. (2015). Improved rolling horizon approaches to the aircraft sequencing problem. Journal of Scheduling, 18, 435-447. Gahm, C., Uzunoglu, A., Wahl, S., Ganschinietz, C., & Tuma, A. (2022). Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning. European Journal of Operational Research, 296(3), 819-836. Geyer, R., Jambeck, J. R., & Law, K. L. (2017). Production, use, and fate of all plastics ever made. Science advances, 3(7), e1700782. 55 Ghaedy-Heidary, E., Nejati, E., Ghasemi, A., & Torabi, S. A. (2023). A simulation optimization framework to solve Stochastic Flexible Job-Shop Scheduling Problems—Case: Semiconductor manufacturing. Computers & Operations Research, 106508. Glomb, L., Liers, F., & Rösel, F. (2022). A rolling-horizon approach for multi-period optimization. European Journal of Operational Research, 300(1), 189-206. Goerigk, M., & Kurtz, J. (2023). Data-driven robust optimization using deep neural networks. Computers & Operations Research, 151, 106087. Goli, A., Tirkolaee, E. B., & Aydın, N. S. (2021). Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors. IEEE transactions on fuzzy systems, 29(12), 3686-3695. Gondal, A. H., Bhat, R. A., Gómez, R. L., Areche, F. O., & Huaman, J. T. (2023). Advances in plastic pollution prevention and their fragile effects on soil, water, and air continuums. International Journal of Environmental Science and Technology, 20(6), 6897-6912. González Rodríguez, G., Gonzalez-Cava, J. M., & Méndez Pérez, J. A. (2020). An intelligent decision support system for production planning based on machine learning. Journal of Intelligent Manufacturing, 31(5), 1257-1273. Guo, X., Zhang, Z., Qi, L., Liu, S., Tang, Y., & Zhao, Z. (2021). Stochastic hybrid discrete grey wolf optimizer for multi-objective disassembly sequencing and line balancing planning in disassembling multiple products. IEEE Transactions on Automation Science and Engineering, 19(3), 1744-1756. Hahladakis, J. N., & Iacovidou, E. (2019). An overview of the challenges and trade-offs in closing the loop of post-consumer plastic waste (PCPW): Focus on recycling. Journal of hazardous materials, 380, 120887. Hameed, M. S. A., & Schwung, A. (2023). Graph neural networks-based scheduler for production planning problems using reinforcement learning. Journal of Manufacturing Systems, 69, 91-102. Hubbs, C. D., Li, C., Sahinidis, N. V., Grossmann, I. E., & Wassick, J. M. (2020). A deep reinforcement learning approach for chemical production scheduling. Computers & Chemical Engineering, 141, 106982. Jaganmohan, M. (2024). Annual production of plastics worldwide from 1950 to 2022. Retrieved March 6, 2024, from https://www.statista.com/statistics/282732/global-production-of-plastics-since-1950/#statisticContainer. Jayathilaka, R. M. R. M., Weerakoon, W. R. W. M. A. P., Indika, K. W., Arulananthan, K., & Kithsiri, H. M. P. (2022). Spatio-temporal variation of plastic pellets dispersion in the coastline of Sri Lanka: An assessment of pellets originated from the X-Press Pearl incident during the Southwest monsoon in 2021. Marine Pollution Bulletin, 184, 114145. Jones, A. Q., Majowicz, S. E., Edge, V. L., Thomas, M. K., MacDougall, L., Fyfe, M., ... & Kovacs, S. J. (2007). Drinking water consumption patterns in British Columbia: an investigation of associations with demographic factors and acute gastrointestinal illness. Science of the total environment, 388(1-3), 54-65. 56 Joseph, B., James, J., Kalarikkal, N., & Thomas, S. (2021). Recycling of medical plastics. Advanced Industrial and Engineering Polymer Research, 4(3), 199-208. Iwakin, O., & Moazeni, F. (2024). Improving urban water demand forecast using conformal prediction-based hybrid machine learning models. Journal of Water Process Engineering, 58, 104721. Kamal, M., Gupta, S., Chatterjee, P., Pamucar, D., & Stevic, Z. (2019). Bi-level multi-objective production planning problem with multi-choice parameters: a fuzzy goal programming algorithm. Algorithms, 12(7), 143. Kamran, M. A., Karimi, B., Dellaert, N., & Demeulemeester, E. (2019). Adaptive operating rooms planning and scheduling: A rolling horizon approach. Operations Research for Health Care, 22, 100200. Kassotis, C. D., Klemp, K. C., Vu, D. C., Lin, C. H., Meng, C. X., Besch-Williford, C. L., ... & Nagel, S. C. (2015). Endocrine-disrupting activity of hydraulic fracturing chemicals and adverse health outcomes after prenatal exposure in male mice. Endocrinology, 156(12), 4458-4473. Kibria, M. G., Masuk, N. I., Safayet, R., Nguyen, H. Q., & Mourshed, M. (2023). Plastic waste: Challenges and opportunities to mitigate pollution and effective management. International Journal of Environmental Research, 17(1), 20. Kim, T., Kim, Y. W., & Cho, H. (2020). Dynamic production scheduling model under due date uncertainty in precast concrete construction. Journal of Cleaner Production, 257, 120527. Kisomi, M. S., Solimanpur, M., & Doniavi, A. (2016). An integrated supply chain configuration model and procurement management under uncertainty: a set-based robust optimization methodology. Applied Mathematical Modelling, 40(17-18), 7928-7947. Koskinen, J., Raduly-Baka, C., Johnsson, M., & Nevalainen, O. S. (2020). Rolling horizon production scheduling of multi-model PCBs for several assembly lines. International Journal of Production Research, 58(4), 1052-1073. Kühnert, C., Gonuguntla, N. M., Krieg, H., Nowak, D., & Thomas, J. A. (2021). Application of LSTM networks for water demand prediction in optimal pump control. Water, 13(5), 644. Kumar, R. (2022). Operations management. Jyothis Publishers. Kurniawan, S. B., Said, N. S. M., Imron, M. F., & Abdullah, S. R. S. (2021). Microplastic pollution in the environment: Insights into emerging sources and potential threats. Environmental Technology & Innovation, 23, 101790. Lee, Y. H., & Lee, S. (2022). Deep reinforcement learning based scheduling within production plan in semiconductor fabrication. Expert Systems with Applications, 191, 116222. Li, Z., Ding, R., & Floudas, C. A. (2011). A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization. Industrial & engineering chemistry research, 50(18), 10567-10603. 57 Li, Z., & Ierapetritou, M. G. (2010). Rolling horizon based planning and scheduling integration with production capacity consideration. Chemical Engineering Science, 65(22), 5887-5900. Lu, C., Maciejewski, M., Wu, H., & Nagel, K. (2023). Optimization of demand-responsive transport: The rolling horizon approach. Procedia Computer Science, 220, 145-153. Lu, C. C., Ying, K. C., & Chen, H. J. (2016). Real-time relief distribution in the aftermath of disasters–A rolling horizon approach. Transportation research part E: logistics and transportation review, 93, 1-20. Marquant, J. F., Evins, R., & Carmeliet, J. (2015). Reducing computation time with a rolling horizon approach applied to a MILP formulation of multiple urban energy hub system. Procedia Computer Science, 51, 2137-2146. Mohammadi, S., Al-e-Hashem, S. M., & Rekik, Y. (2020). An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company. International Journal of Production Economics, 219, 347-359. Mohseni, S., & Pishvaee, M. S. (2020). Data-driven robust optimization for wastewater sludge-to-biodiesel supply chain design. Computers & Industrial Engineering, 139, 105944. Morariu, C., Morariu, O., Răileanu, S., & Borangiu, T. (2020). Machine learning for predictive scheduling and resource allocation in large scale manufacturing systems. Computers in Industry, 120, 103244. Muncke, J., Andersson, A. M., Backhaus, T., Boucher, J. M., Carney Almroth, B., Castillo Castillo, A., ... & Scheringer, M. (2020). Impacts of food contact chemicals on human health: a consensus statement. Environmental Health, 19, 1-12. Nasser, A. A., Rashad, M. Z., & Hussein, S. E. (2020). A two-layer water demand prediction system in urban areas based on micro-services and LSTM neural networks. IEEE Access, 8, 147647-147661. Oliveira, M., Visintin, F., Santos, D., & Marques, I. (2022). Flexible master surgery scheduling: combining optimization and simulation in a rolling horizon approach. Flexible Services and Manufacturing Journal, 34(4), 824-858. Oluyisola, O. E., Bhalla, S., Sgarbossa, F., & Strandhagen, J. O. (2022). Designing and developing smart production planning and control systems in the industry 4.0 era: a methodology and case study. Journal of Intelligent Manufacturing, 33(1), 311-332. Plastics – the facts. (2022). Retrieved March 6, 2024, from https://plasticseurope.org/knowledge-hub/plastics-the-facts-2022/. Plastic waste and pollution reduction. (2023). Retrieved March 6, 2024, from https://www.canada.ca/en/environment-climate-change/services/managing-reducing-waste/reduce-plastic-waste.html. Pu, Z., Yan, J., Chen, L., Li, Z., Tian, W., Tao, T., & Xin, K. (2023). A hybrid Wavelet-CNN-LSTM deep learning model for short-term urban water demand forecasting. Frontiers of Environmental Science & Engineering, 17(2), 22. 58 Rabnawaz, M., Wyman, I., Auras, R., & Cheng, S. (2017). A roadmap towards green packaging: the current status and future outlook for polyesters in the packaging industry. Green Chemistry, 19(20), 4737-4753. Ramasamy, R., Aragaw, T. A., & Balasaraswathi Subramanian, R. (2022). Wastewater treatment plant effluent and microfiber pollution: focus on industry-specific wastewater. Environmental Science and Pollution Research, 29(34), 51211-51233. Reijonen, H., Bellman, S., Murphy, J., & Kokkonen, H. (2021). Factors related to recycling plastic packaging in Finland’s new waste management scheme. Waste Management, 131, 88-97. Rossit, D. A., Tohmé, F., & Frutos, M. (2019). A data-driven scheduling approach to smart manufacturing. Journal of Industrial Information Integration, 15, 69-79. Santander, O., Betts, C. L., Archer, E. E., & Baldea, M. (2020). On the interaction and integration of production planning and (advanced) process control. Computers & Chemical Engineering, 133, 106627. Shalaby, A. A., Shaaban, M. F., Mokhtar, M., Zeineldin, H. H., & El-Saadany, E. F. (2022). A dynamic optimal battery swapping mechanism for electric vehicles using an LSTM-based rolling horizon approach. IEEE Transactions on Intelligent Transportation Systems, 23(9), 15218-15232. Shamsuyeva, M., & Endres, H. J. (2021). Plastics in the context of the circular economy and sustainable plastics recycling: Comprehensive review on research development, standardization and market. Composites Part C: open access, 6, 100168. Shen, L., & Worrell, E. (2024). Plastic recycling. In Handbook of recycling (pp. 497-510). Elsevier. Tolio, T., & Urgo, M. (2007). A rolling horizon approach to plan outsourcing in manufacturing-to-order environments affected by uncertainty. CIRP annals, 56(1), 487-490. Torkaman, S., Jokar, M. R. A., Mutlu, N., & Van Woensel, T. (2022). Rolling horizon-based heuristics for solving a production-routing problem with price-dependent demand. Computers & Operations Research, 148, 105973. Tosarkani, B. M., & Amin, S. H. (2020). A robust optimization model for designing a wastewater treatment network under uncertainty: Multi-objective approach. Computers & Industrial Engineering, 146, 106611. Tosarkani, B. M., Amin, S. H., & Ghiasvand, M. R. (2024). Designing a sustainable plastic bottle reverse logistics network: A data-driven optimization approach. Expert Systems with Applications, 123918. Vieira, M., Moniz, S., Gonçalves, B. S., Pinto-Varela, T., Barbosa-Póvoa, A. P., & Neto, P. (2022). A two-level optimisation-simulation method for production planning and scheduling: the industrial case of a human–robot collaborative assembly line. International Journal of Production Research, 60(9), 2942-2962. Villalonga, A., Negri, E., Biscardo, G., Castano, F., Haber, R. E., Fumagalli, L., & Macchi, M. (2021). A decision-making framework for dynamic scheduling of cyber-physical production systems based on digital twins. Annual Reviews in Control, 51, 357-373. 59 Walker, S., & Rothman, R. (2020). Life cycle assessment of bio-based and fossil-based plastic: A review. Journal of Cleaner Production, 261, 121158. Williams, I. D., & Phillips, J. (2022). Leading the World: A Review of Household Recycling in Wales. Recycling, 7(4), 46. Wong, J. S., Zhang, Q., & Chen, Y. D. (2010). Statistical modeling of daily urban water consumption in Hong Kong: Trend, changing patterns, and forecast. Water resources research, 46(3). Wu, O., Dalle Ave, G., Harjunkoski, I., & Imsland, L. (2021). A rolling horizon approach for scheduling of multiproduct batch production and maintenance using generalized disjunctive programming models. Computers & Chemical Engineering, 148, 107268. Yağmur, E., & Kesen, S. E. (2023). Bi-objective coordinated production and transportation scheduling problem with sustainability: formulation and solution approaches. International Journal of Production Research, 61(3), 774-795. Zaneti, L. A., Arias, N. B., de Almeida, M. C., & Rider, M. J. (2022). Sustainable charging schedule of electric buses in a University Campus: A rolling horizon approach. Renewable and Sustainable Energy Reviews, 161, 112276. Zero plastic waste. (2021). Retrieved May 11, 2024, from https://www.canada.ca/en/environment-climate-change/services/managing-reducing-waste/reduce-plastic-waste/need-action.html. Zhang, C., Kuppannagari, S. R., Kannan, R., & Prasanna, V. K. (2018, October). Generative adversarial network for synthetic time series data generation in smart grids. In 2018 IEEE international conference on communications, control, and computing technologies for smart grids (SmartGridComm) (pp. 1-6). IEEE. Zhang, F., Zhao, Y., Wang, D., Yan, M., Zhang, J., Zhang, P., ... & Chen, C. (2021). Current technologies for plastic waste treatment: A review. Journal of Cleaner Production, 282, 124523. Zhang, W., Zheng, Y., & Ahmad, R. (2023). The integrated process planning and scheduling of flexible job-shop-type remanufacturing systems using improved artificial bee colony algorithm. Journal of Intelligent Manufacturing, 34(7), 2963-2988. Zhang, X., Liao, Z., Ma, L., & Yao, J. (2022). Hierarchical multistrategy genetic algorithm for integrated process planning and scheduling. Journal of Intelligent Manufacturing, 33, 223-246. Zhang, Y., Zhu, H., Tang, D., Zhou, T., & Gui, Y. (2022). Dynamic job shop scheduling based on deep reinforcement learning for multi-agent manufacturing systems. Robotics and Computer-Integrated Manufacturing, 78, 102412. Ziarnetzky, T., Mönch, L., & Uzsoy, R. (2018). Rolling horizon, multi-product production planning with chance constraints and forecast evolution for wafer fabs. International Journal of Production Research, 56(18), 6112-6134. 60 Appendices Appendix A: The Static Counterpart In this approach, the entire production scheme is planned all at once in advance. Orders for raw materials, whether virgin plastics or plastic waste, can be placed at any time (without restrictions on the timing of orders). Similar to the DRHP approach, demand and recycling rate are uncertain parameters. The MILP model developed for the static counterpart is as follows: Indices: 𝑡 Days; t = 1, …., 𝑇. 𝑝 Type of raw materials/products; 𝑝 = 1, … , 𝑃. Parameters: 𝜐 Raw material preparation efficiency, equivalent to rolling duration (Θ𝜏) in the DRHP approach (day). 𝐷′𝑝𝑡 Predicted demand of product p on day t (unit). 𝑅𝑅′𝑝𝑡 Predicted recycling rate of plastic waste type p on day t (percentage). 𝑃𝑐𝑎𝑝𝑝𝑡 Production capacity for product type p on day t (unit). 𝐶𝑖𝑛𝑣𝑟𝑝𝑡 Inventory cost of raw material type p on day t ($ per kg). 𝐶𝑖𝑛𝑣𝑓𝑝𝑡 Inventory cost of final products type p on day t ($ per unit). 𝐶𝑝𝑟𝑜𝑝𝑡 Production cost of product type p on day t ($ per unit). 𝐶𝑏𝑙𝑝𝑡 Backlog cost of product type p on day t ($ per unit). 𝐶𝑣𝑝𝑝𝑡 Cost of virgin plastic type p on day t ($ per kg). 𝐶𝑤𝑝𝑝𝑡 Cost of plastic waste type p on day t ($ per kg). 𝐶𝑟𝑝𝑡 Cost of recycling plastic waste type p on day t ($ per kg). 61 𝐶𝑐𝑣𝑝𝑡 Contract cost for virgin plastic type p on day t ($). 𝐶𝑐𝑤𝑝𝑡 Contract cost for plastic waste type p on day t ($). 𝐼𝑛𝑣𝑟𝑝 Inventory of raw material type p at the beginning of planning scheme (kg). 𝐼𝑛𝑣𝑓𝑝 Inventory of final product type p at the beginning of planning scheme (unit). 𝛼𝑝 Unitary raw material consumption for product type p (percent). 𝑀 A very large positive number. 𝜀 A very small positive number. Decision variables: 𝑥𝑝𝑡 Amount of virgin plastic type p ordered on day t (kg). 𝑦𝑝𝑡 Amount of plastic waste type p ordered on day t (kg). 𝑧𝑝𝑡 Amount of virgin plastic type p received on day t (kg). 𝑙′𝑝𝑡 Amount of raw material type p expected to be sourced through recycling stream on day t (kg). 𝑝𝑞𝑝𝑡 Number of product type p produced on day t (unit). 𝑠𝑞𝑝𝑡 Number of product type p sold on day t (unit). 𝑖𝑛𝑣𝑟𝑝𝑡 Inventory of raw material type p on the end of day t (kg). 𝑖𝑛𝑣𝑓𝑝𝑡 Inventory of final product type p on the end of day t (kg). 𝑣𝑝𝑡 Equals 1 if virgin material contributes to the raw material sourcing of product type p on day t, otherwise 0. 𝑤𝑝𝑡 Equals 1 if recycling contributes to the raw material sourcing of product type p on day t, otherwise 0. Objective function: 62 𝑀𝑖𝑛 𝑍ℎ = ∑ ∑ (𝐶𝑣𝑝𝑝𝑡𝑥𝑝𝑡 + 𝐶𝑤𝑝𝑝𝑡𝑦𝑝𝑡 + 𝐶𝑟𝑝𝑡𝑙′𝑝𝑡 + 𝐶𝑐𝑣𝑝𝑡𝑣𝑝𝑡 + 𝐶𝑐𝑤𝑝𝑡𝑤𝑝𝑡𝑇𝑡=1𝑃𝑝=1+ 𝐶𝑖𝑛𝑣𝑟𝑝𝑡𝑖𝑛𝑣𝑟𝑝𝑡 + 𝐶𝑖𝑛𝑣𝑓𝑝𝑡𝑖𝑛𝑣𝑓𝑝𝑡 + 𝐶𝑝𝑟𝑜𝑝𝑡𝑝𝑞𝑝𝑡 + 𝐶𝑏𝑙𝑝𝑡(𝐷′𝑝𝑡 − 𝑠𝑞𝑝𝑡)) (30) Constraints: 𝑝𝑞𝑝𝑡 ≤ 𝑃𝑐𝑎𝑝𝑝𝑡 ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (31) 𝑠𝑞𝑝𝑡 ≤ 𝐷′𝑝𝑡 ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (32) 𝑧𝑝𝑡 = 0 ∀𝑡 ∈ {1, … , 𝜐}, ∀𝑝 ∈ {1, … , 𝑃} (33) 𝑧𝑝𝑡 = 𝑥𝑝(𝑡−υ) ∀𝑡 ∈ {𝜐 + 1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (34) 𝑙′𝑝𝑡 = 0 ∀𝑡 ∈ {1, … , 𝜐}, ∀𝑝 ∈ {1, … , 𝑃} (35) 𝑙′𝑝𝑡 = 𝑦𝑝(𝑡−υ). 𝑅𝑅′𝑝(𝑡−υ) ∀𝑡 ∈ {𝜐 + 1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (36) 𝐼𝑛𝑣𝑟𝑝 − 𝛼𝑝𝑝𝑞𝑝𝑡 = 𝑖𝑛𝑣𝑟𝑝𝑡 𝑡 = 1, ∀𝑝 ∈ {1, … , 𝑃} (37) 𝑖𝑛𝑣𝑟𝑝(𝑡−1) − 𝛼𝑝𝑝𝑞𝑝𝑡 + 𝑧𝑝𝑡 + 𝑙′𝑝𝑡 = 𝑖𝑛𝑣𝑟𝑝𝑡 ∀𝑡 ∈ {2, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (38) 𝐼𝑛𝑣𝑓𝑝 + 𝑝𝑞𝑝𝑡 − 𝑠𝑞𝑝𝑡 = 𝑖𝑛𝑣𝑓𝑝𝑡 𝑡 = 1, ∀𝑝 ∈ {1, … , 𝑃} (39) 𝑖𝑛𝑣𝑓𝑝(𝑡−1) + 𝑝𝑞𝑝𝑡 − 𝑠𝑞𝑝𝑡 = 𝑖𝑛𝑣𝑓𝑝𝑡 ∀𝑡 ∈ {2, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (40) 𝜀. 𝑣𝑝𝑡 ≤ 𝑥𝑝𝑡 ≤ 𝑀. 𝑣𝑝𝑡 ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (41) 𝜀. 𝑤𝑝𝑡 ≤ 𝑦𝑝𝑡 ≤ 𝑀. 𝑤𝑝𝑡 ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (42) 𝑥𝑝𝑡 , 𝑦𝑝𝑡 , 𝑧𝑝𝑡 , 𝑙𝑝𝑡 , 𝑝𝑞𝑝𝑡 , 𝑠𝑞𝑝𝑡 , 𝑖𝑛𝑣𝑟𝑝𝑡, 𝑖𝑛𝑣𝑓𝑝𝑡, 𝑣𝑝𝑡, 𝑤𝑝𝑡 ∈ 𝑅+ ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (43) 𝑣𝑝𝑡 , 𝑤𝑝𝑡 ∈ {0,1} ∀𝑡 ∈ {1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (44) Objective (30) minimizes the production cost over the entire planning scheme. Constraint (31) accounts for production capacity limits. Constraint (32) ensures demand satisfaction. Constraints (33) and (34) specify the daily amount of raw material received through the virgin plastic stream. Constraints (35) and (36) determine the daily amount of raw material received through the recycling stream. Constraints (37) and (38) monitor the flow of raw material inventory throughout 63 the entire planning process. Constraints (39) and (40) ensure a balanced inventory flow for final products. Constraints (41) and (42) determine the quantity of raw material sourced through virgin plastics and the recycling stream, respectively. Constraints (43) and (44) specify the range of the decision variables. It is worth mentioning that the ATC in the static approach is also determined at the end of the planning scheme (after the disclosure of actual data of demand and recycling rate) as follows: ATC ∶= ∑ ∑ (𝐶𝑣𝑝𝑝𝑡𝑥𝑝𝑡 + 𝐶𝑤𝑝𝑝𝑡𝑦𝑝𝑡 + 𝐶𝑟𝑝𝑡𝐿𝑝𝑡 + 𝐶𝑐𝑣𝑝𝑡𝑣𝑝𝑡 + 𝐶𝑐𝑤𝑝𝑡𝑤𝑝𝑡 +𝑇𝑡=1𝑃𝑝=1𝐶𝑖𝑛𝑣𝑟𝑝𝑡𝑖𝑛𝑣𝑟𝑝𝑡 + 𝐶𝑖𝑛𝑣𝑓𝑝𝑡𝑖𝑛𝑣𝑓𝑝𝑡 + 𝐶𝑝𝑟𝑝𝑡𝑝𝑞𝑝𝑡 + 𝐶𝑑𝑜𝑝𝑡𝑃𝑑𝑜𝑝𝑡(𝑙′𝑝𝑡 − 𝐿𝑝𝑡) +𝐶𝑏𝑙𝑝𝑡𝑌𝑏𝑙𝑝𝑡(𝐷𝑝𝑡 − 𝑠𝑞𝑝𝑡) + 𝐶𝑒𝑥𝑝𝑡(1 − 𝑌𝑏𝑙𝑝𝑡)𝑝𝑡(𝑠𝑞𝑝𝑡 − 𝐷𝑝𝑡)) (45) where 𝐿𝑝𝑡 = 0 ∀𝑡 ∈ {1, … , 𝜐}, ∀𝑝 ∈ {1, … , 𝑃} (46) 𝐿𝑝𝑡 = 𝑦𝑝(𝑡−𝜐). 𝑅𝑅𝑝(𝑡−𝜐) ∀𝑡 ∈ {𝜐 + 1, … , 𝑇}, ∀𝑝 ∈ {1, … , 𝑃} (47) and 𝐿𝑝𝑡 Actual Amount of raw material type p sourced through recycling stream on day t (kg). 𝐷𝑝𝑡 Actual demand of product p on day t (unit). 𝑅𝑅𝑝𝑡 Actual recycling rate of plastic waste type p on day t (percentage). 𝐶𝑑𝑜𝑝𝑡 Late-order cost for virgin plastic type p on day t ($ per kilogram). 𝐶𝑒𝑥𝑝𝑡 Cost of excessive production of product type p on day t ($ per unit). 𝑃𝑑𝑜𝑝𝑡 Equals 1 if 𝐿𝑝𝑡 ≤ 𝑙′𝑝𝑡, otherwise 0. 𝑌𝑏𝑙𝑝𝑡 Equals 1 if 𝑠𝑞𝑝𝑡 ≤ 𝐷𝑝𝑡, otherwise 0. 64 Appendix B: Synthetic Daily Demands #Libraries import numpy as np # Constants total_days = 365 average_demand = 28500 # Generate time series data with seasonal pattern and noise time = np.arange(total_days) ##Scenario1 seasonality_pattern1 = (20000 * np.sin (2 * np.pi * time / total_days - np.pi/2) + 10000 * np.sin (4 * np.pi * time / total_days - np.pi/4) + 5000 * np.sin (6 * np.pi * time / total_days + np.pi/4)) noise_std1 = 4000 noise1 = np.random.normal (scale=noise_std1, size=total_days) daily_demand1 = average_demand + seasonality_pattern1 + noise1 daily_demand1 = np.maximum(daily_demand1, 5000) ##Scenario2 seasonality_pattern2 = (15000 * np.sin(2 * np.pi * time / total_days) + 5000 * np.cos(4 * np.pi * time / total_days) + 1000 * time / total_days) noise_std2 = 4000 noise2 = np.random.normal (scale=noise_std2, size=total_days) daily_demand2 = average_demand + seasonality_pattern2 + noise2 daily_demand2 = np.maximum(daily_demand2, 5000) 65 ##Scenario 3 seasonality_pattern3 = (25000 * np.sin(2 * np.pi * time / total_days) + 15000 * np.sin(4 * np.pi * time / total_days) + 10000 * np.sin(6 * np.pi * time / total_days)) noise_std3 = 3000 * np.abs(np.sin(2 * np.pi * time / total_days)) noise3 = np.random.normal (scale=noise_std3, size=total_days) daily_demand3 = average_demand + seasonality_pattern3 + noise3 daily_demand3 = np.maximum(daily_demand3, 5000) 66 Appendix C: Synthetic Daily Recycling Rates #Libraries import numpy as np ##Scenario1 ### Constants supplier_rates1 = {'Supplier 1': {'mean': 66, 'std_dev': 3}, 'Supplier 2': {'mean': 63, 'std_dev': 3}, 'Supplier 3': {'mean': 70, 'std_dev': 2}, 'Supplier 4': {'mean': 87, 'std_dev': 1}, 'Supplier 5': {'mean': 90, 'std_dev': 10}, 'Supplier 6': {'mean': 52, 'std_dev': 4}, 'Supplier 7': {'mean': 81, 'std_dev': 2}} num_days = 365 ### Generate time series data for recycling rates with facility switches data1 = [] current_supplier1 = np.random.choice (list(supplier_rates1.keys())) days_with_current_supplier1 = np.random.randint (3, 8) for day in range (1, num_days + 1): if days_with_current_supplier1 == 0: current_supplier1 = np.random.choice (list(supplier_rates.keys1())) days_with_current_supplier1 = np.random.randint (3, 8) supplier_name1 = current_supplier1 mean_rate1 = supplier_rates1 [supplier_name1]['mean'] 67 std_dev1 = supplier_rates1 [supplier_name1]['std_dev'] recycling_rate1 = np.random.normal (mean_rate1, std_dev1) recycling_rate1 = min (recycling_rate1, 98) data1.append ((day, round (recycling_rate1, 1))) ##Scenario2 ### Constants supplier_rates2 = {'Supplier 1': {'mean': 0.92, 'std': 0.004, 'probability': 0.7, 'next_prob': 0.9}, 'Supplier 2': {'mean': 0.85, 'std': 0.012, 'probability': 0.25, 'next_prob': 0.7}, 'Supplier 3': {'mean': 0.75, 'std': 0.013, 'probability': 0.05}} num_days = 365 ### Generate time series data recycling rates based on the selected supplier suppliers2 = list (supplier_rates2.keys()) selected_suppliers2 = [] for day in range (num_days): if day == 0 or (selected_suppliers2 [day - 1] == 'Supplier 1' and np.random.random () < supplier_rates2 ['Supplier 1']['next_prob']): current_supplier2 = 'Supplier 1' elif day == 0 or (selected_suppliers2 [day - 1] == 'Supplier 2' and np.random.random () < supplier_rates2 ['Supplier 2']['next_prob']): current_supplier2 = 'Supplier 2' else: current_supplier2 = np.random.choice (suppliers2, p=[supplier_rates2[s]['probability'] for s in suppliers2]) selected_suppliers2.append (current_supplier2) 68 recycling_rates2 = np.array ([supplier_rates2[supplier]['mean'] for supplier in selected_suppliers2]) recycling_rates2 += np.random.normal (0, [supplier_rates2[supplier]['std'] for supplier in selected_suppliers2], num_days) recycling_rates2 = np.clip (recycling_rates2, 0, 1) ##Scenario3 ### Constants supplier_rates3= {'Supplier 1': {'mean': 0.80, 'std': 0.004, 'probability': 0.7, 'next_prob': 0.33}, 'Supplier 2': {'mean': 0.85, 'std': 0.012, 'probability': 0.25, 'next_prob': 0.33}, 'Supplier 3': {'mean': 0.75, 'std': 0.013, 'probability': 0.05}} num_days = 365 ### Generate time series data recycling rates based on the selected supplier suppliers3 = list (supplier_rates3.keys()) selected_suppliers3 = [] for day in range (num_days): if day == 0 or (selected_suppliers3[day - 1] == 'Supplier 1' and np.random.random () < supplier_rates3['Supplier 1']['next_prob']): current_supplier3 = 'Supplier 1' elif day == 0 or (selected_suppliers3[day - 1] == 'Supplier 2' and np.random.random () < supplier_rates3['Supplier 2']['next_prob']): current_supplier3 = 'Supplier 2' else: current_supplier3 = np.random.choice (suppliers3, p=[ supplier_rates3[s]['probability'] for s in suppliers3]) selected_suppliers3.append (current_supplier3) 69 recycling_rates3 = np.array ([supplier_rates3[supplier]['mean'] for supplier in selected_suppliers3]) recycling_rates3 += np.random.normal (0, [supplier_rates3[supplier]['std'] for supplier in selected_suppliers3], num_days) recycling_rates3 = np.clip (recycling_rates3, 0, 1)
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Tosarkani, Babak Mohamadpour
A novel data-driven rolling horizon production planning approach for the plastic industry under the uncertainty of demand and recycling rate
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