Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Shaker Ardakani, Elham
Master of Applied Science - MASc
University of British Columbia
Global trade agreements (GTAs) have transformed global food supply chains (GFSCs) by facilitating the international flow of food products and reducing barriers such as tariffs and quotas. However, uncertainties in GTAs lead to several challenges, including panic buying and fluctuating demand, transportation delays, expiration of perishable food products, and increased operational costs, all of which threaten the stability and resilience of food supply chains (FSCs). For instance, the termination of the North American Free Trade Agreement (NAFTA) can result in tariff increases of up to 150% in some products, leading to significant cost surges in cross-border food trade and disrupting supply continuity (Swanson & Granville, 2017). This study investigates the impact of such disruptions and the subsequent effects of panic buying on GFSCs and food security. To address the uncertainty in demand, this research develops a two-stage stochastic programming model to optimize a global multi-product FSC during disruptions, aiming to enhance profitability and resilience. Various products with different shelf lives and transportation modes are incorporated into the model to meet logistical requirements. The model integrates supply and distribution decision-making and considers multiple disruption scenarios. The Monte Carlo simulation is employed to simulate the demand parameter by generating a large number of scenarios based on historical data. The K-means clustering method is then applied to reduce the number of generated scenarios. Moreover, the sample average approximation method is employed to mitigate the large-scale nature of the problem and reduce the computational time. A real-world case study demonstrates the model’s applicability, particularly highlighting the impact of a potential NAFTA termination on the FSC between Canada and the United States. The results demonstrate that terminating NAFTA can reduce profit by up to 41.67% due to unmet demand, leading to food shortages first in Canada and then in the United States, with some products being less resilient than others. Finally, the numerical experiments confirm the model’s effectiveness across various problem sizes.
The Role of Global Trade Agreements in Global Food Supply Chain and Food Security by Elham Shaker Ardakani B.Sc., Islamic Azad University, 2015 M.Sc., Alzahra University, 2018 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) April 2025 © Elham Shaker Ardakani, 2025 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis/dissertation entitled: The Role of Global Trade Agreements in Global Food Supply Chain and Food Security submitted by Elham Shaker Ardakani in partial fulfillment of the requirements of the degree of Master of Applied Science . Dr. Babak Mohamadpour Tosarkani, School of Engineering Supervisor Dr. Eric Li, Faculty of Management Co-Supervisor Dr. Wouter Bam, School of Engineering Supervisory Committee Member Dr. Hossein Zolfagharinia, Toronto Metropolitan University Supervisory Committee Member Dr. Liwei Wang, School of Engineering University Examiner iii Abstract Global trade agreements (GTAs) have transformed global food supply chains (GFSCs) by facilitating the international flow of food products and reducing barriers such as tariffs and quotas. However, uncertainties in GTAs lead to several challenges, including panic buying and fluctuating demand, transportation delays, expiration of perishable food products, and increased operational costs, all of which threaten the stability and resilience of food supply chains (FSCs). For instance, the termination of the North American Free Trade Agreement (NAFTA) can result in tariff increases of up to 150% in some products, leading to significant cost surges in cross-border food trade and disrupting supply continuity (Swanson & Granville, 2017). This study investigates the impact of such disruptions and the subsequent effects of panic buying on GFSCs and food security. To address the uncertainty in demand, this research develops a two-stage stochastic programming model to optimize a global multi-product FSC during disruptions, aiming to enhance profitability and resilience. Various products with different shelf lives and transportation modes are incorporated into the model to meet logistical requirements. The model integrates supply and distribution decision-making and considers multiple disruption scenarios. The Monte Carlo simulation is employed to simulate the demand parameter by generating a large number of scenarios based on historical data. The K-means clustering method is then applied to reduce the number of generated scenarios. Moreover, the sample average approximation method is employed to mitigate the large-scale nature of the problem and reduce the computational time. A real-world case study demonstrates the model’s applicability, particularly highlighting the impact of a potential NAFTA termination on the FSC between Canada and the United States. The results demonstrate that terminating NAFTA can reduce profit by up to 41.67% due to unmet demand, leading to food shortages first in iv Canada and then in the United States, with some products being less resilient than others. Finally, the numerical experiments confirm the model’s effectiveness across various problem sizes. v Lay Summary Global trade agreements (GTAs) have revolutionized food supply chains (FSCs) by facilitating international trade and reducing tariffs. However, disruptions in GTAs, such as the potential termination of North American Free Trade Agreement (NAFTA), can trigger panic buying, increase shortages and operational costs, and ultimately threaten food security and economic stability. This study develops a two-stage stochastic optimization model to help food producers, government agencies, and supply chain partners assess risks and make informed decisions under GTA disruptions. The model incorporates multiple products with varying shelf lives and transportation needs, allowing firms to minimize shortages and waste while maximizing total profit. A real-world case study analyzes the impact of NAFTA termination and compares FSC resilience between Canada and the United States. Findings reveal that GTA disruptions can reduce profitability by over 40%, with shortages appearing first in Canada before affecting the United States, and disproportionately impacting certain food products. vi Preface This thesis, entitled “The Role of Global Trade Agreements in Global Food Supply Chain and Food Security”, is an original work conducted by Elham Shaker Ardakani under the supervision of Dr. Babak Mohamadpour Tosarkani at the Industrial & Systems Engineering Research Group and the co-supervision of Dr. Eric Li. I was responsible for the design and execution of the research, the performance of the research tasks, and the analysis of the data. This work reflects my individual efforts in these areas, with guidance and support from my supervisors. To provide this thesis, generative AI was not used for any aspects of the work. vii Table of Contents Abstract .............................................................................................................. iii Lay Summary ...................................................................................................... v Preface ................................................................................................................. vi Table of Contents ..............................................................................................vii List of Tables ....................................................................................................... x List of Figures ..................................................................................................... xi List of Abbreviations ...................................................................................... xiii Acknowledgements............................................................................................ xv Dedication ......................................................................................................... xvi Chapter 1: Introduction ..................................................................................... 1 1.1 Background .................................................................................................................... 1 1.2 Motivation ...................................................................................................................... 5 1.3 Objectives ....................................................................................................................... 7 1.4 Thesis Outline ................................................................................................................. 9 Chapter 2: Literature Review .......................................................................... 10 viii 2.1 Disruptions in Global Food Supply Chains ................................................................. 10 2.2 Resilience Strategies for Enhancing Food Supply Chain Robustness ......................... 12 2.3 The Impact of Global Trade Agreements on Strengthening Food Supply Chain ........ 13 2.4 Stochastic Programming and Sample Average Approximation................................... 16 Chapter 3: Problem Definition ........................................................................ 24 3.1 Problem Formulation ................................................................................................... 26 3.2 Two-stage Stochastic Programming ............................................................................ 32 Chapter 4: Solution Approach, Numerical Experiments, and Sensitivity Analysis .............................................................................................................. 37 4.1 Solution Approach ....................................................................................................... 37 4.1.1 Scenario Generation Method ................................................................................... 39 4.1.2 Scenario Reduction Method .................................................................................... 39 4.1.3 Sample average Approximation .............................................................................. 41 4.2 The Numerical Experiments ........................................................................................ 43 4.3 Case Study .................................................................................................................... 47 Chapter 5: Conclusions and Future Directions ............................................. 65 5.1 Research Summary....................................................................................................... 65 5.2 Research Contributions ................................................................................................ 69 ix 5.3 Research Limitations .................................................................................................... 70 5.4 Future Research ............................................................................................................ 71 Bibliography ...................................................................................................... 74 x List of Tables Table 2.1: An overview of related studies. ............................................................................. 19 Table 3.1: List of notations, parameters, and decision variables ............................................ 26 Table 4.1: Numerical examples .............................................................................................. 43 Table 4.2: Values of 𝑑𝑐𝑚𝑡(lb.) ............................................................................................... 48 Table 4.3: Parameter setting.................................................................................................... 49 xi List of Figures Figure 1.1: Impact of disruptions in GTAs and GFSCs on food security ................................ 4 Figure 3.1: The configuration of the proposed model ............................................................ 25 Figure 4.1: The overall solution framework for optimizing the FSC ..................................... 38 Figure 4.2: The optimal value of the number of clusters ........................................................ 41 Figure 4.3: The convergence of lower bound and upper bound by increasing the sample size.................................................................................................................................................. 46 Figure 4.4: The value of gap (%) and computational time (seconds) based on the number of scenarios ................................................................................................................................... 47 Figure 4.5: The configuration of the FSC with NAFTA ........................................................ 50 Figure 4.6: The configuration of the FSC with termination of NAFTA................................. 51 Figure 4.7: The impact of increasing demand on the total profit and unmet demand (%) .... 53 Figure 4.8: The impact of NAFTA termination and panic buying on the total profit ............ 55 Figure 4.9: The allocation of products under NAFTA disruption .......................................... 57 Figure 4.10: The rate of unmet demand for each product under disruption ........................... 59 Figure 4.11: Impact of production level on unmet demand and rate of waste in factories ..... 61 Figure 4.12: Impact of production level on unmet demand and total inventory .................... 62 Figure 4.13: Impact of production level on total profit and unmet demand .......................... 63 xii Figure 4.14: Impact of minimum level of inventory at retailers and shelf life extension on total waste and profit ................................................................................................................ 64 xiii List of Abbreviations ACO Ant Colony Optimization AHP Analytic Hierarchy Process A𝜀 −C Augmented 𝜀-Constraint BDA Benders Decomposition Algorithm CGE Computable General Equilibrium CPTPP Comprehensive and Progressive Agreement for Trans-Pacific Partnership C. T. (S) Computational Time (Seconds) DA Decomposition Algorithm DRCCP Distributionally Robust Chance-Constrained Programming DRO Distributionally Robust Optimization 𝜀 −C 𝜀-Constraint FSC Food Supply Chain GFSC Global food supply chains GTA Global trade agreement GVAR Global Vector Autoregression LR Lagrangian Relaxation MIP Mixed Integer Programming MILP Mixed Integer Linear Programming MKA Modified Keshtel Algorithm MOCE Multi-objective Cross Entropy NAFTA North American Free Trade Agreement PC Production Center P. NO. Problem Number xiv RCEP Regional Comprehensive Economic Partnership RO Robust Optimization RPP Robust Possibilistic Programming SAA Sample Average Approximation SBRO Scenario-based Robust Optimization SP Stochastic Programming USMCA The United States-Mexico-Canada Agreement WGPA Weighted Goal Programming Approach xv Acknowledgements My sincere gratitude goes to my supervisors, Dr. Babak Mohamadpour Tosarkani and Dr. Eric Li, for their invaluable guidance, support, and wisdom throughout my academic journey. Their continuous encouragement and insightful feedback have greatly contributed to this thesis. Additionally, I express my appreciation to my committee members, Dr. Hossein Zolfagharinia and Dr. Wouter Bam, for their informative suggestions and precious insights. I would like to extend my heartfelt thanks to Dr. Mahsa Mohammadi for her unwavering support, encouragement, and mentorship. Her invaluable guidance has played a significant role in shaping my academic growth. I am deeply thankful for the support provided by colleagues at the Industrial & Systems Engineering Research Group, especially Mohammadreza Khodoomi, Mohsen Roytvand Ghiasvand, and Dr. 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. xvi Dedication For my mother, whose love and belief in me have been the driving force behind this journey. This thesis is dedicated to you with heartfelt gratitude.1 Chapter 1: Introduction In this section, the background on the critical role of Global Trade Agreements (GTAs) in shaping and stabilizing global food supply chains (GFSCs), as well as the vulnerabilities they face due to disruptions is explained. Subsection 1.1 explores the foundational aspects of GTAs, their impact on GFSCs, and their role in global trade, with a particular focus on the North American Free Trade Agreement (NAFTA) as the most important GTA in the North America. Subsection 1.2 explains the motivations behind this research, highlighting the need for more resilient food supply chains (FSCs) throughout the growing global uncertainties. Subsection 1.3 defines the specific objectives of this study, including the development of a stochastic programming model to address the challenges posed by disruptions to GTAs. Finally, Subsection 1.4 provides an overview of the thesis outline. 1.1 Background GTAs have facilitated GFSC by enhancing the flow of food products across international borders and playing as a key driver for international trade. A comprehensive analysis of global grain trade data from 1993 to 2015 reveals the significant impact of GTAs on the formation of new trade links and expanding trade volumes. The implementation of a trade agreement between countries can increase the probability of establishing a new trade link by more than sixfold. Moreover, the continued presence of trade agreements enhances market stability by reducing the probability of link deactivation by more than 50%. Trade links governed by trade agreements not only exhibit larger trade flows but also experience fewer annual fluctuations (Falsetti et al., 2022). The Regional Comprehensive Economic Partnership (RCEP) and the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP) are two of the most important 2 GTAs that are committed to reducing tariffs and quotas in various sectors, including agricultural and food products (Schott, 2023). Similarly, NAFTA, implemented in 1994, played a crucial role in eliminating tariffs and expanding the food market between the United States, Canada, and Mexico (Zahniser et al., 2015). While NAFTA nearly doubled the United States’ agricultural trade with its partners and improved economic welfare, it also drew criticism for disproportionately impacting small-scale farmers in Mexico, ultimately leading to its replacement by the United States-Mexico-Canada Agreement (USMCA) in 2020 (Zahniser and Link, 2002; Wise, 2019; Khan, 2020; Rioux et al., 2021). However, due to its broader recognition, the term “NAFTA” is employed throughout this thesis instead of “USMCA” to maintain consistency and clarity. GTAs have a substantial impact on national economies and the food industry. RCEP and CPTPP account for 29% and 14.5% of the global gross domestic product, respectively (Schott, 2023) and contribute to the food industry’s substantial revenue of $10.07 trillion in 2024 (Statista, 2024). However, poorly designed FSCs continue to contribute to global malnutrition and related health issues (Khan et al., 2022). The United Nations (2023) reported that approximately 9.2% of the global population experienced hunger in 2022, with an estimated 692 to 783 million people affected by food insecurity. Additionally, disruptions within FSCs further intensify these challenges, leading to more profound health and economic repercussions. A notable example of this impact is the potential termination of NAFTA, which can raise tariffs by 150%, threatening both consumer affordability and company profitability (Swanson and Granville, 2017). As the GFSCs become increasingly interconnected, disruptions can spread throughout the network; therefore, it is crucial to understand how they spread to effectively mitigate their impact (Davis et al., 2021). Although some disruptions may be temporary, their effects can be 3 long-lasting and may arise from man-made disasters (e.g., war, political unrest, and pandemics) or natural events (e.g., floods, wildfires, and earthquakes). A notable example is the ongoing conflict between Russia and Ukraine, two major food suppliers, which has drastically impacted GFSCs (Jagtap et al., 2022), leading to a 60% drop in trade and pushing millions of people into severe food insecurity (Lin et al., 2023). Moreover, recent attacks and blockages in the Red Sea have threatened agricultural exports from Italy to China, valued at over €570 million annually. As a result, shipments have been rerouted via the Cape of Good Hope, increasing transit times by 10 to 15 days, depending on the destination. This alternative route not only increases transit time but also raises costs, as it requires more fuel and reduces available capacity. Consequently, the cost per container could increase by 30% to 70%. Disruptions in GFSCs are also expected to affect global food markets, with reports indicating that the global export price of basmati rice could rise by 15% to 20% (Coyne, 2024). Demand uncertainties during disasters can further disrupt FSCs through panic buying, which can be challenging to control (Song et al., 2018; Xu et al., 2023). Panic buying occurs when consumers anticipate shortages, leading to a sudden surge in demand that can quickly deplete inventories, which was notably observed during the COVID-19 pandemic (Islam et al. 2021). This demand surge not only causes immediate shortages but also disrupts supply-demand balance, making it challenging for suppliers to restock efficiently. The best way to deal with these challenges is to increase the FSC’s resilience, which is defined as FSC system’s capacity to maintain a desired food security state under disruptions and uncertainties (Poo et al., 2024). Moreover, GFSCs present greater challenges due to the perishable nature of food products, as perishability introduces various sources of uncertainty, including limited shelf life, safety requirements, and pricing considerations (Behzadi et al., 2017). This makes the design of FSCs a compelling subject for study. A product is considered perishable if its quality or quantity 4 visibly declines, its functionality decreases, or its value diminishes over time. Food products are typically classified as perishable because their quality deteriorates rapidly, not only during production and storage but also throughout the distribution process (Jouzdani et al., 2021). Given the inherent perishability of food products, maintaining quality at each stage of the supply chain is crucial (Kirci et al., 2022). The limited shelf life of perishable products introduces significant complexities in FSC management, as it imposes a strict timeframe within which food products must be consumed before deterioration (Pan et al. 2023). Therefore, effective FSC management requires strategic planning and precise coordination to minimize waste, reduce economic losses, and ensure consumers receive high-quality food products. Figure 1.1 illustrates the impact of disruptions in GTAs and GFSCs on food security, highlighting that enhancing FSC resilience is crucial. Frequent disruptions can severely compromise FSC stability, leading to significant food insecurity and economic losses. Figure 1.1: Impact of disruptions in GTAs and GFSCs on food security 5 1.2 Motivation The role of food in human survival cannot be overstated. Food is indispensable for human existence, and its absence can result in starvation and ultimately lead to death. Moreover, reliable access to food is not only fundamental for individual well-being but also essential for societal stability. As global populations rise and demand for food increases, the importance of FSCs becomes critical. Efficient FSCs ensure that food products reach markets and consumers on time at a reasonable price, that wastage is minimized, and food security is achieved. While significant attention has been directed toward the logistics and operational challenges within FSCs, the role of GTAs in shaping and stabilizing these systems remains underexplored. Given the increasing reliance on international trade to meet food demand, disruptions to GTAs can have severe implications for global food security. Despite their importance, the cascading effects of such disruptions on FSCs have not been sufficiently studied. For instance, the potential termination of a key GTA, such as NAFTA, or disruptions caused by geopolitical conflicts, can destabilize FSCs, leading to widespread consequences, including heightened food insecurity. Recent events, such as the COVID-19 pandemic and political conflicts in major food-producing regions, have demonstrated the vulnerability of FSCs to external shocks. These disruptions often trigger panic buying, exacerbating supply-demand imbalances. Therefore, investigating the impact of GTA disruptions on the resilience of FSCs and identifying strategies to mitigate their impacts are crucial for ensuring global food security. Another critical motivation for this study lies in the increasing complexity and interdependence of GFSCs, as the intricacies of international trade are becoming more evident. As GTAs shape the flow of goods, especially in the food sector, their disruptions have far-reaching consequences rippling across borders. Events such as the Russia-Ukraine conflict and Red Sea blockages illustrate how disruptions to key trade routes can severely impact food security, 6 disrupt market stability, and elevate global food prices. These disruptions are further complicated by the perishability of food products, which magnifies the urgency for efficient supply chain management. It is therefore essential to investigate the effects of disruptions to GTAs on the resilience of FSCs and to explore strategies for managing these shocks to minimize their detrimental impact on food security. With growing geopolitical tensions and environmental changes, the global food trade faces unprecedented levels of uncertainty, reinforcing the need for resilient and adaptable food systems. Moreover, with rising populations and evolving consumer demand, the role of FSCs in ensuring equitable food distribution is more crucial than ever. As demonstrated during the COVID-19 pandemic, panic buying highlighted the fragility of these systems when disruptions arise. The imbalance between supply and demand can lead to food shortages, price inflation, and exacerbate food insecurity, particularly for vulnerable populations. Addressing these vulnerabilities requires a deeper understanding of how GTAs can either stabilize or destabilize supply chains during crises. By examining how disruptions to trade agreements impact FSCs, this research seeks to contribute to the development of more resilient systems that can withstand future disruptions and ensure consistent food availability, even under adverse conditions. In response to these motivations and the pressing need to better understand the impact of GTA disruptions on FSC resilience and food security, this research is designed to answer the following key questions: How do changes in GTAs affect the resilience and efficiency of the GFSC? Which parameters are most impacted when a disruption in GTA occurs? What is the optimal quantity of products that should be produced and distributed to meet demand during disruptive scenarios? And finally, which food products demonstrate the highest level of resilience during GTA disruptions? 7 1.3 Objectives Despite the extant literature on GFSCs, studies on the quantitative impacts of disruptions in GTAs and their direct implications for food security are limited; thus, it is necessary to model the role of GTAs in GFSCs to ensure the economic efficiency of GFSCs and enhancing food security. Therefore, for the first time, in this study, a novel two-stage stochastic programming model is proposed to optimize a global multi-product FSC considering various shelf lives during disruptions. The model is designed to enhance both profitability and resilience, addressing a critical gap in current FSC and trade policy research. A key contribution of this model lies in its integration of supply and distribution decision-making under uncertainty in parameters, allowing for the efficient allocation of limited food resources to maximize profit and minimize waste and shortage during disruptions. Recognizing that demand fluctuations significantly impact food security; this study accounts for multiple potential demand scenarios. The Monte Carlo simulation (MCS) is employed to generate a large number of scenarios based on historical data and an assigned probability function, ensuring that the model captures an adequate range of demand variations, reflecting the real-world complexity of GFSCs. However, to analyze large numbers of demand scenarios, scenario reduction techniques are necessary. To address this challenge, the K-means clustering algorithm is applied to effectively group similar demand scenarios into clusters. This approach allows for a more manageable number of representative scenarios while preserving the diversity of demand fluctuations. Given the inclusion of multiple demand scenarios, the model requires a scalable solution approach. Thus, the Sample Average Approximation (SAA) method is utilized to tackle the large-scale nature of the problem with providing solutions within a short time frame. Finally, a real-world case study focused on the potential termination of NAFTA as the most influential GTA in the North America, is used to demonstrate the model’s applicability. The case study 8 provides valuable insights into the cascading effects of GTA disruptions on both national and cross-border food security, highlighting the comparative vulnerability of the customer regions and food products. The main contributions of this study are presented as follows: 1. This research introduces a two-stage stochastic model designed to optimize GFSCs under uncertainties related to GTAs. The model aims to enhance both resilience and profitability by integrating the supply and distribution phases while accounting for various disruption scenarios, such as panic buying, as well as uncertainties in production costs and capacities. To manage the demand uncertainty, an MCS is utilized to create numerous demand scenarios. The K-means method is then applied to reduce the generated scenarios, and the SAA approach is used to reduce the computational time. Furthermore, a thorough analysis assesses how uncertainties in GTAs and disruptions in GFSCs affect food security. 2. The study considers various perishable food products with differing shelf lives and incorporates different transportation vehicles based on each product’s logistical needs. It also illustrates how extended shelf life and inventory levels at retail locations influence waste and profitability, providing retailers with insights on how to minimize both shortages and spoilage effectively. 3. The proposed model is implemented through a real-world case study that examines the potential effects of NAFTA’s termination on food security in the United States and Canada. This analysis reveals that Canada’s FSC exhibits lower resilience, with shortages occurring first in Canada before affecting the United States. Additionally, it compares the resilience of different food products, showing that meat shortages arise before those of bread. 4. The research analyzes the impact of production uncertainty, emphasizing the trade-off between minimizing shortages and waste across factories operating at varying production 9 levels. It concludes that while increasing production levels can effectively reduce the occurrence of shortage, it also introduces a new constraint within the model that leads to higher waste levels and diminished profits. 1.4 Thesis Outline The remainder of this thesis is structured as follows: Section 2 provides an in-depth review of the relevant literature on disruptions in GFSCs, resilience strategies for enhancing GFSCs, the impact of GTAs on GFSCs, and stochastic programming and the solution approach used to solve the model. Section 3 presents the problem statement and introduces the mathematical model. Section 4 details the solution approaches employed to solve the proposed model, discusses numerical results, including sensitivity analysis and model validation through a case study. Finally, Section 5 concludes with key findings and recommendations for future research on enhancing the resilience of GFSCs through strategic trade agreements. 10 Chapter 2: Literature Review This literature review investigates the key aspects of GTAs and their influence on GFSCs, focusing on how disruptions in GFSCs affect FSCs worldwide. The review is structured into distinct subsections, each examining a critical area of research. Subsection 2.1 examines disruptions in GFSCs, highlighting the growing interconnectivity of global food systems and the vulnerabilities created by geopolitical and environmental crises. Moreover, this section also explains the role of transportation and logistics disruptions, focusing on how disruptions in key maritime routes and other transportation networks can exacerbate supply chain vulnerabilities. Subsection 2.2 explores various resilience strategies implemented within FSCs to address uncertainties such as demand fluctuations and supply chain interruptions. Subsection 2.3 studies the role of GTAs, such as CPTPP, RCEP, and NAFTA, in enhancing the resilience of GFSCs. Finally, Subsection 2.4 discusses stochastic programming techniques, including MCS for generating demand scenarios, K-means clustering for scenario reduction, and the SAA method for reducing the computational time. 2.1 Disruptions in Global Food Supply Chains The globalization of FSCs has significantly influenced the transmission of fluctuations within the network and the growing interconnectivity between producers and consumers, leading to increasingly complex relationships (Herold and Marzantowicz, 2023). This interconnectedness, combined with an increasing number of disruptions, requires decision-makers to prioritize resilience strategies to strengthen FSCs against uncertainties. The Russia-Ukraine conflict is a clear example of how geopolitical disruptions can severely affect supply chains. Jagtap et al. (2022) examined the impact of this conflict on FSCs, which caused profound changes in demand among nations reliant on imports from Ukraine. They explored key areas of the FSCs that were significantly impacted, and they proposed several strategies to 11 mitigate the conflict’s impact, including alternative food raw materials, diversification of suppliers, and the involvement of supply chain partners. The recent Red Sea crisis has further demonstrated the fragility of global trade routes, particularly in regions dependent on maritime imports. This crisis has emphasized the necessity for international cooperation and resilient GTAs to ensure that FSCs can adapt and recover from such disruptions (Notteboom et al., 2024; Glauber and Mamun, 2024). Glauber and Mamun (2024) analyzed the impacts of the Red Sea disruption on exports and food markets in East Africa and Asia. They showed that this disruption can lead to higher retail prices, lower producer prices, and reduced food security in import-dependent countries. The blockage of the Suez Canal by the Ever Given in March 2021 also significantly disrupted global trade, including FSCs, and exposed the vulnerabilities of GSCs to unexpected events (Macfarlane, 2022). Meanwhile, a severe drought at the Panama Canal has led authorities to implement restrictions that have significantly reduced daily ship crossings since October 2023. This phenomenon has slowed maritime trade, which typically accounts for about 5% of global maritime trade (Kamali et al., 2024). Several studies have considered the role of disruptions in FSCs. For example, Diabat et al. (2019) developed a two-stage stochastic optimization model for designing a perishable supply chain network with reliability and disruption considerations. The goal of their model was to minimize the time and cost of delivering perishable products where facilities and routes could become inaccessible. Yavari et al. (2020) explored a location-inventory-routing problem for perishable products under route disruptions. They employed dynamic and disruptive pricing strategies to enhance the resilience of the model. Foroozesh et al. (2022) designed a green and resilient supply chain network for perishable products considering disruption risks, including risks affecting transportation routes. They addressed the uncertainties through various 12 approaches such as multiple sourcing and horizontal collaboration, and they applied a novel robust possibilistic programming approach to address uncertainties. In more recent studies, Hashemi-Amiri et al. (2023) proposed a perishable multi-product FSC network that optimizes supplier selection, production scheduling, and vehicle routing problems to mitigate the demand and supply uncertainties while reinforcing the distribution-related decisions. The aim of their model was minimizing the total network costs and maximizing suppliers’ reliability. Sasi et al. (2024) developed a GFSC model and introduced a novel heuristic algorithm to reoptimize the model in response to various disruptions in supply and transportation. The disruptions could occur sequentially or simultaneously within a short time frame, without resolving the entire problem. 2.2 Resilience Strategies for Enhancing Food Supply Chain Robustness The dynamic global environment imposes various risks, highlighting the need for food and agribusiness firms to establish proactive and predictive risk management strategies (Enyinda and Mbah, 2017). Several studies have proposed models incorporating risk to enhance the resilience of FSCs against disruptions. Bottani et al. (2019) developed a mathematical model for a resilient FSC to mitigate the impact of uncertain market demand and disruptions in the supply of raw materials. Their goal was to maximize the total profit and minimize the total lead time. To enhance the resilience of the model, the multiple sourcing policy was employed. Gholami-Zanjani et al. (2021a) designed an FSC model with location-allocation and inventory-replenishment decisions under disruptive conditions. To manage the uncertainties in the model, they implemented various resilience strategies, including readiness, flexibility, and responsiveness. Gholami-Zanjani et al. (2021b) further contributed by proposing a two-stage scenario-based mathematical model for a resilient FSC under demand uncertainty and 13 disruptions. They compared various resilience strategies, demonstrating that fortification and backup supplier strategies can effectively improve resilience. In more recent studies, Kalantari and Hosseininezhad (2022) developed a four-stage sustainable GFSC model considering various risk factors such as time delay risk, exchange rate fluctuations, and production quality. They applied a robust optimization approach to address uncertainties. Gholian-Jouybari et al. (2023) developed a multi-objective stochastic model to analyze an agricultural FSC network and utilized a robust optimization approach to address uncertainties in the production capacity and demand. Li and Zhao (2023) developed a resilient retail supply network for fresh products to address the risk of disruption. Their model helped retailers select suppliers, distribution centers, and transportation routes across various scenarios using three resilience strategies: priority supply, multiple sourcing, and lateral transshipment. Gitinavard et al. (2024) designed a new location-routing model under uncertainty for a dairy logistics system and used fuzzy uncertainty modeling to address strategic and operational aspects of perishable FSCs. Sharifi et al. (2024) integrated resilience, sustainability, and responsiveness in designing agri-FSCs to operate under uncertain conditions. Reducing node criticality, complexity, and customer dissatisfaction were considered the resilience-related objectives. They applied their proposed model to a Canadian wheat supply chain to validate its applicability. 2.3 The Impact of Global Trade Agreements on Strengthening Food Supply Chain GTAs play a crucial role in shaping the structure and dynamics of GFSCs. As GFSCs become increasingly complex, GTAs such as CPTPP, RCEP, and NAFTA have facilitated the flow of food products across borders, thereby enhancing the efficiency and resilience of food distribution networks. CPTPP is one of the most significant developments in international trade, especially within the Asia-Pacific region. This agreement includes 11 member countries 14 and the United Kingdom, all of which have committed to eliminating nearly all tariffs and import charges on each other’s products over time (Innovation, Science and Economic Development Canada, 2023). This reduction in trade barriers is particularly impactful for FSCs, as it reduces costs, facilitates operations, and enhances food safety and regulatory standards across the member countries. Ciuriak et al. (2017) demonstrated that CPTPP could increase the income of the member countries by US$13.47 billion by 2035, largely due to increased trade in agricultural products. RCEP, which came into effect in January 2022, is another critical GTA influencing FSCs, particularly within Asia. This agreement includes 15 member countries and focuses on reducing trade costs and enhancing regional collaboration. While it is not as comprehensive as CPTPP in terms of tariff elimination, RCEP is expected to provide substantial economic benefits by creating a more integrated regional market (Schott, 2023). Estrades et al. (2023) estimated that the income gains from RCEP could range between 0.21% and 2.5% across member countries, contributing to regional food security by making food imports more affordable and accessible. Thangavelu (2022) also demonstrated that RCEP could help mitigate the impact of global trade disruptions, such as the ones caused by the COVID-19 pandemic, by making regional supply chains more resilient and reducing dependency on external markets. NAFTA, which was implemented in 1994, has also played a pivotal role in integrating agricultural markets across the United States, Mexico, and Canada. NAFTA’s members committed to gradually remove thousands of barriers and tariffs from various products, including agricultural products. Although the flows of products, services, capital, and labor across borders had increased (Zahniser et al., 2015), NAFTA still faced criticism for its uneven impacts on small-scale farmers and local food systems. This was particularly evident in Mexico, where the influx of cheap agricultural imports led to significant disruptions in the rural 15 economy (Wise, 2019). Therefore, in 2020, NAFTA was replaced with an updated agreement known as the USMCA (Khan, 2020). Khan (2020) conducted an analysis of the economic impacts of NAFTA and the transition to USMCA, using a global vector autoregression model. His findings demonstrated that while NAFTA significantly contributed to economic growth, wage increases, and lower unemployment in the region, the USMCA is expected to enhance the associated benefits. This enhancement is achieved by providing greater market access and strengthening regulatory alignment among member countries. Similarly, Regmi (2020) performed a comprehensive analysis of the impacts of USMCA on agricultural trade, examining the continuation and expansion of trade liberalization efforts that began under NAFTA, with a focus on the agreement’s effects on market access. She concluded that the USMCA provides several new market access opportunities, particularly in the dairy and poultry sectors. However, its overall impact on food security and supply chains may be modest due to the continuation of pre-existing trade patterns. In contrast, Vorhaben (2021) highlighted the potential benefits of the USMCA in enhancing food security by increasing trade in agricultural products. By facilitating greater access to diverse and affordable food products, the USMCA can strengthen FSCs across North America and improve food security outcomes, particularly for low-income consumers. However, Eldridge (2021) examined the transition from NAFTA to the USMCA, focusing on its implications for food safety standards and public health throughout North America. She highlighted concerns regarding the establishment of equivalent food safety standards among the USMCA members, emphasizing the potential risks posed by differing regulatory approaches, particularly for Canadian consumers. She deduced that a more equitable and 16 sustainable economic model is required to mitigate the adverse effects on public health and food security. 2.4 Stochastic Programming and Sample Average Approximation Deterministic models are useful in scenarios with fixed and known parameters but are unable to effectively handle problems under uncertainties or provide solutions with a significant level of risk, as they fail to incorporate the variability and risks inherent in real-world situations. This limitation is particularly evident in GFSCs with multiple sources of uncertainty, such as demand fluctuation and supply or transportation disruptions, which can significantly impact outcomes. However, stochastic programming offers solutions to address uncertainties by incorporating random variables into mixed integer programming models (Nguyen et al., 2021; Huang et al., 2023). Extensive research has been conducted on implementing large-scale techniques to solve stochastic programming models for disruptions. Notably, the SAA method has proven to be an effective approach for solving stochastic optimization problems with numerous possible scenarios (Chang et al., 2022). Several studies have applied the SAA method to solve stochastic optimization problems by considering possible scenarios. Shehadeh and Tucker (2022) developed a resilient model to prepare for disaster seasons by determining the location of warehouses and amount of inventory relief items. To address uncertainty, they utilized a two-stage stochastic programming model, and they used the SAA method to solve the model. Wang et al. (2022) formulated a dynamic scenario-based two-stage stochastic programming model to optimize the emergency response time during a disaster using the SAA method. Liu et al. (2023) proposed a two-stage optimization model for facilities location and capacity adjustment during large-scale emergencies. In the first stage, prepositioning strategies are determined to meet predetermined fill-rate requirements using the SAA method, while the second stage dynamically adjusts 17 capacity for fluctuating demand. Geiger (2024) developed a two-stage production routing problem under demand uncertainty and introduced two solution methods based on the SAA to address a large number of scenarios. They demonstrated that the simple heuristic within an adjustable SAA approach yields better results compared to the metaheuristic within a non-adjustable approach. Gómez-Rocha et al. (2024) considered shortages and demand distribution in the capacitated facility location problem and applied the SAA method to conduct computational experiments on a set of instances. Moreover, MSC is a statistical technique that simulates uncertainty by generating random samples from probability distributions (Roozkhosh et al., 2024). This technique has been utilized in several studies to address uncertainties in stochastic models. Kabiri et al. (2022) proposed a multi-objective closed-loop supply chain with multiple recycling, manufacturing/remanufacturing, and distribution centers. To address the uncertainty in the demand parameter, they employed the MCS method, integrating the NSGA-II algorithm. Ghanei et al. (2023) developed a two-stage stochastic model to improve the intertwined supply network considering various resilience strategies. The transportation costs and available capacity at facilities were considered as uncertain parameters, and they employed an MSC-based algorithm that uses the SAA method for generating solutions. Roozkhosh et al. (2024) developed a supply chain model with the aim of improving performance and reducing costs. Due to the fluctuations in purchase price of raw materials and fuel in their model, the cost parameters were considered uncertain. They employed machine learning-based performance measures and MCS to address the cost uncertainties and improve the accuracy of the model. Additionally, K-means clustering has been used in stochastic programming and supply chain optimization to reduce the complexity of scenario sets and improve computational efficiency. Shahbazbegian et al. (2020) proposed a power plant supply chain optimization model to 18 minimize costs and find suitable locations for facilities. They employed the fuzzy-robust programming approach to address the uncertainty in demand parameter, and the K-Means clustering method to assess the installed photovoltaic capacity of different cities during each period. Chen et al. (2023) proposed a two-stage stochastic model to fully utilize mobile energy storage systems under various scenarios, including normal, severe, and extreme conditions. To improve model efficiency and accuracy, they employed the SAA and K-means clustering algorithms to eliminate redundant scenarios. Yunusoglu et al. (2024) developed a two-stage optimization problem for a biomass-to-bioenergy supply chain network. They utilized the K-means clustering algorithm in the first stage to reduce the complexity of the problem. Bahmani et al. (2024) proposed a robust-stochastic approach for a biodiesel supply chain considering the disruption in facilities and transportation links. They applied the MCS and K-means clustering methods to generate and reduce probable scenarios to mitigate the uncertainties in the model. Table 2.1 illustrates the characteristics of the present study in comparison with previous ones, highlighting the key features, such as the inclusion of GTA concepts in GFSCs, the role of uncertainty and perishability, and the modeling frameworks used. The table underscores the gaps in literature, particularly the lack of comprehensive studies that integrate these critical factors to address disruptions in GTAs and their impact on food security. 19 Table 2.1: An overview of related studies. Study Trade Agreements Supply Chain Framework Model Feature Methodology Approach Application Area / Case Study Multi-period Multi-product Perishability Uncertainty Modeling Approach Solution Approach Zahniser (2015) NAFTA - Conceptual - - - - - - - Enyinda and Mbah (2017) - ✓ Analytical - - - ✓ AHP - Food (Agribusiness) Ciuriak et al. (2017) CPTPP - Analytical - - - - CGE Simulation - Automobile, Textiles, & Agriculture Diabat et al. (2019) - ✓ Analytical ✓ ✓ ✓ ✓ RO LR & 𝜀-C Blood Bottani et al. (2019) - ✓ Analytical - ✓ - ✓ MIP ACO Food Regmi (2020) NAFTA - Conceptual - - - - - - - Khan (2020) NAFTA - Analytical - - - ✓ GVAR - - 20 Table 2.1: An overview of related studies Study Trade Agreements Supply Chain Framework Model Feature Methodology Approach Application Area / Case Study Multi-period Multi-product Perishability Uncertainty Modeling Approach Solution Approach Gholami-Zanjani et al. (2021a) - ✓ Analytical ✓ - ✓ ✓ SP & RO SBRO Food Eldridge (2021) NAFTA - Conceptual - - - - - - - Gholami-Zanjani et al. (2021b) - ✓ Analytical ✓ - ✓ ✓ SP BDA Food Kalantari and Hosseininezhad (2022) - ✓ Analytical ✓ - ✓ ✓ RO MOCE Food Jagtap et al. (2022) - ✓ Conceptual - ✓ - - - - Food Foroozesh et al. (2022) - ✓ Analytical ✓ ✓ ✓ ✓ RPP A𝜀-C Food 21 Table 2.1: An overview of related studies Study Trade Agreements Supply Chain Framework Model Feature Methodology Approach Application Area / Case Study Multi-period Multi-product Perishability Uncertainty Modeling Approach Solution Approach Shehadeh and Tucker (2022) - ✓ Analytical - - - ✓ SP & DRO SAA & DA - Wang et al. (2022) - ✓ Analytical ✓ - - ✓ SP SAA Transportation Sector Gholian-Jouybari et al. (2023) - ✓ Analytical ✓ ✓ ✓ ✓ SP MKA Food (Saffron) Schott (2023) RCEP, CPTPP - Conceptual - - - - - - - Estrades (2023) RCEP - Conceptual - - - - - - - Hashemi-Amiri et al. (2023) - ✓ Analytical ✓ ✓ ✓ ✓ DRCCP WGPA Food (Poultry Industry) 22 Table 2.1: An overview of related studies Study Trade Agreements Supply Chain Framework Model Feature Methodology Approach Application Area / Case Study Multi-period Multi-product Perishability Uncertainty Modeling Approach Solution Approach Li and Zhao (2023) - ✓ Analytical ✓ ✓ ✓ ✓ MILP LR & ε-C Retail Stores Glauber and Mamun (2024) - ✓ Conceptual - - - ✓ - - Food (Wheat) Sasi et al. (2024) - ✓ Analytical ✓ ✓ ✓ ✓ MILP Heuristic Algorithm Food (Rice and Wheat) Gitinavard et al. (2024) - ✓ Analytical - - - - Possibilistic RO Hesitant Fuzzy Food (Diary) Geiger (2024) - ✓ Analytical ✓ - - ✓ SP SAA - This Research NAFTA ✓ Analytical ✓ ✓ ✓ ✓ Two-stage SP SAA Food 23 While GTAs have substantially improved GFSCs by reducing trade barriers and facilitating cross-border food flow, existing studies have largely focused on the benefits and economic growth facilitated by GTAs. However, a significant gap remains in understanding the impacts of uncertainties within GTAs, such as potential terminations or modifications, on the resilience of FSCs and food security. Furthermore, although stochastic programming models have been applied to optimize FSCs under disruption, comprehensive studies that integrate supply and distribution decision-making to address uncertainty in GTAs are still scarce. For instance, panic buying and demand fluctuations caused by the termination of GTAs can exacerbate shortages and inflate operational costs. However, to the best of our knowledge, this study is the first to bridge these gaps by proposing a two-stage stochastic programming model tailored for multi-product perishable FSCs considering uncertainty in GTAs. To address the uncertainties in the demand parameter, this parameter is simulated using the MCS. Then, to reduce the number of scenarios, the K-means method is implemented to cluster the generated scenarios. Moreover, to address the computational complexity associated with evaluating the large-scale nature of the problem, the SAA method is employed. A real-world case study on the NAFTA termination underscores the model’s applicability, revealing critical insights into the resilience differentials among food products and the broader implications for food security in Canada and the United States. This research not only contributes to the theoretical understanding of uncertainty in GTAs but also offers practical strategies for enhancing the resilience and adaptability of GFSCs in an era of growing global uncertainties. 24 Chapter 3: Problem Definition To ensure global food security during disruptions, a resilient GFSC is essential, as the frequency of natural disasters and political instability is increasing. The frequency of weather and climate disasters in the United States, for instance, has significantly increased, experiencing over 338 disasters since 1980 (Siddig and Song, 2025). These challenges often result in shortages, price fluctuations, and ultimately food insecurity, particularly in regions heavily reliant on imports. For instance, over 67% of food insecurity crises in East Africa are due to unanticipated droughts (Krishnamurthy et al., 2022). The interconnected nature of modern GFSCs implies that disruptions in one node can have global cascading effects. Therefore, enhancing resilience in FSCs is crucial by mitigating shocks, recovering quickly, and continuing to deliver essential food products to consumers. This resilience is especially important in the context of GTAs, as they facilitate food trades but remain vulnerable to uncertainties. Additionally, the inherent uncertainties in the global environment, such as fluctuating demand, perishability of food, and logistical challenges, complicate decision-making. These complexities highlight the necessity for resilient models that optimize supply chain operations under varying conditions. By considering possible disruption scenarios, the model identifies effective strategies for resource allocation, cost minimization, and profit maximization under uncertainties, ensuring that the demand for food products is met. The configuration of the proposed GFSC model is demonstrated in Figure 3.1, which illustrates the delivery of food product 𝑚 ∈ {1, 2, … , 𝑀} from production center (PC) 𝑝 ∈ {1, 2, … , 𝑃} to retailer 𝑖 ∈ {1, 2, … , 𝐼} through vehicle 𝑣 ∈{1, 2, … , 𝑉} to meet the demand of customer 𝑐 ∈ {1, 2, … , 𝐶} in period 𝑡 ∈ {1, 2, … , 𝑇} under uncertainty. The proposed model aims to maximize the total expected profit of retailers during a disruption over a multi-period planning horizon. The main decisions addressed by the 25 proposed FSC model involve the selection of PCs and their capacities, along with planning decisions regarding the flow of food products. The selection of PCs and their capacities is made from a set of potential candidates at the beginning of the planning horizon. Figure 3.1: The configuration of the proposed model The main characteristics and assumptions of the FSC considered here are as follows: • Food production involves processing facilities that collect primary food ingredients from various sources and transform them for storage and distribution. • Two different types of food products are considered in this model. The food products in the first group are perishable and necessitate refrigeration and controlled temperatures on refrigerated platforms. • The products delivered to retailers are ready to be sold. It is not mandatory to satisfy all demand as this model is assumed to be disrupted, and unmet demand is considered a lost sale. However, there is a penalty cost associated with each unit of unsatisfied demand. 26 • The products under discussion have a limited shelf life and must be consumed within a specific period. It is important to note that the shelf life of a product begins when it is produced at the PCs, and any expired products must be disposed of. • Countries are assumed to have similar food standards, allowing food products produced in one country to be exported to another and imported without significant regulatory barriers. The aim of this study is to answer the following key research questions: 1. How do changes in GTAs affect the resilience and efficiency of the GFSC? 2. What parameters are most impacted when a disruption in GTA occurs? 3. What is the optimal quantity of products that should be produced and distributed to meet demand during disruptive scenarios? 4. Which food product is the most resilient during a disruption in a GTA? 3.1 Problem Formulation The parameters and decision variables utilized to formulate the mathematical model are outlined in Table 3.1 as follows: Table 3.1: List of notations, parameters, and decision variables Indices: 𝑃 Set of PCs indexed by 𝑝 (𝑝 ∈ 𝑃) 𝐼 Set of retailers indexed by 𝑖 (𝑖 ∈ 𝐼) 𝐶 Set of customers indexed by 𝑐 (𝑐 ∈ 𝐶) 𝑀 Set of products indexed by 𝑚 (𝑚 ∈ 𝑀) 𝑉 Set of vehicles indexed by 𝑣 (𝑣 ∈ 𝑉) 𝑇 Set of periods indexed by 𝑡 & 𝑡′ (𝑡 & 𝑡′ ∈ 𝑇) Parameters: 27 𝑓𝑝𝑚 Order cost for product 𝑚 to PC 𝑝 𝑐𝑎𝑝𝑝𝑝𝑚 Maximum throughput of PC 𝑝 for product 𝑚 𝑐𝑎𝑝𝑖𝑖𝑚 Maximum inventory capacity of retailer 𝑖 for product 𝑚 𝑞𝑝𝑝𝑚 Production capacity of PC 𝑝 for product 𝑚 𝑐𝑣𝑝𝑖𝑚𝑣 Unit transportation cost for product 𝑚 from PC 𝑝 to retailer 𝑖 using vehicle 𝑣 𝑐𝑝𝑝𝑚 Unit production cost at PC 𝑝 for product 𝑚 ℎ𝑝𝑝𝑚 Unit inventory holding cost for PC 𝑝 for product 𝑚 ℎ𝑖𝑖𝑚 Unit inventory holding cost for retailer 𝑖 for product 𝑚 𝑙𝑠𝑐𝑚𝑡 Unit lost-sale cost of customer 𝑐 for product 𝑚 at period 𝑡 𝑑𝑐𝑚𝑡 Demand of customer 𝑐 for product 𝑚 at period 𝑡 𝑠𝑙𝑚 Shelf life of product 𝑚 𝜔𝑖𝑚 Price of product 𝑚 in retailer 𝑖 𝑐𝑒𝑝𝑝𝑚 Unit expiration cost of product 𝑚 at PC 𝑝 𝑐𝑒𝑖𝑖𝑚 Unit expiration cost of product 𝑚 at retailer 𝑖 𝑀𝑙𝑎𝑟𝑔𝑒 A large number Decision Variables: 𝐿𝑝𝑚 Equals 1 if PC 𝑝 is selected among potential PCs for product 𝑚, otherwise 0 𝐴𝑃𝑝𝑖𝑚𝑣 Equals 1 if retailer 𝑖 is assigned to PC 𝑝 for product 𝑚 to be delivered by vehicle 𝑣, otherwise 0 𝐴𝐼𝑖𝑐𝑚 Equals 1 if customer 𝑐 is assigned to retailer 𝑖 for product 𝑚, otherwise 0 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡 Amount of product 𝑚 produced at period 𝑡′ and transferred to retailer 𝑖 from PC 𝑝 by vehicle 𝑣 in period 𝑡 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡 Amount of product 𝑚 produced at period 𝑡′ and purchased by customer 𝑐 from retailer 𝑖 in period 𝑡 28 𝑃𝑅𝑝𝑚𝑡′ Amount of product 𝑚 produced at period 𝑡′ in PC 𝑝 𝐼𝑃𝑝𝑚𝑡′𝑡 Amount of product 𝑚 produced in period 𝑡′ and remains until end of period 𝑡 in PC 𝑝 𝐼𝐼𝑖𝑚𝑡′𝑡 Amount of product 𝑚 produced in period 𝑡′ and remains until end of period 𝑡 in retailer 𝑖 𝐷𝑐𝑚𝑡− Amount of lost sale for customer area 𝑐 for product 𝑚 in period 𝑡 𝐸𝑃𝑝𝑚𝑡 Amount of product 𝑚 expired at period 𝑡 in PC 𝑝 𝐸𝐼𝑖𝑚𝑡 Amount of product 𝑚 expired at period 𝑡 at retailer 𝑖 The mathematical model for the problem is formulated as follows: The objective of this model, which is shown in Equation (3.1), is to maximize the total expected profit of retailers by maximizing the difference between revenue and costs. The costs include production cost, transportation cost, inventory holding cost at PC 𝑝, inventory holding cost at retailer 𝑖, disposal cost at PC 𝑝, disposal cost at retailer 𝑖, shortage cost, and order cost to PC 𝑝. 29 𝑀𝑎𝑥 𝑍 = ∑ ∑ ∑ ∑ ∑ 𝜔𝑖𝑚𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑡∈𝑇|𝑡′≤𝑡𝑡′∈𝑇𝑚∈𝑀𝑐∈𝐶𝑖∈𝐼− (∑ ∑ ∑ 𝑐𝑝𝑝𝑚𝑃𝑅𝑝𝑚𝑡′ 𝑡′∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ ∑ ∑ ∑ 𝑐𝑣𝑝𝑖𝑚𝑣𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑡∈𝑇|𝑡′≤𝑡𝑡′∈𝑇𝑣∈𝑉𝑚∈𝑀𝑖∈𝐼𝑝∈𝑃+ ∑ ∑ ∑ ∑ ℎ𝑝𝑝𝑚 (𝐼𝑃𝑝𝑚𝑡′(𝑡−1) + 𝐼𝑃𝑝𝑚𝑡′𝑡2)𝑡∈𝑇|𝑡′<𝑡𝑡′∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ ∑ ℎ𝑖𝑖𝑚 (𝐼𝐼𝑖𝑚𝑡′(𝑡−1) + 𝐼𝐼𝑖𝑚𝑡′𝑡2)𝑡∈𝑇|𝑡′<𝑡𝑡′∈𝑇𝑚∈𝑀𝑖∈𝐼+ ∑ ∑ ∑ 𝑐𝑒𝑝𝑝𝑚𝐸𝑃𝑝𝑚𝑡𝑡∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ 𝑐𝑒𝑖𝑖𝑚𝐸𝐼𝑖𝑚𝑡𝑡∈𝑇𝑚∈𝑀𝑖∈𝐼+ ∑ ∑ ∑ 𝑙𝑠𝑐𝑚𝑡𝐷𝑐𝑚𝑡−𝑡∈𝑇𝑚∈𝑀𝑐∈𝐶+ ∑ ∑ 𝑓𝑝𝑚𝐿𝑝𝑚𝑚∈𝑀𝑝∈𝑃) (3.1) Subject to: Constraint (3.2) ensures that each retailer can be assigned to a PC if that PC has been selected. ∑ 𝐴𝑃𝑝𝑖𝑚𝑣𝑣∈𝑉≤ 𝐿𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀 (3.2) Constraint (3.3) demonstrates that customers can be assigned only to retailers that are linked to a PC. ∑ 𝐴𝐼𝑖𝑐𝑚𝑐∈𝐶≤ ∑ ∑ 𝐴𝑃𝑝𝑖𝑚𝑣𝑣∈𝑉𝑝∈𝑃, ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀 (3.3) Constraint (3.4) ensures that products can be transported from a PC to retailers if that PC is selected and the product has not expired. 30 ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑖∈𝐼≤ 𝑀𝑙𝑎𝑟𝑔𝑒 × 𝐿𝑝𝑚 , ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|0 ≤ 𝑡 − 𝑡′ < 𝑆𝐿𝑚 (3.4) In Constraint (3.5), product 𝑚 in retailer 𝑖 can be allocated to customer 𝑐 if and only if customer 𝑐 is assigned to retailer 𝑖. 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡 ≤ 𝑀𝑙𝑎𝑟𝑔𝑒 × 𝐼𝐴𝑖𝑐𝑚, ∀ 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|0 ≤ 𝑡 − 𝑡′ < 𝑆𝐿𝑚 (3.5) Constraint (3.6) shows that the amount of production cannot exceed the production capacity of selected PCs for each product. 𝑃𝑅𝑝𝑚𝑡′ ≤ 𝑞𝑝𝑝𝑚 × 𝐿𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′ ∈ 𝑇 (3.6) Constraint (3.7) ensures that the total number of products sent from PC 𝑝 to retailers cannot exceed the total number of products produced at that PC. ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑖∈𝐼≤ 𝑃𝑅𝑝𝑚𝑡′ , ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|𝑡′ ≤ 𝑡 (3.7) Constraints (3.8) - (3.10) show the inventory balance in PCs for each period. In other words, at the end of each period, the amount of product 𝑚, which is produced in period 𝑡′ is equal to total amount of product 𝑚 at the end of the previous period minus the total amount of products sent to retailers, or it expires if it exceeds the considered shelf life. 𝐼𝑃𝑝𝑚𝑡′𝑡 = 𝑃𝑅𝑝𝑚𝑡′ − ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑖∈𝐼, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|𝑡′ = 𝑡 (3.8) 𝐼𝑃𝑝𝑚𝑡′𝑡 = 𝐼𝑃𝑝𝑚𝑡′(𝑡−1) − ∑ ∑ 𝑃𝑋𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑖∈𝐼 (3.9) ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|0 < 𝑡 − 𝑡′ ≤ 𝑆𝐿𝑚 ∑ 𝐼𝑃𝑝𝑚𝑡′𝑡𝑡′∈𝑇|𝑆𝐿𝑚≤𝑡−𝑡′= 𝐸𝑃𝑝𝑚𝑡 , ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇 (3.10) 31 Constraints (3.11) - (3.13) show the inventory balance at retailers for each period. Here, all orders are assumed to be received by customers within less than a period, which equals zero. 𝐼𝐼𝑖𝑚𝑡′𝑡 = ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑝∈𝑃− ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑐∈𝐶, ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|𝑡′ = 𝑡 (3.11) 𝐼𝐼𝑖𝑚𝑡′𝑡 = 𝐼𝐼𝑖𝑚𝑡′(𝑡−1) + ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑣∈𝑉𝑝∈𝑃− ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑐∈𝐶 (3.12) ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|0 < 𝑡 − 𝑡′ ≤ 𝑆𝐿𝑚 ∑ 𝐼𝐼𝑖𝑚𝑡′𝑡𝑡′∈𝑇|𝑆𝐿𝑚≤𝑡−𝑡′= 𝐼𝐸𝑖𝑚𝑡 , ∀𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇 (3.13) Constraint (3.14) balances the demand, lost sales and products delivered to customers. 𝐷𝑐𝑚𝑡− = 𝑑𝑐𝑚𝑡 − ∑ ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑡′∈𝑇𝑖∈𝐼, ∀𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇 (3.14) Constraints (3.15) and (3.16) demonstrate the inventory capacity of PCs and retailers, respectively. ∑ 𝐼𝑃𝑝𝑚𝑡′𝑡𝑡′∈𝑇|0≤𝑡′≤𝑡≤ 𝑐𝑎𝑝𝑝𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇 (3.15) ∑ 𝐼𝐼𝑖𝑚𝑡′𝑡𝑡′∈𝑇|0≤𝑡′≤𝑡≤ 𝑐𝑎𝑝𝑖𝑖𝑚, ∀𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇 (3.16) Constraint (3.17) defines binary variables. 𝐿𝑝𝑚, 𝐴𝑃𝑝𝑖𝑚𝑣, 𝐴𝐼𝑖𝑐𝑚 ∈ {0,1}, ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑣 ∈ 𝑉 (3.17) Constraint (3.18) describes continues variables. 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡, 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡, 𝑃𝑅𝑝𝑚𝑡′ , 𝐼𝑃𝑝𝑚𝑡′𝑡, 𝐼𝐼𝑖𝑚𝑡′𝑡, 𝐷𝑐𝑚𝑡− , 𝐸𝑃𝑝𝑚𝑡 , 𝐸𝐼𝑖𝑚𝑡 ≥ 0 (3.18) 32 ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑣 ∈ 𝑉, 𝑡′ ∈ 𝑇, 𝑡 ∈ 𝑇 3.2 Two-stage Stochastic Programming Various approaches can be employed for decision making during uncertain situations, one of which is stochastic programming which demonstrates efficient performance. In two-stage stochastic programming, decision variables are categorized into two sets. The first stage involves selecting variables that are independent of specific scenarios, while the second stage allows for the optimization of additional variables once uncertainty is realized. The goal is to minimize costs by optimizing first-stage actions, with the key idea that considering second-stage decisions improves first-stage strategic decisions (Ahmed et al., 2004; Bertsimas and Mundru, 2023; Hajipour et al., 2025). The two-stage stochastic program is represented by Equations (3.19) and (3.20) (Birge and Louveaux, 2011; Bertsimas and Mundru, 2023; Ding et al., 2024). In this formulation, uncertain parameters are denoted by 𝜉 and scenarios by 𝑠. The uncertain parameters in the second stage are represented as 𝜉 ≔ (𝑞, 𝐾, 𝑊, ℎ), with a known probability distribution of 𝜉(𝑠). Moreover, the first stage decision variable is denoted as ?̇?, with A as the coefficient of the objective function for the first-stage decision variable. Min?̇?∈?̇?𝑔(?̇?) ≔ 𝐴𝑈?̇? + 𝔼[𝑄(?̇?, 𝜉(𝑠))] (3.19) Where: 𝑄(?̇?, 𝜉(𝑠)) = inf𝑦∈𝑌(𝑞𝑈𝑦: 𝑊𝑦 ≥ ℎ − 𝐾?̇?) (3.20) Equation (3.19) represents a two-stage stochastic model where the first stage variables ?̇? ∈ ℝ𝑛1 are determined without considering uncertainty. In the second stage, represented by Equation (3.20), scenario-dependent variables 𝑦 ∈ ℝ𝑛2 serve as recourse for the decision made in the first stage when uncertainty 𝜉 is taken into account (Bertsimas and Mundru, 2023). 33 The mathematical formulation of the problem is shown in Equation (3.21). 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒: ∑ ∑ 𝑓𝑝𝑚𝐿𝑝𝑚𝑚∈𝑀𝑝∈𝑃− 𝔼[𝑄(?̇?, 𝜉(𝑠))] (3.21) The aim of Equation (3.21) is to minimize cost, which is equivalent to maximizing profit (Weskamp et al., 2019). Therefore, the proposed model, represented by Equations (3.22) to (3.40), is structured as a two-stage stochastic problem including strategic decisions made in the first stage and other decision variables as second-stage decisions. Moreover, scenario set 𝑠 ∈[1,2, … , 𝑆] is defined to represent the uncertainty of parameters and decision variables. The probability of scenario s is indicated by 𝑝𝑠. 𝑀𝑎𝑥 𝑍 = 𝔼[𝑄(?̇?, 𝜉(𝑠))] − ∑ ∑ 𝑓𝑝𝑚𝐿𝑝𝑚𝑚∈𝑀𝑝∈𝑃 (3.22) 𝑄(?̇?, 𝜉(𝑠)) is the optimal value of the following problem: 34 𝑄(?̇?, 𝜉(𝑠)) = ∑ 𝑝𝑠 (∑ ∑ ∑ ∑ ∑ 𝜔𝑖𝑚𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠𝑡∈𝑇|𝑡′≤𝑡𝑡′∈𝑇𝑚∈𝑀𝑐∈𝐶𝑖∈𝐼𝑠− (∑ ∑ ∑ 𝑐𝑝𝑝𝑚𝑃𝑅𝑝𝑚𝑡′𝑠𝑡′∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ ∑ ∑ ∑ 𝑐𝑣𝑝𝑖𝑚𝑣𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑡∈𝑇|𝑡′≤𝑡𝑡′∈𝑇𝑣∈𝑉𝑚∈𝑀𝑖∈𝐼𝑝∈𝑃+ ∑ ∑ ∑ ∑ ℎ𝑝𝑝𝑚 (𝐼𝑃𝑝𝑚𝑡′(𝑡−1)𝑠 + 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠2)𝑡∈𝑇|𝑡′<𝑡𝑡′∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ ∑ ℎ𝑖𝑖𝑚 (𝐼𝐼𝑖𝑚𝑡′(𝑡−1)𝑠 + 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠2)𝑡∈𝑇|𝑡′<𝑡𝑡′∈𝑇𝑚∈𝑀𝑖∈𝐼+ ∑ ∑ ∑ 𝑐𝑒𝑝𝑝𝑚𝐸𝑃𝑝𝑚𝑡𝑠𝑡∈𝑇𝑚∈𝑀𝑝∈𝑃+ ∑ ∑ ∑ 𝑐𝑒𝑖𝑖𝑚𝐸𝐼𝑖𝑚𝑡𝑠𝑡∈𝑇𝑚∈𝑀𝑖∈𝐼+ ∑ ∑ ∑ 𝑙𝑠𝑐𝑚𝑡𝐷𝑐𝑚𝑡−𝑠𝑡∈𝑇𝑚∈𝑀𝑐∈𝐶)) (3.23) Subject to: ∑ 𝐴𝑃𝑝𝑖𝑚𝑣𝑣∈𝑉≤ 𝐿𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀 (3.24) ∑ 𝐴𝐼𝑖𝑐𝑚𝑐∈𝐶≤ ∑ ∑ 𝐴𝑃𝑝𝑖𝑚𝑣𝑣∈𝑉𝑝∈𝑃, ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀 (3.25) ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑖∈𝐼≤ 𝑀𝑙𝑎𝑟𝑔𝑒 × 𝐿𝑝𝑚 (3.26) ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|0 ≤ 𝑡 − 𝑡′ < 𝑆𝐿𝑚, 𝑠 ∈ 𝑆 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠 ≤ 𝑀𝑙𝑎𝑟𝑔𝑒 × 𝐴𝐼𝑖𝑐𝑚 (3.27) 35 ∀ 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|0 ≤ 𝑡 − 𝑡′ < 𝑆𝐿𝑚, 𝑠 ∈ 𝑆 𝑃𝑅𝑝𝑚𝑡′𝑠 ≤ 𝑞𝑝𝑝𝑚 × 𝐿𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′ ∈ 𝑇, 𝑠 ∈ 𝑆 (3.28) ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑖∈𝐼≤ 𝑃𝑅𝑝𝑚𝑡′𝑠 , ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′& 𝑡 ∈ 𝑇|𝑡′ ≤ 𝑡, 𝑠 ∈ 𝑆 (3.29) 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠 = 𝑃𝑅𝑝𝑚𝑡′𝑠 − ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑖∈𝐼, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|𝑡′ = 𝑡, 𝑠 ∈ 𝑆 (3.30) 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠 = 𝐼𝑃𝑝𝑚𝑡′(𝑡−1)𝑠 − ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑖∈𝐼 (3.31) ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|0 < 𝑡 − 𝑡′ ≤ 𝑆𝐿𝑚, 𝑠 ∈ 𝑆 ∑ 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠𝑡′∈𝑇|𝑆𝐿𝑚≤𝑡−𝑡′= 𝐸𝑃𝑝𝑚𝑡𝑠 , ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.32) 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠 = ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑝∈𝑃− ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠𝑐∈𝐶, ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|𝑡′ = 𝑡, 𝑠 ∈ 𝑆 (3.33) 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠 = 𝐼𝐼𝑖𝑚𝑡′(𝑡−1)𝑠 + ∑ ∑ 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠𝑣∈𝑉𝑝∈𝑃− ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠𝑐∈𝐶 ∀ 𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡′&𝑡 ∈ 𝑇|0 < 𝑡 − 𝑡′ ≤ 𝑆𝐿𝑚, 𝑠 ∈ 𝑆 (3.34) ∑ 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠𝑡′∈𝑇|𝑆𝐿𝑚≤𝑡−𝑡′= 𝐸𝐼𝑖𝑚𝑡𝑠 , ∀𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.35) 𝐷𝑐𝑚𝑡−𝑠 = 𝑑𝑐𝑚𝑡𝑠 − ∑ ∑ 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠𝑡′∈𝑇𝑖∈𝐼, ∀𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.36) ∑ 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠𝑡′∈𝑇|0≤𝑡′≤𝑡≤ 𝑐𝑎𝑝𝑝𝑝𝑚, ∀ 𝑝 ∈ 𝑃, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.37) 36 ∑ 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠𝑡′∈𝑇|0≤𝑡′≤𝑡≤ 𝑐𝑎𝑝𝑖𝑖𝑚, ∀𝑖 ∈ 𝐼, 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.38) 𝐿𝑝𝑚, 𝐴𝑃𝑝𝑖𝑚𝑣, 𝐴𝐼𝑖𝑐𝑚 ∈ {0,1}, ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑣 ∈ 𝑉 (3.39) 𝑋𝑃𝑝𝑖𝑚𝑣𝑡′𝑡𝑠 , 𝑋𝐼𝑖𝑐𝑚𝑡′𝑡𝑠 , 𝑃𝑅𝑝𝑚𝑡′𝑠 , 𝐼𝑃𝑝𝑚𝑡′𝑡𝑠 , 𝐼𝐼𝑖𝑚𝑡′𝑡𝑠 , 𝐷𝑐𝑚𝑡−𝑠 , 𝐸𝑃𝑝𝑚𝑡𝑠 , 𝐸𝐼𝑖𝑚𝑡𝑠 ≥ 0 ∀ 𝑝 ∈ 𝑃, 𝑖 ∈ 𝐼, 𝑐 ∈ 𝐶, 𝑚 ∈ 𝑀, 𝑣 ∈ 𝑉, 𝑡′ ∈ 𝑇, 𝑡 ∈ 𝑇, 𝑠 ∈ 𝑆 (3.40) 37 Chapter 4: Solution Approach, Numerical Experiments, and Sensitivity Analysis In this section, the methodologies employed to address the uncertainty in the proposed FSC model are explored, and a real-world case study is provided to demonstrate the model’s applicability. Subsection 4.1 explains the solution approach, detailing the steps taken to generate scenarios using MCS, utilize K-means clustering for efficient scenario reduction, and employ the SAA method for addressing the large-scale nature of the problem. Subsection 4.2 presents numerical experiments designed to demonstrate the model’s performance across varying problem sizes and computational settings. Finally, Subsection 4.3 provides a case study to perform sensitivity analysis and validate the model. 4.1 Solution Approach Although disruption risks are infrequent, they mostly have significant impacts on systems (Aldrighetti, 2021). Disruptions in GTAs and other types of disruptions in FSCs, such as transportation route blockages and geopolitical conflicts can result in uncertainties and threaten the supply of essential food ingredients. Recent global instances include the potential termination of NAFTA, the Russia-Ukraine conflict, and the attacks and blockages in the Red Sea (Swanson and Granville, 2017; Jagtap et al., 2022; Lin et al., 2023; Coyne, 2024). These disruptions introduce uncertainty into FSCs, which in turn leads to fluctuations in demand, creating additional challenges in efficient FSCs management (Davis et al., 2021). In this subsection, the methodology used to address the uncertainties in the FSC optimization model is presented. Subsection 4.1.1 explores the MCS for generating scenarios, Subsection 4.1.2 details the K-means clustering method to reduce the scenarios, and Subsection 4.1.3 explains the SAA algorithm. The overall framework of the proposed solution approach is shown in Figure 4.1. 38 Figure 4.1: The overall solution framework for optimizing the FSC 39 4.1.1 Scenario Generation Method MCS is an effective statistical method for modeling uncertainties by creating random samples from the probability distributions of stochastic parameters. By repeatedly sampling and simulating the system, it provides a statistical estimate of the parameters (Roozkhosh et al., 2024). In this study, MCS method is first implemented to generate possible future scenarios along the planning horizon for 𝑑𝑐𝑚𝑡𝑠 using pseudo-random numbers. For this study, 𝑍 is the objective function value, which depends on the uncertain parameter 𝑑𝑐𝑚𝑡𝑠 . The steps for generating scenarios via the MCS are as follows: 1. Based on the historical data, the probability distribution (e.g., Normal or Uniform) is assigned to 𝑑𝑐𝑚𝑡𝑠 2. 𝑁 random samples are generated for 𝑑𝑐𝑚𝑡𝑠 . 3. The value of 𝑍 = 𝑓(𝑑𝑐𝑚𝑡𝑠 ) for each sample is obtained, which results in 𝑁 output value. 4. The average of 𝑍 is calculated through equation (4.1) (Roozkhosh and Ghorbani, 2025). 𝑍 = 𝐸[𝑍] ≈ (1𝑁) ∑ 𝑍𝑛𝑁𝑛=1 (4.1) The MCS is then combined with K-means clustering and the Elbow method, as presented in the following subsections to reduce the complexity of the model. 4.1.2 Scenario Reduction Method Scenario reduction and sampling methods are employed to reduce the number of scenarios while ensuring that the reduced numbers remain representative of the entire scenario set. The Fuzzy C-means and K-means clustering algorithms are the two recognized approaches to group a specified number of scenarios with similar attributes into a predetermined number of clusters, thereby reducing the number of representative scenarios (Bezdek, 1973; Gholami-Zanjani et al., 2021b). Following related studies (Chen et al., 2023; Yunusoglu et al., 2024), and the ability 40 of the Elbow method for determining the optimal number of clusters (Chen et al., 2021), the K-means clustering algorithm is employed in this study. Moreover, the K-means algorithm is efficient in finding the best possible solutions for clustering errors by iteratively adjusting cluster centers. This method, commonly used in various clustering applications, starts with cluster centers at random positions and continuously moves them to reduce clustering errors (Likas et al., 2003; Tao et al., 2024). Consider the data set 𝑋 = {𝑥1, … , 𝑥𝑁} in a 𝑑-dimentional Euclidean space 𝑅𝑑. Consider 𝐴 ={𝑎1, … , 𝑎𝐶} be the set of cluster centers, where 𝐶 is the total number of clusters. Moreover, 𝑧 =[𝑧𝑖𝑘]𝑁×𝐶 where 𝑧𝑖𝑘 ∈ {0,1}, indicating if data point 𝑥𝑖 is allocated to 𝑘-th cluster where 𝑘 ∈{1, … , 𝐶}. Th objective function of K-means algorithm is calculated via equation (4.2). 𝐽(𝑧, 𝐴) = ∑ ∑ 𝑧𝑖𝑘𝐶𝑘=1(||𝑥𝑖 − 𝑎𝑘||)2𝑁𝑖=1 (4.2) The K-means algorithm performs the required steps to minimize the K-means objective function 𝐽(𝑧, 𝐴), including updating equations for cluster centers and memberships, as shown in Equations (4.3) and (4.4), respectively. 𝑎𝑘 =∑ 𝑧𝑖𝑘 𝑥𝑖𝑁𝑖=1∑ 𝑧𝑖𝑘 𝑁𝑖=1 (4.3) 𝑧𝑖𝑘 = {1 𝑖𝑓 ||𝑥𝑖 − 𝑎𝑘||2 = min1≤𝑘≤𝐶||𝑥𝑖 − 𝑎𝑘||2 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. (4.4) where ||𝑥𝑖 − 𝑎𝑘||2 is the Euclidean distance between 𝑥𝑖 and 𝑎𝑘 (Sinaga and Yang, 2020). However, determining the optimal number of clusters is required to achieve accurate results. Elbow criterion technique, which is a heuristic method, can be applied for this purpose. This technique determines the best number of clusters based on the quadratic difference calculation on various test 𝑘 values. As the value of 𝑘 increases, the average degree of distortion decreases. At the optimal value of 𝑘, there is a sudden increase in distortion, creating an elbow point. The 41 best number for 𝑘 can be determined by visually inspecting the data; the optimal number of clusters is reached when each cluster forms distinct groups without overlapping, minimizing grouping errors (Permadi et al., 2023). However, in this study, the KneeLocator approach is employed from the kneed Library to determine the number of clusters (Harrington, 2021). The optimal number of clusters is determined to be 3, which is illustrated in Figure 4.2. Figure 4.2: The optimal value of the number of clusters 4.1.3 Sample average Approximation The uncertainties in the model make evaluating the exact value of the expected profit in the second stage challenging; thus, SAA method is applied to address this issue. SAA is a widely used method for validating large-scale two-stage stochastic models, which is based on sampling (Liu et al, 2023). The approach involves approximating the objective value through 𝑠 scenarios and repeating the procedure for 𝑅𝑒𝑝 times. As presented in Algorithm 4.1, the number of scenarios, the number of replications, and the accepted gap between upper and lower bounds are determined initially, after which the lower and upper bounds are set to negative and positive infinity, respectively. Step 7 computes the mean objective function value across all replications, Step 8 updates the gap between upper and lower bounds, and Step 9 initiates a loop that 42 continues until the deviation between upper and lower bounds falls below the accepted gap. Steps 10 and 11 calculate and record the second-stage objective function and variables in each replication. Upon completing the loop in Step 12, Step 13 updates the lower bound, within the obtained decision variables of the first-stage model as the feasible solutions for the second-stage problem. Steps 14 to 16 involve updating the upper bound based on deviations in the objective function value from the mean across scenarios. Step 17 calculates the deviation between updated upper and lower bounds, while Step 18 terminates the loop if the gap falls below the predefined threshold. Provided that the gap value is less than the predefined acceptable gap, the second stage of the model will be updated (Mohammadi et al. 2021). The SAA method steps are depicted in the algorithm 4.1 as follows: Algorithm 4.1: SAA Initialize: 1. 𝑆 ← 𝑺 (Number of scenarios) 2. 𝑆′ ← 𝑺′ (Number of scenarios) 3. 𝑅𝑒𝑝 ← 𝑹𝒆𝒑 (Number of replications) 4. 𝛼% ← 𝛼% (Pre-defined accepted gap) 5. 𝐿𝐵 ← −∞ (Lower bound) 6. 𝑈𝐵 ← +∞ (Upper bound) 7. ?̅? (Updated lower bound) 8. 𝛾 ← [] (Gap) 9. while 𝛾 ≤ 𝛼 10. for 𝑠 = [1: 𝑆] 11. 𝑀𝑎𝑥 𝑄(𝑋) =1𝑆∑ 𝑄(𝑋, 𝑠)𝑠∈𝑆 − ∑ ∑ 𝑓𝑝𝑚𝐿𝑝𝑚𝑚∈𝑀𝑝∈𝑃 12. end for 43 13. 𝐿𝐵 ← ?̅? = 1𝑅∑ 𝑍𝑟∈𝑅 14. for 𝑠′ = [1: 𝑆′] 15. 𝑈𝐵 = 𝑄𝑆′(?̅?, 𝑠′) =1(𝑆′−1)𝑆′∑ (𝑓(?̅?, 𝑠) −𝑓(𝑓(?̅?,𝑠))𝑆′𝑠′∈𝑆′ )2 16 end for 17. 𝛾 = 𝑄𝑆′(?̅?, 𝑠′) − ?̅? 18. end while 4.2 The Numerical Experiments In this section, four main test problems with different sizes have been generated to show the applicability of this model across various problem sizes, solved via the Jupyter Notebook version 7.0.8 and a Ryzen 5 7000 series processor. Details regarding the size of the test problems and results are provided in Table 4.1. The value of 𝑆′ and 𝑅𝑒𝑝 in all tests are set to 5000 and 25, respectively. Table 4.1: Numerical examples P. NO. Set 𝑆 Lower-bound Upper-bound Gap (%) C. T. (S) 𝑃 𝐼 𝐶 𝑀 𝑉 𝑇 1 1 1 1 1 1 1 50 9,591.43 9,589.92 0.0158 4.90 100 9,590.35 9,589.92 0.0045 5.37 150 9,588.06 9,589.95 0.0197 6.16 300 9,589.05 9,589.94 0.0092 7.82 500 9,589.64 9,590.01 0.0038 10.31 44 Table 4.1: Numerical examples P. NO. Set 𝑆 Lower-bound Upper-bound Gap (%) C. T. (S) 𝑃 𝐼 𝐶 𝑀 𝑉 𝑇 1 1 1 1 1 1 1 700 9,589.68 9,589.90 0.0022 13.15 900 9,590.10 9,589.63 0.0049 15.09 2 1 2 2 2 1 2 50 76,766.57 76,778.55 0.0156 35.14 100 76,769.38 76,778.55 0.0119 43.01 150 76,777.81 76,778.58 0.0010 50.81 300 76,780.41 76,778.41 0.0026 74.22 500 76,778.42 76,778.95 0.0007 104.58 700 76,777.89 76,779.57 0.0022 135.94 900 76,778.93 76,779.47 0.0007 166.70 3 1 2 3 3 2 3 50 259,123.49 259,169.29 0.0177 136.39 100 259,165.25 259,168.98 0.0014 173.18 150 259,168.81 259,169.01 0.0001 210.42 300 259,159.49 259,170.36 0.0042 327.16 500 259,166.20 259,170.08 0.0015 488.18 700 259,167.19 259,171.34 0.0016 637.83 900 259,169.70 259,170.62 0.0004 835.00 45 Table 4.1: Numerical examples As Table 4.1 demonstrates, by increasing the sample size (𝑆), the computational time grows significantly, while the gap value decreases. For better illustration, Figure 4.3 is provided to P. NO. Set 𝑆 Lower-bound Upper-bound Gap (%) C. T. (S) 𝑃 𝐼 𝐶 𝑀 𝑉 𝑇 4 2 3 4 3 2 4 50 460,731.86 460,770.45 0.0084 596.40 100 460,753.35 460,770.67 0.0038 930.58 150 460,764.92 460,770.33 0.0012 1,338.20 300 460,750.94 460,771.75 0.0045 2,618.85 500 460,749.57 460,750.98 0.0003 4,229.44 700 460,763.61 460,769.82 0.0013 5,478.48 900 460,764.87 460,768.41 0.0008 6,916.09 46 depict the convergence of the upper bound and lower bound through increasing the sample size for problem number (P. NO.) 3. Figure 4.3: The convergence of lower bound and upper bound by increasing the sample size Figure 4.4 also highlights the relationship between the reduction in the percentage gap between the upper and lower bounds and the required computation time as the number of scenarios increases. The figure clearly demonstrates that as more scenarios are introduced, the gap percentage steadily decreases, indicating enhanced accuracy and convergence in solving the problem. However, this improvement comes at a cost, as the required computational time increases sharply with each added scenario. 47 Figure 4.4: The value of gap (%) and computational time (seconds) based on the number of scenarios 4.3 Case Study To demonstrate the applicability of the proposed mathematical model for GFSCs, a case study is provided. Among various GTAs, NAFTA is selected due to its critical importance in both North America and the global economy, making it one of the most significant and impactful GTAs worldwide. Across globally traded food categories, grain, meat, and dairy are identified as the three main food products contributing the most to food security and representing over 75% of the food industry (Rogachev and Antamoshkina, 2019). Specifically, the model focuses on bread and meat, which are significant commodities in NAFTA, with Canada and the United States serving as major importers and exporters on a global scale. For instance, in 2024, Canada exported CAD $670,269,901 worth of meat to the United States (Agriculture and Agri-Food Canada, 2024). 48 To calculate customer demand (𝑑𝑐𝑚𝑡) for each product in each period, the consumption of meat and bread in the three largest cities in Canada and five major cities in the United States is considered. Using per capita consumption data for meat (38.56 lb. in Canada and 89.23 lb. in the United States) and bread (79.45 lb. in Canada and 44.75 lb. in the United States) (Shahbandeh, 2023; Wunsch, 2024; Shahbandeh, 2024), it is determined that on average, individuals in Canada consume 0.22 lb. of bread and 0.11 lb. of meat daily, while individuals in the United States consume 0.12 lb. of bread and 0.24 lb. of meat daily. By scaling these values to the population size of each city, 𝑑𝑐𝑚𝑡 is calculated and presented in Table 4.2. Table 4.2: Values of 𝑑𝑐𝑚𝑡(lb.) City Demand City Demand Bread Meat Bread Meat Toronto 564,200 317,200 Los Angeles 409,368 951,294.3 Montreal 347,200 195,200 Chicago 288,370 670,118.7 Calgary 221,327 124,432.9 Houston 241,980 562,317.5 New York City 924,439 2,148,222 Phoenix 168,854 392,385.9 The selected cities are divided into 25 different regions as customer areas, and 7 periods are considered, with each period representing one day. The value of 𝜔𝑖𝑚 for bread and meat in Canada is 2.01 CAD $/lb. and 5.22 CAD $/lb. and for the United States is respectively 2.73 CAD $/lb. and 7.03 CAD $/lb (Wunsch, 2024). According to D’Arcy et al. (2012), 𝑐𝑝𝑝𝑚 is 75% of 𝜔𝑖𝑚. Moreover, the values of ℎ𝑝𝑝𝑚 and ℎ𝑖𝑖𝑚 are estimated to be between 0.005 and 0.01 times 𝑐𝑝𝑝𝑚, while parameter 𝑐𝑒𝑝𝑝𝑚is assumed to be equal to 𝑝𝑐𝑝𝑚 (Haijema at al., 2007). The value of parameter 𝑐𝑒𝑖𝑖𝑚 is also assumed to be equal to 𝜔𝑖𝑚. The shelf life of bread is 49 determined to be 4 days, while refrigerated meat has a shelf life of 5 days (Makoveev and Kozak, 2022; Sabila et al., 2023). Moreover, 𝑙𝑠𝑚𝑡 is projected to be approximately 0.6 times 𝜔𝑖𝑚. Two different trucks are also considered to meet the logistical requirements. Reefer trucks are utilized for transporting perishable food products from PCs to retailers, and standard trucks are used to transport durable products. The cost of transportation based on the type of vehicle, food product, and the origin and destination is assumed to be between 0.03 to 0.4 CAD. The value of the parameters used in this model is provided in Table 4.3. Table 4.3: Parameter setting Parameter Value Parameter Value 𝑓𝑝𝑚 (100, 2,600) ℎ𝑝𝑝𝑚 (0.016, 0.056) 𝑐𝑎𝑝𝑝𝑝𝑚 850,000 ℎ𝑖𝑖𝑚 (0.02, 0.07) 𝑐𝑎𝑝𝑖𝑖𝑚 500,000 𝑙𝑠𝑐𝑚𝑡 (1.47, 4.92) 𝑐𝑣𝑝𝑖𝑚𝑣 (0.03, 0.4) 𝑐𝑒𝑝𝑝𝑚 (1.608, 5.62) 𝑞𝑝𝑝𝑚 (50,000, 2750,000) 𝑐𝑒𝑖𝑖𝑚 (2.01, 7.03) 𝑐𝑝𝑝𝑚 (1.608, 5.62) 𝜔𝑖𝑚 (2.01, 7.03) Figure 4.5 depicts the flow of food products between Canada and the United States under the NAFTA agreement, depicting an efficient system where PCs, retailers, and customers are interconnected through multiple routes. The extensive lines connecting various nodes across the map underscore the smooth flow of food products, facilitated by the elimination of tariffs and minimal trade barriers. This configuration ensures that food products are readily available across the border. The free trade framework under NAFTA allows for the easier and faster 50 exchange of food products, optimizing the FSC and ensuring a steady flow of food products to meet consumer demands in both countries. Figure 4.5: The configuration of the FSC with NAFTA However, Figure 4.6 illustrates the flow of food products between Canada and the United States under conditions where NAFTA faces uncertainty due to political instability, trade disputes, economic sanctions, or other destabilizing factors. A noticeable reduction in connectivity among PCs, retailers, and consumers is evident in this figure. This diminished interconnection results in fewer routes and a fragmented network structure that can cause delays and inefficiencies within the FSC. The constrained flow of food products highlighted under the disrupted scenario underscores the pivotal role that trade agreements like NAFTA play in maintaining a reliable FSC. 51 Figure 4.6: The configuration of the FSC with termination of NAFTA To demonstrate the impact of panic buying on the FSC due to increased demand, Figure 4.7 is provided, which also illustrates the vulnerability of the FSC to disruptions. The initial stability in profit shows the system can handle a moderate demand increase, with profit rising slightly when demand increases by 5%. This is due to the system’s ability to distribute the remaining food products from previous periods or increase production output, thereby generating more profit. When demand increases by 10%, a minor shortage appears in the stochastic model, yet total profit still improves slightly. This occurs because the percentage of unmet demand represents the shortage-to-demand ratio. Therefore, the stochastic model can still fulfill more demand and generate higher profit. However, beyond a 10% increase in demand, profit begins to drop. A significant drop occurs when demand increases by about 11%, due to unmet demand. Since food is an indispensable part of human survival, the model incorporates a significant penalty cost for shortages to prioritize meeting demands. The increase in total shortage due to 52 the increase in demand indicates the growing pressure on the system to maximize the level of production and distribution. Although the model strives to meet all demands, shortages still occur due to the production capacity constraints. Even if PCs utilize 100% of their production capacity, they cannot meet total demand. Moreover, the comparison of deterministic and stochastic models shows that with demand increasing up to 10%, both models maintain relatively similar profit, with the stochastic model slightly outperforming the deterministic one. However, beyond this point, the deterministic model results in higher profit and less unmet demand. This occurs because stochastic models account for demand uncertainty, and demand fluctuates randomly, leading to a higher total demand than in the deterministic model. Additionally, as demand increases, the percentage of unmet demand for both models rises substantially, reflecting the growing pressure on the system. Although the stochastic model generally provides more adaptability, it results in higher unmet demand as demand surges, further highlighting the limitations of production capacity, even with full utilization. 53 Figure 4.7: The impact of increasing demand on the total profit and unmet demand (%) Disruptions in GTAs, such as NAFTA, can impact various sectors. One key aspect is transportation, which is a critical factor in GFSC, as it directly impacts the timely delivery of food products. Various transportation methods are used in FSCs; however, given the perishable nature of many food products, any disruption in transportation networks can lead to delays, potentially resulting in spoilage and loss of goods. These disruptions not only cause delays in food product delivery but also increase expenses for the transportation sector. One major indirect cost imposed on FSCs is insurance expenses. There has been a notable increase in insurance rates for voyages through the Red Sea and Bab al-Mandab. Typically, the insurance rates are approximately 0.6% of a ship’s cargo value under normal circumstances, but this rate has been escalated to as much as 2%. Additionally, cargo insurers have begun including an extra war risk premium due to the increased risks in these areas. (Denamiel et al., 2024). The impact of the disruptions is felt throughout the FSC, leading to increased production costs, wheat shipments, and ultimately, bread production. The primary food ingredients, wheat in this 54 case, would be delivered to the manufacturers with higher costs and with long delays. Moreover, the World Trade Organization reported a 40% drop in wheat shipments through the Suez Canal due to rerouting around South Africa’s Cape of Good Hope (World Trade Organization, 2024). This decline can result in decreased production capacity and higher expenses for food manufacturers. Moreover, tariffs and quotas can escalate additional costs such as order fees, transportation costs, and raw material prices. Tariffs, which are the direct expenses added to the FSC when a trade agreement terminates, vary based on the product type and the countries involved. For instance, NAFTA termination can lead to increased costs for raw materials imported for food production, thereby affecting overall production costs. Moreover, order fees may increase due to more time-consuming processes required for acquiring licenses and completing paperwork. The increases in costs will ultimately elevate the final cost of food products, potentially leading to panic buying. Figure 4.8 is provided to depict the impacts of increasing the production cost and reducing the production capacity. It compares the total profit of a system under three different disruption scenarios in which demand rises, production capacity declines, and production costs surge simultaneously. Three scenarios are shown: the baseline scenario, which assumes no changes in production capacity and production costs; scenario 1, which incorporates a 5% reduction in production capacity and a corresponding increase in production costs compared to the baseline; and scenario 2, with a 10% decrease in production capacity and a corresponding rise in production costs relative to the baseline. 55 Figure 4.8: The impact of NAFTA termination and panic buying on the total profit Figure 4.8 (a) and (b) illustrate total profit under varying demand changes for three different production scenarios. The deterministic model (a) and the stochastic model (b) exhibit similar trends, highlighting the impact of increasing production costs and reduced capacity on profitability. The baseline scenario consistently yields the highest profits across all demand levels, underscoring the financial advantage of maintaining stable production conditions. 56 However, once demand exceeds a 10% increase, profitability declines significantly. This drop occurs because, at higher demand levels, the production system reaches its capacity limits and is unable to meet all demand, resulting in shortages. This trend is observed in Scenarios 1 and 2 as well, with Scenario 2 experiencing the steepest decline due to the combined effects of higher production costs and reduced capacity. While the stochastic model generally follows the same pattern, it exhibits slightly different profit behaviors in some cases. This variation arises because demand uncertainties in the stochastic model can occasionally result in a higher number of demands compared to the deterministic model. As a result, the stochastic model may fulfill more demand, leading to slightly higher profits. However, as demand increases beyond 10%, the stochastic model encounters greater shortages than the deterministic model, leading to a sharper decline in profitability where capacity constraints become a limiting factor. This highlights the need for resilient capacity planning and cost-control strategies to mitigate financial risks in uncertain market environments and ensure profitability even under fluctuating demand conditions. Figure 4.9 illustrates which retailers and customer areas have experienced the highest unmet demand during the disruption. 57 Figure 4.9: The allocation of products under NAFTA disruption As illustrated in Figure 4.9, due to a substantial shortage, no food products have been allocated to retailers in Canada. Consequently, retailers located in Canada were unable to meet the demand of their allocated customers. This outcome is primarily driven by the shortage costs, which vary based on the customer’s geographic location, and the customer area in this case is the country where the customers live. In scenarios of limited production capacity and supply in general, the model prioritizes satisfying demand in regions with higher associated shortage costs to minimize the shortage costs imposed on the system. Given that these costs are significantly higher in the United States than in Canada, the model opts to allocate resources 58 to meet the demand of customers in the United States first, even though transportation and total production costs in the United States are higher. Figure 4.10 compares unmet demand rates for bread (Figure 4.10 (a)) and meat (Figure 4.10 (b)) under the same three scenarios described in Figure 4.8 (baseline scenario: no change in production capacity and production cost; scenario 1: 5% decrease in production capacity and 5% increase in production cost; scenario 2: 10% decrease in production capacity and 10% increase in production cost). Both figures show that as demand rises, unmet demand increases for each product, but the rate of increase differs between bread and meat. For bread, shortages begin even with a 5% increase in demand, and by the time demand rises by 25%, unmet demand reaches approximately 8% in the baseline scenario. In scenarios 1 and 2, the unmet demand for bread rises sharply, peaking at around 18% when demand increases by 25%. In contrast, meat shortages are more pronounced, particularly in scenarios 1 and 2 relative to the baseline scenario. Shortages begin with a 5% increase in demand, and when demand reaches 25%, unmet demand reaches approximately 19% in scenario 2. Moreover, in the baseline scenario, the unmet demand for meat reaches about 10% when demand increases by 25%, indicating that the meat supply chain is less resilient than bread under similar demand surges. 59 Figure 4.10: The rate of unmet demand for each product under disruption 60 The meat supply chain is significantly more vulnerable to disruptions compared to the bread supply chain due to its greater complexity and resource-intensive processes. Meat production involves lengthy cycles, from raising livestock to processing and distribution, which makes it more prone to supply shortages. In contrast, bread benefits from a shorter and less complex production cycle. Wheat, the primary ingredient in bread, is mostly grown domestically in the United States, a leading global wheat exporter. This local production base provides greater resilience to the bread supply chain, as it is less reliant on international imports and experiences fewer bottlenecks. As a result, even under scenarios of reduced production capacity or increased costs, the bread supply chain remains more stable, leading to fewer supply disruptions and a smaller rise in unmet demand than meat. Ensuring an optimal production level is crucial for supply chains, especially in FSCs, where both shortages and excessive waste can have significant financial and operational consequences. A key challenge in managing production is balancing unmet demand, inventory levels, and waste generation to maintain efficiency. The relationship between unmet demand and waste generation across varying production levels is shown in Figure 4.11. When production is set at 1,000,000 units, unmet demand is at its highest level (6.39%), indicating a severe shortage. However, as production increases, unmet demand rapidly declines, reaching the zero level beyond 1,150,000 units. This behavior demonstrates the system’s ability to mitigate shortages as production capacity expands. However, once the production level surpasses 1,370,000 units, another critical issue arises: the PC waste rate begins to rise sharply, reaching 0.28% at 1,400,000 units. This trend highlights 61 a trade-off; while higher production effectively eliminates shortages, it eventually leads to operational inefficiencies as excess inventory surpasses system capacity, resulting in waste. Figure 4.11: Impact of production level on unmet demand and rate of waste in factories The shift from shortage mitigation to overproduction is further illustrated in Figure 4.12. As production exceeds demand, surplus products are retained in PC inventories until they are either transported to retailers or expire. While inventory accumulation provides a buffer against shortages, it also introduces higher storage costs. Between 1,150,000 and 1,370,000 units, the system operates at peak efficiency, all demands are met while the excess products are stored for future use. However, beyond 1,370,000 units, the storage capacity reaches its limit, and additional production results in an increase in waste instead of inventory. This critical threshold marks the transition from efficient stockpiling to overproduction, where excess products can no longer be absorbed into inventory. 62 Figure 4.12: Impact of production level on unmet demand and total inventory The financial implications of the observed trends in Figures 4.11 and 4.12 are reflected in Figure 4.13. Initially, as production increases, profitability rises, peaking between 1,100,000 and 1,150,000 units, when unmet demand is fully addressed, and inventory is efficiently managed. This range represents the optimal production threshold, where the system benefits from maximum sales profit without incurring excessive waste or inventory holding costs. However, as Figure 4.11 highlighted, surpassing 1,370,000 units leads to an increase in waste generation. As Figure 4.12 demonstrated, inventory capacity reaches its saturation point, meaning additional production does not translate to higher availability but rather leads to increased disposal rates. These inefficiencies directly impact profitability, as seen in Figure 4.13, where profits begin to decline beyond the peak production range. 63 Figure 4.13: Impact of production level on total profit and unmet demand This finding underscores a critical insight, higher production does not always yield better financial performance. Instead, overproduction beyond the system’s absorption capacity leads to financial inefficiencies, diminishing overall returns. A strategic approach to production planning is essential to maintaining long-term FSC resilience and profitability. Maintaining a minimum level of inventory in retail stores plays a critical role in ensuring product availability, enhancing customer satisfaction, and providing operational flexibility. Lack of sufficient inventory levels can result in shortage of products and consequently result in customer dissatisfaction. By considering a certain level of inventory, retailers can address fluctuations in demand more efficiently, preventing shortage cost as well as revenue loss. This also allows retailers to be more resilient in the face of supply chain disruptions, as they can continue to meet customer needs despite unexpected delays. Figure 4.14 provides a detailed analysis of the impact of maintaining minimum inventory levels at retail stores as well as the extension of shelf life, by comparing scenarios with minimum inventory levels of 0, 50, and 100 units. 64 Figure 4.14: Impact of minimum level of inventory at retailers and shelf life extension on total waste and profit Figure 4.14 illustrates the relationship between total profit and total waste as a function of product shelf life extension. As shelf life extension increases from 0 to 3 periods, total waste decreases, with the most significant reduction observed at the 100-unit minimum inventory level. This highlights the effectiveness of extending product shelf life in minimizing waste, particularly at higher inventory levels. Moreover, total profit shows a slight yet consistent increase as shelf life extends, with the highest profit achieved when the minimum inventory is set at 100 units, followed by 50 and 0 units. This suggests that maintaining higher inventory levels, combined with extended shelf life, can simultaneously reduce waste and improve profit. This approach provides an optimal strategy for retailers to meet customer demand while minimizing shortage units and spoilage. 65 Chapter 5: Conclusions and Future Directions In this section, the key conclusions of the study are discussed, and potential future directions are proposed. The findings regarding the impact of disruptions in GTAs on GFSCs are summarized, along with the proposed optimization model for managing disruptions. Furthermore, areas for future research are suggested, with a focus on how alternative strategies can further strengthen supply chains and ensure long-term food security. 5.1 Research Summary This thesis explores the role of GTAs in GFSCs and food security, emphasizing the effects of GTA disruptions on FSC stability, costs, and food availability. A particular focus is given to NAFTA and the potential consequences of its termination. Chapter 2 provides an extensive literature review on key topics related to GFSC disruptions, transportation and logistic challenges, resilience strategies, the role of GTAs in ensuring food security, and the SAA method for optimizing a large-scale FSC model. This chapter explores the increasing complexities of modern FSCs and how they are highly exposed to disruptions caused by factors such as geopolitical conflicts, trade policy shifts, environmental changes, and logistical inefficiencies. A particular focus is given to the vulnerabilities caused by these disruptions, including supply shortages, price volatility, increased operational costs, and cascading effects on food accessibility. Moreover, the chapter critically examines the impact of transportation and logistics disruptions, such as those caused by maritime blockages and infrastructure failures, which play a crucial role in determining the stability and efficiency of GFSCs. Various resilience strategies employed to enhance supply chain resilience are also reviewed, including inventory management approaches, multiple sourcing, and flexible distribution networks. One of the key 66 contributions of this chapter is identifying research gaps, particularly concerning the quantitative modeling of GTA disruptions and their effects on FSCs. While previous studies have examined trade policies and their economic implications, there remains a lack of comprehensive stochastic models that incorporate uncertainty, perishability, demand fluctuations, and transportation constraints. Based on the reviewed literature and the research gap in Chapter 2, Chapter 3 introduces the stochastic optimization model, which serves as the foundation of the research’s mathematical approach. This model is designed to integrate supply and distribution decisions while considering critical uncertainties such as demand variability, perishability of food products, and disruptions in trade policies. Multiple products, each with a specific shelf life, were considered model, and various transportation vehicles were incorporated to meet the logistical requirements. The model ensures that food security is maintained even in uncertain environments by optimizing resource allocation, inventory management, and distribution logistics. By considering multiple disruption scenarios, the model provides practical insights into supply chains responses to GTA uncertainties, enabling decision-makers to develop a resilient FSC. Additionally, the model is structured to maximize profitability while maintaining resilience, allowing businesses and policymakers to evaluate trade-offs between cost efficiency and risk mitigation. To enable the model to handle a large number of scenarios and tackle the complexity of large-scale problems, Chapter 4 presents a comprehensive solution approach that integrates multiple advanced computational techniques. Specifically, this chapter employs MCS for scenario generation, K-means clustering for scenario reduction, and the SAA method for reducing the computational time. These methodologies are selected to enhance computational efficiency and optimize decision-making under uncertainty. MCS allows for the creation of diverse and 67 representative scenarios by generating different possible demand scenarios, capturing the stochastic nature of the problem. Given the vast number of scenarios generated, solving the problem is not practical. To address this, K-means clustering is used to reduce the number of scenarios while maintaining the statistical characteristics of the original dataset. Finally, the SAA method is applied to address the large-scale nature of the problem. The applicability and effectiveness of the proposed model are then demonstrated through a real-world case study that assesses the potential impact of NAFTA termination on food trade between Canada and the United States. Given the integral role of GTAs in stabilizing GFSCs, the study highlights the economic and logistical consequences resulting from disruptions to these agreements. GTAs facilitate the exchange of food products across borders, promoting lower tariffs, economic integration, and efficient food distribution. However, the study underscores that political and economic disruptions, including NAFTA termination, can lead to severe consequences, such as increased operational costs, supply shortages, and broader food security risks. The findings reveal that disruptions in GTAs reduce profit by up to over 40% due to unmet demand. In addition to financial losses, disruptions cause supply chain inefficiencies, leading to delayed food shipments and shortages of staple food products. The study also examines the cascading effects of such disruptions on food security, demonstrating that shortages first impact Canada, then the United States. This outcome is attributed to the prioritization of high-shortage-cost regions, where resources are allocated based on economic and logistical considerations. Beyond trade disruptions, the study incorporates various perishable food products with different shelf lives and considers multiple transportation modes to meet each product’s logistical requirements. The impact of extended shelf life and inventory levels at retailers is analyzed, revealing their role in minimizing shortages and spoilage simultaneously. By 68 extending shelf life, retailers can mitigate waste, improve overall supply chain efficiency, and reduce financial losses. However, improper inventory management can lead to overstocking or understocking, exacerbating food shortages and waste. These findings highlight the importance of integrating storage optimization and supply chain forecasting strategies to enhance resilience in perishable food distribution. The study further explores how variations in shelf life influence food distribution efficiency and supply chain profitability, highlighting the need for strategic decision-making in inventory and transportation management. Additionally, the case study compares the resilience of different food products, demonstrating that shortages occur first for meat and later for bread. This discrepancy stems from differences in production capacity and supply chain dependencies. The findings indicate that meat shortages occur earlier due to its dependence on cross-border supply chains and lower production capacity. In contrast, bread is more resilient due to more localized production. This analysis of food resilience underscores the importance of diversified sourcing strategies and adaptive logistics to mitigate disruptions across different food categories. The study also examines the impact of production uncertainty, revealing the inherent trade-offs between reducing shortages and increasing waste. It finds that higher production levels effectively reduce shortages; however, they impose new constraints within the supply chain, leading to increased waste and reduced profitability. This observation suggests that increasing production alone is not a viable long-term strategy for ensuring food security. Instead, a balanced approach that considers production capacity, waste management, and demand fluctuations is essential for optimizing FSCs efficiency. The findings emphasize the need for strategic production planning that minimizes excess inventory while maintaining adequate supply levels to prevent shortages. 69 5.2 Research Contributions This thesis makes several substantial contributions to the FSC field, particularly in addressing the impact of disruptions in GTAs on the FSCs. The primary contributions of this thesis can be summarized as follows: • A two-stage stochastic model is introduced that optimizes global multi-product FSCs under GTA-related uncertainties. The model enhances resilience and profitability by integrating supply and distribution phases under various disruption scenarios, such as panic buying, and uncertainties in production costs and capacities. To address the uncertainty in demand, MCS is applied to generate a large number of scenarios for the demand parameter. The K-means method is used to reduce the number of scenarios, and the SAA approach is employed to obtain results in a computationally feasible timeframe. Additionally, a comprehensive analysis is conducted to evaluate the impacts of uncertainties in GTAs and disruptions in GFSCs on food security. • Various perishable food products with different shelf lives are considered, and various transportation modes are considered to meet each product’s logistical requirements. In addition, the impacts of extended shelf life and inventory levels at retailers on the amount of waste and profit are demonstrated, helping retailers in minimizing shortages and spoilage simultaneously. • The proposed model is applied to a real-world case study, evaluating the potential impact of the termination of NAFTA on food security in the United States and Canada. This contribution demonstrates the lower resilience in Canada’s FSC with shortages occurring first in Canada and then in the United States. Moreover, the resilience of food products is compared, illustrating shortages occurring first for meat and later for bread. 70 • The role of uncertainty in production is analyzed, highlighting the trade-off between reducing shortages and waste in factories with different production levels. It is concluded that while higher production levels effectively reduce shortages, it acts similarly to a new constraint in the model, leading to increased waste and lower profitability. 5.3 Research Limitations While this study makes significant contributions to understanding the impact of disruptions in GTAs on GFSCs and food security, several limitations must be acknowledged. These limitations highlight areas where the study can be expanded in future research to enhance its applicability and robustness. This study primarily focuses on perishable food products due to their vulnerability to supply chain disruptions, particularly in transportation and storage. However, the exclusion of non-perishable goods, frozen products, and specialty foods limits the applicability of the findings. Expanding the model to include these additional product categories will provide a more comprehensive analysis of FSC resilience. Non-perishable food items, such as grains, canned goods, and dried products, can have different logistical and demand fluctuations, which may change the study’s findings. Moreover, specialty food products, such as organic food products, may be subject to distinct regulatory requirements, which might introduce further vulnerabilities in trade agreements. Another limitation is that this study examines various transportation methods for perishable goods but does not fully assess the role of alternative and emerging transportation methods in mitigating disruptions. Multimodal logistics (integrating road, rail, air, and sea transportation) and advancements in cold chain logistics present potential solutions to enhance FSC resilience. Additionally, the study does not consider the impact of transportation disruptions and delays caused by regulatory challenges or infrastructural constraints. These delays may cause food 71 spoilage and waste. Examining these factors will offer deeper insights into the resilience and adaptability of FSCs. While the study evaluates disruptions in GTAs, it does not incorporate the full complexity of evolving trade policies, regulatory changes, or geopolitical influences. Trade agreements are dynamic and prone to renegotiations, political shifts, and external economic pressures that can significantly alter their structure and effectiveness. The research assumes a relatively static trade policy framework, which does not reflect real-world complexities such as new tariffs. Additionally, the role of non-tariff barriers, such as sanitary and phytosanitary regulations, remains unexplored in this study. Another limitation of this study is the assumption that product prices remain fixed and certain across all scenarios. However, the uncertainty or termination of GTAs can lead to significant price volatility due to the introduction of tariffs, increased transportation costs, currency fluctuations, or shifts in supply and demand. Finally, the model assumes that food products produced in one country comply with the standards of the importing country. However, real-world trade barriers, including differences in food safety standards, labeling requirements, and import/export restrictions, can significantly impact FSCs. In practice, regulatory differences between trading partners can result in delays, additional compliance costs, and even complete barriers to trade. 5.4 Future Research While the current research primarily examines disruptions caused by human-induced sources (such as disruptions in GTAs), future studies can expand the model to include natural sources of uncertainty, such as wildfires, hurricanes, earthquakes, and other extreme weather events. These natural disasters can significantly impact FSCs by destroying critical infrastructure, 72 limiting access to food distribution points, disrupting transportation networks, and increasing logistical costs. Incorporating these elements into future models will provide a more comprehensive approach to resilience planning, ensuring food security even in the face of climate-related disruptions. Another avenue for future research is the inclusion of transportation network disruptions in the model. The current study has primarily focused on supply-related uncertainties; however, future models should consider constraints on routes between retailers, warehouses, and PCs. Disruptions, such as road infrastructure damages, can lead to the deactivation of critical transportation routes, affecting supply chain continuity. By integrating these factors into optimization models, future research can develop more robust strategies to mitigate disruptions in supply chain networks. Furthermore, the impact of alternative routing strategies, emergency logistics planning, and adaptive rerouting algorithms can be explored to assess their effectiveness in maintaining stable food distribution networks under varying disruption intensities. Future research can also explore and compare different resilience strategies, such as fortification, multimodal transportation strategies, and lateral transshipment, to enhance the resilience of FSCs. By evaluating their effectiveness under various disruption scenarios, future studies can provide insights into the most suitable approaches for improving supply chain resilience. For instance, lateral transshipment, where inventory is shared across multiple distribution centers to address shortages, can be implemented, and its impact on total profit, costs, and shortages can be analyzed with and without this approach. Another important direction for future research is considering the price uncertainty into the model. Under scenarios involving GTA disruptions or terminations, prices of food products may fluctuate due to changes in tariffs, increased operational costs, and shifts in supply and 73 demand. Future models could integrate stochastic price parameter or scenario-based price variations to capture market volatility more accurately. This would allow for a more realistic analysis of profitability, supply chain behavior, and policy interventions under uncertain trade environments. Additionally, integrating environmental sustainability considerations will enhance the model’s comprehensiveness and relevance to sustainable development goals. Future studies could incorporate emissions and other environmental impacts, such as waste, pollution, and energy consumption, to evaluate the ecological footprint of FSCs. Considering these impacts can enable the development of greener and more sustainable strategies for production, transportation, and waste management. Lastly, future research could expand the focus on food security by incorporating nutritional dimensions. While this study focuses on product availability and profitability, food insecurity is also influenced by access to nutritious food. Future models could investigate the supply chain dynamics of nutrient-rich foods and assess trade-offs between fresh produce and packaged or processed foods in global distribution networks. 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Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Mohamadpour Tosarkani, Babak
Li, Eric Ping Hung, 1978-
The role of global trade agreements in global food supply chain and food security
Text