Using a Just-In-Time Approach in the Green Supply Chain, Taking Into Account CO2 Emissions, Under Uncertainty in the Pre- and Post-COVID-19 Situation

Abstract

The main objective of this study is to develop a fuzzy-based approach for building a multistage, multiproduct, and multiperiod supply chain network (SCN) after and before the COVID-19 pandemic. The proposed model optimizes production and distribution planning under uncertainty in a multiperiod stochastic process network. The model is designed to help decision-makers manage the green supply chain (GSC) of their organizations. It was developed using the mixed-integer linear programming (MILP) approach. The model aims to maximize customer satisfaction in the pre- and post-COVID-19 era by reducing the total cost and delivery time they face. The model also estimates production, asset locations, order allocation, and inventory levels. Under uncertain conditions, a new probabilistic MILP model addresses the multiproduct, multiperiod SCN design (SCND) problem. The two objectives of this model are to maximize time and cost by using the concepts of total cost of ownership, activity-based costing, and just-in-time (JIT) production. The model’s outputs include the quantity of goods purchased, produced, inventoried, delivered, and transported and the selection of suppliers before and after the COVID situation. A numerical example solved using the above technique is given to evaluate and validate the model and the proposed solution approach. Finally, the results of the study are presented.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Fuzzy set theory and possibility theory are simpler and need less information than probability theory, yet they could be more effective at handling uncertainty in the supply chain (SC) than probability theory [1]. Overall, the research shows that even in the face of post-COVID-19 uncertainty, green closed-loop SC (GCLSC) may be constructed that are both environmentally sustainable and cost-effective by carefully balancing operational, economic, and legal considerations [2]. Most SC planning researchers model the uncertainties in the SC using probability distributions, which frequently utilize historical data. Given that reliable historical statistical data are not always accessible, probabilistic models may not be the best choice [3].

It is possible to optimize closed-loop SCs (CLSCs) to save expenses and carbon emissions simultaneously. This calls for prudence while choosing a site, paying for transportation, and handling regulatory fees, among other variables [4, 5]. A range of carbon policies, including carbon taxes and emissions trading programs, have been put in place by governments to encourage companies to reduce their environmental effect. These shifting constraints must be included in SC models [6]. Due to the COVID-19 pandemic, SC operations are now incredibly opaque. Strong optimization strategies may make it easier to create CLSC networks (CLSCNs) that are durable and environmentally sustainable [7].

Figure 1 shows the general structure of the just-in-time (JIT). Operations management’s JIT system makes it possible to develop production in response to demand at that specific time. No previous manufacturing was performed to meet any expected demand. The manufacturing process is extremely efficient when JIT is implemented; there is very little waste, excellent quality control, schedule adherence, and a smooth continuous flow. The goals include removing unprofitable processes, enhancing the production system’s flexibility, and doing away with the related expenses of inventory transportation and storage. There is no room for further goods. Toyota was the first to implement this at their facilities.

[figure(s) omitted; refer to PDF]

The main contribution and motivation of this paper are as follows:

• Based on what is known about the research in this field and reviewing the cited publications, there are not many studies on SCN design (SCND) that simultaneously consider the three components of cost, time, and CO₂ emissions taking into account uncertainty in the pre- and post-COVID-19 era.

• Total operating costs and process costing were included in the model for the cost factor, while JIT production was used for the time factor. Due to their simplicity, multiproduct, multistage, multiperiod, and multiobjective (MO) aspects were generally ignored in previous models; however, the current research model includes all these key aspects of true SC situations. Unlike most previous models, the current model calculates the values for early and late deliveries and attempts to minimize them.

• As a sort of cognitive uncertainty, the uncertainty of the parameters utilized in the problem has led to the usage of a probabilistic planning technique to simulate it in the pre- and post-COVID-19 period. Determining the ideal levels of production, distribution, and procurement for facilities situated at various SC levels at both the tactical and strategic levels is the aim of this work.

• Fuzzy sets are used to model the uncertainty. Since the supply, manufacturing, and distribution components of the model are all simultaneously present, the optimality of each component’s actions has been examined while considering other components.

The rest of the paper is organized as follows.

In Section 2 of the article, the literature review is explained. In Section 3, the problem is defined and its model is presented. In Section 4, the approach solution method is presented. In Section 5, results and discussion are presented. In Section 6, the conclusion and outlook are explained.

2. Literature Review

In this section, we provide an overview of the JIT approach, green SC (GSC), uncertainty, and pre- and post-COVID-19 in the context of the SC literature. After careful consideration of the problem and review of the previous work, we are convinced that the innovation of this paper is to be taken seriously. Moreover, incorporating JIT concepts into a GSC framework can improve operational efficiency and solve environmental problems. The fuzzy sets can be used to address uncertainty in SC networks (SCNs). For this purpose, a multiproduct, multilevel, and multiperiod SCN could be used.

2.1. GSCs

Customers are becoming increasingly aware of environmental and social sustainability. Companies that prioritize customer-centric green practices can improve their perception of customer resilience in general and environmental and social sustainability in particular [8–10]. Ultimately, a mutually agreeable CLSCN may be constructed by meeting at the level of common satisfaction of opposing objectives in a MO mixed-integer linear programming (MOMILP) model. This approach, which performs SC management (SCM) recycling, remanufacturing, and destruction, may help decision-makers manage GCLSC in firms more expertly [11]. The goal of reducing CO₂ emissions becomes crucial in the context of the GSC. Environmental impact assessment in times of disaster was performed using the rapid impact assessment matrix method by Abbasi et al. [12]. Pratondo et al. [13] advocated a conceptual framework that incorporates economic, environmental, and social elements to improve SC performance during and after crises, also emphasizing the need for supply networks to move toward sustainability.

The economy is changing quickly, and businesses today need to focus on SCs and integrated logistics to meet the demands of a highly competitive market. Businesses that employ a well-organized SCN can manage the increasing environmental disturbances and obtain a competitive advantage [14]. According to Ahmed et al. [15], the use of optimization techniques promotes the creation of CLSCs that are environmentally friendly and reduce costs and emissions through the use of reliable mathematical models. Ab Halim et al.’s [16] research on the problem of green inventory management highlights the importance of transportation efficiency in the SC by showing how logistics can be managed to reduce carbon emissions. Given that transportation contributes significantly to overall SC emissions, this is crucial. Abbasi et al. [17] created a network for vaccine SC considering the environment. Salehi Sarbijan and Behnamian [18] proposed hybrid particle swarm optimization and adaptive learning techniques to study the challenges of vehicle routing in a collaborative context. Tiwari et al. [19] investigated how pressure on SCs, environmental policy stringency, energy transition, and circular economy affect CO₂ emissions in emerging economies. Zhu et al. [20] identified critical transmission sectors, pathways, and carbon communities for CO₂ reduction in global SCs. Galdos-Urbizu et al. [21] assessed the moderating effects and impact of GSCM on corporate environmental performance. Yang et al. [22] investigated how SC decisions under low-carbon regulations are affected by asymmetric carbon information. Guan et al. [23] proposed a coordinated optimization model for a complex GSC distribution network system. Using a case study, Abdolazimi et al. [24] created a sustainable, forward-looking SC configuration for the construction sector in an unpredictable environment.

The introduction of green ammonia in shipping was examined by Fullonton et al. [25], considering both the advantages and disadvantages of SC fuel. In an unpredictable environment, Chen et al. [26] dealt with decision-making in logistics services for e-commerce SSCs considering fairness. Zhou et al. [27] suggested the model for business and management empirical data from China on the idiosyncratic risk of carbon suppliers. The impact of GSCM techniques on firms’ environmental performance was proposed by Wiredu et al. [28]. Saeedi et al. [29] investigated the vulnerabilities in building SC under an unfavorable microenvironment.

2.2. Uncertainty in SCs

Taking into consideration the uncertainty condition, a MO fuzzy technique may be used to build a CLSCN. This approach may be used to condense MO models to a single objective using fuzzy mathematical programming. A dynamic pricing method may be used to determine the purchase price of used products, which might encourage customers to return their used items. This tactic may be applied to minimize supplier returns of raw materials, maximize profit, and shorten customer delivery delays [30]. A fuzzy method may be used to optimize the decentralized production–distribution planning problem in a multiperiod SCN under unpredictable conditions. By considering the uncertainty in the SCN, this approach may be used to optimize the production–distribution planning problem [31]. Within SC, rationalizing the movement of materials within the network is an important and practical problem. It could bring great benefits to the company if it receives enough attention. The complicated and dynamic structure of SC has a great impact on the overall performance of the chain and leads to a significant degree of uncertainty in planning decisions [32]. To achieve flexibility, fuzzy sets are used to characterize a flexible number of constraints and objectives. To deal with this type of uncertainty, flexible mathematical programming models are used [33]. Cognitive uncertainty is the result of incomplete coverage of the model parameters; this type of uncertainty is handled by the possibility planning technique [34]. When analyzing digitally enabled SC innovation and carbon emissions, the role of structural weaknesses of first-tier suppliers was considered by Wang and Gong [35]. The best practice for a fuzzy two-echelon SC was investigated by Song et al. [36]. Green logistics networks (GLNs) were created as part of carbon pricing policies in the post-COVID-19 era [37, 38]. Baykasoglu and Göçken [39] have made a classification of fuzzy mathematical programming problems, identified 15 different types of fuzzy mathematical programming models, and provided many methods to solve each category. Dehshiri and Amiri [40] utilized a resilient scenario-based possibilistic–stochastic programming approach to construct a CLSC under hybrid uncertainty, considering the circular economy. Dolatabad et al. [41] used a fuzzy multicriteria method to evaluate agile approaches in GSCM. Sharifi et al. [42] used a MO approach to design a wheat SC that is resilient, responsive, and sustainable in the face of mixed uncertainty. This provides an integrated Type-II fuzzy approach that considers tactical and operational constraints in determining the best course of action for production, distribution, procurement, and location selection [43].

2.3. JIT in SCs

This suggests that a JIT methodology can be successfully modified to increase responsiveness in unpredictable situations. El-Gibaly [44] proposed a pricing system with reverse flow and throughput accounting for flexible JIT on SCs. Finance SC (FSC) and JIT considered a hierarchical model development, which was examined by Zaman et al. [45]. A key tactic in contemporary SCM is JIT inventory management, which aims to match production schedules with demand to cut waste and increase efficiency. JIT was first introduced in the automobile business, namely, with Toyota, and has since spread to other industries, such as manufacturing and healthcare. JIT’s main goal is to reduce inventory levels while guaranteeing that goods and resources are accessible exactly when needed, which improves operational effectiveness and lowers expenses [46]. It has been demonstrated that JIT implementation has a major effect on business performance. Research shows that companies that use JIT techniques may increase cash flow, reduce inventory costs, and become more sensitive to changes in the market [47]. Kannan and Tan’s research, for example, shows how SCM, JIT, and total quality management are related, showing that dedication to quality and knowledge of SC dynamics may result in better corporate performance [48]. In addition, by lowering excess inventory and enhancing material flow, the combination of JIT and other inventory management strategies, such as vendor-managed inventory (VMI), can further enhance SC performance [49]. However, outside variables such as the COVID-19 epidemic, which revealed weaknesses in supply networks that depend on JIT principles, might undermine the efficacy of JIT. The necessity for adaptability and resilience in inventory management systems was highlighted by disruptions in the supply of necessities, especially in the healthcare industry [50]. Due to this, businesses are realizing more and more how crucial it is to balance JIT with backup plans to reduce the risks of SC interruptions [51]. Furthermore, by improving visibility and control over inventory levels, the use of cutting-edge technology such as real-time data analytics and enterprise resource planning (ERP) systems has increased the efficacy of JIT [52]. The advantages of JIT methods are strengthened by these technologies, which let firms make decisions quickly and react quickly to changes in demand [53].

2.4. Pre- and Post-COVID-19 Disaster in SCs

Santibanez Gonzalez et al. [54] created a trustworthy aggregated production planning for the time of the COVID-19 disaster. Li et al. [55] investigated the operation of SSCs under COVID-19 considering factors and response tactics. Satpathy et al. [56] used agent-based simulation to investigate how adaptive collaboration between heterogeneous manufacturers in the face of fluctuating demand affects the viability of SSCs in the post-COVID-19 era. During a medical emergency disaster, Abbasi, Sıcakyüz, Erdebilli [57], the home healthcare SC was utilized. Ivanov [58] has survived the COVID-19 pandemic, avoiding the risks of SC disruption and postshock. Zhu et al. [59] analyzed the impact of adaptive cooperation among heterogeneous manufacturers on SC viability under fluctuating demand post-COVID-19. Abbasi et al. [60] considered a case study in the US and proposed hybrid data mining and data-driven algorithms for a green logistics transportation network in the post-COVID-19 era. According to Golan et al. [61], the timing and sequencing of operations have a significant impact on performance outcomes, highlighting the need for enhanced resilience analysis to ensure SCNs continue to function amidst global disruptions during COVID-19. Abbasi et al. [62] examined a network of financial and logistical suppliers during the COVID-19 pandemic. Abbasi et al. [63] offered the network for the provision of necessary goods during the simultaneous COVID-19 pandemic and seismic circumstances. The need for agility and adaptability in SC strategies is also supported by Wang and Wang [64], who argue that SC agility is critical to corporate sustainability in the post-COVID-19 era as it enables companies to respond quickly to environmental changes. Global SCs have been severely impacted by the COVID-19 epidemic, highlighting the need for resilience analysis to maintain business continuity. During COVID-19 and lockdowns, Abbasi et al. [65] proposed a triobjective, sustainable, closed, and multiechelon SC. Corporate social responsibility (CSR) also serves as a moderator. External CSR measures strengthen the relationship between customer-oriented GSCM and COVID-19 anxiety. On the other hand, internal CSR has a significant moderating effect [66]. During the COVID-19 pandemic, the sustainable SC (SSC) was assessed [67]. This is consistent with the research findings of Özdemir et al. [68], who found that during the pandemic, both proactive and reactive resilience–building initiatives increased SC velocity. The location routing problem for a cold SC was devised by Abbasi et al. [69] in the COVID-19 tragedy. This is particularly important in the post-COVID-19 environment, where companies are under increasing pressure to adopt sustainable practices that meet regulatory and consumer requirements Abbasi et al. [70]. Given the uncertainties of the COVID-19 period, Moadab et al. [71] have created a SCN that is responsive, robust, and sustainable. In addition, the interval-valued intuitionistic fuzzy analytic hierarchy process can be used to assess the resilience of GSCs in the pre- and post-COVID-19 era [72]. Based on a thorough review of the literature and recommendations for future research, Ahmed et al. [73] offered SSCs in emerging countries both during and after the COVID-19 pandemic. During the COVID-19 pandemic, Abbasi et al. [74] created a sustainable network for end-of-life (EOL) asset recovery. During the pandemic, Zahari and Zakuan [75] presented a viable SCM model that prioritizes sustainability and demonstrates that efficient SC tactics can reduce environmental impacts while maintaining company profitability.

3. Problem Statement and Assumptions

3.1. Proposed Problem

This research attempts to give a suitable MILP model for the design of the multiproduct, multilevel, and multiperiod SCN in the three components of procurement, manufacturing, and distribution since the SC mostly consists of a network structure pre- and post-COVID-19 situation. The aforementioned model is used to calculate the production, distribution, and purchase quantities for facilities at various SC levels at both the tactical and strategic levels. The problem under consideration is depicted in Figure 2. The aforementioned network is built on a material production plant’s material transfer network, which is represented by fuzzy sets of uncertainty. During the planning horizon, the purchasing firm makes a supplier choice. Fees at this level include extra research and development expenses incurred by hiring a specific supplier as well as quality audit fees incurred by the buyer to assess a supplier. Order-level characteristics contain expenses and requirements that must be satisfied each time a certain provider fills an order, such as acceptance, invoicing, shipping, and ordering fees. Costs and circumstances related to the units of items for which buying choices are made are included at the unit level. These conditions and costs include price, internal error, external error, and inventory holding costs. This section first presents the problem’s sets, indices, parameters, and variables, followed by the problem’s mathematical model.

[figure(s) omitted; refer to PDF]

3.2. Assumptions of the Problem

During modeling the problem, the following presumptions are taken into account:

• The distance between various facilities is such that there is no waiting period between placing the order and getting the items

• The client receives the goods they ordered in each period

• The problem is considered in the situation before and after the COVID-19 pandemic

• Every objective function and constraint utilized in this problem is linear

• It is assumed that the producer is part of the supplier of goods for the customers

• The problem’s unknown parameters are represented as triangle fuzzy numbers

• A traction mechanism moves various commodities ahead along the network

• The facilities are situated in fixed, planned places

3.3. Formulation Process and Model Components

3.3.1. Indexes

• s: The index of suppliers, s ∈ {1.2, 3, …, S}

• j: The index of distribution centers, j ∈ {1.2, 3, …, J}

• k: The index of retailers, k ∈ {1.2, 3, …, K}

• l: The index of the shipping method, l ∈ {1.2, 3, …, L}

• r: The index of raw materials, r ∈ {1.2, 3, …, R}

• p: The index of products, p ∈ {1.2, 3, …, P}

• t: The index of periods, t ∈ {1.2, 3, …, T}

3.3.2. Parameters and Variables

3.3.2.1. Parameters

• ${\widetilde{lc}}_{st}$: The total cost for inventory from the supplier and producer s in period t

• ${\widetilde{oc}}_{st}$: The total cost for order level from supplier s in period t

• $\tilde{C}{x}_{rst}$: The cost of each unit of raw material r that is assigned from the supplier s in period t

• ${\widetilde{ac}}_{rst}$: The extra costs of raw material r that is purchased from the supplier s in period t

• ${\widetilde{Mr}}_{rt}$: The maintenance cost of each unit of raw material r in period t

• ${\widetilde{Mf}}_{pt}$: The maintenance cost of each unit of product p in period t

• ${\widetilde{Pc}}_{pt}$: The production cost of each unit of product p in period t

• ${\tilde{C}}_{pjt}^l$: The cost for shipping one unit of product p by method l from the production center to the distribution center j in period t considering CO₂ emissions

• $\tilde{C}{\tilde{C}}_{pkt}^l$: The cost for shipping one unit of product p by method l from the production center to retailer k in period t considering CO₂ emissions

• $\tilde{C}\tilde{C}{\tilde{C}}_{pjkt}^l$: The cost of shipping one unit of product p by method l from distribution center j to retailer k in period t considering CO₂ emissions

• ${\tilde{H}}_{pjt}$: The cost of keeping one unit of product p in the distribution center j in period t

• $\tilde{H}{\tilde{H}}_{pkt}$: The cost of keeping one unit of product p in the retailer k in period t

• ${\phi }_{rpt}$: The amount of raw material r needed to produce one unit of product p in period t

• $\tilde{d}e{m}_{pkt}$: The demand for product p by retailer k in period t

• ${\widetilde{Cap}}_{jt}$: The capacity of distribution j in period t

• ${\widetilde{Capp}}_{kt}$: The capacity of retailer k in period t

• ${\tilde{Q}}_{pjt}$: Storage capacity of product p in distribution center j in period t

• ${\widetilde{S\max }}_{pkt}$: The maximum storage capacity of retailer k for product p in period t

• $\tilde{\mathrm{\partial }}{\max }_{pkt}$: The maximum amount allowed for the shortage of product p in retailer k in period t

• ${\widetilde{Qr}}_{rt}$: The storage capacity of raw materials r in the producer center in period t

• ${\widetilde{Qf}}_{pt}$: The storage capacity of product p in the producer center in period t

• ${\widetilde{Qu}}_{rst}$: The average failure rate of raw material r in supplier s in period t

• ${\tilde{Q}}_{rst}$: The acceptable rate of failure for raw material r in supplier s in period t

• ${\widetilde{Su}}_{st}$: The average service level in the supplier s in period t

• $\widetilde{Sl{o}_t}$: The acceptable service level in the production center in period t

• ${\widetilde{BQX}}_{rst}$: The maximum allowed value for $Q{U}_{rst}$

• ${\psi }_{pkt}$: The surplus amount of product p not delivered to retailer k in period t

• $P_{pt}$: The production p in period t

• $Shor{\mathrm{t}}_{\text{pkt}}$: The shortage quantity of product p delivered to retailer k in period t

3.3.2.2. Variables

• ${\theta }_s$: If supplier s is opened in all periods of time, equal 1, otherwise 0

• ${\lambda }_{st}$: If supplier s is opened during the period t, equal 1, otherwise 0

• $V{S}_{pkt}$: If surplus or shortage of product p delivered to retailer k in period t, equal 1, otherwise 0

• $Q{X}_{rst}$: The quantity units of raw material r from supplier s in period t

• $\varphi r_{rt}$: The quantity of stock units of raw material r in period t

• $\varphi f_{pt}$: The quantity of inventory units of product p in period t

• $X_{pjtl}$: The quantity of product p that is shipped by method l in the period t from the production to the distribution center j

• $Y_{pktl}$: The quantity of product p that is shipped by method l in the period t from the production to the retailer k

• ${\Omega }_{pjktl}$: The quantity of product p that is shipped from distribution center j to retailer k in period t by method l

3.4. Mathematical Model of the Problem

The mathematical modeling of the problem is presented as follows:$$\begin{array}{c}\text{(1)}& \mathrm{Min}{Z}_1={\displaystyle \sum }_{s=1}^S{\displaystyle \sum }_{t=1}^T{\widetilde{lc}}_{st}{\theta }_{st}+{\displaystyle \sum }_{s=1}^S{\displaystyle \sum }_{t=1}^T{\widetilde{oc}}_{st}{\lambda }_{st}+{\displaystyle \sum }_{r=1}^R{\displaystyle \sum }_{s=1}^S{\displaystyle \sum }_{t=1}^T\tilde{C}{x}_{rst}+{\widetilde{ac}}_{rst}Q{X}_{rst}+{\displaystyle \sum }_{r=1}^R{\displaystyle \sum }_{t=1}^T{\widetilde{Mr}}_r\varphi r_{rt}+{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{t=1}^T{\widetilde{Pc}}_{pt}M{P}_{pt}+{\widetilde{Mf}}_p\varphi f_{pt}+{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{\tilde{C}}_{pj}^l{X}_{pjtl}\\ +{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L\tilde{C}{\tilde{C}}_{pkt}^l{Y}_{pktl}+{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L\tilde{C}\tilde{C}{\tilde{C}}_{pjkt}^l.{\mathrm{\Omega }}_{pjktl}\\ +{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{\tilde{H}}_{pjt}{X}_{pjtl}-{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{\tilde{H}}_{pjt}{\mathrm{\Omega }}_{pjktl}\\ +{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{t=1}^T\tilde{H}{\tilde{H}}_{pkt}+{\psi }_{pkt},\\ \text{(2)}& \mathrm{Min}{Z}_2={\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{t=1}^{T}Shor{t}_{pkt}+{\psi }_{pkt},\end{array}$$$\text{which\hspace{0.17em}is\hspace{0.17em}subject\hspace{0.17em}to}$$$\begin{array}{}\text{(3)}& {\displaystyle \sum }_{r=1}^R\varphi r_{rt-1}+{\displaystyle \sum }_{s=1}^S{\displaystyle \sum }_{r=1}^{R}Q{X}_{rst}-\varphi r_{rt}={\displaystyle \sum }_{r=1}^R{\phi }_{rpt}.M{P}_{pt}\forall p,\forall t,\text{(4)}& \varphi f_{pt-1}+P_{pt}+\varphi f_{pt}={\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{l=1}^L{X}_{pjtl}+{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{l=1}^L{Y}_{pktl}\forall p,\forall t,\text{(5)}& {\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{l=1}^L{X}_{pjtl}+{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{l=1}^L{Y}_{pktl}\le \varphi f_{pt}\forall p,\forall t,\text{(6)}& {\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{X}_{pjtl}-{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{l=1}^L{\displaystyle \sum }_{t=1}^T{\mathrm{\Omega }}_{pjktl}=0\forall p,\forall j,\text{(7)}& {\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{Y}_{pktl}+{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{l=1}^L{\displaystyle \sum }_{t=1}^T{\mathrm{\Omega }}_{pjktl}={\displaystyle \sum }_{t=1}^T\tilde{d}e{m}_{pkt}\forall p,\forall k,\text{(8)}& {\displaystyle \sum }_{l=1}^L{X}_{pjtl}-{\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{l=1}^L{\mathrm{\Omega }}_{pjktl}\le {\tilde{Q}}_{pjt}\forall p,\forall j,\forall t,\text{(9)}& {\displaystyle \sum }_{k=1}^K{\displaystyle \sum }_{l=1}^L{\mathrm{\Omega }}_{pjktl}\le {\displaystyle \sum }_{l=1}^L{X}_{pjtl}\forall p,\forall j,\forall t,\text{(10)}& {\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{l=1}^L{X}_{pjtl}\le {\widetilde{Cap}}_{jt}\forall j,\forall \mathrm{t},\text{(11)}& {\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{l=1}^L{Y}_{pktl}+{\displaystyle \sum }_{p=1}^P{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{l=1}^L{\mathrm{\Omega }}_{pjktl}\le {\widetilde{Capp}}_{kt}\forall k,\forall t,\text{(12)}& {\displaystyle \sum }_{t=1}^T{\displaystyle \sum }_{l=1}^L{Y}_{pktl}+{\displaystyle \sum }_{j=1}^J{\displaystyle \sum }_{l=1}^L{\displaystyle \sum }_{t=1}^T{\mathrm{\Omega }}_{tjktl}-{\displaystyle \sum }_{t=1}^T\tilde{d}e{m}_{pkt}=\forall p,\forall k,\text{(13)}& {\psi }_{pkt}\le {\widetilde{S\max }}_{pkt}.V{S}_{pkt}\forall p,\forall k,\forall t,\text{(14)}& Shor{t}_{pkt}\le \tilde{\mathrm{\partial }}\underset{pkt}{\max }.1-V{S}_{pkt}\forall p,\forall k,\forall t,\text{(15)}& \varphi r_{rt}\le {\widetilde{Qr}}_{rt}\forall r,\forall t,\text{(16)}& \varphi f_{pt}\le {\widetilde{Qf}}_{pt}\forall p,\forall t,\text{(17)}& {\displaystyle \sum }_{s=1}^S{\widetilde{Qu}}_{rst}.Q{X}_{rst}\le {\widetilde{Qt}}_r.{\displaystyle \sum }_{s=1}^{S}Q{X}_{rst}\forall r,\forall t,\text{(18)}& {\displaystyle \sum }_{s=1}^S{\displaystyle \sum }_{r=1}^R{\widetilde{Su}}_{st}.Q{X}_{rst}\ge \widetilde{Sl{o}_t}.{\displaystyle \sum }_{r=1}^R{\displaystyle \sum }_{s=1}^{S}Q{X}_{rst}\forall t,\text{(19)}& Q{X}_{rst}\le {\widetilde{BQX}}_{rst}.{\lambda }_{st}\forall r,\forall s,\forall t,\text{(20)}& {\theta }_s\le {\displaystyle \sum }_{t=1}^T{\lambda }_{st}\forall s,\text{(21)}& {\lambda }_{st}\le {\theta }_s\forall t,\forall s,\text{(22)}& {\theta }_s,{\lambda }_{st},V{S}_{pkt}\in 0,1\forall s,\forall t,\forall p,\forall k,\text{(23)}& Q{X}_{rst},\varphi r_{rt},\varphi f_{pt},X_{pjtl},{\mathrm{\Omega }}_{pjktl},Y_{pktl}\ge 0\forall r,\forall s,\forall t,\forall p,\forall j,\forall l,\forall k.\end{array}$$

The first objective function ($Z_1$) shows the costs at the supplier level, the second term denotes the costs at the order level, and the third and fourth terms reflect the costs at the unit level in the pre- and post-COVID-19 era. The producer’s costs are represented in the fifth term, which also includes the costs of producing and storing the products. The costs associated with the transfer of goods between different facilities are shown in terms six, seven, and eight. The last two terms show the warehousing costs at the distribution facility or store. Of course, it should be emphasized that the retail department has no inventory in its natural state; instead, the inventory of this part consists of the surplus items sent to these sections. The purpose of the second objective function ($Z_2$) is on-time delivery, which reduces the sum of shortages and surpluses made available to retailers in all periods.

The equilibrium between the goods produced and the raw materials on the producer’s side is shown in Constraints (3) and (4). Constraint (5) ensures that the total quantity of items ordered in a given period does not exceed the capacity of that period. Constraint (6) shows that the inventory of the distribution centers is zero after the planning horizon by controlling the balance between the goods entering and leaving the centers over the entire planning period. After the time horizon, Constraint (7) guarantees that all demand is satisfied. The difference between the items entering and leaving each distribution center must not be greater than the capacity of the center, as shown in Constraint (8). Constraint (9) ensures that the quantity of items taken from each center does not exceed the center’s stock. The ability of the distribution facilities and the stores to receive items at any time is represented in Constraints (10) and (11), respectively. The amount of surplus or deficit of items delivered to the retailers at any time is represented in Constraint (12). Constraints (13) and (14) state that only a deficit or a surplus of delivered items may occur in a given period, that is, neither value may be positive at the same time. These restrictions also specify the upper limit that is allowed for both a surplus and a deficit of products in a given time frame. The producer’s storage capacities for raw materials and products are specified in Constraints (15) and (16) for each point in time. The quality criterion for the raw materials purchased from the suppliers is specified in Constraint (17). The restriction on the timely delivery of raw materials from the suppliers to the manufacturer is the subject of Constraint (18). The maximum quantity of raw materials that can be purchased is subject to Constraint (19). The integrity Constraints (20) and (21) are components of the structural constraints of the problem. Constraints (22) and (23) outline the type and scope of the variables used for the problem.

4. Approach Solution Method

A mathematical optimization method called MILP blends integer restrictions with aspects of linear programming. When dealing with complicated decision-making issues where certain variables must take on integer values while others can stay continuous, this method is quite helpful. In conclusion, by utilizing linear connections between variables and taking integer restrictions into account, MILP is a potent optimization tool that empowers decision-makers to address challenging issues in a variety of fields. The majority of the model’s parameters, such as the objective function’s parameters, right-hand side values, and technical coefficients, are fuzzy, as can be observed in the primary problem model, while the problem’s constraints, objective functions, and variables are deterministic. The model provided in this article is solved in two steps. The original fuzzy model is converted into an equivalent auxiliary deterministic model in the first stage. The recommended final consensus solution is determined in the second stage by the application of a fuzzy technique. The aforementioned approach maintains the linearity characteristic and adds no new objective functions or inequality restrictions, making it incredibly computationally efficient. The imprecise character of the fuzzy parameters of the issue is modeled by the trigonometric fuzzy distribution because of its ease in data collection and processing efficiency.

Suppose that $\tilde{c}=c^p,c^m,c^0$ is a triangular fuzzy number, then its membership function ${\mu }_{\tilde{c}}x$ is as follows:$$\begin{array}{}\text{(24)}& {\mu }_{\tilde{c}}x=\begin{array}{c}\begin{array}{cc}{f}_{c}x=\frac{x-c^p}{c^m-c^p},& \text{if\hspace{0.17em}}{c}^p\le x\le c^m,\end{array}\\ \begin{array}{cc}1,& \text{if\hspace{0.17em}}x=c^m,\end{array}\\ \begin{array}{cc}{q}_{c}x=\frac{c^o-x}{c^0-c^m},& \text{if\hspace{0.17em}}{c}^m\le x\le c^0,\end{array}\\ \begin{array}{cc}0,& \text{if\hspace{0.17em}}x<c^p\text{\hspace{0.17em}or\hspace{0.17em}}\mathrm{x}\succ c^0.\end{array}\end{array}.\end{array}$$

According to [76], the expected interval (EI) and expected value (EV) of the fuzzy number $\tilde{c}$ are defined as follows:$$\begin{array}{}\text{(25)}& EI\tilde{c}=E_1^C,E_2^C={\int }_0^1{f}_c^{-1}xdx,{\int }_0^1{q}_c^{-1}xdx,\text{(26)}& EV\tilde{c}=\frac{E_1^C,E_2^C}{2}.\end{array}$$

Considering that the triangular fuzzy distribution is used to display the parameters in (27) and (28), we have$$\begin{array}{}\text{(27)}& EI\tilde{c}=\frac{1}{2}{c}^p+c^m,\frac{1}{2}{c}^m+c^o,\text{(28)}& EV\tilde{c}=\frac{c^p,2c^m+c^o}{4}.\end{array}$$

Now, we consider the following fuzzy mathematical programming model in which all parameters are defined in the fuzzy form as$$\begin{array}{c}\text{(29)}& \mathrm{Min}\mathrm{Z}=\tilde{c}x,\text{Subject\hspace{0.17em}to}:\\ {\tilde{a}}_{i}x\ge {\tilde{b}}_i,i=1,\dots ,l,\\ {\tilde{a}}_{i}x={\tilde{b}}_i,i=l+1,\dots ,m,\\ \mathrm{x}\ge 0.\end{array}$$

Due to the problem’s imprecise and nondeterministic parameters, we must compare fuzzy numbers, which naturally raises two important considerations: optimality and feasibility. As a result, the following two challenges must be addressed [77]:

1. When fuzzy numbers are present in the constraints, how should the decision vector x be defined?

2. How can the objective function’s optimality with fuzzy coefficients be defined?

The degree that is greater for each pair of fuzzy numbers is defined in (30) by the [78] ranking method as follows:$$\begin{array}{}\text{(30)}& {\mu }_M\tilde{a},\tilde{b}=\begin{array}{c}\begin{array}{cc}0,& \text{if\hspace{0.17em}}{E}_2^a-E_1^a\prec 0,\end{array}\\ \begin{array}{cc}\frac{E_2^a-E_1^b}{E_2^a-E_1^b-E_1^a-E_2^b},& \text{if\hspace{0.17em}}0\in E_1^a-E_2^b;E_2^a-E_1^b,\end{array}\\ \begin{array}{cc}1,& \text{if\hspace{0.17em}}{E}_1^a-E_2^b\succ 0.\end{array}\end{array}.\end{array}$$

When ${\mu }_M\tilde{a},\tilde{b}\ge \alpha$, then it is said that $\tilde{a}$ is greater than or equal to $\tilde{b}$ at least in degree $\alpha$, and it is represented as $\tilde{a}{\ge }_{\alpha }\tilde{b}$. According to Jimenez et al.’s method [77], the decision vector $x\mathfrak{\in }\mathfrak{R}$ is possible in degree $\alpha$ if ${\min }_{i=1,\dots ,m}{\mu }_M\widetilde{a_i}x,{\tilde{b}}_i=\alpha$.

Therefore, for (31), we have$$\begin{array}{}\text{(31)}& \frac{E_2^{a_{i}x}-E_1^{b_i}}{E_2^{a_{i}x}-E_1^{a_{i}x}+E_2^{b_i}-E_1^{b_i}}\ge \alpha ,i=1,\dots ,l.\end{array}$$

Now, by simplifying the time relation, we have$$\begin{array}{}\text{(32)}& 1-\alpha E_2^{a_i}+\alpha E_1^{a_i}x\ge \alpha E_2^{b_i}+1-\alpha E_1^{b_i},\text{(33)}& \tilde{a}{\ge }_{\alpha /2}\tilde{b},\tilde{a}{\le }_{\alpha /2}\widetilde{b,}\text{(34)}& \frac{\alpha }{2}\le {\mu }_M\tilde{a},\tilde{b}\le 1-\frac{\alpha }{2}.\end{array}$$

The feasible solution of $x^0$ is the acceptable optimal solution for (35) if the following condition is true:$$\begin{array}{}\text{(35)}& {\mu }_M\tilde{c}x,\tilde{c}{x}^0\ge \frac{1}{2}.\end{array}$$

Therefore, $x^0$ provides a better solution at least in a degree 1/2 than other feasible vectors (for the purpose of minimization), and we have$$\begin{array}{}\text{(36)}& \tilde{c}x{\ge }_{1/2}\tilde{c}{x}^0.\end{array}$$

By using the previous equation, we have$$\begin{array}{}\text{(37)}& \frac{E_2^{cx}-E_1^{c{x}^0}}{E_2^{cx}-E_1^{cx}+E_2^{c{x}^0}-E_1^{c{x}^0}}\ge \frac{1}{2},\text{(38)}& \frac{E_2^{cx}+E_1^{cx}}{2}\ge \frac{E_2^{c{x}^0}+E_1^{c{x}^0}}{2}.\end{array}$$

By considering in model, its $-\alpha$ parametric model is obtained as follows:$$\begin{array}{c}\text{(39)}& \mathrm{Min}\mathrm{Z}=\text{EV}\tilde{c}x,\text{Subject\hspace{0.17em}to}:\\ 1-\alpha .E_2^{a_i}+\alpha .E_1^{a_i}x\ge \alpha .E_2^{b_i}+1-\alpha .E_1^{b_i},i=1,\dots ,m,\\ 1-\frac{\alpha }{2}.E_2^{a_i}+\frac{\alpha }{2}.E_1^{a_i}x\ge \frac{\alpha }{2}{E}_2^{b_i}+1-\frac{\alpha }{2}.E_1^{b_i},i=l+1,\dots ,m,\\ \frac{\alpha }{2}.E_2^{a_i}+1-\frac{\alpha }{2}.E_1^{a_i}x\le 1-\frac{\alpha }{2}.E_2^{b_i}+\frac{\alpha }{2}.E_1^{b_i},i=l+1,\dots ,m,\\ x\ge 0.\end{array}$$

This paper creates an auxiliary deterministic model that is comparable to the primary problem model as described above using the information from the previous section. As can be observed, every equal constraint in the main model has been translated into two unequal constraints in the equivalent auxiliary model, resulting in a larger number of constraints in the equivalent accessory issue than in the primary issue. The authors in [79] were the first to design the fuzzy solution strategy for MILP. The relevant research has offered several approaches to dealing with probabilistic models [35, 80, 81]. This article solves the given deterministic model using the technique of [82, 83]. The following are the stages involved in the procedure mentioned:

• Step 1: Create the problem model and choose appropriate trapezoidal or triangular distributions for the problem parameters.

• Step 2: Using the predicted value based on the imprecise parameters, convert the model’s imprecise objective function to a deterministic objective function.

• Step 3: Calculate the value of the minimum acceptable scaling of the decision vector, transform the problem’s fuzzy constraints into deterministic constraints, and then create the problem’s corresponding auxiliary deterministic model.

• Step 4: For every possible level and objective function, find the positive ideal solution (α-PIS) and the negative ideal solution (α-NIS).

• Step 5: Use the following method to get each objective function’s linear membership function as:$$\begin{array}{}\text{(40)}& {\mu }_{1}x=\begin{array}{c}\begin{array}{cc}1,& \text{if}{Z}_1\le Z_1^{\alpha -Pis},\end{array}\\ \begin{array}{cc}\frac{Z_1^{\alpha -Nis}-Z_1}{Z_1^{\alpha -Nis}-Z_1^{\alpha -Pis}},& \text{if\hspace{0.17em}}{Z}_1^{\alpha -Pis}\le Z_1\le Z_1^{\alpha -Nis},\end{array}\\ \begin{array}{cc}0,& \text{if\hspace{0.17em}}{Z}_1\succ Z_1^{\alpha -Nis},\end{array}\end{array}\text{(41)}& {\mu }_{2}x=\begin{array}{c}\begin{array}{cc}1,& \text{if\hspace{0.17em}}{Z}_2\le Z_2^{\alpha -Pis},\end{array}\\ \begin{array}{cc}\frac{Z_2^{\alpha -Nis}-Z_2}{Z_2^{\alpha -Nis}-Z_2^{\alpha -Pis}},& \text{if\hspace{0.17em}}{Z}_2^{\alpha -Pis}\le Z_2\le Z_2^{\alpha -Nis},\end{array}\\ \begin{array}{cc}0,& \text{if\hspace{0.17em}}{Z}_2\succ Z_2^{\alpha -Nis}.\end{array}\end{array},\end{array}$$

• Step 6: Using the cumulative function of [83], convert the problem’s corresponding two-objective deterministic model into a MILP model. The aforementioned cumulative function in (42) is as follows:$$\begin{array}{c}\text{(42)}& \max \lambda \mathrm{X}=\gamma {\lambda }_0+1-\gamma .{\displaystyle \sum }_h{\theta }_h{\mu }_{h}x,\text{Subject\hspace{0.17em}to}:\\ {\lambda }_0\le {\mu }_{h}x,h=12,\\ x\in Fx,{\lambda }_0\text{\hspace{0.17em}and\hspace{0.17em}}\lambda \in 0,1,\end{array}$$

  where $\mu hx$ refers to the degree of satisfaction with the objective function h. F(x) specifies the feasible region including the variables of the equivalent deterministic model, and ${\theta }_h$ and $\gamma$ specify, respectively, the importance of the objective function h and the correction coefficient. It should be noted that ${\lambda }_0={\min }_h{\mu }_{h}x$ shows the minimum degree of satisfaction with the objective functions.

• Step 7: Determine the values of $\gamma$ and ${\theta }_h$ and solve the corresponding single-objective complex integer linear programming model. If the decision maker is satisfied with the current solution, stop, otherwise create another consensus solution by changing the values of $\gamma$ and $\alpha$ (and if necessary, ${\theta }_h$) and go to Step 3.

5. Results and Discussion

In this study, in which a JIT strategy was applied in the GSC considering under uncertainty in the pre- and post-COVID-19 situation, several important conclusions about the operational effectiveness and environmental impact of the GSC under different scenarios influenced by the COVID-19 pandemic are presented. A viable way to achieve sustainability while overcoming the challenges of the COVID-19 pandemic is to implement JIT concepts within GSC. Companies can create SCs that meet environmental regulations and consumer demands by focusing on reducing emissions and improving responsiveness through efficient resource management and creative modeling approaches. Over time, the JIT approach to SCM has grown in popularity, particularly due to its ability to reduce waste and increase productivity. To strengthen sustainability and overcome emerging uncertainties, a reassessment of JIT processes is necessary as the COVID-19 pandemic has exposed vulnerabilities in SCs. This study examines the impact of cost and time from a pre- and post-COVID-19 pandemic perspective and explores the intricacies of applying JIT in GSC. Dealing with cost and time within GSC requires the introduction of a JIT strategy, particularly given the unpredictability of global issues such as the COVID-19 pandemic. Although operational efficiency has been at the heart of the JIT approach in the past, the current environment requires a shift to more robust and sustainable methods. Companies that successfully combine JIT approaches with flexible tactics and environmental concerns not only improve their sustainability but are also better equipped to deal with unforeseen circumstances in the future. Ultimately, maintaining long-term environmental sustainability and operational success will depend heavily on companies’ continued commitment to improving JIT within the GSC.

This section presents a numerical example that demonstrates the applicability, validity, and efficiency of both the model and the solution strategy. The problem is then solved using the previously indicated solution technique. For every inaccurate parameter, three sensitive points, the most probable value, the pessimistic value, and the optimistic value, are evaluated to produce triangle fuzzy numbers. To do this, each parameter’s most likely value is first randomly generated. Next, two random integers ($r_1$ and $r_2$) between 0.1 and 0.5 are created using a uniform distribution to maintain the problem’s generality. The fuzzy number’s optimistic ($c^o$) and pessimistic ($c^p$) values are then computed as follows: $$\begin{array}{}\text{(43)}& c^o=1+r_1{c}^m,\text{(44)}& c^p=1+r_2{c}^m.\end{array}$$

Before addressing the problem with fuzzy parameters, the problem is initially seen as deterministic and nonfuzzy, and its solutions are investigated. In the following, an efficient solution for the deterministic model was used for the one-step method, so that the value of the first objective function and the value of the second objective function were found [34, 84].

The problem’s fuzzy model solutions are looked at in the sections that follow. The models were solved using LINGO 19. These results demonstrate how the objective function values in the fuzzy state differ dramatically from those in the deterministic state, highlighting the significance of taking the uncertainty state into account. In addition, for some values, it is unmanageable. A personal computer with an Intel CORE I7 @ 2.40 GHZ processor and 8 GB of internal RAM was used to code and solve the designed problems using the LINGO Version 19 software and to obtain the answers to the design problems.

Table 1 shows the values of the suggested model parameters. Table 2 illustrates the description of the problems. Table 3 displays the optimal $Z_1$ solutions in the pre- and post-COVID-19 era. Figure 3 shows the results of solving the first objective function for different alpha-cuts in the pre- and post-COVID-19 era. Table 4 demonstrates the optimality of $Z_2$ solutions in the pre- and post-COVID-19 era. Figure 4 shows the results of solving the second objective function for different alpha-cuts in the pre -and post-COVID-19 era.

Table 1

The values of the suggested model parameters.

Parameters	Value
${\widetilde{lc}}_{st}$	U (1000, 2600)
${\widetilde{oc}}_{st}$	U (20, 500)
$\tilde{C}{x}_{rst}$	U (50, 700)
${\widetilde{ac}}_{rst}$	U (0.1, 0.8)
${\widetilde{Mr}}_{rt}$	U (20, 100)
${\widetilde{Mf}}_{pt}$	U (100, 1000)
${\widetilde{Pc}}_{pt}$	U (10, 200)
${\tilde{C}}_{pjt}^l$	U (50, 500)
$P_{pt}$	U (50, 500)
${\tilde{Q}}_{rst}$	U (0.01, 0.09)
$\tilde{C}{\tilde{C}}_{pkt}^l$	U (100, 500)
$\tilde{C}\tilde{C}{\tilde{C}}_{pjkt}^l$	U (50, 100)
${\tilde{H}}_{pjt}$	U (10, 100)
$\tilde{H}{\tilde{H}}_{pkt}$	N (10, 100)
$\tilde{d}e{m}_{pkt}$	U (200, 1000)
${\widetilde{Cap}}_{jt}$	U (300, 500)
${\widetilde{Capp}}_{kt}$	U (500, 1000)
${\tilde{Q}}_{pjt}$	U (500, 1000)
${\psi }_{pkt}$	U (50, 500)
${\phi }_{rpt}$	U (1, 1000)
${\widetilde{S\max }}_{pkt}$	U (100, 500)
$\tilde{\mathrm{\partial }}{\max }_{pkt}$	U (100, 500)
${\widetilde{Qr}}_{rt}$	U (100, 500)
${\widetilde{Qf}}_{pt}$	U (100, 1000)
${\widetilde{Qu}}_{rst}$	U (0.01, 0.09)
${\tilde{Q}}_{pjt}$	U (0.01, 0.09)
${\widetilde{Su}}_{st}$	U (0.01, 0.09)
$\widetilde{Sl{o}_t}$	U (0, 1)
${\widetilde{BQX}}_{rst}$	U (100, 1000)
$Shor{t}_{pkt}$	U (50, 500)

Table 2

The description of the problems.

Facilities	Number
Suppliers	2
Distribution centers	5
Retailers	3
Shipping method	4
Kind of raw materials	1
Kind of products	3
Periods	2

Table 3

The optimal $Z_1$ solutions in the pre- and post-COVID-19 era.

$\alpha$	Pre-COVID-19	Post-COVID-19
0.1	11,110,450	12,110,450
0.2	10,628,320	11,628,320
0.3	9,713,400	10,713,410
0.4	9,104,215	9,104,215
0.5	8,207,510	8,204,110
0.6	8,554,200	7,554,200
0.7	7,001,219	6,004,210
0.8	6,504,290	5,554,290
0.9	3,532,143	4,532,178

[figure(s) omitted; refer to PDF]

Table 4

The optimal of $Z_2$ solutions in the pre- and post-COVID-19 era.

$\alpha$	Pre-COVID-19	Post-COVID-19
0.1	4,520,135	3,520,132
0.2	5,908,135	4,988,130
0.3	6,908,130	6,998,130
0.4	7,955,100	7,955,100
0.5	9,910,125	8,900,120
0.6	9,907,123	9,900,120
0.7	11,918,005	10,911,155
0.8	12,040,184	11,040,184
0.9	14,045,133	13,044,199

[figure(s) omitted; refer to PDF]

A drop in alpha considerably affects the cost objective functions of the alpha-cuts for the fuzzy set. Lowering the alpha value leads to a more accurate representation of the data and reduces the uncertainty associated with the fuzzy set in the prea- and post-COVID-19 era. One of the important results of this analysis is that during the COVID-19 period, the costs were higher due to the increase in health costs and also the time of movement in the SC.

This reduction in uncertainty might have the following effects on the delivery time and cost objective functions.

Lowering the alpha number improves the accuracy of the data by enhancing the fuzzy set’s membership, nonmembership, and indeterminacy values. This increased precision might lead to a more accurate cost computation inside the target function. A lower alpha can aid in the optimization process by highlighting the boundaries and differences within the fuzzy set. This clarity can improve the effectiveness of the cost goal function optimization, leading to potential cost savings or improvements in delivery times, expenses, and environmental impact. Lowering alpha might have an impact on the weighting components of the goal function. Lower alpha values may come from the alterations made to the fuzzy set, changing the weighting of different components in the cost function and perhaps altering the overall strategy for cost optimization. Variations in the alpha value may have an impact on how sensitive the cost and delivery time effect objective functions are to changes in the input data. A lower alpha may cause the three-goal functions to become more sensitive to changes, highlighting the importance of accurate data representation and how it affects judgments about delivery time and cost. In summary, decreasing the alpha value in the fuzzy set’s alpha-cuts can lead to improved optimization, enhanced accuracy, weighting factor modifications, and sensitivity changes in the two objective functions. These outcomes can affect decisions about costs and optimization techniques.

6. Conclusion and Outlook

6.1. Finding

This study proposes a novel interpretation of JIT production using a fuzzy approach to SCN design. The recommended method takes into account the imprecision and uncertainty of SCN parameters, which are sometimes difficult to measure accurately in the pre- and post-COVID-19 era. A fuzzy optimization approach is used to solve the fuzzy linear programming problem posed by the proposed model. The results of the study show that the proposed method can successfully create SCNs that are more sensitive to fluctuations in supply and demand and are more efficient. In addition, by reducing the possibility of stock-outs and overstocks, the proposed strategy can help save a considerable amount of money. For this reason, the proposed strategy may prove to be a useful tool for SC managers looking to improve their SCND in the pre- and post-COVID-19 era. The simulation of material and product movement in SCN under unpredictable conditions is presented in this paper. To evaluate the previous research, the SCND requirements were categorized into five categories: problem definition and assumptions, constraints, outcomes, objectives, and solution technique. Of course, there are several subcriteria for each of these criteria. The publications and research papers on SCND are then coded using this model. This is a coding system for these criteria, which is shown as follows.

In addition, different levels of uncertainty are explained and a potential planning model has been selected to characterize the problem based on its features. During the modeling phase, all three components of supply, manufacturing, and distribution are included in the model. In this paper, a complete model is presented that includes early and late deliveries, cost, quality, on-time delivery, multistage, multiperiod, and multiproduct chain structure. The model was solved in two steps: first, the potential model of the problem was transformed into an analog deterministic model, and then an interactive method was used to obtain the final answers. A numerical example is used to demonstrate the applicability and validity of the model and the methodology used in the solution. This study was investigated and compared using a deterministic methodology as well as a proposed solution technique for both single and MO modes and for different solution parameters and final solutions. A sensitivity analysis was also performed for some of the parameters of the problem. The obtained answers show the importance of including uncertainty aspects in the modeling process, since it can be observed that for certain problem parameters, the deterministic and fuzzy answers are very close to each other, while for other parameters, there is a significant difference between the answers.

6.2. Limitation

The limitations such as the research method and approach of this study are as follows:

• The COVID-19 pandemic has significantly impacted SCM, revealing vulnerabilities and necessitating strategy changes across industries. Here is a detailed examination of the limitations faced in SCM pre- and post-COVID-19.

• The COVID-19 pandemic has fundamentally altered the landscape of SCM. While prepandemic strategies focused on efficiency through globalization and JIT principles, the crisis has highlighted the need for resilience, flexibility, and robust risk management. Moving forward, companies are likely to adopt more diversified sourcing strategies and leverage technology to create SCs that can adapt to unforeseen disruptions.

• Research may be predicated on assumptions that are subject to change throughout time and are not always true.

• Using stochastic programming models might add complexity and might not account for all the uncertainties that exist in real-world situations, such as abrupt shifts in customer behavior or interruptions in the SC brought on by outside forces.

• The availability and dependability of data on CO₂ emissions and SC performance indicators before and after the COVID-19 pandemic will determine how accurate the model’s predictions are. Insufficient data may result in less reliable results.

• The emphasis on a JIT method may restrict the findings’ applicability to alternative SC tactics that could be more robust in the face of uncertainty, particularly during emergencies such as pandemics.

• The study’s focus on CO₂ emissions could oversimplify the environmental evaluation by ignoring other important environmental effects linked to CLSCs, such as waste production or water use.

• The study looks at pre- and post-COVID-19 scenarios, which might make the analysis more difficult because the circumstances and reactions were different in each of these time periods. This dual context may make it difficult to distinguish the implications of COVID-19 from other current SCM developments.

• These drawbacks draw attention to areas where more study might deepen knowledge and advance techniques for examining GSC, especially in unstable contexts impacted by international crises such as COVID-19.

• The suggested method is more accurate than heuristic and metaheuristic approaches, which are needed to address the problem in big dimensions.

6.3. Recommendation for Future

A wider variety of risks than those examined in this work should be taken into account in future research, including shifts in consumer demand, SC interruptions brought on by geopolitical issues, and the effects of climate change on logistics. More reliable frameworks for making decisions in the face of uncertainty may result from the use of sophisticated stochastic modeling approaches. The efficiency of GSCs may be greatly increased by integrating technologies such a blockchain, artificial intelligence (AI), and the internet of things (IoT). Assessing the efficacy of policies such as carbon pricing, tariffs, and trading systems can assist firms in determining how to strike a balance between environmental compliance and operational efficiency. It is recommended to consider uncertainties in model variables, other than the parameters considered in this paper. Integrating flexible scheduling problem solving and feasibility planning is another recommendation we have for future collaborations. Considering multiple operational choices in the problem can also be useful for the future. Considering temporary storage facilities in the model is also a useful suggestion for researchers interested in studying these issues. The final proposal is to solve the model in larger dimensions, which is proposed to solve the model using metaheuristic techniques if the problem’s dimensions and temporal complexity grow. Long-term research looking at how JIT methods affect GSC over time would be very helpful in determining how resilient and sustainable they are. Best practices and tactics that adjust to shifting market conditions may be found with the use of such research. It is essential to comprehend how consumer behavior relates to sustainable practices. Future studies should look at how customer preferences affect how successful GSCs are as well as how businesses can better adapt their operations to suit these demands.

6.4. Theoretical and Practical Implications

By integrating JIT concepts with sustainability and green logistics, this study makes a significant contribution to the theoretical framework of SCM. The theoretical and practical implications are explained as follows.

The study examines how JIT can be modified to improve the sustainability of CLSC. The idea that a properly deployed JIT system can reduce waste and CO₂ emissions through improved inventory management and transportation logistics makes this integration essential as it addresses both operational efficiency and environmental responsibility. The study underlines the need for adaptable SC strategies, taking into account the uncertainties caused by the COVID-19 pandemic. This aspect underlines the importance of SCs being resilient, which means that traditional models need to be adapted to take unforeseen disruptions into account. The theoretical framework includes models that assess how different carbon policies affect SC operations, especially during pandemics. This approach provides a quantitative way to assess the trade-offs between environmental sustainability and economic performance and serves as a basis for future research on the impact of regulations on SCM.

The results of this study have several applications for companies that operate in green CLSCs, especially given the current global issues. Companies can use JIT approaches that not only save lead time but also incorporate environmentally friendly techniques such as recycling programs and reverse logistics. This dual focus can reduce environmental impact while increasing overall operational efficiency. The report highlights how companies need to adapt to changing carbon laws, particularly those caused by pandemics. Companies need to create flexible plans to maximize SC efficiency and comply with carbon regulations. The study offers decision-makers a methodical way to assess their SCs in the face of uncertainty. Using mathematical models such as MILP, managers can decide on production locations, transportation modes, and inventory levels that support both sustainability and economic goals. To promote a culture of sustainability in companies, the report calls on them to introduce metrics that assess both economic performance and environmental performance. This comprehensive approach can motivate efforts to continuously improve SC processes. In summary, this study contributes to the theoretical debates on JIT and GSC while providing practitioners with practical advice on how to successfully deal with the complicated issues of today’s SCs.

Ethics Statement

The authors have nothing to report.

Consent

The authors have nothing to report.

Author Contributions

All authors contributed equally at all stages.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

References

[1] D. Dubois, H. Fargier, P. Fortemps, "Fuzzy Scheduling: Modelling Flexible Constraints vs. Coping With Incomplete Knowledge," European Journal of Operational Research, vol. 147 no. 2, pp. 231-252, DOI: 10.1016/s0377-2217(02)00558-1, 2003.

[2] J. Amirian, H. Amoozad Khalili, A. Mehrabian, "Designing an Optimization Model for Green Closed-Loop Supply Chain Network of Heavy Tire by Considering Economic Pricing Under Uncertainty," Environmental Science and Pollution Research, vol. 29 no. 35, pp. 53107-53120, DOI: 10.1007/s11356-022-19578-0, 2022.

[3] R. C. Wang, T. F. Liang, "Applying Possibilistic Linear Programming to Aggregate Production Planning," International Journal of Production Economics, vol. 98 no. 3, pp. 328-341, DOI: 10.1016/j.ijpe.2004.09.011, 2005.

[4] S. Abbasi, B. Erdebilli, "Green Closed-Loop Supply Chain Networks’ Response to Various Carbon Policies During COVID-19," Sustainability, vol. 15 no. 4,DOI: 10.3390/su15043677, 2023.

[5] S. Abbasi, M. Daneshmand-Mehr, A. Ghane Kanafi, "Green Closed-Loop Supply Chain Network Design During the Coronavirus (COVID-19) Pandemic: A Case Study in the Iranian Automotive Industry," Environmental Modeling & Assessment, vol. 28 no. 1, pp. 69-103, DOI: 10.1007/s10666-022-09863-0, 2023.

[6] Z. Asadi, M. V. Khatir, M. Rahimi, "Robust Design of a Green-Responsive Closed-Loop Supply Chain Network for the Ventilator Device," Environmental Science and Pollution Research, vol. 29 no. 35, pp. 53598-53618, DOI: 10.1007/s11356-022-19105-1, 2022.

[7] M. Taherifar, N. Hasani, M. Zokaee, A. Aghsami, F. Jolai, "A Scenario-Based Sustainable Dual-Channel Closed-Loop Supply Chain Design with Pickup and Delivery Considering Social Conditions in a Natural Disaster Under Uncertainty: A Real-Life Case Study," Environment, Development and Sustainability, vol. 26 no. 8, pp. 19443-19490, DOI: 10.1007/s10668-023-03421-8, 2023.

[8] T. Singh, S. Tripathi, A. Dwivedi, Á. Acevedo-Duque, "Post-COVID Green Supply Chain Management of Used Products: A Study towards Awareness for Vaccination," Environmental Science and Pollution Research, vol. 30 no. 15, pp. 42526-42540, DOI: 10.1007/s11356-022-21321-8, 2022.

[9] Q. A. Nisar, S. Haider, I. Ameer, M. S. Hussain, S. S. Gill, A. Usama, "Sustainable Supply Chain Management Performance in Post COVID-19 Era in an Emerging Economy: A Big Data Perspective," International Journal of Emerging Markets, vol. 18 no. 12, pp. 5900-5920, DOI: 10.1108/ijoem-12-2021-1807, 2022.

[10] F. Jalil, J. Yang, S. U. Rehman, M. M. Khan, "Post-COVID-19’s Impact on Green Supply Chain Management and Sustainable E-Commerce Performance: The Moderating Role of Big Data Analytics," Environmental Science and Pollution Research, vol. 30 no. 54, pp. 115683-115698, DOI: 10.1007/s11356-023-30581-x, 2023.

[11] S. Akin Bas, B. Ahlatcioglu Ozkok, "A Fuzzy Approach to Multi-Objective Mixed-Integer Linear Programming Model for Multi-Echelon Closed-Loop Supply Chain With Multi-Product Multi-Time Period," Operations Research and Decisions, vol. 30 no. 1,DOI: 10.37190/ord200102, 2020.

[12] S. Abbasi, U. M. Modibbo, H. Jafari Kolashlou, I. Ali, N. Kavousi, "Environmental Impact Assessment With Rapid Impact Assessment Matrix Method: During Disaster Conditions," Frontiers in Applied Mathematics and Statistics, vol. 10,DOI: 10.3389/fams.2024.1344158, 2024.

[13] K. Pratondo, T. Kusmantini, S. Sabihaini, "Gaining Supply Chain Resilience and Performance Sustainability Through Supply Chain Agility in Furniture Smes in Yogyakarta," International Journal of Social Science and Business, vol. 5 no. 3,DOI: 10.23887/ijssb.v5i3.37945, 2021.

[14] W. Dullaert, O. Bräysy, M. Goetschalckx, B. Raa, A. Center, "Supply Chain (Re)Design: Support for Managerial and Policy Decisions," European Journal of Transport and Infrastructure Research, vol. 7 no. 2, pp. 73-92, DOI: 10.18757/ejtir.2007.7.2.3378, 2007.

[15] M. Ahmed, S. Iqbal, T. Priyanka, M. Arani, M. Momenitabar, M. Billal, "An Environmentally Sustainable Closed-Loop Supply Chain Network Design Under Uncertainty: Application of Optimization," pp. 343-358, DOI: 10.1007/978-3-030-66501-2_28, 2021.

[16] H. Z. Ab Halim, N. N. Mohd Azliana, N. Baharom, N. Fauzi, N. S. Ahmad Bakhtiar, N. Khairudin, "Green Inventory Routing Problem Using Hybrid Genetic Algorithm," Journal of Computing Research and Innovation, vol. 6 no. 4, pp. 10-19, DOI: 10.24191/jcrinn.v6i4.254, 2021.

[17] S. Abbasi, S. Zahmatkesh, A. Bokhari, M. Hajiaghaei-Keshteli, "Designing a Vaccine Supply Chain Network Considering Environmental Aspects," Journal of Cleaner Production, vol. 417,DOI: 10.1016/j.jclepro.2023.137935, 2023.

[18] M. Salehi Sarbijan, J. Behnamian, "Feeder Vehicle Routing Problem in a Collaborative Environment Using Hybrid Particle Swarm Optimization and Adaptive Learning Strategy," Environment, Development and Sustainability,DOI: 10.1007/s10668-023-04123-x, 2023.

[19] S. Tiwari, K. Si Mohammed, G. Mentel, S. Majewski, I. Shahzadi, "Role of Circular Economy, Energy Transition, Environmental Policy Stringency, and Supply Chain Pressure on CO 2 Emissions in Emerging Economies," Geoscience Frontiers, vol. 15 no. 3,DOI: 10.1016/j.gsf.2023.101682, 2024.

[20] Q. Zhu, C. Xu, Y. Pan, J. Wu, "Identifying Critical Transmission Sectors, Paths, and Carbon Communities for CO 2 Mitigation in Global Supply Chains," Renewable and Sustainable Energy Reviews, vol. 191,DOI: 10.1016/j.rser.2023.114183, 2024.

[21] L. Galdos-Urbizu, E. Zubeltzu-Jaka, A. Erauskin-Tolosa, I. A. Etxeberria, "The Impact of Green Supply Chain Management on Corporate Environmental Performance and the Moderating Roles: A Meta-Analysis," Business Strategy & Development, vol. 7 no. 1,DOI: 10.1002/bsd2.351, 2024.

[22] L. Yang, J. Ji, C. Zheng, "Impact of Asymmetric Carbon Information on Supply Chain Decisions Under Low-Carbon Policies," Discrete Dynamics in Nature and Society, vol. 2016 no. 1,DOI: 10.1155/2016/1369589, 2016.

[23] Y. Guan, M. Aamir, Z. A. Dayo, "A Coordinated Optimization Model of the Complex System of the Green Supply Chain Distribution Network," Discrete Dynamics in Nature and Society, vol. 2021 no. 1, pp. 4077151-4077212, DOI: 10.1155/2021/4077151, 2021.

[24] O. Abdolazimi, S. Entezari, D. Shishebori, M. A. Ardakani, A. Kashef, "Developing a Sustainable Forward Supply Chain Configuration for Construction Industry Under Uncertainty Condition: A Case Study," Clean Technologies and Environmental Policy, vol. 26 no. 4, pp. 1197-1225, DOI: 10.1007/s10098-023-02672-3, 2024.

[25] A. Fullonton, A. R. Lea-Langton, F. Madugu, A. Larkin, "Green Ammonia Adoption in Shipping: Opportunities and Challenges Across the Fuel Supply Chain," Marine Policy, vol. 171,DOI: 10.1016/j.marpol.2024.106444, 2025.

[26] L. Chen, Y. Wang, L. Zeng, J. Jiang, X. Zhu, J. Peng, "Logistics Service Decision for E-Commerce Supply Chain With Fairness Concern Under Uncertain Environment," International Journal of General Systems, vol. 54 no. 1,DOI: 10.1080/03081079.2024.2359037, 2025.

[27] Z. Zhou, Y. Dai, S. Han, T. Zhang, J. Liu, X. Chen, "Supplier Carbon Management and Firm Idiosyncratic Risk: Empirical Evidence From China," Journal of Supply Chain Management, vol. 61 no. 1, pp. 34-61, DOI: 10.1111/jscm.12334, 2025.

[28] J. Wiredu, Q. Yang, A. K. Sampene, B. A. Gyamfi, S. A. Asongu, "The Effect of Green Supply Chain Management Practices on Corporate Environmental Performance: Does Supply Chain Competitive Advantage Matter?," Business Strategy and the Environment, vol. 33 no. 3, pp. 2578-2599, DOI: 10.1002/bse.3606, 2024.

[29] S. Saeedi, K. Koohestani, M. Poshdar, S. Talebi, "Investigation of the Construction Supply Chain Vulnerabilities Under an Unfavorable Macro-Environmental Context," Proceedings of the 30th Annual Conference of the International Group for Lean Construction (IGLC30), .

[30] S. A. Darestani, F. Pourasadollah, "A Multi-Objective Fuzzy Approach to Closed-Loop Supply Chain Network Design With Regard to Dynamic Pricing," Journal of Optimization in Industrial Engineering, vol. 12 no. 1, pp. 173-194, 2019.

[31] R. Nourifar, I. Mahdavi, N. Mahdavi-Amiri, M. M. Paydar, "Optimizing Decentralized Production–Distribution Planning Problem in a Multi-Period Supply Chain Network Under Uncertainty," Journal of Industrial Engineering International, vol. 14 no. 2, pp. 367-382, DOI: 10.1007/s40092-017-0229-3, 2018.

[32] W. Klibi, A. Martel, A. Guitouni, "The Design of Robust Value-Creating Supply Chain Networks: A Critical Review," European Journal of Operational Research, vol. 203 no. 2, pp. 283-293, DOI: 10.1016/j.ejor.2009.06.011, 2010.

[33] R. E. Bellman, L. A. Zadeh, "Decision Making in a Fuzzy Environment," Management Science, vol. 17 no. 4, pp. B-141-B-164, DOI: 10.1287/mnsc.17.4.b141, 1970.

[34] M. S. Pishvaee, S. A. Torabi, "A Possibilistic Programming Approach for Closed-Loop Supply Chain Network Design Under Uncertainty," Fuzzy Sets and Systems, vol. 161 no. 20, pp. 2668-2683, DOI: 10.1016/j.fss.2010.04.010, 2010.

[35] X. Wang, T. Gong, "Digital-Enabled Supply Chain Innovation and CO 2 Emissions: The Contingent Role of First-Tier Supplier’s Structural Holes," Technological Forecasting and Social Change, vol. 201,DOI: 10.1016/j.techfore.2024.123252, 2024.

[36] Q. Song, K. Shi, S. Lin, G. Xu, "Optimal Decisions for a Fuzzy Two-Echelon Supply Chain," Discrete Dynamics in Nature and Society, vol. 2014 no. 1,DOI: 10.1155/2014/705839, 2014.

[37] S. Abbasi, S. Mazaheri, H. R. Talaie, P. Ghasemi, "Designing Green Logistics Networks Under Carbon Tax Policy: Post-COVID Condition," Results in Engineering, vol. 23,DOI: 10.1016/j.rineng.2024.102830, 2024.

[38] S. Abbasi, S. S. Mousavi, E. Farbod, M. Yousefi Sorkhi, M. Parvin, "Hybrid Data Mining and Data-Driven Algorithms for a Green Logistics Transportation Network in the Post-COVID Era: A Case Study in the USA," Systems and Soft Computing, vol. 6,DOI: 10.1016/j.sasc.2024.200156, 2024.

[39] A. Baykasoglu, T. Göçken, "A Review and Classification of Fuzzy Mathematical Programs," Journal of Intelligent and Fuzzy Systems, vol. 3, 2008.

[40] S. J. Dehshiri, M. Amiri, "Considering the Circular Economy for Designing Closed-Loop Supply Chain Under Hybrid Uncertainty: A Robust Scenario-Based Possibilistic-Stochastic Programming," Expert Systems With Applications, vol. 238,DOI: 10.1016/j.eswa.2023.121745, 2024.

[41] M. J. Dolatabad, M. Azhdarifard, N. K. Acwin Dwijendra, A. Q. Ali Sharhan Al-Sudani, "Evaluating Agile Practices in Green Supply Chain Management Using a Fuzzy Multicriteria Approach," Discrete Dynamics in Nature and Society, vol. 2022 no. 1,DOI: 10.1155/2022/4290848, 2022.

[42] E. Sharifi, S. H. Amin, L. Fang, "Designing a Sustainable, Resilient, and Responsive Wheat Supply Chain Under Mixed Uncertainty: A Multi-Objective Approach," Journal of Cleaner Production, vol. 434,DOI: 10.1016/j.jclepro.2023.140076, 2024.

[43] J. S. Sarah, K. Khalili-Damghani, A. R. Abtahi, A. Rashidi-Komijan, "Type-II Fuzzy Multi-Product, Multi-Level, Multi-Period Location-Allocation, Production-Distribution Problem in Supply Chains: Modelling and Optimisation Approach," Fuzzy Information and Engineering, vol. 10 no. 2, 2018.

[44] M. M. El-Gibaly, "A Proposed Costing System for Agile Just-In-Time Supply Chains With Back-Flush and Throughput Accounting," Asian Journal of Economics, Business and Accounting, vol. 24 no. 5, pp. 126-145, DOI: 10.9734/ajeba/2024/v24i51298, 2024.

[45] S. I. Zaman, M. R. Ali, S. A. Khan, "Just-In-time and Supply Chain Finance: A Hierarchal Model Development," International Journal of Industrial and Systems Engineering, vol. 47 no. 4, pp. 518-556, DOI: 10.1504/ijise.2024.140332, 2024.

[46] W. Wang, S. Wang, X. Ma, J. Gong, "Recent Advances in Catalytic Hydrogenation of Carbon Dioxide," Chemical Society Reviews, vol. 40 no. 7, pp. 3703-3727, DOI: 10.1039/C1CS15008A, 2011.

[47] N. Khourshed, A. Abdelaziz, "Testing the Just-In-Time Inventory Model Effect on Organizational Effectiveness for Egyptian Manufacturing Industries," Arab Journal of Management,DOI: 10.21608/aja.2023.191418.1393, 2023.

[48] V. R. Kannan, K. C. Tan, "Just in Time, Total Quality Management, and Supply Chain Management: Understanding Their Linkages and Impact on Business Performance," Omega, vol. 33 no. 2, pp. 153-162, DOI: 10.1016/j.omega.2004.03.012, 2005.

[49] A. E. Mohamed, Inventory Management, 2024.

[50] B. Balkhi, A. Al-Shahrani, A. Khan, "Just-In-time Approach in Healthcare Inventory Management: Does it Really Work?," Saudi Pharmaceutical Journal, vol. 30 no. 12, pp. 1830-1835, DOI: 10.1016/j.jsps.2022.10.013, 2022.

[51] Y. D. Elijah, D. P. K. Ngugi PhD, "Inventory Management Strategies and Performance of Commercial Government Entities in Kenya," Strategic Journal of Business & Change Management, vol. 8 no. 3, pp. 87-106, DOI: 10.61426/sjbcm.v8i3.2029, 2021.

[52] A. M. Obadire, B. L. Boitshoko, N. T. Moyo, "Analysis of the Impact of Inventory Management Practices on the Effectiveness of Retail Stores in South Africa," Global Journal of Management and Business Research,DOI: 10.34257/gjmbrcvol22is5pg1, 2022.

[53] J. Achuora, A. Robert, "Lean Inventory Management Systems and Performance of Supermarkets in Nairobi County, kenya," European Journal of Business and Management Research, vol. 5 no. 2,DOI: 10.24018/ejbmr.2020.5.2.280, 2020.

[54] E. D. Santibanez Gonzalez, S. Abbasi, M. Azhdarifard, "Designing a Reliable Aggregate Production Planning Problem During the Disaster Period," Sustainable Operations and Computers, vol. 4, pp. 158-171, DOI: 10.1016/j.susoc.2023.08.004, 2023.

[55] Z. Li, Y. Sheng, Q. Meng, X. Hu, "Sustainable Supply Chain Operation Under COVID-19: Influences and Response Strategies," International Journal of Logistics Research and Applications, vol. 28 no. 1, pp. 24-50, DOI: 10.1080/13675567.2022.2110220, 2025.

[56] A. S. Satpathy, S. K. Sahoo, A. Mohanty, P. P. Mohanty, "Strategies for Enhancements of MSME Resilience and Sustainability in the Post-COVID-19 Era," Social Sciences & Humanities Open, vol. 11,DOI: 10.1016/j.ssaho.2024.101223, 2025.

[57] S. Abbasi, Ç. Sıcakyüz, B. Erdebilli, "Designing the Home Healthcare Supply Chain During a Health Crisis," Journal of Engineering Research, vol. 11 no. 4, pp. 447-452, DOI: 10.1016/j.jer.2023.100098, 2023.

[58] D. Ivanov, "Exiting the COVID-19 Pandemic: After-Shock Risks and Avoidance of Disruption Tails in Supply Chains," Annals of Operations Research, vol. 335 no. 3, pp. 1627-1644, DOI: 10.1007/s10479-021-04047-7, 2024.

[59] A. Zhu, Y. Han, H. Liu, "Effects of Adaptive Cooperation Among Heterogeneous Manufacturers on Supply Chain Viability Under Fluctuating Demand in Post-COVID-19 Era: An Agent-Based Simulation," International Journal of Production Research, vol. 62 no. 4, pp. 1162-1188, DOI: 10.1080/00207543.2023.2178370, 2024.

[60] S. Abbasi, S. S. Mousavi, E. Farbod, M. Yousefi Sorkhi, M. Parvin, "Hybrid Data Mining and Data-Driven Algorithms for a Green Logistics Transportation Network in the Post-COVID Era: A Case Study in the USA," Systems and Soft Computing, vol. 6,DOI: 10.1016/j.sasc.2024.200156, 2024.

[61] M. Golan, L. Jernegan, I. Linkov, "Trends and Applications of Resilience Analytics in Supply Chain Modeling: Systematic Literature Review in the Context of the COVID-19 Pandemic," Environment Systems and Decisions, vol. 40 no. 2, pp. 222-243, DOI: 10.1007/s10669-020-09777-w, 2020.

[62] S. Abbasi, I. Vlachos, A. Samadzadeh, S. Etemadifar, M. Afshar, M. Amra, "Modelling a Logistics and Financial Supply Chain Network During the COVID-19 Era," Logistics, vol. 8 no. 1,DOI: 10.3390/logistics8010032, 2024.

[63] S. Abbasi, I. Vlachos, S. Rekabi, M. Talooni, "Designing the Distribution Network of Essential Items in the Critical Conditions of Earthquakes and COVID-19 Simultaneously," Sustainability, vol. 15 no. 22,DOI: 10.3390/su152215900, 2023.

[64] M. Wang, B. Wang, "Supply Chain Agility as the Antecedent to Firm Sustainability in the Post COVID-19," International Journal of Logistics Management, vol. 35 no. 1, pp. 281-303, DOI: 10.1108/ijlm-02-2022-0059, 2023.

[65] S. Abbasi, M. Daneshmand-Mehr, A. G. Kanafi, "Designing a Tri-Objective, Sustainable, Closed-Loop, and Multi-Echelon Supply Chain During the COVID-19 and Lockdowns," Foundations of Computing and Decision Sciences, vol. 48 no. 3, pp. 269-312, DOI: 10.2478/fcds-2023-0011, 2023.

[66] M. M. N. H. K. Kholaif, X. Ming, G. K. Getele, "Post COVID-19’s Opportunities for Customer-Centric Green Supply Chain Management and Customers’ Resilience; the Moderate Effect of Corporate Social Responsibility," International Journal of Emerging Markets, vol. 18 no. 6, pp. 1397-1424, DOI: 10.1108/ijoem-11-2021-1730, 2022.

[67] S. Abbasi, H. A. Khalili, M. Daneshmand-Mehr, M. Hajiaghaei-Keshteli, "Performance Measurement of the Sustainable Supply Chain During the COVID-19 Pandemic: A Real-Life Case Study," Foundations of Computing and Decision Sciences, vol. 47 no. 4, pp. 327-358, DOI: 10.2478/fcds-2022-0018, 2022.

[68] D. Özdemir, M. Sharma, A. Dhir, T. Daim, "Supply Chain Resilience During the COVID-19 Pandemic," Technology in Society, vol. 68,DOI: 10.1016/j.techsoc.2021.101847, 2022.

[69] S. Abbasi, M. Moosivand, I. Vlachos, M. Talooni, "Designing the Location–Routing Problem for a Cold Supply Chain Considering the COVID-19 Disaster," Sustainability, vol. 15 no. 21,DOI: 10.3390/su152115490, 2023.

[70] S. Abbasi, S. Abbaspour, M. Eskandari Nasab Siahkoohi, M. Yousefi Sorkhi, P. Ghasemi, "Supply Chain Network Design Concerning Economy and Environmental Sustainability: Crisis Perspective," Results in Engineering, vol. 22,DOI: 10.1016/j.rineng.2024.102291, 2024.

[71] A. Moadab, G. Kordi, M. M. Paydar, A. Divsalar, M. Hajiaghaei-Keshteli, "Designing a Sustainable-Resilient-Responsive Supply Chain Network Considering Uncertainty in the COVID-19 Era," Expert Systems With Applications, vol. 227,DOI: 10.1016/j.eswa.2023.120334, 2023.

[72] E. Ayyildiz, "Interval Valued Intuitionistic Fuzzy Analytic Hierarchy Process-Based Green Supply Chain Resilience Evaluation Methodology in Post COVID-19 Era," Environmental Science and Pollution Research, vol. 30 no. 15, pp. 42476-42494, DOI: 10.1007/s11356-021-16972-y, 2021.

[73] H. N. Ahmed, S. Ahmed, M. A. Khan, S. M. Ali, "Sustainable Supply Chain in Emerging Economies During and Post COVID-19 Pandemic: A Systematic Literature Review and Future Research Directions," International Journal of Emerging Markets, vol. 19 no. 9, pp. 2472-2498, DOI: 10.1108/ijoem-01-2022-0092, 2024.

[74] S. Abbasi, M. Daneshmand-Mehr, A. Ghane Kanafi, "Designing Sustainable Recovery Network of End-Of-Life Product During the COVID-19 Pandemic: A Real and Applied Case Study," Discrete Dynamics in Nature and Society, vol. 2022 no. 1,DOI: 10.1155/2022/6967088, 2022.

[75] M. K. Zahari, N. Zakuan, "Viable Supply Chain Management Model Towards Company Sustainability During COVID-19 Pandemic: A Measurement Model Analysis," International Journal of Academic Research in Business and Social Sciences, vol. 12 no. 12,DOI: 10.6007/ijarbss/v12-i12/15772, 2022.

[76] S. Heilpern, "The Expected Value of a Fuzzy Number," Fuzzy Sets and Systems, vol. 47 no. 1, pp. 81-86, DOI: 10.1016/0165-0114(92)90062-9, 1992.

[77] M. Jimenez, M. Arenas, A. Bilbao, M. V. Rodrı´guez, "Linear Programming With Fuzzy Parameters: An Interactive Method Resolution," European Journal of Operational Research, vol. 177 no. 3, pp. 1599-1609, DOI: 10.1016/j.ejor.2005.10.002, 2007.

[78] M. Jimenes, "Ranking Fuzzy Numbers Through the Comparison of its Expected Intervals," International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 4, pp. 379-883, 1996.

[79] H. J. Zimmermann, "Fuzzy Programming and Linear Programming With Several Objective Functions," Fuzzy Sets and Systems, vol. 1 no. 1, pp. 45-55, DOI: 10.1016/0165-0114(78)90031-3, 1978.

[80] M. Inuiguchi, J. Ramík, "Possibilistic Linear Programming: A Brief Review of Fuzzy Mathematical Programming and a Comparison With Stochastic Programming in Portfolio Selection Problem," Fuzzy Sets and Systems, vol. 111 no. 1, 2000.

[81] M. A. Parra, A. B. Terol, B. P. Gladish, M. Rodriguez Uria, "Solving a Multiobjective Possibilistic Problem Through Compromise Programming," European Journal of Operational Research, vol. 164 no. 3, pp. 748-957, 2005.

[82] S. A. Torabi, E. Hassini, "Multi-Site Production Planning Integrating Procurement and Distribution Plans in Multi-Echelon Supply Chains: An Interactive Fuzzy Goal Programming Approach," International Journal of Production Research, vol. 47 no. 19, pp. 5475-5499, DOI: 10.1080/00207540801905460, 2009.

[83] S. A. Torabi, E. Hassini, "An Interactive Possibilistic Programming Approach for Multiple Objective Supply Chain Master Planning," Fuzzy Sets and Systems, vol. 159 no. 2, pp. 193-214, DOI: 10.1016/j.fss.2007.08.010, 2008.

[84] A. Fallah-Tafti, R. Sahraeian, R. Tavakkoli Moghaddam, M. Moeinipour, "An Interactive Possibilistic Programming Approach for a Multi-Objective Closed-Loop Supply Chain Network Under Uncertainty," International Journal of Systems Science, vol. 45 no. 3, pp. 283-299, DOI: 10.1080/00207721.2012.720296, 2014.