A differential game model for closed-loop supply chain participants under carbon emission permits

The adoption of closed-loop supply chain (CLSC) network is one of the effective approaches to reduce carbon emissions. In current globalization, inherent uncertainty exists in business environment so there is a need to be design robust supply chains. This paper proposes a deterministic mixed integer linear programming (MILP) model integrating economics and carbon emission considerations including selection of production technologies and transportation mode as a part of CLSC network strategic and tactical decisions. The robust counterpart of the proposed deterministic model is developed based on three alternative uncertainty sets to represent the imprecise input parameters. The robust counterpart is used to study the supply chain performance by considering the two most globally practiced carbon regulatory policies; carbon tax policy and carbon trading policy. Numerical results show that total cost of the proposed robust optimization model under each uncertainty set is greater than the total cost of deterministic model. The additional cost is due to solution space of each uncertainty set to accommodate any uncertainty level. As uncertainty level increases the overall supply chain cost worsen. Moreover, the results suggest that carbon tax rate has direct relation with overall supply chain cost whereas having carbon market trading flexibility in carbon trading policy, this policy is more efficient policy as compared to carbon tax policy. Furthermore, the proposed robust optimization model is useful for mangers to achieve not only a robust supply chain network design which can withstand any possible uncertainty level but also significant reduction in carbon emissions by choosing suitable carbon-efficient policy.

PurposeThis study aims to address the inherent uncertainties within closed-loop supply chain (CLSC) networks through the application of a multi-objective approach, specifically focusing on the optimization of integrated production and transportation processes. The primary purpose is to enhance decision-making in supply chain management by formulating a robust multi-objective model.Design/methodology/approachIn dealing with uncertainty, this study uses Pythagorean fuzzy numbers (PFNs) to effectively represent and quantify uncertainties associated with various parameters within the CLSC network. The proposed model is solved using Pythagorean hesitant fuzzy programming, presenting a comprehensive and innovative methodology designed explicitly for handling uncertainties inherent in CLSC contexts.FindingsThe research findings highlight the effectiveness and reliability of the proposed framework for addressing uncertainties within CLSC networks. Through a comparative analysis with other established approaches, the model demonstrates its robustness, showcasing its potential to make informed and resilient decisions in supply chain management.Research limitations/implicationsThis study successfully addressed uncertainty in CLSC networks, providing logistics managers with a robust decision-making framework. Emphasizing the importance of PFNs and Pythagorean hesitant fuzzy programming, the research offered practical insights for optimizing transportation routes and resource allocation. Future research could explore dynamic factors in CLSCs, integrate real-time data and leverage emerging technologies for more agile and sustainable supply chain management.Originality/valueThis research contributes significantly to the field by introducing a novel and comprehensive methodology for managing uncertainty in CLSC networks. The adoption of PFNs and Pythagorean hesitant fuzzy programming offers an original and valuable approach to addressing uncertainties, providing practitioners and decision-makers with insights to make informed and resilient decisions in supply chain management.

ABSTRACTOne of the basic requirements of the companies to survive in real-world competitive environments is to make their supply chains as efficient as possible. Due to recent governmental regulations, environmental issues, and the development of the concept of social responsibility, the closed-loop supply chain management has been focused by many researchers. A closed-loop supply chain includes both forward and reverse supply chain networks with the purpose of combining environmental considerations with the traditional supply chain network designs through the collection of used products and activities related to their reuse. In this paper, a bi-objective, multi-period, multi-product, closed-loop supply chain network is designed under environmental considerations, discounts, and uncertainties. The deterministic model of the chain is first solved by three multi-objective decision-making methods. Then, based on real-world uncertainties involved in some of the parameters, a robust optimization model is proposed and solved using decision-making methods. At the end, the best deterministic and robust models are selected based on the displaced ideal solution.

A novel multi-objective optimization model for integrated problem of green closed loop supply chain network design and quantity discount

PurposeThe purpose of this paper is to assist a manufacturing firm in designing the closed-loop supply chain network under risks that are affecting its supply quality and logistics operations. The modeling approach adopted aims at the embedding supply chain risks in a closed-loop supply chain (CLSC) network design process and suggests optimal supply chain configuration and risk mitigation strategies.Design/methodology/approachThe method proposes a closed-loop supply chain network and identifies the network parameter and variables required for closing the loop. Mixed-integer-linear-programming-based mathematical modeling approach is used to formulate the research problem. The solutions and test results are obtained from CPLEX solver.FindingsThe outcomes of the proposed model were demonstrated through a case study conducted in an Indian hospital furniture manufacturing firm. The modern supply chain is mapped to make it closed loop, and potential risks in its supply chain are identified. The supply chain network of the firm is redesigned through embedding risk in the modeling process. It was found that companies can be in great profit if they follow closed-loop practices and simultaneously keep a check on risks as well. The cost of making the supply chain risk averse was found to be insignificant.Practical implicationsAlthough the study was conducted in a practical case situation, the obtained results are not indiscriminate to the other circumstances. However, the approach followed and proposed methodology can be applied to many industries once a firm decides to redesign its supply chain for closing its loop or model under risks.Originality/valueBy using the identified CLSC parameters and applying the proposed network design methodology, a firm can design/redesign their supply chain network to counter the risk and accordingly come up with planned mitigation strategies to achieve a certain degree of robustness.

In recent times, sustainable supply chain management has been a prominent area of research due to the growing concern over carbon emissions and their environmental impact. There has been limited research on sustainable supply chain management that considers the three pillars of sustainability simultaneously, viz. economic, environmental, and social. This study addresses this gap and provides a multi-objective optimization framework for designing a sustainable, uncertain, closed-loop supply chain network while considering three sustainability dimensions. The maximum entropy method has been utilized to deal with uncertainties. Lagrangian relaxation, linear relaxation, and Monte Carlo simulation techniques have been used to solve the model for computational purposes. The results demonstrate that the proposed approach may help improve supply chain efficiency by balancing cost reduction, environmental responsibility, and social impact. This study contributes to the literature on sustainable supply chains by offering a comprehensive decision-making framework that simultaneously integrates the three sustainability pillars.

Increasing global warming, climate change and stringent governmental legislations are driving industry practitioners and decision makers to implement various strategies to reduce carbon emissions. One of the effective approaches to mitigate carbon emissions is the implementation of closed-loop supply chain (CLSC). The key motivation for considering multiple recovery options in the CLSC is to capture the remaining economic value and to reduce carbon emissions in the collection and recovery operations. Customer's willingness to return used product depends on the acquisition price and nearness to the collection center. This research proposes a deterministic mixed-integer linear programming (MILP) model for a multi-period and multi-product CLSC network under carbon pricing and carbon trading policies consideration. The model includes different acquisition price for returned products and multiple recovery options. Further, the study takes into consideration uncertainty in procurement cost, demand, and quantity of returned products. A robust optimization approach is adopted to address uncertainty in network parameters. Numerical results show that the proposed model captures trade-offs between total cost and carbon emission. Overall, the study reveals that the carbon trading policy incurs relatively lower total cost compared to the carbon pricing policy. Repair and recycling activities in the reverse supply chain contribute significantly to the total cost and carbon emission. This study provide evidence that it is possible to achieve an optimal CLSC network with reduced carbon emission at a moderate total supply chain cost. The proposed model could be used to guide firms to choose an appropriate budget of uncertainty toward achieving a robust supply chain network.

Green or closed-loop supply chain had been the focus of many manufacturers during the last decade. The application of closed-loop supply chain in today’s manufacturing is not only due to growing environmental concerns and the recognition of its benefits in reducing greenhouse gas emissions, energy consumption, and meeting a more strict environmental regulations but it also offers economic competitive advantages if appropriately managed. First-order hybrid Petri nets represent a powerful graphical and mathematical formalism to map and analyze the dynamics of complex systems such as closed-loop supply chain networks. This article aims at illustrating the use of first-order hybrid Petri nets to model a closed-loop supply chain network and evaluate its operational, financial, and environmental performance measures under different management policies. Actual data from auto manufacturer in the United States are used to validate network’s performance under both tactical and strategic decision-making, namely, (1) tactical decision—production policies: increase of recovered versus new components and (2) strategic decision—closed-loop supply chain network structure: manufacturer internal recovery process or recovery process done by a third-party collection and recovery center. The work presented in this article is an extension of the use of first-order hybrid Petri nets as a modeling and performance analysis tool from supply chain to closed-loop supply chain. The modularity property of first-order hybrid Petri nets has been used in the modeling process, and the simulation and analysis of the modeled network are done in MATLAB® environment. The results of the experiments depict that first-order hybrid Petri nets are a powerful modeling and analysis formalism for closed-loop supply chain networks and can be further used as an efficient decision-making tool at both tactical and strategic levels. Unlike other researches on modeling supply chain networks that focus on evaluating individually cost, operational, or environmental aspects, the research here shows how first-order hybrid Petri nets can be extended to assess simultaneously operational, financial, and environmental network’s performance measures at different managerial decision-making levels. The results particularly are compelling for researchers and industrial practitioners who can use the same methodology in evaluating their network’s performance and making educated management decisions based on the performance results and the impact of their selected supply chain and manufacturing strategies.

Climate change, increased carbon regulations, and globalized supply chains are driving industry practitioners and decision makers to implement various carbon policies to reduce carbon emissions. One of the effective approaches to mitigate carbon emissions is the implementation of closed-loop supply chain (CLSC). This paper proposes a deterministic mixed integer linear programming (MILP) model for a multi-period and multi-product closed loop supply chain network with multiple recovery, quality returns and carbon emission considerations. Transportation mode selection decision for logistic activities is also incorporated in the model. Results show that the model captures trade-offs between the total cost and carbon emission. Further, results suggest that carbon price directly effects on the total cost. Conversely, in carbon trading policy, due to having carbon buying and selling flexibility, both total cost and carbon emission are significantly reduced. Sensitivity analysis shows that the operational costs of various recovery activities impact on the total cost. This study provide evidence that besides achieving optimal closed-loop supply chain network design (CLSCND) and planning, it also reduces carbon emissions significantly without increasing the total cost.

Supply chain network design is an important decision-making problem affecting the long-term profitability of firms. Evaluating the performance of supply chain network designs can help decision-makers to select the network configuration that meets the business specifications while operating at a reasonable cost. In this study, Social Network Analysis (SNA) metrics are used to evaluate the performance of closed-loop supply chain (CLSC) Network designs in terms of resilience when exposed to disruptions and the balance of flows. CLSC Networks accommodate the flow of returned products from the customers for recycling, remanufacturing, or disposal, increasing the design complexity compared to traditional supply chain networks. The proposed approach involves custom-designed network-level SNA metrics and random forest (RF) feature selection which are computationally low-cost approaches. The proposed metrics are implemented in an R package titled NetworkSNA and shared on GitHub, and RF feature selection method is performed in python. The optimal and near-optimal network designs from a CLSC Network based on real data are used as a case study. The metric values are interpreted into practical recommendations to compare the alternative CLSC Networks.

Robust optimization and modified genetic algorithm for a closed loop green supply chain under uncertainty: Case study in melting industry

ABSTRACTThe increase in the development of proper channels for recycling and disposal of the manufactured products have motivated the study of closed loop supply chains. The closed loop supply chain networks can be considered as a strong tool for attaining the goals of sustainable development. The customers are not the terminating destination for the products in closed loop supply chain networks. However, after some recycling or refurbishing processes the product once again enters the supply chain networks. The involvement of forward and reverse flow of the products makes the closed loop supply chain networks very complex. As, there may be several conflicting objectives related to the closed loop supply chains, in this paper, we have proposed a bi-level multi-objective programming model for these networks. Bi-level programming problems deal with the situations where decisions are to be taken at two different hierarchical levels. We have considered three objective functions which are distributed among these two levels in such a manner that the decision makers solves for a single objective at each level. A solution procedure is also discussed for solving the proposed model.

With two chains cooperation, Hinfin control methods of bullwhip effects in closed-loop supply chain (CLSC) networks are studied. In each chain, the products which hold by the consumer part are considered as the virtual inventory and the remanufacturing part is defined as a rate to the virtual inventory. The inventory state difference equations of the manufacturers, retailers and consumers are built respectively. Considering CLSCs based on remanufacturing, the model of CLSC networks is established. Bullwhip effects are described as the variance proportion. In the worse case of the demand fluctuation, Hinfin control methods of bullwhip effects in the system are presented with two chains cooperation. To prove it, some number examples are given. The essence of the method is that in the worse case the optimum strategy of the normal manufacturing and order are made by cooperation control of node enterprises in the CLSC networks to restrain bullwhip effects. As a result, it presents a new method to study the stability of CLSC networks and control corporately their bullwhip effects.

A robust leader-follower approach for closed loop supply chain network design considering returns quality levels

Closed-loop supply chain network with interaction of forward and reverse logistics