Document Type : Research Paper


1 Associate Professor, Dept. of Applied Mathematics, Ayat Amoly Unit, Islamic Azad University, Amoly, Iran

2 Master of Industrial Engineering, Masjid Sulaiman branch, Islamic Azad University, Masjid Sulaiman, Iran

3 Associate Professor, Department of Industrial Engineering, Firozabad Higher Education Center, Firozabad, Fars, Iran


The closed-loop supply chain is used in practice for several reasons. Firstly, returning products to the production cycle is important for its operation. Secondly, sustainability in the supply chain is a topic of interest for researchers, as the environmental impacts of industries are significant. In this paper, a multi-objective integer fuzzy mathematical programming model is presented to design a sustainable closed-loop supply chain under uncertain conditions. The proposed model aims to maximize profit and social impacts, while minimizing gas emissions into the environment. Since decision makers face uncertainty and doubt, trapezoidal intuitionistic fuzzy numbers are employed to determine the parameter values in the model. To convert the objective functions and model constraints into crisp forms, the expected value and the intuitionistic credibility measure are developed for the objectives and constraints, respectively. Finally, an interactive fuzzy programming approach is utilized to solve the crisp multi-objective problem. Three numerical examples are designed and solved to validate the model and assess the efficiency of the proposed solution method.
Supply chain management encompasses techniques aimed at coordinating all aspects of the supply chain, from raw material procurement to product delivery or recovery, with the objective of minimizing total costs while addressing conflicts among chain partners. Once raw materials have traversed the forward chain and been transformed into products or services, they may require repair, transformation, or proper disposal, which occurs within the reverse chain. The integration of forward and reverse supply chain methods gives rise to a closed-loop supply chain.
Today, one of the primary concerns for organizational managers in supply chain network design is the presence of uncertainties, such as disruptions and uncertain input parameters. Uncertainties can have adverse effects on supply chain performance and decision-making at various network levels, including tactical, strategic, and operational decisions. As probabilistic planning necessitates historical data, which may not always be available or accurate, the theory of fuzzy sets can serve as a suitable option for expressing ambiguity and lack of certainty in parameters. In recent years, environmental factors have received increasing attention. There has been a growing recognition of the importance of environmental effects and the need to incorporate these effects alongside traditional indicators in supply chain design. Environmental considerations are crucial not only for compliance with government regulations but also for improving the organization's social standing from the customers' perspective. Moreover, with the rise of global warming and the accumulation of waste (both renewable and non-renewable, as well as electronic waste and ozone-depleting gases), the importance of managing and controlling these factors has become even more prominent. Despite the significance of environmental issues, there remains a noticeable gap in the supply chain literature concerning the provision of mathematical models based on real-world conditions and efficient solution methods for this problem. This paper focuses on the design of a sustainable closed-loop logistics network that aims to maximize profitability and social factors while minimizing environmental factors. The proposed integrated network considers multi-product and multi-state customer demand under conditions of uncertainty. The significance of this research lies in simultaneously addressing economic, environmental, and social considerations in the modeling process, as previous studies have mostly focused on single or dual objectives. Another innovative aspect of this article is the consideration of parameters in the form of intuitive fuzzy numbers for the design of a sustainable supply chain network.
Materials and Methods
In this research, a comprehensive model addressing the problem of sustainable closed-loop supply chain under intuitionistic fuzzy uncertainty is selected through library studies and internet research. Subsequently, the model is transformed into a deterministic multi-objective model utilizing the intuitionistic credibility measure. Recognizing that decision makers face not only uncertainty but also doubts, trapezoidal intuitionistic fuzzy numbers are employed to determine parameter values within the proposed model. To convert the objective functions and model constraints into their crisp equivalents, the expected value and intuitionistic credibility measure are respectively developed for the objective functions and constraints.
Based on the selected confidence levels and numerical examples, the following observations can be made: In numerical example 1, the first objective function demonstrated that the ABS, SO, and TH methods performed best, respectively. However, in the second objective function, the order shifted to SO, ABS, and TH. Interestingly, all three methods performed equally in the third objective function. The performance of the solution methods in numerical example 2 mirrored that of numerical example 1. Moving on to numerical example 3, the first objective function indicated that the SO, TH, and ABS methods were the most effective, respectively. The order remained similar in the second objective function, and once again, all three methods performed equally in the third objective function. These results indicate the relative superiority of the SO solution method compared to the other methods employed. Additionally, concerning the execution time of the solution methods, numerical examples 1 and 2 exhibited nearly equal execution times for the methods. However, in numerical example 3, the SO, TH, and ABS methods displayed the best performance in terms of execution time, respectively. These findings further emphasize the relative superiority of the SO solution method compared to the others in terms of execution time. It is worth noting that the execution time of each method alone increases significantly with the problem's dimensions across all numerical examples.
This paper presents a multi-objective fuzzy optimization model for the design problem of a sustainable closed-loop supply chain. The model takes into account the concept of sustainability and aims to maximize the income and minimize the costs of the entire supply chain, while also minimizing environmental effects and maximizing social effects. The parameters are considered uncertain and are represented by intuitionistic trapezoidal fuzzy numbers. To handle this uncertainty, the model is transformed into a deterministic multi-objective optimization model using the expected value definition and a chance constraint based on the size of intuitionistic. The obtained deterministic multi-objective model is then solved using the interactive fuzzy mathematical programming method.


Main Subjects

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