Developing a Mathematical Model for a Green Closed-Loop Supply Chain with a Multi-Objective Gray Wolf Optimization Algorithm

Abstract Intense competition in today’s market and quick change in customer preferences, along with the rapid development of technology and globalization, have forced companies to work as members of a supply chain instead of individual companies. The success of the supply chain depends on the integration and coordination of all its institutions to form an efficient network structure. An efficient network leads to cost savings throughout the supply chain and helps it respond to customer needs faster. Accordingly, and with respect to the importance of the supply chain, in this study a developed mathematical model for the design of a green closed-loop supply chain is presented. In this mathematical model, the economic and environmental objectives are simultaneously optimized. In order to tackle this mathematical model, two methods of epsilon constraint and multi-objective gray wolf optimization (MOGWO) algorithm have been applied. The results of comparisons between the two mentioned methods show that MOGWO reduce the average solving time from about 1300 seconds to 88 seconds. In the last step of this research, in order to show the application of the proposed mathematical model and the method of solving the research problem, it was implemented in the supply chain of Dalan Kouh diary product and the Pareto optimal solutions were analyzed.