Mathematical Modeling of Closed-loop Supply Chain Network based on Environmental and Social Impacts

With the expansion and intensification of competitive environment in today's world, supply chain management has become one of the key issues facing businesses. It has influenced all the activities of organizations to produce products, improve quality, reduce costs and provide the services required by customers. On the other hand, as the volume of pollutants increased, the researchers sought to design networks that, in addition to economic optimization, focused on environmental factors in all sectors. Supply chain network design is a strategic and critical issue that provides an optimal framework for effective and efficient supply chain management. One of the most suitable areas for integration in supply chain networks is the design of closed-loop supply chain networks, which can prevent the overlap caused by the design of separate direct and reverse networks. In this paper, a mixed integer linear programming model for closed loop supply chain network design is presented. The latter model seeks to minimize costs, minimize environmental impact, maximize the amount of worn-out product collected, and maximize supply chain social responsiveness. The proposed model is implemented by Saba Battery Company, which produces various types of batteries. Since the proposed model belongs to the NP-hard category, an exact solution method and two multi-objective genetic algorithms and a multicomponent particle swarm were used to solve the model. Based on the research results, the cost objective function tends to create a supply chain network with a centralized structure in order to achieve a lower cost. The environmental objective function tends to create a network with a decentralized structure to reduce environmental impacts. The proposed models are able to provide a range of Pareto optimal solutions according to the different levels of applying fuzzy constraints to determine the final decision. The two algorithms differ in terms of time; NSGA-II is superior to MOPSO. Also, two algorithms are different in the MID criterion, MOPSO is superior to NSGA-II, and in the rest of the criteria, they are not significantly superior to each other. The proposed model was determined with Jimenez's deterministic approach and a deterministic auxiliary model was proposed. This model was solved using the epsilon constraint method and two multi-objective genetic algorithms and multi-objective particle swarm