A Robust Multi Objective Optimization Model for Sustainable Closed-Loop Supply Chain Network Design

Reverse logistic has attracted a lot of attention from researchers in recent years due to government regulations، environmental problems، extension of social responsibility and customer demands. In addition، the decline in the natural resources and raw materials combined with the increase in production costs and problems of dealing with trash of the industry and consumer products makes the cycle of consumption very interesting to researchers from the production point to the last stage of recycling. This subject gave way to newer concepts like integrated، closed-loop and stable supply chain in the past decade. This paper presents a robust design for a multi-product، multi-echelon، closed-loop logistic network model in an uncertain environment. To this aim، a multi-objective mathematical programming model is developed wherein its objective functions include profit، social and environmental impacts. First، a deterministic mixed-integer linear programming model is developed for designing a closed-loop supply chain network. Then، the robust counterpart of the proposed mixed-integer linear programming model is presented by using the recent extensions in robust optimization theory. Finally، to assess the robustness of the solutions obtained by the novel robust optimization model، they are compared to those generated by the deterministic mixed-integer linear programming model in a number of realizations under different test problems.