Sustainable closed-loop supply chain network design with discount supposition

Supply chain network design (SCND) is one of the important, primary and strategic decisions affecting competitive advantages and all other decisions in supply chain management. Although most of papers in SCND focus only on the economic performance, this study considers simultaneously economic, social and environmental aspects. In this study, a new mixed integer nonlinear programming model is developed to formulate a multi-objective sustainable closed-loop supply chain network design problem by considering discount supposition in the transportation costs for the first time. In order to address the problem, not only traditional and recent metaheuristics are utilized, but also the algorithms are hybridized according to their strengths especially in intensification and diversification. To evaluate the efficiency and effectiveness of these algorithms, they are compared with each other by four assessment metrics for Pareto optimal analyses. Although the results indicate the performance of three proposed new hybridization algorithms, KAGA achieves better solutions compared with the others, but it needs more time. At the end, we introduced a real industrial example in glass industry to verify the proposed model and the algorithms.