Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques

•We model a closed-loop supply chain network with six echelons.•The triple bottom lines of sustainability are modeled as three distinct objectives.•We compare our three proposed algorithms with three benchmark algorithms.•The nested method generates better Pareto-optimal solutions but needs more time.

Recently, there is a growing concern about the environmental and social footprint of business operations. While most of the papers in the field of supply chain network design focus on economic performance, recently, some studies have considered environmental dimensions.However, there still exists a gap in quantitatively modeling social impacts together with environmental and economic impacts. In this study, this gap is covered by simultaneously considering the three pillars of sustainability in the network design problem. A mixed integer programming model is developed for this multi-objective closed-loop supply chain network problem. In order to solve this NP-hard problem, three novel hybrid metaheuristic methods are developed which are based on adapted imperialist competitive algorithms and variable neighborhood search. To test the efficiency and effectiveness of these algorithms, they are compared not only with each other but also with other strong algorithms. The results indicate that the nested approach achieves better solutions compared with the others. Finally, a case study for a glass industry is used to demonstrate the applicability of the approach.