A parallel variable neighborhood search for the multi-objective sustainable post-sales network design problem

Environmental and sustainability awareness in societies has attracted many academics and professionals from various disciplines to revise their thoughts and philosophies such as supply chain management. In particular, implementation of reverse logistics systems and closed-loop supply chain often results in reduced environmental pollution and costs, as well as increased customer satisfaction. In this study, a multi-objective post-sales network design model considering strategic and tactical decisions is proposed to minimize total fixed and variable costs, total tardiness, and environmental pollution. In addition to common network design decisions, various decisions such as technology and capacity level decisions as well as product selection at recovery facilities are considered. To tackle the proposed model, a parallel multi-objective heuristic based on variable neighborhood search (VNS) is developed to find Pareto-optimal solutions. The efficiency of proposed method is compared with an available efficient multi-objective memetic algorithm (MOMA). In addition, its results are compared with those of branch and bound methods of two commercial optimization packages for small and medium-sized test instances. Computational results demonstrate the superiority of the proposed algorithm in terms of solution quality and computational time over MOMA as well as the single-thread and multi-thread branch and bound methods. Furthermore, comparing the proposed heuristic with a standard VNS demonstrates the success of parallelization in thoroughly exploring solution space as well as improving number and quality of Pareto-optimal solutions.