A multi-objective model for closed-loop supply chain optimization and efficient supplier selection in a competitive environment considering quantity discount policy

Supplier selection and allocation of optimal order quantity are two of the most important processes in closed-loop supply chain (CLSC) and reverse logistic (RL). So that providing high quality raw material is considered as a basic requirement for a manufacturer to produce popular products, as well as achieve more market shares. On the other hand, considering the existence of competitive environment, suppliers have to offer customers incentives like discounts and enhance the quality of their products in a competition with other manufacturers. Therefore, in this study, a model is presented for CLSC optimization, efficient supplier selection, as well as orders allocation considering quantity discount policy. It is modeled using multi-objective programming based on the integrated simultaneous data envelopment analysis–Nash bargaining game. In this study, maximizing profit and efficiency and minimizing defective and functions of delivery delay rate are taken into accounts. Beside supplier selection, the suggested model selects refurbishing sites, as well as determining the number of products and parts in each network’s sector. The suggested model’s solution is carried out using global criteria method. Furthermore, based on related studies, a numerical example is examined to validate it.