A robust leader-follower approach for closed loop supply chain network design considering returns quality levels

This paper aims to assess the effect of governmental policies on a closed loop supply chain network design to achieve the optimum decision level of the collection policies for the government. For this purpose, a robust closed loop supply chain network design model with an incentive strategy for different return quality levels with a bi-level programming approach is proposed. The government will act as a leader in the outer problem and maximize the total collected returned products with different quality levels. A predefined ratio of customer demand should be satisfied as a constraint for the outer problem. In the inner problem, a closed loop supply chain designer is considered as a follower and tries to maximize the supply chain net profit with respect to government regulations. A heuristic method based on enumeration and a solution methodology consisting of particle swarm optimization for the outer problem and a genetic algorithm for the inner problem are proposed. In addition, we investigate the impact of demand uncertainty on government regulations and the closed loop supply chain configuration by a robust optimization approach. Finally, numerical examples are generated to evaluate the performance of the proposed model. The results show the necessity of using bi-level programming and the superiority of the proposed solution methodology compared with the proposed enumeration method in large-size problems.