A robust bi-level programming model for designing a closed-loop supply chain considering government's collection policy

This study aims to provide a new approach to the design of a closed-loop supply chain network by emphasizing the impact of the government's environmental policies based on a bi-level mixed integer linear programming model. Government is considered as the leader at the rst level and tends to set a collection rate policy, which leads to collecting more used products in order to ensure a minimum distribution ratio to satisfy minimum demands. At the second level, the private sector is considered as a follower and tries to maximize its prot by designing its own closed-loop supply chain network according to the government's used products collection policy. A heuristic algorithm and an adaptive genetic algorithm based on the enumeration method are proposed, and their performances are evaluated through computational experiences. The comparison among numerical examples reveals that there is an obvious con ict between the government and CLSC goals. Moreover, it shows that this con ict should be considered and elaborated in uncertain environment by applying the min-max regret scenario based robust optimization approach. The results show the necessity of applying robust bi-level programming to the closed-loop supply chain network design under the governmental legislative decisions as a leader-follower conguration.