Multi-period multi-scenario optimal design for closed-loop supply chain network of hazardous products with consideration of facility expansion

Increased concern for the environment has led to urgent need to design the closed-loop supply chain network of hazardous products economically and ecologically. In this paper, we focus on the optimal design problem of multi-period closed-loop supply chain network of hazardous products considering uncertain demands and returns, expandable facility capacities and social acceptable risk simultaneously. In each period, the built facilities have the ability to expand within a certain scope. The problem is formulated as a mixed-integer nonlinear programming model, which can determine the number, location and expansion scale of the facilities and the forward and reverse logistics quantities between the facilities in each period simultaneously. The goal is to minimize the expected cost over the multi-period planning horizon, including the facilities building, operating and expansion costs and the costs related to manufacturing, collection, processing, recovery and transportation. In order to solve the proposed model, two classes of dummy variables are introduced to equivalently transform it into a mixed-integer linear programming, which can be optimally solved by LINGO. A case study is presented to illustrate the validity of the proposed model. The dynamic design with expansion strategy addressed in this paper is compared with two different strategies of static design and dynamic design without expansion. The results highlight that the dynamic design with expansion strategy has the advantages in saving expenses and raising the average expected collection rate of hazardous wastes.