A Robust Optimization Model for Closed-Loop Supply Chain Network Under Uncertain Returns

An effective closed-loop supply chain (CLSC) is increasingly important for corporate sustainable development, where used products are returned, remanufactured and/or recycled. Optimized planning of CLSC network is required and is influenced by uncertainties of recovery. So, this study seeks to establish a robust optimal model for CLSC network, considering both uncertainties in quantity and quality of returned products. After the general framework of CLSC is discussed, the measurements for uncertain quantity and quality of returned products are formulated mathematically, respectively as a number of discrete scenarios and Quality Index. A mixed integral linear programming (MILP) model for a CLSC network design is established and then translated into a robust optimization model based on regret value, to determine facilities' locations and quantity of flows between facilities in the network. A numerical example is given, and the simulation results show that the operation strategies of the CLSC are relatively stable under different recycling scenarios. Therefore, the optimization model for CLSC network has good robustness.