Distributionally robust optimization for the closed-loop supply chain design under uncertainty

The closed-loop supply chain network (CLSCN) contains reverse flows that collect products from customers and recycle or remanufacture usable parts. The CLSCN design problem is becoming more and more prominent under the context of Sustainable Development and Circular Economy. Parameters associated with a CLSCN including customer demands, transportation costs, or disposal rates are usually subject to uncertainty. Furthermore, natural or man-made disruptions may cause part of the CLSCN to malfunction. We herein propose a hybrid stochastic and distributionally robust optimization (DRO) approach to hedge against discrete disruption scenarios and uncertain customer demands. We also tailor a Benders decomposition-based algorithm to efficiently solve the resulting large-scale mixed integer linear programming reformulations. Computational experiments demonstrate that the proposed algorithm can outperform commercial solvers such as CPLEX, and the DRO approach can produce solutions with low average costs and low variance in out-of-sample tests.