Closed-loop supply chain network design under demand, return and quality uncertainty

We consider the problem of designing a closed-loop supply chain (CLSC) network in the presence of uncertainty in demand quantities, return rates, and quality of the returned products. We formulate the problem as a two-stage stochastic mixed-integer program (SMIP) that maximizes the total expected profit. The first-stage decisions in our model are facility location and capacity decisions, and the second-stage decisions are the forward/reverse flows on the network and hence the production/recovery quantities defined by the flow amounts. We solve the problem by using the L-shaped method in iterative and branch-and-cut frameworks. To improve the computational efficiency, we consider various cut generation strategies. Besides testing the performance of the considered solution methods, we also use our numerical results to estimate the value of the stochastic solution (VSS), the expected value of perfect information (EVPI), and the benefit of utilizing a CLSC network. Our results indicate that the uncertainty in demand has the highest impact and the uncertainty in return rate has the lowest impact on VSS and EVPI values, and including reverse chain increases the expected profit significantly.