Multi-period design and planning of closed-loop supply chains withuncertain supply and demand

A design and planning approach is proposed for addressing general multi-period, multi-product closed-loop supply chains (CLSCs), structured as a 10-layer network (5 forward plus 5 reverse flows), with uncertain levels in the amount of raw material supplies and customer demands. The consideration ofa multi-period setting leads to a multi-stage stochastic programming problem, which is handled by amixed-integer linear programming (MILP) formulation. The effects of uncertain demand and supply onthe network are considered by means of multiple scenarios, whose occurrence probabilities are assumed to be known. Several realistic supply chain requirements are taken into account, such as those relatedto the operational and environmental costs of different transportation modes, as well as capacity limitson production, distribution and storage. Moreover, multiple products are considered, which are groupedaccording to their recovery grade. The objective function minimizes the expected cost (that includes facil-ities, purchasing, storage, transport and emissions costs) minus the expected revenue due to the amount of products returned, from repairing and decomposition centers to the forward network. Finally, com-putational results are discussed and analyzed in order to demonstrate the effectiveness of the proposedapproach. Due to the large size of the addressed optimization problem containing all possible scenariosfor the two uncertain parameters, scenario reduction algorithms are applied to generate a representative,albeit smaller, subset of scenarios