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

• General multi-period multi-product closed-loop supply chains (CLSCs).
• Multi-stage stochastic approach for design and planning of CLSCs with uncertain conditions.
• The effects of uncertain demand and supply on the network are considered by means of multiple scenarios.
• The problem goal is to minimize the expected cost minus the expected revenue.
• Scenario reduction algorithm is applied to generate a representative representation of the problem.

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 of a multi-period setting leads to a multi-stage stochastic programming problem, which is handled by a mixed-integer linear programming (MILP) formulation. The effects of uncertain demand and supply on the 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 related to the operational and environmental costs of different transportation modes, as well as capacity limits on production, distribution and storage. Moreover, multiple products are considered, which are grouped according to their recovery grade. The objective function minimizes the expected cost (that includes facilities, 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, computational results are discussed and analyzed in order to demonstrate the effectiveness of the proposed approach. Due to the large size of the addressed optimization problem containing all possible scenarios for the two uncertain parameters, scenario reduction algorithms are applied to generate a representative, albeit smaller, subset of scenarios.