Multi-stage stochastic optimization of the design and planning of a Closed-Loop Supply Chain

Abstract

This paper addresses the multi-period, multi-product Closed-Loop Supply Chain (CLSC) design and planning problem with uncertain levels in the amount of raw material and customer demands. In addition, several aspects of practical significance are taken into account, such as those related with the operational and environmental costs of different transportation modes, as well as capacity limits on production, distribution and storage. The considered SC is structured as a 10-layer network (5 forward plus 5 reverse). It is important to note that the structure incorporates most of the network nodes plausible in practice. The consideration of the multi-period setting leads to a multi-stage stochastic programming problem, which is handled by a mathematical model based on a multi-stage stochastic mixed-integer linear programming formulation. The objective is to minimize the total cost of facilities, including operational, purchasing, storage, transportation and emissions costs, while guaranteeing costumers demands and maximizing the amount of products returned from repairing and decomposition centers. Thus, the performance measure seeks to obtain low-cost solutions subjected to environmental concerns.