A Lagrangian relaxation heuristic for solving the multi-echelon, multi-commodity, close-loop supply chain network design problem

In some industries such as e-tailing, e-auction and catalog sales, returns account for significant portions of total shipments, causing substantial increases in cost. As cost pressures continue to mount in this era of economic slowdowns, returns management has become a top priority for companies seeking to increase their bottom lines. As such, there is a growing need for developing a close-loop supply chain network that can help companies coordinate and manage both forward and reverse logistics flows associated with product sales and recovery. However, most of the existing studies on closed-loop supply chains focus on the backward flow of returned products and neglect the multi-echelon, integrated aspects of both forward and reverse logistics activities. To study this aspect of the problem, this paper proposes a Lagrangian relaxation heuristic for solving the practical size return centre location-allocation problem within closed-loop supply chains.