Closed-loop supply chains involve forward flows of products from production facilities to customer zones as well as reverse flows from customer zones back to remanufacturing facilities. We present an integrated modeling framework for configuring a distribution system with reverse flows so as to minimize the total cost of satisfying customer demand and remanufacturing the returned items that are recoverable. Given a set of existing plants and customer zones, our basic model identifies the optimal number and location of distribution centers and return centers assuming that all plants have remanufacturing capability. We devise a Lagrangian heuristic for this problem. The proposed solution method proved to be computationally efficient for solving large-scale instances of the closed-loop supply chain design problem. The potential benefits of the integrated model are demonstrated by comparing its results with those obtained from an alternative approach that determines optimal forward and reverse network structures sequentially. We also extend the basic model to determine the optimal locations for establishing remanufacturing facilities. Using the extended model, we study the conditions under which the return centers can be co-located with remanufacturing facilities rather than being established at the downstream echelons of the supply chain. Different from the existing works on facility location-allocation models for closed-loop supply chain network design, the main focus in this paper is on the investigation of structural properties of the network such as co-locating return centers with remanufacturing facilities and quantifying the benefit of modeling forward and reverse flows simultaneously rather than sequentially.
Reverse logistics Facility location-allocation Lagrangian relaxation Mixed-integer programming model