Solving a reverse supply chain design problem by improved Benders decomposition schemes

In this paper we propose improved Benders decomposition schemes for solving a remanufacturing supply chain design problem (RSCP). We introduce a set of valid inequalities in order to improve the quality of the lower bound and also to accelerate the convergence of the classical Benders algorithm. We also derive quasi Pareto-optimal cuts for improving convergence and propose a Benders decomposition scheme to solve our RSCP problem. Computational experiments for randomly generated networks of up to 700 sourcing sites, 100 candidate sites for locating reprocessing facilities, and 50 reclamation facilities are presented. In general, according to our computational results, the Benders decomposition scheme based on the quasi Pareto-optimal cuts outperforms the classical algorithm with valid inequalities. Adopting a friendly sustainable management approach implies a number of changes for companies from the strategic level up to the operational point of view, affecting their employees and impacting their business processes and technology. In this regard, Simchi-Levi, Kaminsky, and Simchi-Levi (2007) point out, ''the strategic level deals with decisions that have a long-lasting effect on the firm. These include decisions regarding the number, location and capacities of warehouses and manufacturing plants, or the flow of material through the logistics network.'' The problem of locating facilities and allocating customers is not new to the operations research community and involves the key aspects of supply chain design (Daskin, Snyder, & Berger, 2005). This problem is one of ''the most comprehensive strategic decision problems that need to be optimized for long-term efficient operation of the whole supply chain'' (Altiparmak, Gen, Lin, & Paksoy, 2006). As observed by Farahani and Hekmatfar (2009), some small changes to classical facility location models can make the problems much harder to solve. In the last few years, mathematical modeling and solution methods for the efficient management of return flows (and/or integrated with forward flows) have been studied in the context of reverse logistics, closed-loop supply chains, and sustainable supply chains. Fleischmann, Krikke, Dekker, and Flapper (2000) discussed new issues that arise in the context of reverse logistics, and they reviewed the mathematical models proposed in the literature. Fleischmann, Beullens, Bloemhof-Ruwaard, and Va (2001) proposed a generic recovery network model based on the elementary characteristics of return networks identified in Fleischmann et al. (2000). Zhou and Wang (2008) proposed a generic mixed integer model for the design of a reverse distribution network including repairing and remanufacturing options simultaneously. Regarding reverse logistics networks in …