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

• We provide a more efficient algorithm for a class of reverse SC problem.
• We propose a primal Benders decomposition approach to solve the SC problem.
• We study valid inequalities to improve the lower bound and also to accelerate the convergence of the classical Benders algorithm problem.
• We derive quasi Pareto-optimal cuts for improving convergence of Benders decomposition scheme.
• Computational results for large instances of the problem are discussed.

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.