Tabu search and Benders decomposition approaches for a capacitated closed-loop supply chain network design problem

We consider a network design problem in a multiproduct closed-loop supply chain setting consisting of remanufacturing facilities and finite-capacity manufacturing, distribution, and collection facilities that serve a set of retailers. We first present a mixed-integer linear program to determine the optimal locations of the collection centers and remanufacturing facilities along with the integrated forward and reverse flows such that the total cost of facility location, processing, and transportation associated with forward and reverse flows in the network is minimized. Second, we devise two tabu search heuristics – sequential and random neighborhood search procedures – in which we effectively combine search functions using move and exchange neighborhoods to improve efficiency in exploring the solution space. We also suggest a transshipment heuristic to quickly, but effectively, estimate the objective function value (goodness) of a feasible solution in the course of a tabu search. Third, we present a Benders decomposition solution approach that incorporates the tabu search heuristics as well as Benders cuts that are strengthened to facilitate faster convergence and improved computational efficiency, especially for large-scale instances. While the solutions using tabu search heuristics make the applicability of the Benders decomposition approach possible via providing initial upper bounds and facilitating the generation of good initial Benders cuts, the lower bounds obtained by the Benders approach computationally verify the high quality of the tabu search heuristic solutions. We present computational results illustrating the efficient performance of the solution algorithms in terms of both solution quality and time, especially for larger size problems.