A closed-loop supply chain network design problem with integrated forward and reverse channel decisions

This article considers a multi-product closed-loop logistics network design problem with hybrid manufacturing/remanufacturing facilities and finite-capacity hybrid distribution/collection centers to serve a set of retail locations. First, a mixed integer linear program is presented that determines the optimal solution that characterizes facility locations, 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, a solution method based on Benders' decomposition with strengthened Benders' cuts for improved computational efficiencies is devised. In addition to this method, an alternative formulation is presented and a new dual solution method for the associated Benders' decomposition to obtain a different set of strengthened Benders' cuts is developed. In the Benders' decomposition framework, the strengthened cuts obtained from original and alternative formulations simultaneously are used to obtain an improved efficiency. Computational results illustrating the performance of the solution algorithms in terms of both solution quality and time are presented. It is inferred that the simultaneous use of the strengthened cuts obtained using different formulations facilitates tighter bounds and improves computational efficiency of Benders' algorithm.