Large-scale reverse supply chain network design: An accelerated Benders decomposition algorithm

Reverse logistics (RL) is a term that captures any process that involves the movement of goods or services from their destination back to their source. RL is increasingly gaining recognition as an essential component in the design process of supply chains. In this paper, we formulate a mixed-integer linear programming (MILP) model that aims to determine the optimal locations and capacities of various nodes such as inspection centers and remanufacturing facilities and to help decision makers find optimal transportation decisions and to determine the number and type of transportation units required in the network. We develop an exact method to solve large-scale real-sized instances of this problem. We initially attempt to solve the problem using the traditional Benders Decomposition (BD) technique which fails to solve the problem in reasonable computational times. We improve the traditional BD technique by adding several accelerating methods such as trust-region, logistics constraints, Pareto-optimal cuts, restructuring of the problem, and continuous relaxation of the integer variables to increase the convergence rate and to reduce the total number of cuts required in the master problem. In almost all the instances, we were able to reach optimal solutions. For the remaining instances, we succeed in solving the largest problem with an optimality gap of 0.5% and within a reasonable running time. The paper highlights and evaluates the performance and effectiveness of the different acceleration techniques of our improved BD algorithm along with the computational results.