A multi-stage facility location problem with staircase costs and splitting of commodities: model, heuristic approach and application

Abstract

In this paper a multi-stage facility location problem with staircase costs and splitting of commodities is introduced and formulated as a mixed integer program. The problem is motivated by an application in the context of a reverse supply chain for end-of-life vehicles. We propose a two-phase heuristic solution approach: The greedy construction heuristic utilizes the solution obtained by the LP-relaxation of the problem. In the improvement heuristic we combine ADD, DROP and SWAP neighborhoods with a diversification strategy to a Variable Neighborhood Descent (VND) and to a Variable Neighborhood Search (VNS) approach. Computational results show that this approach is able reduce the duality gap provided by state-of-the-art MIP solver CPLEX for small and medium-sized instances and is also able to provide high-quality solutions for large-scale instances with up to 2,900 candidate facilities. The building blocks of the solution approach can easily be rearranged in order to solve other facility location problems.