Solving Detour-Based Fuel Stations Location Problems

This article studies the problem of locating fuel stations to minimize the extra cost spent in refueling detours, which belongs to a class of discretionary service facility location problems. Unlike many studies of similar problems in the literature, the proposed model considers capacity constraints and compares different ways to incorporate them in the formulation. Note that ignoring the capacity constraint results in nonoptimal and unrealistic solutions. The proposed models are solved using both an off-the-shelf solver CPLEX and a specialized meta-heuristic method Simulated Annealing developed in this study. The solution methods are tested and compared in two case studies; a test benchmark network and a large-scale network. An effort to overcome the memory limitation of CPLEX through more compact formulation was partially successful: it results in a model that is less tightly bounded by its linear relaxation and hence is much more difficult to solve. In contrast, the Simulated Annealing algorithm scales better and is able to consistently yield high-quality solutions with a reasonable amount of computation time.