Solving a Location-Allocation Problem with Logic-Based Benders’ Decomposition

Abstract

We address a location-allocation problem that requires deciding the location of a set of facilities, the allocation of customers to those facilities under facility capacity constraints, and the allocation of the customers to trucks at those facilities under per truck travel-distance constraints. We present a hybrid approach that combines integer programming and constraint programming using logic-based Benders’ decomposition. Computational performance against an existing integer programming model and a tabu search approach demonstrates that the Benders’ model is able to find and prove optimal solutions an order of magnitude faster than an integer programming model while also finding better feasible solutions in less time for the majority of problem instances when compared to the tabu search.