A Modified Benders Method for the Single- and Multiple Allocation P-Hub Median Problems

Abstract

We consider the well-known uncapacitated p-hub median problem with multiple allocation (UMApHMP), and single allocation (USApHMP). These problems have received significant attention in the literature because while they are easy to state and understand, they are hard to solve. They also find practical applications in logistics and telecommunication network design. Due to the inherent complexity of these problems, we apply a modified Benders decomposition method to solve large instances of the UMApHMP and USApHMP. The Benders decomposition approach does, however, suffer from slow convergence mainly due to the high degeneracy of subproblems. To resolve this, we apply a novel method of accelerating Benders method. We improve the performance of the accelerated Benders method by more appropriately choosing parameters for generating cuts, and by solving subproblems more efficiently using minimum cost network flow algorithms. We implement our approach on well-known benchmark data sets in the literature and compare our computational results for our implementations of existing methods and commercial solvers. The computational results confirms that our approach is efficient and enables us to solve larger single- and multiple allocation hub median instances. We believe this paper is the first implementation of Benders method to solve USA$p$HMP and UMA$p$HMP.