A new Benders decomposition acceleration procedure for large scale multiple allocation hub location problems

Abstract

We consider the well-known uncapacitated multiple allocation hub location problem (UMAHLP). Hub location problems are widely used to model and solve problems that arise from network telecommunications, transport networks, and delivery systems. Due to the high complexity of hub location problems, different approaches have been employed to develop efficient algorithms. We apply a modified Benders decomposition method for solving large UMAHLP instances exactly. Since the derived subproblems possess an inherent high degeneracy, the implementation of Benders method for UMAHLP usually suffers from slow convergence. We adapt an existing state-of-the-art method in the literature, and apply a novel method of accelerating this approach. This is performed with a view to addressing the slow convergence issues. Our approach improves the current best results by more appropriately choosing parameters for the accelerated Benders method. Furthermore, as observed in the literature, the exact solution of subproblems can add an extra complexity to the Benders approach for UMAHLP. We reformulate the subproblems and solve them more efficiently using a minimum cost network flow algorithm. Our computational results show that our acceleration procedures together with our different approach to solve subproblems are computationally efficient. According to our computational results, we are able to solve larger UMAHLP instances with up to 200 nodes in less than 2 hours. On average, our approach improves computational times of around two third of tested instances by 44% over current approaches. Also it requires around 10% fewer Benders iterations in our computational experiment.