Efficient flow models for the uncapacitated multiple allocation p-hub median problem on non-triangular networks

Abstract

This paper examines the uncapacitated multiple allocation p-hub median problem (UMApHMP) in a general setting where a given network may violate the triangle inequality, thus leading to flow paths with more than two hubs connecting origin-to-destination pairs. We present two improved flow formulations using a new ”augmented graph” that allows a substantial reduction in the number of constraints, and significant improvement in performance of a standard off-the-shelf MILP solver compared to the recent 4-index flow model proposed in Brimberg et al. (2020). Results presented even surpass the performance of specialized algorithms developed for solving the standard ”triangular” case. The linear programming relaxations of the presented models are also investigated.