Reformulations and Computational Results for the Uncapacitated Single Allocation Hub Covering Problem

We study the single allocation hub covering problem, which is a special case of the general hub location problem and an important extension to traditional covering problems. Hubs are located at some nodes in the network and are used to facilitate (consolidate, transfer, distribute) flows. An important feature in hub location is that the transfer cost between hub nodes is discounted. The hub covering problem is to locate a minimum number of hubs such that the travel cost between each o-d pair in the network does not exceed a given threshold. We improve the best existing integer programming formulation for this problem by lifting constraints to produce facet-defining inequalities. We also develop a new formulation for the problem. The numerical results show that your new formulation performs better than existing formulations when using lifted constraints and paying special attention the number of non-zero coefficients used.