Polyhedral Analysis of Uncapacitated Single Allocation p-Hub Center Problems

In contrast to p-hub problems with a summation objective (p-hub median), min-max hub problems (p-hub center) have not attained much attention in the literature. In this paper, we give a polyhedral analysis of the uncapacitated single allocation p-hub center problem (USApHCP). The analysis will be based on a radius for-mulation which currently yields the most efficient solution procedures. We show which of the valid inequalities in this formulation are facet-defining and present non-elementary classes of facets, for which we propose separation problems. A major part in our argumentation will be the close connection between polytopes of the USApHCP and the uncapacitated p-facility location (pUFL). Hence, the new classes of facets can also be used to improve pUFL formulations