Efficient solution procedure and reduced size formulations for p-hub location problems

In this paper we consider the uncapacitated p-hub location problems, where multiple and single allocation cases are considered. In the multiple allocation problem, a nonhub node may be allocated to more than one hub. We show that the multiple allocation problem can be solved efficiently by the shortest path algorithm when p is fixed. Also, this algorithm can be applied to the cases in which some other hubbing policies are used. In the single allocation problem, each nonhub node must be allocated to exactly one of the p hubs. We provide a reduced size formulation, and a mixed integer formulation for the model with fixed hub locations, where fixed costs for opening links are considered. Computational experience is provided using the data given in the literature and the instances having fixed costs for opening links. (C) 1998 Elsevier Science B.V. All rights reserved.