Uncapacitated single and multiple allocation p-hub center problems

  • Authors:

  • Andreas T. Ernst;Horst Hamacher;Houyuan Jiang;Mohan Krishnamoorthy;Gerhard Woeginger

  • Affiliations:

  • CSIRO Mathematical and Information Sciences, Private Bag 10, Clayton South MDC, Clayton, VIC 3169, Australia;Fachbereich Mathematik, Universitaet Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany;Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, UK;CSIRO Mathematical and Information Sciences, Private Bag 10, Clayton South MDC, Clayton, VIC 3169, Australia;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2009

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Abstract

The hub median problem is to locate hub facilities in a network and to allocate non-hub nodes to hub nodes such that the total transportation cost is minimized. In the hub center problem, the main objective is one of minimizing the maximum distance/cost between origin destination pairs. In this paper, we study uncapacitated hub center problems with either single or multiple allocation. Both problems are proved to be NP-hard. We even show that the problem of finding an optimal single allocation with respect to a given set of hubs is already NP-hard. We present integer programming formulations for both problems and propose a branch-and-bound approach for solving the multiple allocation case. Numerical results are reported which show that the new formulations are superior to previous ones.