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An Efficient Procedure for Designing Single Allocation Hub and Spoke Systems

  • Hasan Pirkul

    (School of Management, University of Texas at Dallas, P.O. Box 830688, Richardson, Texas 75083)

  • David A. Schilling

    (Department of Management Science, Fisher College of Business, Ohio State University, 2100 Neil Avenue, Columbus, Ohio 43210)

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    Given the widespread use of the hub and spoke network architecture and its growing importance to competitiveness in logistics, communication, and mass transportation, there has been considerable interest by practitioners and researchers alike in finding efficient methods for designing such networks. This paper provides a method that delivers both high quality solutions and firm measures of that quality, and allows problems to be solved in reasonable time on a desktop computer. The approach begins with a previously proposed tight linear programming formulation and uses subgradient optimization on a lagrangian relaxation of the model. However, to dramatically improve the performance of this approach, we augment a subproblem of the lagrangian relaxation model with a cut constraint. In computational experiments on eighty-four standard test problems, average gaps are 0.048%. Maximum gaps are under 1% while average solution times on a Pentium-166 are under five minutes.

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    File URL: http://dx.doi.org/10.1287/mnsc.44.12.S235
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 12-Part-2 (December)
    Pages: S235-S242

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    Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-2:p:s235-s242
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    1. Skorin-Kapov, Darko & Skorin-Kapov, Jadranka, 1994. "On tabu search for the location of interacting hub facilities," European Journal of Operational Research, Elsevier, vol. 73(3), pages 502-509, March.
    2. Hasan Pirkul & David A. Schilling, 1988. "The Siting of Emergency Service Facilities with Workload Capacities and Backup Service," Management Science, INFORMS, vol. 34(7), pages 896-908, July.
    3. Mirchandani, Pitu B. & Oudjit, Aissa & Wong, Richard T., 1985. "`Multidimensional' extensions and a nested dual approach for the m-median problem," European Journal of Operational Research, Elsevier, vol. 21(1), pages 121-137, July.
    4. Bazaraa, Mokhtar S. & Goode, Jamie J., 1979. "A survey of various tactics for generating Lagrangian multipliers in the context of Lagrangian duality," European Journal of Operational Research, Elsevier, vol. 3(4), pages 322-338, July.
    5. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    6. Morton O'Kelly & Darko Skorin-Kapov & Jadranka Skorin-Kapov, 1995. "Lower Bounds for the Hub Location Problem," Management Science, INFORMS, vol. 41(4), pages 713-721, April.
    7. Aykin, Turgut, 1994. "Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem," European Journal of Operational Research, Elsevier, vol. 79(3), pages 501-523, December.
    8. Klincewicz, J. G., 1991. "Heuristics for the p-hub location problem," European Journal of Operational Research, Elsevier, vol. 53(1), pages 25-37, July.
    9. Hasan Pirkul & David A. Schilling, 1991. "The Maximal Covering Location Problem with Capacities on Total Workload," Management Science, INFORMS, vol. 37(2), pages 233-248, February.
    10. Skorin-Kapov, Darko & Skorin-Kapov, Jadranka & O'Kelly, Morton, 1996. "Tight linear programming relaxations of uncapacitated p-hub median problems," European Journal of Operational Research, Elsevier, vol. 94(3), pages 582-593, November.
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