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Exact Solution of Large-Scale Hub Location Problems with Multiple Capacity Levels

Author

Listed:
  • Ivan Contreras

    (Concordia University and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

  • Jean-François Cordeau

    (HEC Montréal and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

  • Gilbert Laporte

    (HEC Montréal and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montréal, Quebec H3T 2A7, Canada)

Abstract

This paper presents an extension of the classical capacitated hub location problem with multiple assignments in which the amount of capacity installed at the hubs is part of the decision process. An exact algorithm based on a Benders decomposition of a strong path-based formulation is proposed to solve large-scale instances of two variants of the problem: the splittable and nonsplittable commodities cases. The standard decomposition algorithm is enhanced through the inclusion of features such as the generation of strong optimality cuts and the integration of reduction tests. Given that in the nonsplittable case the resulting subproblem is an integer program, we develop an efficient enumeration algorithm. Extensive computational experiments are performed to evaluate the efficiency and robustness of the proposed algorithms. Computational results obtained on benchmark instances with up to 300 nodes and five capacity levels confirm their efficiency.

Suggested Citation

  • Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2012. "Exact Solution of Large-Scale Hub Location Problems with Multiple Capacity Levels," Transportation Science, INFORMS, vol. 46(4), pages 439-459, November.
    • Handle: RePEc:inm:ortrsc:v:46:y:2012:i:4:p:439-459
    DOI: 10.1287/trsc.1110.0398
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    References listed on IDEAS

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    1. O'Kelly, M. E. & Bryan, D. L., 1998. "Hub location with flow economies of scale," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 605-616, November.
    2. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    3. Campbell, James F., 1994. "Integer programming formulations of discrete hub location problems," European Journal of Operational Research, Elsevier, vol. 72(2), pages 387-405, January.
    4. Samir Elhedhli & Huyu Wu, 2010. "A Lagrangean Heuristic for Hub-and-Spoke System Design with Capacity Selection and Congestion," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 282-296, May.
    5. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    6. Boland, Natashia & Krishnamoorthy, Mohan & Ernst, Andreas T. & Ebery, Jamie, 2004. "Preprocessing and cutting for multiple allocation hub location problems," European Journal of Operational Research, Elsevier, vol. 155(3), pages 638-653, June.
    7. A.T. Ernst & M. Krishnamoorthy, 1999. "Solution algorithms for the capacitated single allocation hub location problem," Annals of Operations Research, Springer, vol. 86(0), pages 141-159, January.
    8. A. T. Ernst & M. Krishnamoorthy, 1998. "An Exact Solution Approach Based on Shortest-Paths for p -Hub Median Problems," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 149-162, May.
    9. Ricardo Saraiva de Camargo & Gilberto de Miranda & Henrique Pacca L. Luna, 2009. "Benders Decomposition for Hub Location Problems with Economies of Scale," Transportation Science, INFORMS, vol. 43(1), pages 86-97, February.
    10. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "The Dynamic Uncapacitated Hub Location Problem," Transportation Science, INFORMS, vol. 45(1), pages 18-32, February.
    11. 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.
    12. Ivan Contreras & Juan A. Díaz & Elena Fernández, 2011. "Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 41-55, February.
    13. Turgut Aykin, 1995. "Networking Policies for Hub-and-Spoke Systems with Application to the Air Transportation System," Transportation Science, INFORMS, vol. 29(3), pages 201-221, August.
    14. Correia, Isabel & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2010. "Single-assignment hub location problems with multiple capacity levels," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1047-1066, September.
    15. Ebery, Jamie & Krishnamoorthy, Mohan & Ernst, Andreas & Boland, Natashia, 2000. "The capacitated multiple allocation hub location problem: Formulations and algorithms," European Journal of Operational Research, Elsevier, vol. 120(3), pages 614-631, February.
    16. Alumur, Sibel & Kara, Bahar Y., 2008. "Network hub location problems: The state of the art," European Journal of Operational Research, Elsevier, vol. 190(1), pages 1-21, October.
    17. Marshall L. Fisher & R. Jaikumar & Luk N. Van Wassenhove, 1986. "A Multiplier Adjustment Method for the Generalized Assignment Problem," Management Science, INFORMS, vol. 32(9), pages 1095-1103, September.
    18. Mari'n, Alfredo & Canovas, Lazaro & Landete, Mercedes, 2006. "New formulations for the uncapacitated multiple allocation hub location problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 274-292, July.
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