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An improved Benders decomposition algorithm for the tree of hubs location problem

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  • de Sá, Elisangela Martins
  • de Camargo, Ricardo Saraiva
  • de Miranda, Gilberto

Abstract

The tree of hubs location problem is a particularly hard variant of the so called hub location problems. When solving this problem by a Benders decomposition approach, it is necessary to deal with both optimality and feasibility cuts. While modern implementations of the Benders decomposition method rely on Pareto-optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems, a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems. The proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature.

Suggested Citation

  • de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:2:p:185-202
    DOI: 10.1016/j.ejor.2012.10.051
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    1. Jean-François Cordeau & Federico Pasin & Marius Solomon, 2006. "An integrated model for logistics network design," Annals of Operations Research, Springer, vol. 144(1), pages 59-82, April.
    2. Alumur, Sibel A. & Kara, Bahar Y. & Karasan, Oya E., 2009. "The design of single allocation incomplete hub networks," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 936-951, December.
    3. 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.
    4. Mitchell, John E., 1997. "Fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 139-148, February.
    5. John Gleeson & Jennifer Ryan, 1990. "Identifying Minimally Infeasible Subsystems of Inequalities," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 61-63, February.
    6. Mayer, Gabriela & Wagner, Bernd, 2002. "HUBLocator : an exact solution method for the multiple allocation hub location problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 18962, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    7. Shahin Gelareh & Stefan Nickel, 2008. "A Benders Decomposition for Hub Location Problems Arising in Public Transport," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 129-134, Springer.
    8. J. F. Campbell & A. T. Ernst & M. Krishnamoorthy, 2005. "Hub Arc Location Problems: Part I---Introduction and Results," Management Science, INFORMS, vol. 51(10), pages 1540-1555, October.
    9. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    10. 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.
    11. Poojari, C.A. & Beasley, J.E., 2009. "Improving benders decomposition using a genetic algorithm," European Journal of Operational Research, Elsevier, vol. 199(1), pages 89-97, November.
    12. Contreras, Ivan & Cordeau, Jean-François & Laporte, Gilbert, 2011. "Stochastic uncapacitated hub location," European Journal of Operational Research, Elsevier, vol. 212(3), pages 518-528, August.
    13. 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.
    14. Cote, Gilles & Laughton, Michael A., 1984. "Large-scale mixed integer programming: Benders-type heuristics," European Journal of Operational Research, Elsevier, vol. 16(3), pages 327-333, June.
    15. Klincewicz, J. G., 1991. "Heuristics for the p-hub location problem," European Journal of Operational Research, Elsevier, vol. 53(1), pages 25-37, July.
    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. Ebery, Jamie, 2001. "Solving large single allocation p-hub problems with two or three hubs," European Journal of Operational Research, Elsevier, vol. 128(2), pages 447-458, January.
    18. John Klincewicz, 2002. "Enumeration and Search Procedures for a Hub Location Problem with Economies of Scale," Annals of Operations Research, Springer, vol. 110(1), pages 107-122, February.
    19. Alf Kimms, 2006. "Economies of Scale in Hub & Spoke Network Design Models: We Have It All Wrong," Springer Books, in: Martin Morlock & Christoph Schwindt & Norbert Trautmann & Jürgen Zimmermann (ed.), Perspectives on Operations Research, pages 293-317, Springer.
    20. 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.
    21. 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.
    22. Ernst, Andreas T. & Krishnamoorthy, Mohan, 1998. "Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 104(1), pages 100-112, January.
    23. 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.
    24. J. F. Campbell & A. T. Ernst & M. Krishnamoorthy, 2005. "Hub Arc Location Problems: Part II---Formulations and Optimal Algorithms," Management Science, INFORMS, vol. 51(10), pages 1556-1571, October.
    25. Alysson Costa & Jean-François Cordeau & Bernard Gendron, 2009. "Benders, metric and cutset inequalities for multicommodity capacitated network design," Computational Optimization and Applications, Springer, vol. 42(3), pages 371-392, April.
    26. 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.
    27. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "Benders Decomposition for Large-Scale Uncapacitated Hub Location," Operations Research, INFORMS, vol. 59(6), pages 1477-1490, December.
    28. Racunica, Illia & Wynter, Laura, 2005. "Optimal location of intermodal freight hubs," Transportation Research Part B: Methodological, Elsevier, vol. 39(5), pages 453-477, June.
    29. Walter Rei & Jean-François Cordeau & Michel Gendreau & Patrick Soriano, 2009. "Accelerating Benders Decomposition by Local Branching," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 333-345, May.
    30. 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.
    31. Bruno, Giuseppe & Ghiani, Gianpaolo & Improta, Gennaro, 1998. "A multi-modal approach to the location of a rapid transit line," European Journal of Operational Research, Elsevier, vol. 104(2), pages 321-332, January.
    32. 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.
    33. Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    34. M-G Yoon & J Current, 2008. "The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 80-89, January.
    35. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
    36. 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.
    37. Contreras, Ivan & Fernández, Elena & Marín, Alfredo, 2010. "The Tree of Hubs Location Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 390-400, April.
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