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Lower Bounds for the Hub Location Problem

Author

Listed:
  • Morton O'Kelly

    (Department of Geography, The Ohio State University, 1036 Derby Hall, 154 North Oval Mall, Columbus, Ohio 43210)

  • Darko Skorin-Kapov

    (W. A. Harriman School for Management and Policy, State University of New York at Stony Brook, Stony Brook, New York 11794-3775)

  • Jadranka Skorin-Kapov

    (W. A. Harriman School for Management and Policy, State University of New York at Stony Brook, Stony Brook, New York 11794-3775)

Abstract

We present a new lower bound for the Hub Location Problem (HLP) where distances satisfy the triangle inequality. Our lower bound is based on a linearization of the problem and its modification obtained by incorporating the knowledge of a known heuristic solution. A lower bound was computed for some standard data sets from the literature ranging between 10 and 25 nodes, with 2, 3, and 4 hubs, and for different values for the parameter \alpha , representing the discount for the flow between hubs. The novel approach of using a known heuristic solution to derive a lower bound in all cases reduced the difference between the upper and lower bound. This difference measures the quality of the best known heuristic solution in percentages above the best lower bound. As a result of this research, for smaller problems (all instances with 10 and 15 nodes) the average difference is reduced to 3.3%. For larger sets (20 and 25 nodes) the average difference is reduced to 5.9%.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:4:p:713-721
    DOI: 10.1287/mnsc.41.4.713
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    Citations

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    Cited by:

    1. Morton O’Kelly, 2010. "Routing Traffic at Hub Facilities," Networks and Spatial Economics, Springer, vol. 10(2), pages 173-191, June.
    2. Moon-gil Yoon & Young-ho Baek & Dong-wan Tcha, 1998. "Design of a distributed fiber transport network with hubbing topology," European Journal of Operational Research, Elsevier, vol. 104(3), pages 510-520, February.
    3. Yaman, Hande, 2011. "Allocation strategies in hub networks," European Journal of Operational Research, Elsevier, vol. 211(3), pages 442-451, June.
    4. Matsubayashi, Nobuo & Umezawa, Masashi & Masuda, Yasushi & Nishino, Hisakazu, 2005. "A cost allocation problem arising in hub-spoke network systems," European Journal of Operational Research, Elsevier, vol. 160(3), pages 821-838, February.
    5. 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.
    6. Sung, C. S. & Jin, H. W., 2001. "Dual-based approach for a hub network design problem under non-restrictive policy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 88-105, July.
    7. 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.
    8. Sohn, Jinhyeon & Park, Sungsoo, 1998. "Efficient solution procedure and reduced size formulations for p-hub location problems," European Journal of Operational Research, Elsevier, vol. 108(1), pages 118-126, July.
    9. 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.
    10. Racunica, Illia & Wynter, Laura, 2005. "Optimal location of intermodal freight hubs," Transportation Research Part B: Methodological, Elsevier, vol. 39(5), pages 453-477, June.
    11. Nader Azizi & Navneet Vidyarthi & Satyaveer S. Chauhan, 2018. "Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion," Annals of Operations Research, Springer, vol. 264(1), pages 1-40, May.
    12. Chen, Dongxu & Yang, Zhongzhen, 2018. "Systematic optimization of port clusters along the Maritime Silk Road in the context of industry transfer and production capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 174-189.
    13. Milorad Vidović & Slobodan Zečević & Milorad Kilibarda & Jelena Vlajić & Nenad Bjelić & Snežana Tadić, 2011. "The p-hub Model with Hub-catchment Areas, Existing Hubs, and Simulation: A Case Study of Serbian Intermodal Terminals," Networks and Spatial Economics, Springer, vol. 11(2), pages 295-314, June.
    14. Hasan Pirkul & David A. Schilling, 1998. "An Efficient Procedure for Designing Single Allocation Hub and Spoke Systems," Management Science, INFORMS, vol. 44(12-Part-2), pages 235-242, December.
    15. Saberi, Meead & Mahmassani, Hani S., 2013. "Modeling the airline hub location and optimal market problems with continuous approximation techniques," Journal of Transport Geography, Elsevier, vol. 30(C), pages 68-76.
    16. Dongdong Ge & Simai He & Yinyu Ye & Jiawei Zhang, 2011. "Geometric rounding: a dependent randomized rounding scheme," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 699-725, November.

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