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Hub Location as the Minimization of a Supermodular Set Function

Author

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  • Ivan Contreras

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

  • Elena Fernández

    (Statistics and Operations Research Department, Technical University of Catalonia, Barcelona, Spain 08034)

Abstract

This paper highlights how a general class of hub location problems can be modeled as the minimization of a real-valued supermodular set function. Well-known problems such as uncapacitated hub location, p -hub median, and hub arc location, among others, are shown to be particular cases of this class. Two integer programming formulations are introduced and compared. One uses path-based variables, frequently employed in hub location, whereas the other exploits properties of supermodular functions. In addition, several worst case bounds for a greedy and a local improvement heuristic are obtained for the general class and for some particular cases in which sharper bounds can be devised. Computational experiments are performed to compare both formulations when used with a general purpose solver. Computational results obtained on benchmark instances confirm the superiority of the supermodular formulation.

Suggested Citation

  • Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:3:p:557-570
    DOI: 10.1287/opre.2014.1263
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2019. "An Exact Algorithm for Multilevel Uncapacitated Facility Location," Transportation Science, INFORMS, vol. 53(4), pages 1085-1106, July.
    2. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2017. "Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 767-779, November.
    3. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    4. Martins de Sá, Elisangela & Contreras, Ivan & Cordeau, Jean-François, 2015. "Exact and heuristic algorithms for the design of hub networks with multiple lines," European Journal of Operational Research, Elsevier, vol. 246(1), pages 186-198.
    5. Miguel A. Pozo & Justo Puerto & Antonio M. Rodríguez Chía, 2021. "The ordered median tree of hubs location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 78-105, April.
    6. Alibeyg, Armaghan & Contreras, Ivan & Fernández, Elena, 2016. "Hub network design problems with profits," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 40-59.
    7. Alfandari, Laurent & Ljubić, Ivana & De Melo da Silva, Marcos, 2022. "A tailored Benders decomposition approach for last-mile delivery with autonomous robots," European Journal of Operational Research, Elsevier, vol. 299(2), pages 510-525.
    8. Bütün, Cihan & Petrovic, Sanja & Muyldermans, Luc, 2021. "The capacitated directed cycle hub location and routing problem under congestion," European Journal of Operational Research, Elsevier, vol. 292(2), pages 714-734.
    9. Hao-Hsiang Wu & Simge Küçükyavuz, 2018. "A two-stage stochastic programming approach for influence maximization in social networks," Computational Optimization and Applications, Springer, vol. 69(3), pages 563-595, April.
    10. Ivan Contreras & Moayad Tanash & Navneet Vidyarthi, 2017. "Exact and heuristic approaches for the cycle hub location problem," Annals of Operations Research, Springer, vol. 258(2), pages 655-677, November.
    11. Alibeyg, Armaghan & Contreras, Ivan & Fernández, Elena, 2018. "Exact solution of hub network design problems with profits," European Journal of Operational Research, Elsevier, vol. 266(1), pages 57-71.
    12. Milad Keshvari Fard & Laurent Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," Working Papers hal-01821280, HAL.
    13. Alumur, Sibel A. & Campbell, James F. & Contreras, Ivan & Kara, Bahar Y. & Marianov, Vladimir & O’Kelly, Morton E., 2021. "Perspectives on modeling hub location problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 1-17.
    14. Milad , Keshvari Fard & Laurent, Alfandari, 2018. "Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem," ESSEC Working Papers WP1805, ESSEC Research Center, ESSEC Business School.
    15. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2015. "Multi-level facility location as the maximization of a submodular set function," European Journal of Operational Research, Elsevier, vol. 247(3), pages 1013-1016.
    16. Zetina, Carlos Armando & Contreras, Ivan & Cordeau, Jean-François & Nikbakhsh, Ehsan, 2017. "Robust uncapacitated hub location," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 393-410.
    17. Hao Shen & Yong Liang & Zuo-Jun Max Shen, 2021. "Reliable Hub Location Model for Air Transportation Networks Under Random Disruptions," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 388-406, March.
    18. Pearce, Robin H. & Forbes, Michael, 2018. "Disaggregated Benders decomposition and branch-and-cut for solving the budget-constrained dynamic uncapacitated facility location and network design problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 78-88.

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