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The Tree of Hubs Location Problem

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  • Contreras, Ivan
  • Fernández, Elena
  • Marín, Alfredo

Abstract

This paper presents the Tree of Hubs Location Problem. It is a network hub location problem with single assignment where a fixed number of hubs have to be located, with the particularity that it is required that the hubs are connected by means of a tree. The problem combines several aspects of location, network design and routing problems. Potential applications appear in telecommunications and transportation systems, when set-up costs for links between hubs are so high that full interconnection between hub nodes is prohibitive. We propose an integer programming formulation for the problem. Furthermore, we present some families of valid inequalities that reinforce the formulation and we give an exact separation procedure for them. Finally, we present computational results using the well-known AP and CAB data sets.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:390-400
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    References listed on IDEAS

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    10. 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.
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    Citations

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    Cited by:

    1. Contreras, Ivan & Fernández, Elena, 2012. "General network design: A unified view of combined location and network design problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 680-697.
    2. Meng, Qiang & Wang, Xinchang, 2011. "Intermodal hub-and-spoke network design: Incorporating multiple stakeholders and multi-type containers," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 724-742, May.
    3. 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.
    4. Yaman, Hande, 2011. "Allocation strategies in hub networks," European Journal of Operational Research, Elsevier, vol. 211(3), pages 442-451, June.
    5. Aros-Vera, Felipe & Marianov, Vladimir & Mitchell, John E., 2013. "p-Hub approach for the optimal park-and-ride facility location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 277-285.
    6. Alumur, Sibel A. & Kara, Bahar Y. & Karasan, Oya E., 2012. "Multimodal hub location and hub network design," Omega, Elsevier, vol. 40(6), pages 927-939.
    7. 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.
    8. 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.
    9. Alumur, Sibel A. & Yaman, Hande & Kara, Bahar Y., 2012. "Hierarchical multimodal hub location problem with time-definite deliveries," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(6), pages 1107-1120.
    10. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-2091-2 is not listed on IDEAS
    11. Alumur, Sibel A. & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2012. "Hub location under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 529-543.
    12. Liao, Chung-Shou & Hsieh, Tsung-Jung & Guo, Xian-Chang & Liu, Jian-Hong & Chu, Chia-Chi, 2015. "Hybrid search for the optimal PMU placement problem on a power grid," European Journal of Operational Research, Elsevier, vol. 243(3), pages 985-994.
    13. repec:eee:ejores:v:266:y:2018:i:1:p:57-71 is not listed on IDEAS
    14. repec:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2730-x is not listed on IDEAS
    15. Gelareh, Shahin & Neamatian Monemi, Rahimeh & Nickel, Stefan, 2015. "Multi-period hub location problems in transportation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 67-94.
    16. 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.
    17. Valentin CÂRLAN & Eugen ROªCA & Mircea Augustin ROªCA, 2014. "Urban And Peri-Urban Passenger Transport Integration Through Hub-And-Spoke-Network," Theoretical and Empirical Researches in Urban Management, Research Centre in Public Administration and Public Services, Bucharest, Romania, vol. 9(1), pages 74-84, February.
    18. repec:spr:annopr:v:246:y:2016:i:1:d:10.1007_s10479-015-1805-9 is not listed on IDEAS
    19. Lüer-Villagra, Armin & Marianov, Vladimir, 2013. "A competitive hub location and pricing problem," European Journal of Operational Research, Elsevier, vol. 231(3), pages 734-744.
    20. Yazar, Başak & Arslan, Okan & Karaşan, Oya Ekin & Kara, Bahar Y., 2016. "Fiber optical network design problems: A case for Turkey," Omega, Elsevier, vol. 63(C), pages 23-40.
    21. 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.

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