IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v211y2013i1p193-20710.1007-s10479-013-1394-4.html
   My bibliography  Save this article

The planar hub location problem: a probabilistic clustering approach

Author

Listed:
  • Cem Iyigun

Abstract

Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by visiting any of the hubs. The travel cost between hubs is discounted with a factor. It is assumed that each point can be served by multiple hubs. We propose a probabilistic clustering method for the planar hub-location problem which is analogous to the method of Iyigun and Ben-Israel (in Operations Research Letters 38, 207–214, 2010 ; Computational Optmization and Applications, 2013 ) for the solution of the multi-facility location problem. The proposed method is an iterative probabilistic approach assuming that all trips can be taken with probabilities that depend on the travel costs based on the hub locations. Each hub location is the convex combination of all data points and other hubs. The probabilities are updated at each iteration together with the hub locations. Computations stop when the hub locations stop moving. Fermat-Weber problem and multi-facility location problem are the special cases of the proposed approach. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Cem Iyigun, 2013. "The planar hub location problem: a probabilistic clustering approach," Annals of Operations Research, Springer, vol. 211(1), pages 193-207, December.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:193-207:10.1007/s10479-013-1394-4
    DOI: 10.1007/s10479-013-1394-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1394-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-013-1394-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Turgut Aykin, 1988. "On the Location of Hub Facilities," Transportation Science, INFORMS, vol. 22(2), pages 155-157, May.
    2. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    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. 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.
    5. Turgut Aykin & Gary F. Brown, 1992. "Interacting New Facilities and Location-Allocation Problems," Transportation Science, INFORMS, vol. 26(3), pages 212-222, August.
    6. 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.
    7. Aykin, Turgut, 1995. "The hub location and routing problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 200-219, May.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yu, Bin & Zhu, Hanbing & Cai, Wanjun & Ma, Ning & Kuang, Qiji & Yao, Baozhen, 2013. "Two-phase optimization approach to transit hub location – the case of Dalian," Journal of Transport Geography, Elsevier, vol. 33(C), pages 62-71.
    2. 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.
    3. García, Sergio & Landete, Mercedes & Marín, Alfredo, 2012. "New formulation and a branch-and-cut algorithm for the multiple allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 48-57.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Taherkhani, Gita & Alumur, Sibel A., 2019. "Profit maximizing hub location problems," Omega, Elsevier, vol. 86(C), pages 1-15.
    9. Erdoğan, Güneş & Battarra, Maria & Rodríguez-Chía, Antonio M., 2022. "The hub location and pricing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1035-1047.
    10. Tiwari, Richa & Jayaswal, Sachin & Sinha, Ankur, 2021. "Competitive hub location problem: Model and solution approaches," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 237-261.
    11. Marianov, Vladimir & Serra, Daniel & ReVelle, Charles, 1999. "Location of hubs in a competitive environment," European Journal of Operational Research, Elsevier, vol. 114(2), pages 363-371, April.
    12. An, Yu & Zhang, Yu & Zeng, Bo, 2015. "The reliable hub-and-spoke design problem: Models and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 103-122.
    13. 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.
    14. 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.
    15. S Alumur & B Y Kara, 2009. "A hub covering network design problem for cargo applications in Turkey," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1349-1359, October.
    16. Olivera Janković & Stefan Mišković & Zorica Stanimirović & Raca Todosijević, 2017. "Novel formulations and VNS-based heuristics for single and multiple allocation p-hub maximal covering problems," Annals of Operations Research, Springer, vol. 259(1), pages 191-216, December.
    17. 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.
    18. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    19. 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.
    20. Soylu, Banu & Katip, Hatice, 2019. "A multiobjective hub-airport location problem for an airline network design," European Journal of Operational Research, Elsevier, vol. 277(2), pages 412-425.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:193-207:10.1007/s10479-013-1394-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.