IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v136y2005i1p81-9710.1007-s10479-005-2040-6.html
   My bibliography  Save this article

The Stochastic Location-Assignment Problem on a Tree

Author

Listed:
  • Ting Zeng
  • James Ward

Abstract

In the assignment problem units of supply are assigned on a one-to-one basis to units of demand so as to minimize the sum of the cost associated with each supply-to-demand matched pair. Defined on a network, the supplies and demands are located at vertices and the cost of a supply-to-demand matched pair is the distance between them. This paper considers a two-stage stochastic program for locating the units of supply based upon only a probabilistic characterization of demand. The objective of the first-stage location problem is to minimize the expected cost of the second-stage assignment problem. Principal results include showing that the problem is NP-hard on a general network, has a simple solution procedure on a line network, and is solvable by a low order polynomial greedy procedure on a tree network. Potential applications are discussed. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Ting Zeng & James Ward, 2005. "The Stochastic Location-Assignment Problem on a Tree," Annals of Operations Research, Springer, vol. 136(1), pages 81-97, April.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:81-97:10.1007/s10479-005-2040-6
    DOI: 10.1007/s10479-005-2040-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-005-2040-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-005-2040-6?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. Louveaux, F. & Thisse, J.-F., 1984. "Production and location on a network under demand uncertainty," LIDAM Discussion Papers CORE 1984001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Oded Berman & Richard C. Larson & Samuel S. Chiu, 1985. "Optimal Server Location on a Network Operating as an M / G /1 Queue," Operations Research, INFORMS, vol. 33(4), pages 746-771, August.
    3. Margaret L. Brandeau & Samuel S. Chiu, 1989. "An Overview of Representative Problems in Location Research," Management Science, INFORMS, vol. 35(6), pages 645-674, June.
    4. Gilbert Laporte & François V. Louveaux & Luc van Hamme, 1994. "Exact Solution to a Location Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 28(2), pages 95-103, May.
    5. Donald Erlenkotter, 1978. "A Dual-Based Procedure for Uncapacitated Facility Location," Operations Research, INFORMS, vol. 26(6), pages 992-1009, December.
    6. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    7. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
    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. Zuo-Jun Max Shen & Roger Lezhou Zhan & Jiawei Zhang, 2011. "The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 470-482, August.
    2. Kannan Viswanath & James Ward, 2010. "Stochastic Location-assignment on an Interval with Sequential Arrivals," Networks and Spatial Economics, Springer, vol. 10(3), pages 389-410, September.
    3. Liming Yao & Zhongwen Xu & Ziqiang Zeng, 2020. "A Soft‐Path Solution to Risk Reduction by Modeling Medical Waste Disposal Center Location‐Allocation Optimization," Risk Analysis, John Wiley & Sons, vol. 40(9), pages 1863-1886, September.

    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. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    2. 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.
    3. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    4. Vladimir Marianov & Daniel Serra, 2009. "Median problems in networks," Economics Working Papers 1151, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Renata Turkeš & Kenneth Sörensen & Daniel Palhazi Cuervo, 2021. "A matheuristic for the stochastic facility location problem," Journal of Heuristics, Springer, vol. 27(4), pages 649-694, August.
    6. Oded Berman & Dmitry Krass & Mozart B. C. Menezes, 2007. "Facility Reliability Issues in Network p -Median Problems: Strategic Centralization and Co-Location Effects," Operations Research, INFORMS, vol. 55(2), pages 332-350, April.
    7. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    8. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    9. H K Smith & G Laporte & P R Harper, 2009. "Locational analysis: highlights of growth to maturity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 140-148, May.
    10. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Venkateshan, Prahalad & Mathur, Kamlesh & Ballou, Ronald H., 2010. "Locating and staffing service centers under service level constraints," European Journal of Operational Research, Elsevier, vol. 201(1), pages 55-70, February.
    12. Hakimi, S.Louis, 1983. "Network location theory and contingency planning," Energy, Elsevier, vol. 8(8), pages 697-702.
    13. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
    14. Mozhu Wang & Jianming Yao, 2023. "A reliable location design of unmanned vending machines based on customer satisfaction," Electronic Commerce Research, Springer, vol. 23(1), pages 541-575, March.
    15. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    16. Xu, Jianhua & Johnson, Michael P. & Fischbeck, Paul S. & Small, Mitchell J. & VanBriesen, Jeanne M., 2010. "Robust placement of sensors in dynamic water distribution systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 707-716, May.
    17. Mark S. Daskin, 2008. "What you should know about location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 283-294, June.
    18. George L. Vairaktarakis & Panagiotis Kouvelis, 1999. "Incorporation dynamic aspects and uncertainty in 1‐median location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 147-168, March.
    19. Dolores R. Santos Peñate & María del Carmen Martel Escobar, 1996. "Modelos de localización para la planificación escolar en el contexto de la LOGSE," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 5, pages 139-159, Junio.
    20. F Silva & D Serra, 2008. "Locating emergency services with different priorities: the priority queuing covering location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1229-1238, September.

    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:136:y:2005:i:1:p:81-97:10.1007/s10479-005-2040-6. 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.