IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v24y1976i4p628-642.html
   My bibliography  Save this article

Convex Location Problems on Tree Networks

Author

Listed:
  • P. M. Dearing

    (Cornell University, Ithaca, New York)

  • R. L. Francis

    (University of Florida, Gainesville, Florida)

  • T. J. Lowe

    (University of Florida, Gainesville, Florida)

Abstract

This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.

Suggested Citation

  • P. M. Dearing & R. L. Francis & T. J. Lowe, 1976. "Convex Location Problems on Tree Networks," Operations Research, INFORMS, vol. 24(4), pages 628-642, August.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:628-642
    DOI: 10.1287/opre.24.4.628
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.24.4.628
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.24.4.628?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
    ---><---

    Citations

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


    Cited by:

    1. 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.
    2. Dean P. Foster & Rakesh V. Vohra, 1998. "An Axiomatic Characterization of a Class of Locations in Tree Networks," Operations Research, INFORMS, vol. 46(3), pages 347-354, June.
    3. Hakimi, S.Louis, 1983. "Network location theory and contingency planning," Energy, Elsevier, vol. 8(8), pages 697-702.
    4. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    5. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    6. M. C. López-de-los-Mozos & Juan A. Mesa, 2022. "To stop or not to stop: a time-constrained trip covering location problem on a tree network," Annals of Operations Research, Springer, vol. 316(2), pages 1039-1061, September.
    7. Mark-Christoph Körner & Juan Mesa & Federico Perea & Anita Schöbel & Daniel Scholz, 2014. "A maximum trip covering location problem with an alternative mode of transportation on tree networks and segments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 227-253, April.
    8. Burkard, R. E. & Dollani, Helidon, 2003. "Center problems with pos/neg weights on trees," European Journal of Operational Research, Elsevier, vol. 145(3), pages 483-495, March.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:24:y:1976:i:4:p:628-642. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.