IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v28y1994i1p70-76.html
   My bibliography  Save this article

Technical Note—Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel

Author

Listed:
  • Y. P. Aneja

    (Faculty of Business, University of Windsor, Windsor, Ontario, Canada N9B 3P4)

  • M. Parlar

    (Faculty of Business, McMaster University, Hamilton, Ontario, Canada L8S 4M4)

Abstract

We describe algorithms for optimal single facility location problems with forbidden regions and barriers to travel. The former are those where location is not permitted, but one can travel through them, e.g., a lake. The latter are the regions where neither location nor travel is permitted, e.g., large parks in a city. Using the convexity properties of the objective function, in the first case, we develop an algorithm for finding the optimal solution. The objective function in the barrier case is shown to be non-convex. We use the concept of visibility to create a network with the location point as the source and use Dijkstra's algorithm to compute the shortest distance to all the other demand points. Using simulated annealing we find an approximate optimal solution. Numerical examples illustrate the implementation of the algorithms.

Suggested Citation

  • Y. P. Aneja & M. Parlar, 1994. "Technical Note—Algorithms for Weber Facility Location in the Presence of Forbidden Regions and/or Barriers to Travel," Transportation Science, INFORMS, vol. 28(1), pages 70-76, February.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:1:p:70-76
    DOI: 10.1287/trsc.28.1.70
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.28.1.70
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.28.1.70?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. Selçuk Savaş & Rajan Batta & Rakesh Nagi, 2002. "Finite-Size Facility Placement in the Presence of Barriers to Rectilinear Travel," Operations Research, INFORMS, vol. 50(6), pages 1018-1031, December.
    2. Oğuz, Murat & Bektaş, Tolga & Bennell, Julia A., 2018. "Multicommodity flows and Benders decomposition for restricted continuous location problems," European Journal of Operational Research, Elsevier, vol. 266(3), pages 851-863.
    3. J. Brimberg & S. Salhi, 2005. "A Continuous Location-Allocation Problem with Zone-Dependent Fixed Cost," Annals of Operations Research, Springer, vol. 136(1), pages 99-115, April.
    4. Kathrin Klamroth & Margaret M. Wiecek, 2002. "A Bi-Objective Median Location Problem With a Line Barrier," Operations Research, INFORMS, vol. 50(4), pages 670-679, August.
    5. Masashi Miyagawa, 2012. "Rectilinear distance to a facility in the presence of a square barrier," Annals of Operations Research, Springer, vol. 196(1), pages 443-458, July.
    6. Sándor P. Fekete & Joseph S. B. Mitchell & Karin Beurer, 2005. "On the Continuous Fermat-Weber Problem," Operations Research, INFORMS, vol. 53(1), pages 61-76, February.
    7. Andrea Maier & Horst W. Hamacher, 2019. "Complexity results on planar multifacility location problems with forbidden regions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 433-484, June.
    8. Murat Oğuz & Tolga Bektaş & Julia A Bennell & Jörg Fliege, 2016. "A modelling framework for solving restricted planar location problems using phi-objects," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1080-1096, August.
    9. Amiri-Aref, Mehdi & Farahani, Reza Zanjirani & Hewitt, Mike & Klibi, Walid, 2019. "Equitable location of facilities in a region with probabilistic barriers to travel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 66-85.
    10. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.
    11. P.M. Dearing & H.W. Hamacher & K. Klamroth, 2002. "Dominating sets for rectilinear center location problems with polyhedral barriers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 647-665, October.
    12. Malgorzata Miklas-Kalczynska & Pawel Kalczynski, 2024. "Multiple obnoxious facility location: the case of protected areas," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    13. H. W. Hamacher & S. Nickel, 1995. "Restricted planar location problems and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 967-992, September.
    14. Pawel Kalczynski & Zvi Drezner, 2021. "The obnoxious facilities planar p-median problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 577-593, June.
    15. R. Blanquero & E. Carrizosa, 2000. "Optimization of the Norm of a Vector-Valued DC Function and Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 245-260, November.

    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:ortrsc:v:28:y:1994:i:1:p:70-76. 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.