IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i7p647-665.html
   My bibliography  Save this article

Dominating sets for rectilinear center location problems with polyhedral barriers

Author

Listed:
  • P.M. Dearing
  • H.W. Hamacher
  • K. Klamroth

Abstract

In planar location problems with barriers one considers regions which are forbidden for the siting of new facilities as well as for trespassing. These problems are important since they model various actual applications. The resulting mathematical models have a nonconvex objective function and are therefore difficult to tackle using standard methods of location theory even in the case of simple barrier shapes and distance functions. For the case of center objectives with barrier distances obtained from the rectilinear or Manhattan metric, it is shown that the problem can be solved in polynomial time by identifying a dominating set. The resulting genuinely polynomial algorithm can be combined with bound computations which are derived from solving closely connected restricted location and network location problems. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 647–665, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10038

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:7:p:647-665
    DOI: 10.1002/nav.10038
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10038
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10038?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
    ---><---

    References listed on IDEAS

    as
    1. Horst Hamacher & Kathrin Klamroth, 2000. "Planar Weber location problems with barriers and block norms," Annals of Operations Research, Springer, vol. 96(1), pages 191-208, November.
    2. Katz, I. Norman & Cooper, Leon, 1981. "Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle," European Journal of Operational Research, Elsevier, vol. 6(2), pages 166-173, February.
    3. 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.
    4. Robert F. Love & Lowell Yerex, 1976. "An Application of a Facilities Location Model in the Prestressed Concrete Industry," Interfaces, INFORMS, vol. 6(4), pages 45-49, August.
    5. Klamroth, K., 2001. "A reduction result for location problems with polyhedral barriers," European Journal of Operational Research, Elsevier, vol. 130(3), pages 486-497, May.
    6. 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.
    7. Rajan Batta & Anjan Ghose & Udatta S. Palekar, 1989. "Locating Facilities on the Manhattan Metric with Arbitrarily Shaped Barriers and Convex Forbidden Regions," Transportation Science, INFORMS, vol. 23(1), pages 26-36, February.
    8. Viegas, Jose & Hansen, Pierre, 1985. "Finding shortest paths in the plane in the presence of barriers to travel (for any lp - norm)," European Journal of Operational Research, Elsevier, vol. 20(3), pages 373-381, June.
    9. Richard C. Larson & Ghazala Sadiq, 1983. "Facility Locations with the Manhattan Metric in the Presence of Barriers to Travel," Operations Research, INFORMS, vol. 31(4), pages 652-669, August.
    10. Butt, Steven E. & Cavalier, Tom M., 1996. "An efficient algorithm for facility location in the presence of forbidden regions," European Journal of Operational Research, Elsevier, vol. 90(1), pages 56-70, April.
    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. P. Dearing & K. Klamroth & R. Segars, 2005. "Planar Location Problems with Block Distance and Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 117-143, April.
    2. 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.
    3. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.
    4. L. Frießs & K. Klamroth & M. Sprau, 2005. "A Wavefront Approach to Center Location Problems with Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 35-48, April.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. P. Dearing & K. Klamroth & R. Segars, 2005. "Planar Location Problems with Block Distance and Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 117-143, April.
    6. 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.
    7. Klamroth, K., 2004. "Algebraic properties of location problems with one circular barrier," European Journal of Operational Research, Elsevier, vol. 154(1), pages 20-35, April.
    8. Canbolat, Mustafa S. & Wesolowsky, George O., 2010. "The rectilinear distance Weber problem in the presence of a probabilistic line barrier," European Journal of Operational Research, Elsevier, vol. 202(1), pages 114-121, April.
    9. Bischoff, M. & Klamroth, K., 2007. "An efficient solution method for Weber problems with barriers based on genetic algorithms," European Journal of Operational Research, Elsevier, vol. 177(1), pages 22-41, February.
    10. 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.
    11. Klamroth, K., 2001. "A reduction result for location problems with polyhedral barriers," European Journal of Operational Research, Elsevier, vol. 130(3), pages 486-497, May.
    12. 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.
    13. 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.
    14. Sarkar, Avijit & Batta, Rajan & Nagi, Rakesh, 2007. "Placing a finite size facility with a center objective on a rectangular plane with barriers," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1160-1176, June.
    15. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.
    16. 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.
    17. Zhang, Min & Savas, Selçuk & Batta, Rajan & Nagi, Rakesh, 2009. "Facility placement with sub-aisle design in an existing layout," European Journal of Operational Research, Elsevier, vol. 197(1), pages 154-165, August.
    18. 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.
    19. Butt, Steven E. & Cavalier, Tom M., 1997. "Facility location in the presence of congested regions with the rectilinear distance metric," Socio-Economic Planning Sciences, Elsevier, vol. 31(2), pages 103-113, June.
    20. Butt, Steven E. & Cavalier, Tom M., 1996. "An efficient algorithm for facility location in the presence of forbidden regions," European Journal of Operational Research, Elsevier, vol. 90(1), pages 56-70, April.

    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:wly:navres:v:49:y:2002:i:7:p:647-665. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.