IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v136y2008i2d10.1007_s10957-007-9293-y.html
   My bibliography  Save this article

Locating a Central Hunter on the Plane

Author

Listed:
  • M. Cera

    (University of Seville)

  • J. A. Mesa

    (University of Seville)

  • F. A. Ortega

    (University of Seville)

  • F. Plastria

    (Vrije Universiteit)

Abstract

Protection, surveillance or other types of coverage services of mobile points call for different, asymmetric distance measures than the traditional Euclidean, rectangular or other norms used for fixed points. In this paper, the destinations are mobile points (prey) moving at fixed speeds and directions and the facility (hunter) can capture them using one of two possible strategies: either it is smart, predicting the prey’s movement in order to minimize the time needed to capture it, or it is dumb, following a pursuit curve, by moving at any moment in the direction of the prey. In either case, the hunter location in a plane is sought in order to minimize the maximum time of capture of any prey. An efficient solution algorithm is developed that uses the particular geometry that both versions of this problem possess. In the case of unpredictable movement of prey, a worst-case type solution is proposed, which reduces to the well-known weighted Euclidean minimax location problem.

Suggested Citation

  • M. Cera & J. A. Mesa & F. A. Ortega & F. Plastria, 2008. "Locating a Central Hunter on the Plane," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 155-166, February.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9293-y
    DOI: 10.1007/s10957-007-9293-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9293-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-007-9293-y?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. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    2. Christakis Charalambous, 1982. "Technical Note—Extension of the Elzinga-Hearn Algorithm to the Weighted Case," Operations Research, INFORMS, vol. 30(3), pages 591-594, June.
    3. Nimrod Megiddo, 1983. "The Weighted Euclidean 1-Center Problem," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 498-504, November.
    4. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    5. Pelegrin, Blas & Michelot, Christian & Plastria, Frank, 1985. "On the uniqueness of optimal solutions in continuous location theory," European Journal of Operational Research, Elsevier, vol. 20(3), pages 327-331, June.
    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. Plastria, F., 2012. "A note towards improved homeland defense," Omega, Elsevier, vol. 40(2), pages 244-248, April.
    2. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.

    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. Minnie H. Patel & Deborah L. Nettles & Stuart J. Deutsch, 1993. "A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 543-552, June.
    2. Blanco, Víctor & Puerto, Justo, 2021. "Covering problems with polyellipsoids: A location analysis perspective," European Journal of Operational Research, Elsevier, vol. 289(1), pages 44-58.
    3. Hamacher, H. W. & Nickel, S., 1996. "Multicriteria planar location problems," European Journal of Operational Research, Elsevier, vol. 94(1), pages 66-86, October.
    4. Piyush Kumar & E. Alper Yıldırım, 2009. "An Algorithm and a Core Set Result for the Weighted Euclidean One-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 614-629, November.
    5. P. M. Dearing & Mark E. Cawood, 2023. "The minimum covering Euclidean ball of a set of Euclidean balls in $$I\!\!R^n$$ I R n," Annals of Operations Research, Springer, vol. 322(2), pages 631-659, March.
    6. Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    7. Okabe, Atsuyuki & Suzuki, Atsuo, 1997. "Locational optimization problems solved through Voronoi diagrams," European Journal of Operational Research, Elsevier, vol. 98(3), pages 445-456, May.
    8. P. Dearing & Andrea Smith, 2013. "A dual algorithm for the minimum covering weighted ball problem in $${\mathbb{R}^n}$$," Journal of Global Optimization, Springer, vol. 55(2), pages 261-278, February.
    9. Elshaikh, Abdalla & Salhi, Said & Nagy, Gábor, 2015. "The continuous p-centre problem: An investigation into variable neighbourhood search with memory," European Journal of Operational Research, Elsevier, vol. 241(3), pages 606-621.
    10. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    11. Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.
    12. Liu, Yulin & Hansen, Mark & Ball, Michael O. & Lovell, David J., 2021. "Causal analysis of flight en route inefficiency," Transportation Research Part B: Methodological, Elsevier, vol. 151(C), pages 91-115.
    13. Wei-jie Cong & Le Wang & Hui Sun, 2020. "Rank-two update algorithm versus Frank–Wolfe algorithm with away steps for the weighted Euclidean one-center problem," Computational Optimization and Applications, Springer, vol. 75(1), pages 237-262, January.
    14. Frank Plastria & Tom Blockmans, 2015. "Multidimensional Theoretic Consensus Reachability: The Impact of Distance Selection and Issue Saliences," Group Decision and Negotiation, Springer, vol. 24(1), pages 1-44, January.
    15. P. M. Dearing & Pietro Belotti & Andrea M. Smith, 2016. "A primal algorithm for the weighted minimum covering ball problem in $$\mathbb {R}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 466-492, July.
    16. Stefan Nickel & Justo Puerto & Antonio M. Rodriguez-Chia, 2003. "An Approach to Location Models Involving Sets as Existing Facilities," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 693-715, November.
    17. O Berman & Z Drezner, 2003. "A probabilistic one-centre location problem on a network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 871-877, August.
    18. Murray, Alan T., 2021. "Contemporary optimization application through geographic information systems," Omega, Elsevier, vol. 99(C).
    19. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    20. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.

    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:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9293-y. 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.