IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v40y1993i4p543-552.html
   My bibliography  Save this article

A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere

Author

Listed:
  • Minnie H. Patel
  • Deborah L. Nettles
  • Stuart J. Deutsch

Abstract

Whenever n demand points are located on a hemisphere, spherical location problems can be solved easily using geometrical methods or mathematical programming. A method based on a linear programming formulation with four constraints is presented to determine whether n demand points are on a hemisphere. The formulation is derived from a modified minimax spherical location problem whose Karush‐Kuhn‐Tucker conditions are the constraints of the linear program. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:4:p:543-552
    DOI: 10.1002/1520-6750(199306)40:43.0.CO;2-4
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199306)40:43.0.CO;2-4
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199306)40:43.0.CO;2-4?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. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    2. Zvi Drezner & George O. Wesolowsky, 1983. "Minimax and maximin facility location problems on a sphere," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 305-312, June.
    3. Zvi Drezner, 1981. "Technical Note—On Location Dominance on Spherical Surfaces," Operations Research, INFORMS, vol. 29(6), pages 1218-1219, December.
    4. R. Chen & G. Y. Handler, 1987. "Relaxation method for the solution of the minimax location‐allocation problem in euclidean space," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 775-788, December.
    5. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    6. Wen-Hsien Tsai & Maw-Sheng Chern & Tsong-Ming Lin, 1991. "Technical Note—An Algorithm for Determining Whether m Given Demand Points Are on a Hemisphere or Not," Transportation Science, INFORMS, vol. 25(1), pages 91-97, February.
    7. R. K. Chakraborty & P. K. Chaudhuri, 1981. "Letter to the Editor---Note on Geometrical Solution for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 15(2), pages 164-166, May.
    8. 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.
    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. Mordechai Jaeger & Jeff Goldberg, 1997. "Polynomial algorithms for center location on spheres," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(4), pages 341-352, June.

    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. 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.
    2. Mordechai Jaeger & Jeff Goldberg, 1997. "Polynomial algorithms for center location on spheres," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(4), pages 341-352, June.
    3. Zvi Drezner, 1988. "Location strategies for satellites' orbits," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 503-512, October.
    4. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.
    5. Mark E. Cawood & P. M. Dearing, 2024. "The weighted Euclidean one-center problem in $${\mathbb {R}}^n$$ R n," Computational Optimization and Applications, Springer, vol. 89(2), pages 553-574, November.
    6. 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.
    7. Franco Rubio-López & Obidio Rubio & Rolando Urtecho Vidaurre, 2023. "The Inverse Weber Problem on the Plane and the Sphere," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    8. Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Murray, Alan T., 2021. "Contemporary optimization application through geographic information systems," Omega, Elsevier, vol. 99(C).
    15. Zvi Drezner & Vladimir Marianov & George O. Wesolowsky, 2016. "Maximizing the minimum cover probability by emergency facilities," Annals of Operations Research, Springer, vol. 246(1), pages 349-362, November.
    16. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2023. "Obnoxious facility location in multiple dimensional space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-354, July.
    17. Drezner, Zvi & Guyse, Jeffery, 1999. "Application of decision analysis techniques to the Weber facility location problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 69-79, July.
    18. Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    19. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
    20. R. Chen & Y. Handler, 1993. "The conditional p‐center problem in the plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 117-127, February.

    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:40:y:1993:i:4:p:543-552. 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.