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

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  • 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
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    References listed on IDEAS

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    1. Zvi Drezner, 1981. "Technical Note—On Location Dominance on Spherical Surfaces," Operations Research, INFORMS, vol. 29(6), pages 1218-1219, December.
    2. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    3. 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.
    4. 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.
    5. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    6. 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.
    7. 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.
    8. 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.
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    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.

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