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Technical Note—On Location Dominance on Spherical Surfaces

Author

Listed:
  • Zvi Drezner

    (University of Michigan, Dearborn, Michigan)

Abstract

In a recent paper Aly et al. (Aly, A. A., D. C. Kay, D. W. Litwhiler, Jr. 1979. Location dominance on spherical surfaces. Opns. Res. 27 972–981.) proved that an optimal solution to a “minisum” problem on a sphere must lie in the convex hull of the demand points if the demand points are not located entirely on a great circle arc. The case when all demand points are on a great circle arc remains an open question. In this note we prove that if demand points are located on a great circle arc, so is the optimal solution point.

Suggested Citation

  • Zvi Drezner, 1981. "Technical Note—On Location Dominance on Spherical Surfaces," Operations Research, INFORMS, vol. 29(6), pages 1218-1219, December.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:6:p:1218-1219
    DOI: 10.1287/opre.29.6.1218
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    Citations

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    Cited by:

    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. 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. 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.
    4. Zvi Drezner, 1988. "Location strategies for satellites' orbits," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 503-512, October.

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