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Locating a Circle on a Sphere

Author

Listed:
  • Jack Brimberg

    (Royal Military College of Canada, Kingston, Ontario, Canada K7K 7B4, and Groupe d’Études et de Recherche en Analyse des Décisions, Montreal, Quebec, Canada H3T 2A7)

  • Henrik Juel

    (Technical University of Denmark, Informatics and Mathematical Modelling, DK-2800 Kongens Lyngby, Denmark)

  • Anita Schöbel

    (Georg-August-Universität Göttingen, Göttingen, Germany)

Abstract

We consider the problem of locating a spherical circle with respect to existing facilities on a sphere, such that the sum of distances between the circle and the facilities is minimized or such that the maximum distance is minimized. The problem properties are analyzed, and we give solution procedures. When the circle to be located is restricted to be a great circle, some simplifications are possible. The models may be used in preliminary studies on the location of large linear facilities on the earth’s surface, such as superhighways, pipelines, and transmission lines, or in totally different contexts such as search-and-rescue missions and medical or biological studies.

Suggested Citation

  • Jack Brimberg & Henrik Juel & Anita Schöbel, 2007. "Locating a Circle on a Sphere," Operations Research, INFORMS, vol. 55(4), pages 782-791, August.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:4:p:782-791
    DOI: 10.1287/opre.1070.0396
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    References listed on IDEAS

    as
    1. Wesolowsky, G. O., 1982. "Location problems on a sphere," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 495-508, November.
    2. Morris, James G. & Norback, John P., 1983. "Linear facility location -- Solving extensions of the basic problem," European Journal of Operational Research, Elsevier, vol. 12(1), pages 90-94, January.
    3. G O Wesolowsky, 1975. "Location of the Median Line for Weighted Points," Environment and Planning A, , vol. 7(2), pages 163-170, April.
    4. James G. Morris & John P. Norback, 1980. "A Simple Approach to Linear Facility Location," Transportation Science, INFORMS, vol. 14(1), pages 1-8, February.
    5. Diaz-Banez, J. M. & Mesa, J. A. & Schobel, A., 2004. "Continuous location of dimensional structures," European Journal of Operational Research, Elsevier, vol. 152(1), pages 22-44, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jack Brimberg & Henrik Juel & Mark-Christoph Körner & Anita Schöbel, 2014. "Locating an axis-parallel rectangle on a Manhattan plane," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 185-207, April.
    2. Mark-Christoph Körner & Jack Brimberg & Henrik Juel & Anita Schöbel, 2011. "Geometric fit of a point set by generalized circles," Journal of Global Optimization, Springer, vol. 51(1), pages 115-132, September.
    3. Jack Brimberg & Robert Schieweck & Anita Schöbel, 2015. "Locating a median line with partial coverage distance," Journal of Global Optimization, Springer, vol. 62(2), pages 371-389, June.

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