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Locating a Circle on a Sphere

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
Technical University of Denmark, Informatics and Mathematical Modelling, DK-2800 Kongens Lyngby, Denmark
Georg-August-Universität Göttingen, Göttingen, Germany
jack.brimberg{at}rmc.ca
hj{at}imm.dtu.dk
schoebel{at}math.uni-goettingen.de

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.

Subject classifications: facilities/equipment planning; location; continuous; circle on sphere.
History: Received May 2004; revision received February 2006; accepted March 2006.

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