Locating a minisum annulus: a new partial coverage distance model

Loay Alkhalifa () and Jack Brimberg ()
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Loay Alkhalifa: The Royal Military College of Canada
Jack Brimberg: The Royal Military College of Canada

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 25, issue 2, No 11, 373-393

Abstract: Abstract The problem is to find the best location in the plane of a minisum annulus with fixed width using a partial coverage distance model. Using the concept of partial coverage distance, those demand points within the area of the annulus are served at no cost, while for ‘uncovered’ demand points there will be additional costs proportional to their distances to the annulus. The objective of the problem is to locate the annulus such that the sum of distances from the uncovered demand points to the annulus (covering area) is minimized. The distance is measured by the Euclidean norm. We discuss the case where the radius of the inner circle of the annulus is variable, and prove that at least two demand points must be on the boundary of any optimal annulus. An algorithm to solve the problem is derived based on this result.

Keywords: Median circle problem; Covering location models; Minisum annulus; 90B85 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11750-016-0435-y

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