Location and shape of a rectangular facility in ℛn. Convexity properties

Location and shape of a rectangular facility in ℛn. Convexity properties

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Article ID: iaor2000697
Country: Netherlands
Volume: 83
Issue: 2
Start Page Number: 277
End Page Number: 290
Publication Date: Oct 1998
Journal: Mathematical Programming
Authors: , ,
Keywords: programming: mathematical, facilities
Abstract:

In this paper we address a generalization of the Weber problem, in which we seek for the center and the shape of a rectangle (the facility) minimizing the average distance to a given set (the demand-set) which is not assumed to be finite. Some theoretical properties of the average distance are studied, and an expression for its gradient, involving solely expected distances to rectangles, is obtained. This enables the resolution of the problem by standard optimization techniques.

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