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

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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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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, c/Tarfia s/n, 41012, Sevilla, Spain

    E. Carrizosa & J. Puerto

  2. Departamento de Matemáticas, Escuela Politécnica de Cádiz, c/Sacramento 82, 11002, Cádiz, Spain

    M. Muñoz-Márquez

Authors
  1. E. Carrizosa
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  2. M. Muñoz-Márquez
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  3. J. Puerto
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Corresponding author

Correspondence to M. Muñoz-Márquez.

Additional information

The research of the authors is partially supported by Spanish DGICYT grant PB93-0927.

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Carrizosa, E., Muñoz-Márquez, M. & Puerto, J. Location and shape of a rectangular facility in ℝn. Convexity properties. Convexity properties. Mathematical Programming 83, 277–290 (1998). https://doi.org/10.1007/BF02680563

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  • DOI: https://doi.org/10.1007/BF02680563

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