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Locating an axis-parallel rectangle on a Manhattan plane

Author

Listed:
  • Jack Brimberg
  • Henrik Juel
  • Mark-Christoph Körner
  • Anita Schöbel

Abstract

In this paper we consider the problem of locating an axis-parallel rectangle in the plane such that the sum of distances between the rectangle and a finite point set is minimized, where the distance is measured by the Manhattan norm ℓ 1 . In this way we solve an extension of the Weber problem to extensive facility location. As a model, our problem is appropriate for position sensing of rectangular objects. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:1:p:185-207
    DOI: 10.1007/s11750-012-0248-6
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    References listed on IDEAS

    as
    1. F. Plastria & E. Carrizosa, 2001. "Gauge Distances and Median Hyperplanes," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 173-182, July.
    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 & Henrik Juel & Anita Schöbel, 2007. "Locating a Circle on a Sphere," Operations Research, INFORMS, vol. 55(4), pages 782-791, August.
    4. Jack Brimberg & Henrik Juel & Anita Schöbel, 2002. "Linear Facility Location in Three Dimensions---Models and Solution Methods," Operations Research, INFORMS, vol. 50(6), pages 1050-1057, December.
    5. J. Brimberg & G.O. Wesolowsky, 2002. "Minisum Location with Closest Euclidean Distances," Annals of Operations Research, Springer, vol. 111(1), pages 151-165, March.
    6. G O Wesolowsky, 1975. "Location of the Median Line for Weighted Points," Environment and Planning A, , vol. 7(2), pages 163-170, April.
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    Cited by:

    1. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.

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