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Linear Facility Location in Three Dimensions---Models and Solution Methods

Author

Listed:
  • Jack Brimberg

    (University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada, and Groupe d'Études et de Recherche en Analyse des Décisions, Montreal, Quebec, Canada)

  • Henrik Juel

    (Technical University of Denmark, Lyngby, Denmark)

  • Anita Schöbel

    (University of Kaiserslautern, Kaiserslautern, Germany)

Abstract

We consider the problem of locating a line or a line segment in three-dimensional space, such that the sum of distances from the facility represented by the line (segment) to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and efficient solution methods are given.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:6:p:1050-1057
    DOI: 10.1287/opre.50.6.1050.354
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    References listed on IDEAS

    as
    1. Jack Brimberg & Robert F. Love, 1993. "Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with lp Distances," Operations Research, INFORMS, vol. 41(6), pages 1153-1163, December.
    2. Morris, James G. & Norback, John P., 1983. "Linear facility location -- Solving extensions of the basic problem," European Journal of Operational Research, Elsevier, vol. 12(1), pages 90-94, January.
    3. G O Wesolowsky, 1975. "Location of the Median Line for Weighted Points," Environment and Planning A, , vol. 7(2), pages 163-170, April.
    4. James G. Morris & John P. Norback, 1980. "A Simple Approach to Linear Facility Location," Transportation Science, INFORMS, vol. 14(1), pages 1-8, February.
    5. Hamacher, H. W. & Nickel, S., 1996. "Multicriteria planar location problems," European Journal of Operational Research, Elsevier, vol. 94(1), pages 66-86, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
    3. Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    4. Diaz-Banez, J.M. & Ramos, P.A. & Sabariego, P., 2007. "The maximin line problem with regional demand," European Journal of Operational Research, Elsevier, vol. 181(1), pages 20-29, August.

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