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A Simple Approach to Linear Facility Location

Author

Listed:
  • James G. Morris

    (University of Wisconsin-Madison, Madison, Wisconsin)

  • John P. Norback

    (University of Wisconsin-Madison, Madison, Wisconsin)

Abstract

A linear facility is to be located to minimize weighted shortest distances from demand points to the facility. This paper reports on a naive but effective approach. The approach is simple to understand and computer implementation is straightforward. A graphical version may also be used. The approach generalizes to models with more elaborate cost structures than simple proportionality to distance. The analysis addresses uniqueness issues and characterizes the line with respect to other notions of best linear fits.

Suggested Citation

  • James G. Morris & John P. Norback, 1980. "A Simple Approach to Linear Facility Location," Transportation Science, INFORMS, vol. 14(1), pages 1-8, February.
    • Handle: RePEc:inm:ortrsc:v:14:y:1980:i:1:p:1-8
    DOI: 10.1287/trsc.14.1.1
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    Cited by:

    1. Alessandro Agnetis & Pitu B. Mirchandani & Andrea Pacifici, 2002. "Partitioning of biweighted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 143-158, March.
    2. Jianping Li & Suding Liu & Junran Lichen & Wencheng Wang & Yujie Zheng, 2020. "Approximation algorithms for solving the 1-line Euclidean minimum Steiner tree problem," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 492-508, February.
    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. & Mesa, J. A. & Schobel, A., 2004. "Continuous location of dimensional structures," European Journal of Operational Research, Elsevier, vol. 152(1), pages 22-44, January.
    5. Jack Brimberg & Henrik Juel & Anita Schöbel, 2007. "Locating a Circle on a Sphere," Operations Research, INFORMS, vol. 55(4), pages 782-791, August.
    6. Schobel, Anita, 1998. "Locating least-distant lines in the plane," European Journal of Operational Research, Elsevier, vol. 106(1), pages 152-159, April.
    7. Jianping Li & Junran Lichen & Wencheng Wang & Jean Yeh & YeongNan Yeh & Xingxing Yu & Yujie Zheng, 2022. "1-line minimum rectilinear steiner trees and related problems," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2832-2852, November.
    8. 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.
    9. Jack Brimberg & Robert Schieweck & Anita Schöbel, 2015. "Locating a median line with partial coverage distance," Journal of Global Optimization, Springer, vol. 62(2), pages 371-389, June.
    10. 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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