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Technical Note—A New Norm for Measuring Distance Which Yields Linear Location Problems

Author

Listed:
  • J. E. Ward

    (Rensselaer Polytechnic Institute, Troy, New York)

  • R. E. Wendell

    (University of Pittsburgh, Pittsburgh, Pennsylvania)

Abstract

We propose a new norm, called the one-infinity norm, for characterizing distance in facility location problems. This new norm, which is a hybrid version of the rectilinear and Tchebycheff norms, not only gives a good characterization of distance (as compared, for example, to results by Love and Morris) but also has two alternate interpretations of travel. Furthermore, it yields linear programming formulations of location problems.

Suggested Citation

  • J. E. Ward & R. E. Wendell, 1980. "Technical Note—A New Norm for Measuring Distance Which Yields Linear Location Problems," Operations Research, INFORMS, vol. 28(3-part-ii), pages 836-844, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-ii:p:836-844
    DOI: 10.1287/opre.28.3.836
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    Cited by:

    1. Gilbert Laporte & Juan Mesa & Francisco Ortega & Ignacio Sevillano, 2005. "Maximizing Trip Coverage in the Location of a Single Rapid Transit Alignment," Annals of Operations Research, Springer, vol. 136(1), pages 49-63, April.
    2. H Younies & G O Wesolowsky, 2007. "Planar maximal covering location problem under block norm distance measure," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 740-750, June.
    3. Jack Brimberg & Robert F. Love, 1991. "Estimating travel distances by the weighted lp norm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 241-259, April.
    4. Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    5. Enrique R. Venta & Francis J. Nourie, 1989. "Facility location on a grid with a diagonal line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 709-717, October.

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