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General Considerations on the Use of the Weighted lp Norm as an Empirical Distance Measure

Author

Listed:
  • J. Brimberg

    (Royal Military College of Canada, Kingston, Ontario K7K 5L0)

  • R. F. Love

    (Faculty of Business, McMaster University, Hamilton, Ontario L8S 4M4)

Abstract

In this paper, we present a general procedure for fitting the weighted l p norm in order to estimate travel distances in a distribution system. An important finding of our study is that the search for the best-fitting value of the parameter p can be restricted to the interval (0, 2], provided the reference axes of the distance function are oriented to match the directional bias inherent in the transportation network. The advantages of our methodology and particularly the importance of properly aligning the reference axes are demonstrated through a case study of the road system in Southern Ontario. Although attention is restricted to the weighted l p norm, the concepts presented are readily extended to other distance functions such as the block norms of Ward and Wendell.

Suggested Citation

  • J. Brimberg & R. F. Love, 1993. "General Considerations on the Use of the Weighted lp Norm as an Empirical Distance Measure," Transportation Science, INFORMS, vol. 27(4), pages 341-349, November.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:4:p:341-349
    DOI: 10.1287/trsc.27.4.341
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    Cited by:

    1. Brimberg, Jack & Love, Robert F. & Walker, John H., 1995. "The effect of axis rotation on distance estimation," European Journal of Operational Research, Elsevier, vol. 80(2), pages 357-364, January.
    2. Nan Dong & Xiaohuan Yang & Hongyan Cai & Liming Wang, 2015. "A Novel Method for Simulating Urban Population Potential Based on Urban Patches: A Case Study in Jiangsu Province, China," Sustainability, MDPI, vol. 7(4), pages 1-20, April.
    3. Kenneth Carling & Mengjie Han & Johan Håkansson & Pascal Rebreyend, 2015. "Distance measure and the $$p$$ p -median problem in rural areas," Annals of Operations Research, Springer, vol. 226(1), pages 89-99, March.
    4. Brimberg, Jack & Juel, Henrik, 1998. "A bicriteria model for locating a semi-desirable facility in the plane," European Journal of Operational Research, Elsevier, vol. 106(1), pages 144-151, April.

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