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Estimating travel distances by the weighted lp norm

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  • Jack Brimberg
  • Robert F. Love

Abstract

Empirical distance functions are used to estimate actual travel distances in a transportation network, to verify the accuracy of road mileage data, and to formulate continuous location models. In this article we consider the problem of fitting the weighted lp norm to a given network. Mathematical properties are derived for two fitting criteria found in the literature. These properties are used to develop an accurate and efficient methodology to solve for the best‐fitting parameter values. The directional bias of the lp norm is analyzed for its effect on the range of search for the optimal p value. Concepts and methodology are applied to a case study of the road system in Southern Ontario. In conclusion, a general framework for other types of distance functions is briefly discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:2:p:241-259
    DOI: 10.1002/1520-6750(199104)38:23.0.CO;2-Z
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    References listed on IDEAS

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    Cited by:

    1. Dubois, Nicolas & Semet, Frederic, 1995. "Estimation and determination of shortest path length in a road network with obstacles," European Journal of Operational Research, Elsevier, vol. 83(1), pages 105-116, May.
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    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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