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Parametric Facility Location on a Tree Network with an L p -Norm Cost Function

Author

Listed:
  • Margaret L. Brandeau

    (Stanford University, Stanford, California 94305)

  • Samuel S. Chiu

    (Stanford University, Stanford, California 94305)

Abstract

This paper examines the optimal location of a single facility on a tree network with the objective being to minimize the sum of weighted distances from each node measured by an L p -norm-based cost function. Our goal is to trace the trajectory of the optimal location when the L p -norm parameter p varies from one to infinity. Convexity of the objective function, when p is fixed, allows us to perform the parametric analysis. We characterize possible trajectory paths, and show that some surprising trajectory results can occur.

Suggested Citation

  • Margaret L. Brandeau & Samuel S. Chiu, 1988. "Parametric Facility Location on a Tree Network with an L p -Norm Cost Function," Transportation Science, INFORMS, vol. 22(1), pages 59-69, February.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:1:p:59-69
    DOI: 10.1287/trsc.22.1.59
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    Cited by:

    1. Itai Feigenbaum & Jay Sethuraman & Chun Ye, 2017. "Approximately Optimal Mechanisms for Strategyproof Facility Location: Minimizing L p Norm of Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 434-447, May.
    2. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.

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