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An Axiomatic Characterization of a Class of Locations in Tree Networks

Author

Listed:
  • Dean P. Foster

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • Rakesh V. Vohra

    (Ohio State University, Columbus, Ohio)

Abstract

In this paper we describe four axioms that uniquely characterize the class of locations in tree networks that are obtained by minimizing an additively separable, nonnegative, nondecreasing, differentiable, and strictly convex function of distances. This result is analogous to results that have been obtained in the theory of bargaining, social choice, and fair resource allocation.

Suggested Citation

  • Dean P. Foster & Rakesh V. Vohra, 1998. "An Axiomatic Characterization of a Class of Locations in Tree Networks," Operations Research, INFORMS, vol. 46(3), pages 347-354, June.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:347-354
    DOI: 10.1287/opre.46.3.347
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    References listed on IDEAS

    as
    1. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    2. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    3. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    4. Buhl, Hans Ulrich, 1988. "Axiomatic considerations in multi-objective location theory," European Journal of Operational Research, Elsevier, vol. 37(3), pages 363-367, December.
    5. Vohra, Rakesh V., 1989. "Distance weighted voting and a single facility location problem," European Journal of Operational Research, Elsevier, vol. 41(3), pages 314-320, August.
    6. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    7. P. M. Dearing & R. L. Francis & T. J. Lowe, 1976. "Convex Location Problems on Tree Networks," Operations Research, INFORMS, vol. 24(4), pages 628-642, August.
    8. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
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    Cited by:

    1. Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.

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    Keywords

    Facilities; location; discrete;
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