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Convex Location Problems on Tree Networks

Author

Listed:
  • P. M. Dearing

    (Cornell University, Ithaca, New York)

  • R. L. Francis

    (University of Florida, Gainesville, Florida)

  • T. J. Lowe

    (University of Florida, Gainesville, Florida)

Abstract

This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:628-642
    DOI: 10.1287/opre.24.4.628
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    Citations

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    Cited by:

    1. M. C. López-de-los-Mozos & Juan A. Mesa, 2022. "To stop or not to stop: a time-constrained trip covering location problem on a tree network," Annals of Operations Research, Springer, vol. 316(2), pages 1039-1061, September.
    2. Mark-Christoph Körner & Juan Mesa & Federico Perea & Anita Schöbel & Daniel Scholz, 2014. "A maximum trip covering location problem with an alternative mode of transportation on tree networks and segments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 227-253, April.
    3. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    4. 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.
    5. Hakimi, S.Louis, 1983. "Network location theory and contingency planning," Energy, Elsevier, vol. 8(8), pages 697-702.
    6. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    7. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    8. Burkard, R. E. & Dollani, Helidon, 2003. "Center problems with pos/neg weights on trees," European Journal of Operational Research, Elsevier, vol. 145(3), pages 483-495, March.

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