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Duality and Distance Constraints for the Nonlinear p -Center Problem and Covering Problem on a Tree Network

Author

Listed:
  • B. C. Tansel

    (Georgia Institute of Technology, Atlanta, Georgia)

  • R. L. Francis

    (The University of Florida, Gainesville, Florida)

  • T. J. Lowe

    (Purdue University, West Lafayette, Indiana)

  • M. L. Chen

    (The University of Florida, Gainesville, Florida)

Abstract

The problem of locating a fixed number, p , of facilities (centers) on a network, where there are constraints on the center locations and where the centers provide a service to customers (demand points) located at vertices of the network is addressed. The cost or “loss” of servicing a given demand point is a nonlinear function of the distance between the demand point and the closest center. We consider the case where the network has special structure (a tree network), i.e., there is a unique shortest path between any two points on the network. We also provide and interpret a dual to this problem and give polynomially bounded procedures for solving both problems. The primal location problem is solved with the aid of a related problem for which we also give a dual.

Suggested Citation

  • B. C. Tansel & R. L. Francis & T. J. Lowe & M. L. Chen, 1982. "Duality and Distance Constraints for the Nonlinear p -Center Problem and Covering Problem on a Tree Network," Operations Research, INFORMS, vol. 30(4), pages 725-744, August.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:4:p:725-744
    DOI: 10.1287/opre.30.4.725
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    Cited by:

    1. Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    2. Chandra Ade Irawan & Said Salhi & Zvi Drezner, 2016. "Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex $$p$$ p -centre problems," Journal of Heuristics, Springer, vol. 22(4), pages 507-537, August.

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