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The conditional p‐center problem in the plane

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  • R. Chen
  • Y. Handler

Abstract

An algorithm is given for the conditional p‐center problem, namely, the optimal location of one or more additional facilities in a region with given demand points and one or more preexisting facilities. The solution dealt with here involves the minimax criterion and Euclidean distances in two‐dimensional space. The method used is a generalization to the present conditional case of a relaxation method previously developed for the unconditional p‐center problems. Interestingly, its worst‐case complexity is identical to that of the unconditional version, and in practice, the conditional algorithm is more efficient. Some test problems with up to 200 demand points have been solved. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • R. Chen & Y. Handler, 1993. "The conditional p‐center problem in the plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 117-127, February.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:1:p:117-127
    DOI: 10.1002/1520-6750(199302)40:13.0.CO;2-0
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    References listed on IDEAS

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    1. Reuven Chen, 1988. "Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space," Transportation Science, INFORMS, vol. 22(2), pages 157-160, May.
    2. Michael C. Poulton & Adib Kanafani, 1975. "The Application of Location Models to Off-Airport Terminals," Transportation Science, INFORMS, vol. 9(3), pages 224-247, August.
    3. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    4. Robert F. Love & James G. Morris, 1975. "A computation procedure for the exact solution of location‐allocation problems with rectangular distances," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(3), pages 441-453, September.
    5. R. Chen & G. Y. Handler, 1987. "Relaxation method for the solution of the minimax location‐allocation problem in euclidean space," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 775-788, December.
    6. Leon Cooper, 1963. "Location-Allocation Problems," Operations Research, INFORMS, vol. 11(3), pages 331-343, June.
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    Cited by:

    1. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.

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