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Relaxation method for the solution of the minimax location‐allocation problem in euclidean space

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  • R. Chen
  • G. Y. Handler

Abstract

A method previously devised for the solution of the p‐center problem on a network has now been extended to solve the analogous minimax location‐allocation problem in continuous space. The essence of the method is that we choose a subset of the n points to be served and consider the circles based on one, two, or three points. Using a set‐covering algorithm we find a set of p such circles which cover the points in the relaxed problem (the one with m

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:6:p:775-788
    DOI: 10.1002/1520-6750(198712)34:63.0.CO;2-N
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    References listed on IDEAS

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    1. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    2. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    3. Reuven Chen, 1983. "Solution of minisum and minimax location–allocation problems with Euclidean distances," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(3), pages 449-459, September.
    4. Jack Elzinga & Donald Hearn & W. D. Randolph, 1976. "Minimax Multifacility Location with Euclidean Distances," Transportation Science, INFORMS, vol. 10(4), pages 321-336, November.
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    Cited by:

    1. Chen, Doron & Chen, Reuven, 2013. "Optimal algorithms for the α-neighbor p-center problem," European Journal of Operational Research, Elsevier, vol. 225(1), pages 36-43.
    2. Minnie H. Patel & Deborah L. Nettles & Stuart J. Deutsch, 1993. "A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 543-552, June.
    3. Man Yu & Yafang Lv & Yanping Zhao & Chan He & Senlin Wu, 2023. "Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    4. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    5. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.
    6. Pelegrin, B. & Canovas, L., 1998. "A new assignment rule to improve seed points algorithms for the continuous k-center problem," European Journal of Operational Research, Elsevier, vol. 104(2), pages 366-374, January.
    7. 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.

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