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Minimax Location of a Facility in a Network

Author

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  • A. J. Goldman

    (National Bureau of Standards, Washington, D.C.)

Abstract

The problem is that of locating a facility in a network N so as to minimize the largest of its distances from the vertices of N . A method is given that either solves the problem, or else reduces it to an analogous problem for a single “cyclic component” of N . When N is acyclic (a tree), a very efficient solution algorithm results. Partial analogs of these results are given for a “weighted-distance” extension of the problem.

Suggested Citation

  • A. J. Goldman, 1972. "Minimax Location of a Facility in a Network," Transportation Science, INFORMS, vol. 6(4), pages 407-418, November.
    • Handle: RePEc:inm:ortrsc:v:6:y:1972:i:4:p:407-418
    DOI: 10.1287/trsc.6.4.407
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    Cited by:

    1. Lin, Hongying & Zhou, Bo, 2021. "Which numbers are status differences?," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    2. Jesús Muñuzuri & Pablo Cortés & Rafael Grosso & Luis Onieva, 2016. "Teaching Heuristic Methods to Industrial Engineers: A Problem-Based Experience," INFORMS Transactions on Education, INFORMS, vol. 16(2), pages 60-67, January.
    3. Wei Ding & Ke Qiu, 2017. "An FPTAS for generalized absolute 1-center problem in vertex-weighted graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1084-1095, November.
    4. Joseph S. Martinich, 1988. "A vertex‐closing approach to the p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 185-201, April.
    5. Wei Ding & Ke Qiu & Yu Zhou & Zhou Ye, 2022. "A sifting-edges algorithm for accelerating the computation of absolute 1-center in graphs," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 905-920, September.
    6. Hyunwoo Lim & Narushige Shiode, 2011. "Parcel Distribution Networks for Online Shopping Business," Chapters, in: Kenneth Button & Aura Reggiani (ed.), Transportation and Economic Development Challenges, chapter 6, Edward Elgar Publishing.
    7. Mulder, H.M. & Pelsmajer, M.J. & Reid, K.B., 2006. "Generalized centrality in trees," Econometric Institute Research Papers EI 2006-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Chiang Lin & Wei-Han Tsai & Jen-Ling Shang & Yuan-Jen Zhang, 2012. "Minimum statuses of connected graphs with fixed maximum degree and order," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 147-161, October.
    9. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.

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