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Optimal Minimax Path of a Single Service Unit on a Network to Nonservice Destinations

Author

Listed:
  • Oded Berman

    (College of Management, The University of Massachusetts, Boston, Massachusetts, and The University of Calgary, Calgary, Alberta, Canada)

  • Gabriel Y. Handler

    (Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel)

Abstract

In this paper we consider the problem of finding an optimal path of a single service unit that travels toward a “nonservice” destination. Two types of objective functions are examined. One objective function is the minimization of the maximum distance (or weighted distance) between the moving service unit and any demand (node) of the network. The second objective function is the minimization of the total time period that the distance (or weighted distance) between the moving service unit and any node exceeds a response time threshold (lambda). For these two objective functions, we present algorithms which can be calculated, respectively, in 0( n 3 ) and 0( n 3 log n ) elementary operations.

Suggested Citation

  • Oded Berman & Gabriel Y. Handler, 1987. "Optimal Minimax Path of a Single Service Unit on a Network to Nonservice Destinations," Transportation Science, INFORMS, vol. 21(2), pages 115-122, May.
    • Handle: RePEc:inm:ortrsc:v:21:y:1987:i:2:p:115-122
    DOI: 10.1287/trsc.21.2.115
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    Cited by:

    1. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    2. Elena Fernandez & Robert Garfinkel & Roman Arbiol, 1998. "Mosaicking of Aerial Photographic Maps Via Seams Defined by Bottleneck Shortest Paths," Operations Research, INFORMS, vol. 46(3), pages 293-304, June.
    3. Tayyebi, Javad & Mitra, Ankan & Sefair, Jorge A., 2023. "The continuous maximum capacity path interdiction problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 38-52.

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