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Solving min‐max shortest‐path problems on a network

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  • Ishwar Murthy
  • Shenq‐Shyong Her

Abstract

In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest‐path problems. We present a label‐correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label‐correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label‐correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time. © 1992 John Wiley & Sons, Inc.

Suggested Citation

  • Ishwar Murthy & Shenq‐Shyong Her, 1992. "Solving min‐max shortest‐path problems on a network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 669-683, August.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:5:p:669-683
    DOI: 10.1002/1520-6750(199208)39:53.0.CO;2-W
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    1. Krishan Rana & R. G. Vickson, 1988. "A Model and Solution Algorithm for Optimal Routing of a Time-Chartered Containership," Transportation Science, INFORMS, vol. 22(2), pages 83-95, May.
    2. Clifford S. Orloff, 1976. "Route Constrained Fleet Scheduling," Transportation Science, INFORMS, vol. 10(2), pages 149-168, May.
    3. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    4. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
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    1. Schmidt, M. & Schöbel, Anita & Thom, Lisa, 2019. "Min-ordering and max-ordering scalarization methods for multi-objective robust optimization," European Journal of Operational Research, Elsevier, vol. 275(2), pages 446-459.

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