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Arc Reduction and Path Preference in Stochastic Acyclic Networks

Author

Listed:
  • Jonathan F. Bard

    (Department of Mechanical Engineering, Operations Research Group, University of Texas, Austin, Texas 78712)

  • James E. Bennett

    (Department of Mechanical Engineering, Operations Research Group, University of Texas, Austin, Texas 78712)

Abstract

The paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network. The focus is on shortest route problems where a general, nonlinear utility function is used to measure outcomes. For such problems, enumerating all feasible paths is the only way to guarantee that the global optimum has been found. Alternatively, we develop a reduction algorithm based on stochastic dominance to speed up the computations. Monte Carlo simulation is used to evaluate the approach. In all, 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed. The results indicate that the heuristic produces significant computational saving as the size of the network grows, and that the quality of the reduced network solutions are better than those obtained from the original formulation.

Suggested Citation

  • Jonathan F. Bard & James E. Bennett, 1991. "Arc Reduction and Path Preference in Stochastic Acyclic Networks," Management Science, INFORMS, vol. 37(2), pages 198-215, February.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:2:p:198-215
    DOI: 10.1287/mnsc.37.2.198
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    Citations

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    Cited by:

    1. Ishwar Murthy & Sumit Sarkar, 1998. "Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions," Management Science, INFORMS, vol. 44(11-Part-2), pages 125-136, November.
    2. Daniel Reich & Leo Lopes, 2011. "Preprocessing Stochastic Shortest-Path Problems with Application to PERT Activity Networks," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 460-469, August.
    3. Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    4. Nie, Yu (Marco) & Wu, Xing & Dillenburg, John F. & Nelson, Peter C., 2012. "Reliable route guidance: A case study from Chicago," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(2), pages 403-419.
    5. Murthy, Ishwar & Sarkar, Sumit, 1997. "Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function," European Journal of Operational Research, Elsevier, vol. 103(1), pages 209-229, November.
    6. Jian Li & Amol Deshpande, 2019. "Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 354-375, February.

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