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Iterative methods for dynamic stochastic shortest path problems

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  • Raymond K. Cheung

Abstract

We consider a routing policy that forms a dynamic shortest path in a network with independent, positive and discrete random arc costs. When visiting a node in the network, the costs for the arcs going out of this node are realized, and then the policy will determine which node to visit next with the objective of minimizing the expected cost from the current node to the destination node. This paper proposes an approach, which mimics the classical label‐correcting approach, to compute the expected path cost. First, we develop a sequential implementation of this approach and establish some properties about the implementation. Next, we develop stochastic versions of some well‐known label‐correcting methods, including the first‐in‐first‐out method, the two‐queue method, the threshold algorithms, and the small‐label‐first principle. We perform numerical experiments to evaluate these methods and observe that fast methods for deterministic networks can become very slow for stochastic networks. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 769–789, 1998

Suggested Citation

  • Raymond K. Cheung, 1998. "Iterative methods for dynamic stochastic shortest path problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 769-789, December.
  • Handle: RePEc:wly:navres:v:45:y:1998:i:8:p:769-789
    DOI: 10.1002/(SICI)1520-6750(199812)45:83.0.CO;2-#
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    References listed on IDEAS

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    1. Kamburowski, Jerzy, 1985. "An upper bound on the expected completion time of PERT networks," European Journal of Operational Research, Elsevier, vol. 21(2), pages 206-212, August.
    2. Randolph W. Hall, 1986. "The Fastest Path through a Network with Random Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 20(3), pages 182-188, August.
    3. D. R. Fulkerson, 1962. "Expected Critical Path Lengths in PERT Networks," Operations Research, INFORMS, vol. 10(6), pages 808-817, December.
    4. John S. Croucher, 1978. "A note on the stochastic shortest‐route problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(4), pages 729-732, December.
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    1. N Shi & R K Cheung & H Xu & K K Lai, 2011. "An adaptive routing strategy for freight transportation networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 799-805, April.
    2. Tsung-Sheng Chang & Linda K. Nozick & Mark A. Turnquist, 2005. "Multiobjective Path Finding in Stochastic Dynamic Networks, with Application to Routing Hazardous Materials Shipments," Transportation Science, INFORMS, vol. 39(3), pages 383-399, August.
    3. A. Arun Prakash & Karthik K. Srinivasan, 2018. "Pruning Algorithms to Determine Reliable Paths on Networks with Random and Correlated Link Travel Times," Transportation Science, INFORMS, vol. 52(1), pages 80-101, January.
    4. Levering, Nikki & Boon, Marko & Mandjes, Michel & Núñez-Queija, Rudesindo, 2022. "A framework for efficient dynamic routing under stochastically varying conditions," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 97-124.

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