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Minimum Cost Routing on Stochastic Networks

Author

Listed:
  • G. A. Corea

    (University of North Carolina, Chapel Hill, North Carolina)

  • V. G. Kulkarni

    (University of North Carolina, Chapel Hill, North Carolina)

Abstract

In this paper, we consider the minimum cost transshipment problem in a directed network, having a single source node s with supply S and multiple demand nodes. The arc lengths are independent and exponentially distributed random variables. The cost of shipping is $1/unit flow/unit length, and T is the minimum cost of shipping the S units so as to satisfy all the demands. We construct a continuous time Markov chain with an upper triangular generator matrix such that T equals a particular first passage time in this chain. This fact is used to derive numerically stable algorithms for computing the exact distribution and moments of T .

Suggested Citation

  • G. A. Corea & V. G. Kulkarni, 1990. "Minimum Cost Routing on Stochastic Networks," Operations Research, INFORMS, vol. 38(3), pages 527-536, June.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:3:p:527-536
    DOI: 10.1287/opre.38.3.527
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