Minimum Cost Routing on Stochastic Networks

G. A. Corea and V. G. Kulkarni
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G. A. Corea: University of North Carolina, Chapel Hill, North Carolina
V. G. Kulkarni: University of North Carolina, Chapel Hill, North Carolina

Operations Research, 1990, vol. 38, issue 3, 527-536

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 .

Keywords: networks; stochastic: minimum cost routing; probability; Markov processes; first passage times as routing costs (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:38:y:1990:i:3:p:527-536

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