Stochastic Sensitivity Analysis of Maximum Flow and Shortest Route Networks.

by Richard D. Wollmer

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An expansion of earlier work to show the equivalence of (1) the interdiction problem of minimizing flow on a network, and (2) the improvement problem of shortening a route as much as possible. The breakdowns (in the first case) and improvements (in the second) are random variables of known mean and variance. Problem 1 is reduced to Problem 2 by constructing a dual for the maximum flow network: finding a minimum cut for such a network is equivalent to finding the shortest path through its dual, so one solution algorithm is presented for both problems. The labeling procedure is shown to terminate, to be possible of execution, and to find the shortest [n]-improved path to the sink. At termination, the label of highest rank has as its first two components the mean and variance of the path length. 34 pp.

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