Abstract
In various network models the quantities of interest are optimal value functions of the form max ΣX i , min ΣX i , min maxX i , max minX i , where the inner operation is on the nodes of a path/cut and the outer operation on all paths/cuts, e.g. shortest path of a project network, maximal flow of a flow network or lifetime of a reliability system. ForX i random with given marginal distributions, we obtain bounds for the optimal value functions, based on common and on antithetic joint distributions.
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This work was carried out during a visit to RWTH Aachen, supported by DAAD.
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Weiss, G. Stochastic bounds on distributions of optimal value functions with applications to pert, network flows and reliability. Ann Oper Res 1, 59–65 (1984). https://doi.org/10.1007/BF01874452
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DOI: https://doi.org/10.1007/BF01874452