Annals of Operations Research

, Volume 1, Issue 1, pp 59–65 | Cite as

Stochastic bounds on distributions of optimal value functions with applications to pert, network flows and reliability

  • Gideon Weiss
Stochastic Programming


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.

Keywords and phrases

Pert cpm network flows reliability stochastic majorisation convex majorisation antithetic random variables 


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Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1984

Authors and Affiliations

  • Gideon Weiss
    • 1
  1. 1.Department of StatisticsTel Aviv UniversityTel AvivIsrael

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