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

Gideon Weiss

doi:10.1007/BF01874452

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

Research output: Contribution to journal › Article › peer-review

Abstract

In various network models the quantities of interest are optimal value functions of the form max ΣX_i, min ΣX_i, min max X_i, max min X_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. For X_i random with given marginal distributions, we obtain bounds for the optimal value functions, based on common and on antithetic joint distributions.

Original language	English
Pages (from-to)	59-65
Number of pages	7
Journal	Annals of Operations Research
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/BF01874452
State	Published - Feb 1984
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Decision Sciences
Management Science and Operations Research

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10.1007/BF01874452

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abstract = "In various network models the quantities of interest are optimal value functions of the form max ΣXi, min ΣXi, min max Xi, max min Xi, 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. For Xi 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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AB - In various network models the quantities of interest are optimal value functions of the form max ΣXi, min ΣXi, min max Xi, max min Xi, 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. For Xi random with given marginal distributions, we obtain bounds for the optimal value functions, based on common and on antithetic joint distributions.

KW - Pert

KW - antithetic random variables

KW - convex majorisation

KW - cpm

KW - network flows

KW - reliability

KW - stochastic majorisation

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

Abstract

Keywords

ASJC Scopus subject areas

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