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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalAnnals of Operations Research
Volume1
Issue number1
DOIs
StatePublished - Feb 1984
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Decision Sciences (all)
  • Management Science and Operations Research

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