Inequalities for the Completion Times of Stochastic PERT Networks

Luc Devroye

59 citations0/0 files storedMathematics of Operations Research

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Resource-Constrained Project Scheduling Reliability and Maintenance Optimization Probability and Statistical Research

Abstract

A stochastic PERT network is one in which the durations of the activities are random variables. In the absence of complete information about the distribution of these random variables or for the purpose of a fast rough analysis of the network, inequalities relating the mean E{T} and the variance σ 2 {T} of the completion time T of the project (network) to the means and the variances of the individual random variables can be useful. In this note new upper bounds for E{T} and σ 2 {T} are derived that are distribution free: they can be applied for all distributions of the durations of the activities.

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References

1964An Analytical Study of the PERT Assumptions 1962Expected Critical Path Lengths in PERT Networks 1971Bounding Distributions for a Stochastic Acyclic Network 1964Critical Path Analyses Via Chance Constrained and Stochastic Programming 1967On the Expected Duration of PERT Type Networks 1966A Statistical Theory for PERT Critical Path Analysis

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1999Resource-constrained project scheduling: Notation, classification, models, and methods 1985An upper bound on the expected completion time of PERT networks 1986A Multivariate Approach to Estimating the Completion Time for PERT Networks 2003Evaluating project completion times when activity times are Weibull distributed 1989THE ESTIMATION OF SOME NETWORK PARAMETERS IN THE PERT MODEL OF ACTIVITY NETWORKS: REVIEW AND CRITIQUE 1995Bounds on Expected Project Tardiness 1982The bias of an estimate of coupled slack in stochastic PERT networks 1993Estimating the mean completion time of PERT networks with exponentially distributed durations of activities

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