Functional estimation of activity criticality indices and sensitivity analysis of expected project completion time

Abstract

For a PERT network, a new method is developed for estimating the criticality index of activity i (ACI_i) as a function of the expected duration of activity i (μ_i) and for the sensitivity analysis of the expected project completion time (μ_T) with respect to μ_i. The proposed method evaluates the frequency of activity i being on the critical path, and thereby its ACI_i using Monte Carlo simulation or a Taguchi orthogonal array experiment at several values of μ_i, fits a logistic regression model for estimating ACI_i as a function of μ_i, and then, using the estimated ACI_i function, evaluates the amount of change in μ_T when μ_i is changed by a given amount. Unlike the previous works, the proposed method models ACI_i as a nonlinear (ie, logistic) function of μ_i, which can be used to estimate the amount of change in μ_T for a variety of changes in μ_i. Computational results indicate that the performance of the proposed method is comparable to that of direct Monte Carlo simulation.

Keywords:

• PERT
• project management
• regression

Acknowledgements

We thank two anonymous referees for their valuable comments and suggestions that improved the original manuscript. We are also grateful to The Institute for Operations Research and the Management Sciences for permission to use Figure 4 in Kleindorfer (1971).