A new approximation algorithm for obtaining the probability distribution function for project completion time

Authors:
Ming-Jong Yao;Weng-Ming Chu
Affiliations:
Department of Industrial Engineering and Enterprise Information, Tunghai University, P.O. Box 985, Taichung City, 407, Taiwan;Department of Industrial Engineering and Enterprise Information, Tunghai University, P.O. Box 985, Taichung City, 407, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

This paper focuses on the application of the techniques of discretization to obtain an approximated probability density function (pdf) for the completion time of large-size projects, in which we allow any type of pdf for the duration of activities. In this study, we improve the techniques of discretization in the following two ways: first, we propose to replace the max operation with an approximation procedure to save significant computational loading; and second, to reduce the error from assuming independence between paths using a simple heuristic rule. To evaluate the performance of our proposed algorithm, we randomly generated 20 sets of 100-node instances in our numerical experiments. Taking the results from a Monte Carlo simulation using 20,000 samples as a benchmark, we demonstrate that the proposed algorithm significantly outperforms the PERT model and Dodin's [B.M. Dodin, Approximating the distribution function in stochastic networks, Comput. Oper. Res. 12 (3) (1985) 251-264] algorithm in both the running time and the precision aspects.