Evaluating the Project Completion Time When Non-Identical Beta Distributions Govern the Activity Networks

Abstract

The main purpose of this paper is to determine the project completion time using a recursive method, where the activity times are distributed according to a sequence of beta distributions with unequal location parameters. For this purpose, we first evaluate the kth moment of the maximum of independent random variables that follow this sequence of distributions. Some illustrative examples are presented to demonstrate the applicability and appropriateness of this generalized beta model. These examples show that, the suggested estimate of project completion time is situated between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski. Moreover, this estimate has lowest variance among the other known estimates. Comparisons with other exemplary estimates (e.g., exponential, Erlang and Weibull estimates), discussed in literature, are presented.

KEYWORDS AND PHRASES:

• Four-parameter-beta distribution
• moments of order statistics
• project scheduling
• stochastic activity networks

AMS 2010 SUBJECT CLASSIFICATION:

• Primary 90B15
• secondary 62H10

Acknowledgments

The authors are thankful to the reviewers and the Editor-in-chief for their valuable suggestions which have substantially improved the content and the presentation of the paper.