New approach to the distribution of project completion time in PERT networks

Normal distribution has been commonly accepted as the probability function for whole project duration estimation. Nevertheless, this assumption does not hold in complex projects with many activities and paths, particularly when there are several paths with similar mean duration to that of the critical path (dominating paths). In such cases, Extreme Value distribution has been suggested in the literature as a good fit, but the tests carried out in this paper show that its practical utility is limited. In this context, this paper develops a strategy to find another candidate distribution function. The methodology to do this consisted of three phases: (1) an extensive set of tests to corroborate whether Normal and Extreme Value distributions actually fit simulated data; negative results were obtained; (2) a new set of tests were performed to determine the mean and standard deviation of simulated data from the project parameters, and the Gamma distribution was proposed as a new candidate; and (3) a new set of tests was performed in order to validate the proposed model. All data have been taken from the Project Scheduling Problem Library (PSPLIB). The results show a good fit of the Gamma distribution in most of the cases, especially when Beta distribution is the underlying distribution of activity durations. The main contribution of this new approach is to give project managers the potential to obtain a more accurate project duration estimation using the same parameters as other traditional methods with no computational cost increase. The proposed model avoids time underestimations and overestimations, which could result in additional project execution costs.