A distributionally robust analysis of the program evaluation and review technique

Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have been voiced and much research has been devoted to analyzing them. The effect of the beta distribution and corresponding variance PERT assumes is investigated in numerous studies, through analyzing the results for a variety of other distributions. In this paper, we propose a more general method of analyzing PERT’s sensitivity to its assumptions regarding the beta distribution. In particular, we do not assume a singular distribution for the activity duration, but instead assume this distribution to only be partially specified by its support, mean and possibly its mean absolute deviation. The exact worst- and best-case expected project durations over this set of distributions can be calculated through results from distributionally robust optimization on the worst- and best-case distributions themselves. A numerical study of project planning instances from PSPLIB shows that the effect of PERT’s assumption regarding an underlying beta distribution is limited. Furthermore, we find that the added value of knowing the exact mean absolute deviation is also modest.