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A Distributionally Robust Analysis of PERT

Ernst Roos(e.j.roos***at***tilburguniversity.edu)
Dick den Hertog(d.denhertog***at***tilburguniversity.edu)

Abstract: Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is used a lot in practice as it requires specification of 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 these disadvantages. Most of all, numerous studies investigate the effect of the beta distribution and corresponding variance PERT assumes by analyzing the results for a variety of other distributions. In this paper, we propose a more general method of analyzing the sensitivity of PERT's results to its assumptions regarding the beta distribution that addresses three out of the four main disadvantages of PERT. In particular, we do not assume a singular distribution for the activity distribution, 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 duration over this set of distributions can be calculated through results from distributionally robust optimization on the corresponding worst- and best case distributions themselves. Based on these, we can compute tight lower and upper bounds for the expected project duration, which allows us to comment on the ‘value of information’, that is, the potential value of knowing the true distribution. A numerical study of project planning instances from PSPLIB shows that the effect of PERT's assumption regarding an underlying beta distribution is limited. Moreover, we find that the added value of knowing the exact mean absolute deviation or variance is also modest. We advocate to add our method of analysis to project planning software as a means to check whether PERT's assumptions are particularly detrimental to the project of interest.

Keywords: Project Planning, Distributionally Robust Optimization, PERT

Category 1: Robust Optimization

Category 2: Applications -- OR and Management Sciences (Scheduling )


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Entry Submitted: 11/08/2018
Entry Accepted: 11/08/2018
Entry Last Modified: 11/08/2018

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