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A distributionally robust analysis of the program evaluation and review technique

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  • Roos, Ernst
  • den Hertog, Dick

Abstract

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.

Suggested Citation

  • Roos, Ernst & den Hertog, Dick, 2021. "A distributionally robust analysis of the program evaluation and review technique," European Journal of Operational Research, Elsevier, vol. 291(3), pages 918-928.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:3:p:918-928
    DOI: 10.1016/j.ejor.2020.09.027
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    Cited by:

    1. Aakil M. Caunhye & Douglas Alem, 2023. "Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 759-806, September.
    2. Patricia Torres-Lozada & Pablo Manyoma-Velásquez & Jenny Fabiana Gaviria-Cuevas, 2023. "Prioritization of Waste-to-Energy Technologies Associated with the Utilization of Food Waste," Sustainability, MDPI, vol. 15(7), pages 1-13, March.
    3. Zhang, Xihai & Ge, Shaoyun & Liu, Hong & Zhou, Yue & He, Xingtang & Xu, Zhengyang, 2023. "Distributionally robust optimization for peer-to-peer energy trading considering data-driven ambiguity sets," Applied Energy, Elsevier, vol. 331(C).

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