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Fuzzy-probabilistic PERT

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  • Barbara Gładysz

    (Wroclaw University of Science and Technology)

Abstract

Using PERT (Program evaluation and review technique), one assumes that the time required to carry out the individual tasks in a project can be approximated using a beta distribution. It is assumed that the parameters of these distributions (the minimum, maximum and most likely times) are estimated by experts in accordance with the properties of the beta distribution. However, this is not always the case. This article shows how one may analyse the time required to carry out a task. Two approaches to describing uncertainty regarding the duration of tasks are used: probabilistic and fuzzy. This article proposes a mixture of a beta probability distribution with a generative probability distribution to describe the duration of a task. An illustrative examples are given.

Suggested Citation

  • Barbara Gładysz, 2017. "Fuzzy-probabilistic PERT," Annals of Operations Research, Springer, vol. 258(2), pages 437-452, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2315-0
    DOI: 10.1007/s10479-016-2315-0
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    References listed on IDEAS

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    1. Hahn, Eugene David, 2008. "Mixture densities for project management activity times: A robust approach to PERT," European Journal of Operational Research, Elsevier, vol. 188(2), pages 450-459, July.
    2. Abdelkader, Yousry H., 2004. "Evaluating project completion times when activity times are Weibull distributed," European Journal of Operational Research, Elsevier, vol. 157(3), pages 704-715, September.
    3. Frank E. Grubbs, 1962. "Letter to the Editor---Attempts to Validate Certain PERT Statistics or “Picking on PERT”," Operations Research, INFORMS, vol. 10(6), pages 912-915, December.
    4. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    5. Magott, Jan & Skudlarski, Kamil, 1993. "Estimating the mean completion time of PERT networks with exponentially distributed durations of activities," European Journal of Operational Research, Elsevier, vol. 71(1), pages 70-79, November.
    6. Yousry Abdelkader, 2010. "Adjustment of the moments of the project completion times when activity times are exponentially distributed," Annals of Operations Research, Springer, vol. 181(1), pages 503-514, December.
    7. D. G. Malcolm & J. H. Roseboom & C. E. Clark & W. Fazar, 1959. "Application of a Technique for Research and Development Program Evaluation," Operations Research, INFORMS, vol. 7(5), pages 646-669, October.
    8. Catalina García & José Pérez & Salvador Rambaud, 2010. "Proposal of a new distribution in PERT methodology," Annals of Operations Research, Springer, vol. 181(1), pages 515-538, December.
    9. Charles Gallagher, 1987. "Reply---A Note on PERT Assumptions," Management Science, INFORMS, vol. 33(10), pages 1360-1360, October.
    Full references (including those not matched with items on IDEAS)

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