IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v258y2017i2d10.1007_s10479-016-2315-0.html
   My bibliography  Save this article

Fuzzy-probabilistic PERT

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-016-2315-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-016-2315-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pérez, José García & Martín, María del Mar López & García, Catalina García & Sánchez Granero, Miguel Ángel, 2016. "Project management under uncertainty beyond beta: The generalized bicubic distribution," Operations Research Perspectives, Elsevier, vol. 3(C), pages 67-76.
    2. A. Hernández-Bastida & M. P. Fernández-Sánchez, 2019. "How adding new information modifies the estimation of the mean and the variance in PERT: a maximum entropy distribution approach," Annals of Operations Research, Springer, vol. 274(1), pages 291-308, March.
    3. López Martín, M.M. & García García, C.B. & García Pérez, J. & Sánchez Granero, M.A., 2012. "An alternative for robust estimation in Project Management," European Journal of Operational Research, Elsevier, vol. 220(2), pages 443-451.
    4. 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.
    5. HerrerI´as-Velasco, José Manuel & HerrerI´as-Pleguezuelo, Rafael & van Dorp, Johan René, 2011. "Revisiting the PERT mean and variance," European Journal of Operational Research, Elsevier, vol. 210(2), pages 448-451, April.
    6. 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.
    7. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    8. Kotz, Samuel & van Dorp, J. René, 2005. "A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 383-394, March.
    9. Trietsch, Dan & Mazmanyan, Lilit & Gevorgyan, Lilit & Baker, Kenneth R., 2012. "Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation," European Journal of Operational Research, Elsevier, vol. 216(2), pages 386-396.
    10. van Dorp, J. Rene, 2005. "Statistical dependence through common risk factors: With applications in uncertainty analysis," European Journal of Operational Research, Elsevier, vol. 161(1), pages 240-255, February.
    11. Verónica Morales-Sánchez & Antonio Hernández-Mendo & Pedro Sánchez-Algarra & Ángel Blanco-Villaseñor & María-Teresa Anguera-Argilaga, 2009. "Random PERT: application to physical activity/sports programs," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(2), pages 225-236, March.
    12. Colin, Jeroen & Vanhoucke, Mario, 2014. "Setting tolerance limits for statistical project control using earned value management," Omega, Elsevier, vol. 49(C), pages 107-122.
    13. 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.
    14. Hajdu M. & Isaac S., 2016. "Sixty years of project planning: history and future," Organization, Technology and Management in Construction, Sciendo, vol. 8(1), pages 1499-1510, December.
    15. Xiong, Jian & Leus, Roel & Yang, Zhenyu & Abbass, Hussein A., 2016. "Evolutionary multi-objective resource allocation and scheduling in the Chinese navigation satellite system project," European Journal of Operational Research, Elsevier, vol. 251(2), pages 662-675.
    16. Azaron, Amir & Fatemi Ghomi, S.M.T., 2008. "Lower bound for the mean project completion time in dynamic PERT networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 120-127, April.
    17. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    18. Zhen Song & Håkan Schunnesson & Mikael Rinne & John Sturgul, 2015. "An Approach to Realizing Process Control for Underground Mining Operations of Mobile Machines," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-17, June.
    19. V. Sireesha & N. Ravi Shankar, 2013. "A new approach to find project characteristics and multiple possible critical paths in a fuzzy project network," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 69-85, March.
    20. Moayyad Al-Fawaeer & Abdul Sattar Al-Ali & Mousa Khaireddin, 2021. "The Impact of Changing the Expected Time and Variance Equations of the Project Activities on The Completion Time and Cost of the Project in PERT Model," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 20(2), pages 1-22, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2315-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.