IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v181y2010i1p515-53810.1007-s10479-010-0783-1.html
   My bibliography  Save this article

Proposal of a new distribution in PERT methodology

Author

Listed:
  • Catalina García
  • José Pérez
  • Salvador Rambaud

Abstract

The aim of this paper is to present the generalized biparabolic distribution (GBP) as a good candidate to be utilized as the distribution underlying to PERT methodology (Malcolm et al. in Oper. Res. 7:646–669, 1959 ). To do this and following the criteria established by Taha (Investigación de Operaciones, 1981 ) and Herrerías (Estudios de Economía Aplicada, pp. 89–112, 1989 ), we will compare the mean and variance estimates derived from each proposed density function, viz beta, two-sided power (TSP) and GBP distributions. Also we will compare the estimates contributed by the mesokurtic and of constant variance families of the aforementioned distributions. The main conclusion is that the GBP distribution is the most convenient to be used in the PERT methodology because its mean is almost as moderate as that of trapezoidal and its variance is much higher than that of the rest of distributions. As a consequence, it can be stated that the GBP distribution is an alternative to the other four-parameter distributions. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:515-538:10.1007/s10479-010-0783-1
    DOI: 10.1007/s10479-010-0783-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0783-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0783-1?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. C Chapman & S Ward, 2003. "Constructively simple estimating: a project management example," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(10), pages 1050-1058, October.
    2. van Dorp J.R. & Kotz S., 2002. "The Standard Two-Sided Power Distribution and its Properties: With Applications in Financial Engineering," The American Statistician, American Statistical Association, vol. 56, pages 90-99, May.
    3. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    4. Cruz Rambaud, Salvador & García Pérez, José, 2001. "The Aggregate Opinion Of Several Experts In The Fuzzy And Pert Methodologies," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 0(2), pages 23-49, November.
    5. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    6. R A Bowman, 2007. "Efficient sensitivity analysis of PERT network performance measures to significant changes in activity time parameters," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1354-1360, October.
    7. H. O. Hartley & A. W. Wortham, 1966. "A Statistical Theory for PERT Critical Path Analysis," Management Science, INFORMS, vol. 12(10), pages 469-481, June.
    8. M. W. Sasieni, 1986. "Note---A Note on Pert Times," Management Science, INFORMS, vol. 32(12), pages 1652-1653, December.
    9. 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.
    10. Charles Gallagher, 1987. "Reply---A Note on PERT Assumptions," Management Science, INFORMS, vol. 33(10), pages 1360-1360, October.
    11. S Mohan & M Gopalakrishnan & H Balasubramanian & A Chandrashekar, 2007. "A lognormal approximation of activity duration in PERT using two time estimates," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 827-831, June.
    12. Charles E. Clark, 1962. "Letter to the Editor---The PERT Model for the Distribution of an Activity Time," Operations Research, INFORMS, vol. 10(3), pages 405-406, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barbara Gładysz, 2017. "Fuzzy-probabilistic PERT," Annals of Operations Research, Springer, vol. 258(2), pages 437-452, November.

    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. 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.
    5. 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.
    6. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    7. 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.
    8. 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.
    9. Barbara Gładysz, 2017. "Fuzzy-probabilistic PERT," Annals of Operations Research, Springer, vol. 258(2), pages 437-452, November.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Lau, Hon-Shiang & Somarajan, C., 1995. "A proposal on improved procedures for estimating task-time distributions in PERT," European Journal of Operational Research, Elsevier, vol. 85(1), pages 39-52, August.
    15. Colin, Jeroen & Vanhoucke, Mario, 2014. "Setting tolerance limits for statistical project control using earned value management," Omega, Elsevier, vol. 49(C), pages 107-122.
    16. 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.
    17. 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 119-140, September.
    18. Schmidt, Craig W. & Grossmann, Ignacio E., 2000. "The exact overall time distribution of a project with uncertain task durations," European Journal of Operational Research, Elsevier, vol. 126(3), pages 614-636, November.
    19. Samadi, S. Yaser & Billard, Lynne, 2021. "Analysis of dependent data aggregated into intervals," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    20. Lee, Heejung & Suh, Hyo-Won, 2008. "Estimating the duration of stochastic workflow for product development process," International Journal of Production Economics, Elsevier, vol. 111(1), pages 105-117, January.

    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:181:y:2010:i:1:p:515-538:10.1007/s10479-010-0783-1. 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.