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Project management under uncertainty beyond beta: The generalized bicubic distribution

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  • Pérez, José García
  • Martín, María del Mar López
  • García, Catalina García
  • Sánchez Granero, Miguel Ángel

Abstract

The beta distribution has traditionally been employed in the PERT methodology and generally used for modeling bounded continuous random variables based on expert’s judgment. The impossibility of estimating four parameters from the three values provided by the expert when the beta distribution is assumed to be the underlying distribution has been widely debated. This paper presents the generalized bicubic distribution as a good alternative to the beta distribution since, when the variance depends on the mode, the generalized bicubic distribution approximates the kurtosis of the Gaussian distribution better than the beta distribution. In addition, this distribution presents good properties in the PERT methodology in relation to moderation and conservatism criteria. Two empirical applications are presented to demonstrate the adequateness of this new distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:oprepe:v:3:y:2016:i:c:p:67-76
    DOI: 10.1016/j.orp.2016.09.001
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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. Kenneth R. MacCrimmon & Charles A. Ryavec, 1964. "An Analytical Study of the PERT Assumptions," Operations Research, INFORMS, vol. 12(1), pages 16-37, February.
    4. 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.
    5. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    6. M. W. Sasieni, 1986. "Note---A Note on Pert Times," Management Science, INFORMS, vol. 32(12), pages 1652-1653, 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. William H. Parks & Kenneth D. Ramsing, 1969. "The Use of the Compound Poisson in Pert," Management Science, INFORMS, vol. 15(8), pages 397-402, April.
    9. T. K. Littlefield, Jr. & P. H. Randolph, 1987. "Reply---An Answer to Sasieni's Question on PERT Times," Management Science, INFORMS, vol. 33(10), pages 1357-1359, October.
    10. Joseph J. Moder & E. G. Rodgers, 1968. "Judgment Estimates of the Moments of Pert Type Distributions," Management Science, INFORMS, vol. 15(2), pages 76-83, October.
    11. C. García & J. García Pérez & J. Dorp, 2011. "Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 463-486, November.
    12. Charles Gallagher, 1987. "Reply---A Note on PERT Assumptions," Management Science, INFORMS, vol. 33(10), pages 1360-1360, October.
    13. 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.
    14. Sculli, D & Wong, KL, 1985. "The maximum and sum of two beta variables and the analysis of PERT networks," Omega, Elsevier, vol. 13(3), pages 233-240.
    15. C. Perry & I. D. Greig, 1975. "Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis," Management Science, INFORMS, vol. 21(12), pages 1477-1480, August.
    16. 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.
    17. T. C. T. Kotiah & N. D. Wallace, 1973. "Another Look at the PERT Assumptions," Management Science, INFORMS, vol. 20(1), pages 44-49, September.
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    Cited by:

    1. Palit, Niladri & Brint, Andrew, 2020. "The effect of risk aversion on the optimal project resource rate," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1092-1104.

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