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Project management under uncertainty beyond beta: The generalized bicubic distribution

Listed author(s):
  • Pérez, José García
  • Martín, María del Mar López
  • García, Catalina García
  • Sánchez Granero, Miguel Ángel
Registered author(s):

    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.

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    Article provided by Elsevier in its journal Operations Research Perspectives.

    Volume (Year): 3 (2016)
    Issue (Month): C ()
    Pages: 67-76

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    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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    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. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    4. M. W. Sasieni, 1986. "Note---A Note on Pert Times," Management Science, INFORMS, vol. 32(12), pages 1652-1653, December.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Charles Gallagher, 1987. "Reply---A Note on PERT Assumptions," Management Science, INFORMS, vol. 33(10), pages 1360-1360, October.
    10. 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.
    11. 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.
    12. 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.
    13. 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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