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An Analytical Study of the PERT Assumptions

Author

Listed:
  • Kenneth R. MacCrimmon

    (Carnegie Institute of Technology, Pittsburgh, Pennsylvania)

  • Charles A. Ryavec

    (University of Michigan, Ann Arbor, Michigan)

Abstract

This paper presents the results of a mathematical analysis of the standard assumptions used in PERT calculations. The objectives of this analysis were four-fold: (1) to pull together the mathematical aspects of the PERT model, (2) to suggest relevant analytic techniques, (3) to obtain an indication of the magnitude and direction of errors introduced by the assumptions, and (4) to suggest possible modifications and improvements in the model. The first part of the paper analyzes those assumptions relevant to the individual activities. Three possible sources of error are considered here: (1) the beta distribution assumption, (2) the standard deviation assumption and the approximation formula for the mean, and (3) the imprecise time estimates. The second part of the paper deals with the PERT network as a whole and analyzes the calculations underlying the project mean, standard deviation, and probability statements. The concept of relative criticalness is explored for the PERT stochastic model. Techniques for network reduction are outlined.

Suggested Citation

  • Kenneth R. MacCrimmon & Charles A. Ryavec, 1964. "An Analytical Study of the PERT Assumptions," Operations Research, INFORMS, vol. 12(1), pages 16-37, February.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:1:p:16-37
    DOI: 10.1287/opre.12.1.16
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    Cited by:

    1. Finer, David Andrew, 2022. "No Shock Waves through Wall Street? Market Responses to the Risk of Nuclear War," Working Papers 318, The University of Chicago Booth School of Business, George J. Stigler Center for the Study of the Economy and the State.
    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. Tetsuo Iida, 2000. "Computing bounds on project duration distributions for stochastic PERT networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 559-580, October.
    4. Samaddar, Subhashish, 2001. "The effect of setup time reduction on its variance," Omega, Elsevier, vol. 29(3), pages 243-247, June.
    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. Luz Stella Cardona-Meza & Gerard Olivar-Tost, 2017. "Modeling and Simulation of Project Management through the PMBOK® Standard Using Complex Networks," Complexity, Hindawi, vol. 2017, pages 1-12, December.
    7. Kamburowski, J., 1997. "New validations of PERT times," Omega, Elsevier, vol. 25(3), pages 323-328, June.
    8. 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.
    9. García Pérez, J., 1998. "El método de subasta como complemento al PERT clásico," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 10, pages 71-88, Diciembre.
    10. R L Bregman, 2009. "Preemptive expediting to improve project due date performance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 120-129, January.
    11. Banerjee, Arunava & Paul, Anand, 2008. "On path correlation and PERT bias," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1208-1216, September.
    12. 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.

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