# A Practical and Accurate Alternative to PERT

## Abstract

Many real world projects can be represented by stochastic activity network (SAN) models, where the duration of some or all of the project activities are, at best, known in probabilistic sense. These models are known in the literature as PERT networks and they are analyzed using the PERT procedure. It has been known for many years that the Project Evaluation and Review Technique (PERT) provides inaccurate information about the project completion time. Quite often this inaccuracy is large enough to render such estimates as not helpful. As a result of this inaccuracy, many improvements since the introduction of PERT in 1959 have been developed. However, in spite of this inaccuracy and the many improvements, PERT procedure continues to be taught and presented in most text books on Project Management. This is due, perhaps, to its simplicity, and ease of its application. In this paper a new alternative is developed that addresses the issues of accuracy and practicality simultaneously in analyzing SAN models. The new procedure is based on a more accurate representation of the distribution function of the project completion time. We first show that the project completion time can in certain instances be accurately represented by a normal distribution, but in many other instances it can not. In these other instances we show that the project completion time can be more accurately represented by an extreme value distribution. Hence, SAN is first characterized as to when we can use the normal distribution and when we can use extreme value distribution. In the first case, PERT estimates are accurate and will be used; however, in the second case a new procedure is developed that is easy to use, and results in more accurate estimates of the project completion time and its statistics. In this paper examples are also provided that illustrate the above characterization of SANs and the accuracy and practicality of the new procedure.

## Keywords

Stochastic activity networks extreme value distribution normal distribution project completion time estimation## Preview

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## References

- Adlakha, V. G., and Kulkarni, V. G. (1989). A Classified Bibliography of Research on Stochastic PERT Networks: 1966–1987,
*INFOR*, 27(3):272–296.Google Scholar - Burt Jr., J. M. and Garman, M. B. (1971). Conditional Monte Carlo: a Simulation Technique for stochastic network analysis,
*Management Science*, 18:207–217.Google Scholar - Clark, C. E. (1961). The Greatest of a Finite Set of Random Variables,
*Operations Research*, 9:146–162.Google Scholar - Clingen, C. T. (1964). A Modification M Fulkerson’s PERT Algorithm. Letter to the Editor,
*Operations Research*, 12:629–632.Google Scholar - Cramer, H. (1946).
*Mathematical Models of Statistics*, Princeton University Press, Princeton, NJ.Google Scholar - David, H. A. (1981).
*Order Statistics*, 2nd ed. Wiley, New York.zbMATHGoogle Scholar - Demeulemeester, E., Herroelen, W. (2002).
*Project Scheduling: A Research Handbook*, Kluwer Academic Publishing.Google Scholar - Devroye, L. (1979). Inequalities for the Completion Times of Stochastic PERT Networks,
*Mathematics of Operations Research*, 4:441–447.MathSciNetGoogle Scholar - Dodin, B. M. and Elmaghraby, S. E. (1985). Approximating the Criticality Indices of the Activities in PERT Networks,
*Management Science*, 31:207–223.MathSciNetGoogle Scholar - Dodin, B. M. (1985). Bounding the Project Completion Time Distribution in PERT Networks,
*Operations Research*, 24:862–882.Google Scholar - Dodin, B., and Sirvanci, M. (1990). Stochastic Networks and the Extreme Value Distribution,
*Computers and Operations Research*, 17(4):397–409.CrossRefMathSciNetGoogle Scholar - Donaldson, W. A. (1965). Estimation of the Mean and Variance of a PERT Activity Time,
*Operations Research*, 13:382–385.Google Scholar - Downey, P. J. (1990). Distribution-Free Bounds on the Expectation of the Maximum with Scheduling Applications,
*Operations Research Letters*, 9:189–201.CrossRefMathSciNetGoogle Scholar - Dubois, D. and Prade, H. (1987). Fuzzy Numbers: An Overview, in:
*Analysis of Fuzzy Information*, Bezdek, J.C., ed, CRC Press, Boca Raton, pp. 3–39.Google Scholar - Dubois, D. and Prade, H. (1989). Processing Fuzzy Temporal Knowledge,
*IEE Transactions on Systems, Man and Cybernetics*, 19(4):729–744.CrossRefMathSciNetGoogle Scholar - Elmaghraby, S. E. (1977).
*Activity Networks: Project Planning and Control by Network Models*, Wiley and Sons, New York.zbMATHGoogle Scholar - Elmaghraby, S. E. (2000). On Criticality and Sesitivity in Activity Networks,
*European Journal of Operational Research*, 127:220–238.CrossRefGoogle Scholar - Elmaghraby, S. E. (2005). On the fallacy of averages in project risk management,
*European Journal of Operational Research*, 165(2):307–313.CrossRefMathSciNetGoogle Scholar - Esary, J. D., Proschan, F. and Walkup, D. W. (1967). Association of Random Variables with Applications,
*Annals of Mathematical Statistics*, 38:1466–1474.MathSciNetGoogle Scholar - Feller, W. (1968).
*An Introduction to Probability Theory and its Applications*, Vol. I, 3rd ed., John Wiley & Sons, New York.zbMATHGoogle Scholar - Fulkerson, D.R. (1962). Expected critical path lengths in PERT networks,
*Operations Research*, 10:808–817.Google Scholar - Galambos, J. (1978).
*The Asymptotic Theory of Extreme Order Statistics*, John Wiley & Sons, New York.zbMATHGoogle Scholar - Glover, F., Klingman, D., and Phillips, N. V. (1992).
*Network Models in Optimization and their Applications in Practice*, John Wiley & Sons, New York.Google Scholar - Herroelen, W., and Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials,
*European Journal of Operational Research*, 165(2):289–306.CrossRefMathSciNetGoogle Scholar - Iida, T. (2000). Computing Bounds on Project Duration Distributions for Stochastic PERT Networks,
*Naval Research Logistics*, 47:559–580.CrossRefMathSciNetGoogle Scholar - Kamburowski, J. (1997). New Validations of PERT Times,
*OMEGA*, 25(3):323–328.CrossRefGoogle Scholar - Kleindorfer, G. B. (1971). Bounding Distributions for a Stochastic Acyclic Network,
*Operations Research*, 19:1586–1601.MathSciNetGoogle Scholar - Krishnan, V. and Ulrich, K. T. (2001). Product development decisions: A review of the literature,
*Management Science*, 47:1–21.CrossRefGoogle Scholar - Malcolm, D.J., Roseboom, J.H., Clark, C.E. and Fazar, W. (1959). Application of a technique for research and development program evaluation,
*Operations Research*, 7:646–669.CrossRefGoogle Scholar - Martin, J. J. (1965). Distribution of the Time through a Directed Acyclic Network,
*Operations Research*13:46–66.MathSciNetGoogle Scholar - Schmidt, C. W. and Grossmann, I. E. (2000). The Exact Overall Time Distribution of a Project with Uncertain Task Durations,
*European Journal of Operational Research*, 126:614–636.CrossRefGoogle Scholar - Sculli, D. (1983). The Completion Time of PERT Networks,
*Journal of the Operational Research Society*, 34:155–158.CrossRefGoogle Scholar - Shogan, A. W. (1977). Bounding Distributions for a Stochastic PERT Network,
*Networks*, 7:359–381.MathSciNetGoogle Scholar - Sigal, C. E., Pritsker, A. A. B., and Solberg, J. J. (1979). The use of Cutset in Monte Carlo Analysis of Stochastic Networks,
*Mathematics and Computers in Simulation*, 21:379–384.CrossRefMathSciNetGoogle Scholar - Soroush, H. (1994). Risk Taking in Stochastic PERT Networks,
*European Journal of Operational Research*, 67:221–241.CrossRefGoogle Scholar - Van Slyke, R M. (1963). Monte Carlo methods and the PERT problem,
*Operations Research*, 11:839–860.Google Scholar - Williams, T. M. (1995). What are PERT Estimates?,
*Journal of the Operational Research Society*, 46:1498–1504.CrossRefGoogle Scholar