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The Completion Time of PERT Networks

Author

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  • Pierre Robillard

    ((Posthumous) University of Montreal, Montreal, Quebec)

  • Michel Trahan

    (Department of Health and Welfare, Ottawa, Ontario)

Abstract

PERT and critical path techniques have exceptionally wide applications. These techniques and their applications have contributed significantly to better planning, control, and general organization of many programs. This paper is concerned with a technical improvement in PERT methodology by introducing a new approach to approximating, in a computationally efficient way, the total duration distribution function of a program. It is assumed that the activity durations are independent random variables and have a finite range. The first part of the paper considers PERT networks and deals with the lower bound approximation to the total duration distribution function of the program. Then we use this approximation and CPM to propose bounds for the different moments of the distribution function. We illustrate this with numerical examples. In the second part of the paper we adapt our results to PERT decision networks.

Suggested Citation

  • Pierre Robillard & Michel Trahan, 1977. "The Completion Time of PERT Networks," Operations Research, INFORMS, vol. 25(1), pages 15-29, February.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:1:p:15-29
    DOI: 10.1287/opre.25.1.15
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    Cited by:

    1. 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.
    2. Yang, Hsu-Hao & Chen, Yen-Liang, 2000. "Finding the critical path in an activity network with time-switch constraints," European Journal of Operational Research, Elsevier, vol. 120(3), pages 603-613, February.
    3. Badinelli, Ralph D., 1996. "Approximating probability density functions and their convolutions using orthogonal polynomials," European Journal of Operational Research, Elsevier, vol. 95(1), pages 211-230, November.
    4. 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.
    5. Chen, Yen-Liang & Rinks, Dan & Tang, Kwei, 1997. "Critical path in an activity network with time constraints," European Journal of Operational Research, Elsevier, vol. 100(1), pages 122-133, July.

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