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Letter to the Editor---Monte Carlo Methods and the PERT Problem

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  • Richard M. Van Slyke

    (University of California, Berkeley)

Abstract

Many planning problems can be represented as a network in which the arcs represent “activities” with lengths equal to the time required for the activities performance and the nodes represent “events,” marking the beginning and ending in time of activities. For fixed activity durations, a very simple algorithm gives the length of time required for the total project as well as indicating the activities which are particularly obstructive, those on the “critical path” “PERT” generalizes the above model to recognize uncertainty in the activity durations by allowing them to be random variables. A relatively crude solution to this problem is obtained by reducing the problem back to the first case, by means of appropriate approximation. In this paper the results of a Monte Carlo simulation of PERT networks are given. First the concept of using Monte Carlo methods to give solutions to PERT problems under less restrictive assumptions is discussed. Results are given for the accuracy obtainable, for the computing time required and devices for reducing computation are developed. Finally a “critically” index is defined for each activity. This index is simply the probability that the activity will be on the critical path. The ramifications and uses of this parameter, which is not available using current techniques, are developed.

Suggested Citation

  • Richard M. Van Slyke, 1963. "Letter to the Editor---Monte Carlo Methods and the PERT Problem," Operations Research, INFORMS, vol. 11(5), pages 839-860, October.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:5:p:839-860
    DOI: 10.1287/opre.11.5.839
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    Cited by:

    1. Creemers, Stefan, 2018. "Moments and distribution of the net present value of a serial project," European Journal of Operational Research, Elsevier, vol. 267(3), pages 835-848.
    2. Serpell Alfredo Federico & Ferrada Ximena & Rubio Larissa, 2019. "Measuring the performance of project risk management: a preliminary model," Organization, Technology and Management in Construction, Sciendo, vol. 11(1), pages 1984-1991, January.
    3. Hajdu M. & Isaac S., 2016. "Sixty years of project planning: history and future," Organization, Technology and Management in Construction, Sciendo, vol. 8(1), pages 1499-1510, December.
    4. 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.
    5. Stefan Creemers & Erik Demeulemeester & Stijn Vonder, 2014. "A new approach for quantitative risk analysis," Annals of Operations Research, Springer, vol. 213(1), pages 27-65, February.
    6. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    7. Fernando Acebes & Javier Pajares & José M. González-Varona & Adolfo López-Paredes, 2021. "Project risk management from the bottom-up: Activity Risk Index," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1375-1396, December.
    8. Fernando Acebes & Javier Pajares & Jose M Gonzalez-Varona & Adolfo Lopez-Paredes, 2024. "Project Risk Management from the bottom-up: Activity Risk Index," Papers 2406.00078, arXiv.org.
    9. R A Bowman, 2007. "Efficient sensitivity analysis of PERT network performance measures to significant changes in activity time parameters," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1354-1360, October.
    10. Stephen P. Boyd & Seung-Jean Kim & Dinesh D. Patil & Mark A. Horowitz, 2005. "Digital Circuit Optimization via Geometric Programming," Operations Research, INFORMS, vol. 53(6), pages 899-932, December.
    11. N-H Shih, 2005. "Estimating completion-time distribution in stochastic activity networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 744-749, June.
    12. Joel Goh & Melvyn Sim, 2011. "Robust Optimization Made Easy with ROME," Operations Research, INFORMS, vol. 59(4), pages 973-985, August.
    13. Kim, Byung-Cheol, 2022. "Multi-factor dependence modelling with specified marginals and structured association in large-scale project risk assessment," European Journal of Operational Research, Elsevier, vol. 296(2), pages 679-695.
    14. Jarosław Górecki & Manuel Díaz-Madroñero, 2020. "Who Risks and Wins?—Simulated Cost Variance in Sustainable Construction Projects," Sustainability, MDPI, vol. 12(8), pages 1-31, April.
    15. Opabola, Eyitayo A. & Galasso, Carmine, 2024. "A probabilistic framework for post-disaster recovery modeling of buildings and electric power networks in developing countries," Reliability Engineering and System Safety, Elsevier, vol. 242(C).

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