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Efficient Estimation of Arc Criticalities in Stochastic Activity Networks

Author

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  • R. A. Bowman

    (Union College, Graduate Management Institute, Bailey Hall, Schenectady, New York 12308)

Abstract

An algorithm is described for estimating arc and path criticalities in stochastic activity networks by combining Monte Carlo simulation with exact analysis conditioned on node release times. These estimators are proved to be unbiased and to have lower variance than the corresponding standard Monte Carlo estimators. The algorithm is applied to a variety of standard and randomly generated test networks to establish that the estimators are significantly and robustly more efficient than the standard estimators when run time and statistical efficiency are properly combined.

Suggested Citation

  • R. A. Bowman, 1995. "Efficient Estimation of Arc Criticalities in Stochastic Activity Networks," Management Science, INFORMS, vol. 41(1), pages 58-67, January.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:1:p:58-67
    DOI: 10.1287/mnsc.41.1.58
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    Citations

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    Cited by:

    1. Guanglin Xu & Samuel Burer, 2018. "A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming," Computational Management Science, Springer, vol. 15(1), pages 111-134, January.
    2. J-G Cho & B-J Yum, 2004. "Functional estimation of activity criticality indices and sensitivity analysis of expected project completion time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 850-859, August.
    3. Zhichao Zheng & Karthik Natarajan & Chung-Piaw Teo, 2016. "Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty," Operations Research, INFORMS, vol. 64(6), pages 1406-1421, December.
    4. 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.
    5. 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.
    6. 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.
    7. Li, Xiaobo & Natarajan, Karthik & Teo, Chung-Piaw & Zheng, Zhichao, 2014. "Distributionally robust mixed integer linear programs: Persistency models with applications," European Journal of Operational Research, Elsevier, vol. 233(3), pages 459-473.
    8. 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.
    9. Elmaghraby, Salah E., 2000. "On criticality and sensitivity in activity networks," European Journal of Operational Research, Elsevier, vol. 127(2), pages 220-238, December.
    10. Elmaghraby, S. E. & Fathi, Y. & Taner, M. R., 1999. "On the sensitivity of project variability to activity mean duration," International Journal of Production Economics, Elsevier, vol. 62(3), pages 219-232, September.
    11. R. Alan Bowman, 2003. "Sensitivity curves for effective project management," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 481-497, August.
    12. Bregman, Robert L., 2009. "A heuristic procedure for solving the dynamic probabilistic project expediting problem," European Journal of Operational Research, Elsevier, vol. 192(1), pages 125-137, January.
    13. Siqian Shen & J. Cole Smith & Shabbir Ahmed, 2010. "Expectation and Chance-Constrained Models and Algorithms for Insuring Critical Paths," Management Science, INFORMS, vol. 56(10), pages 1794-1814, October.
    14. Madadi, M. & Iranmanesh, H., 2012. "A management oriented approach to reduce a project duration and its risk (variability)," European Journal of Operational Research, Elsevier, vol. 219(3), pages 751-761.

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