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Bounding Distributions for a Stochastic Acyclic Network

Author

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  • George B. Kleindorfer

    (University of California, Berkeley, California)

Abstract

Where the durations of the activities in an acyclic scheduling network are random variables, this paper obtains upper and lower bounding distributions for the activity starting- and finishing-time probability distributions, as well as upper and lower bounds for the expected starting and finishing time of each network activity, and for expected network resource flows. The tightness of the bounds for various networks is examined, and a computational experience with the methods is reported.

Suggested Citation

  • George B. Kleindorfer, 1971. "Bounding Distributions for a Stochastic Acyclic Network," Operations Research, INFORMS, vol. 19(7), pages 1586-1601, December.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:7:p:1586-1601
    DOI: 10.1287/opre.19.7.1586
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    Cited by:

    1. 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.
    2. Fatemi Ghomi, S. M. T. & Hashemin, S. S., 1999. "A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network," European Journal of Operational Research, Elsevier, vol. 114(3), pages 610-625, May.
    3. Jorgensen, Trond & Wallace, Stein W., 2000. "Improving project cost estimation by taking into account managerial flexibility," European Journal of Operational Research, Elsevier, vol. 127(2), pages 239-251, December.
    4. E Saliby & R J Paul, 2009. "A farewell to the use of antithetic variates in Monte Carlo simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 1026-1035, July.
    5. Alessio Angius & András Horváth & Marcello Urgo, 2021. "A Kronecker Algebra Formulation for Markov Activity Networks with Phase-Type Distributions," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    6. Schmidt, Craig W. & Grossmann, Ignacio E., 2000. "The exact overall time distribution of a project with uncertain task durations," European Journal of Operational Research, Elsevier, vol. 126(3), pages 614-636, November.
    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. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    10. Van de Vonder, Stijn & Demeulemeester, Erik & Herroelen, Willy & Leus, Roel, 2005. "The use of buffers in project management: The trade-off between stability and makespan," International Journal of Production Economics, Elsevier, vol. 97(2), pages 227-240, August.
    11. Yousry Abdelkader, 2010. "Adjustment of the moments of the project completion times when activity times are exponentially distributed," Annals of Operations Research, Springer, vol. 181(1), pages 503-514, December.
    12. 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.
    13. Gary Mitchell, 2010. "On Calculating Activity Slack in Stochastic Project Networks," American Journal of Economics and Business Administration, Science Publications, vol. 2(1), pages 78-85, March.
    14. 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.
    15. Xuan Vinh Doan & Karthik Natarajan, 2012. "On the Complexity of Nonoverlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 60(1), pages 138-149, February.

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