IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v10y1962i6p808-817.html
   My bibliography  Save this article

Expected Critical Path Lengths in PERT Networks

Author

Listed:
  • D. R. Fulkerson

    (The Rand Corporation, Santa Monica, California)

Abstract

A method of obtaining a fairly good lower approximation to the expected duration time of a project whose individual job times are discrete random variables is described. It is assumed that jobs that immediately precede any given job may have a joint distribution of times, with independence between immediate predecessors of different jobs. The method provides an estimate that is usually much better, and never worse, than the one obtained by replacing each random job time by its expected value. An application to expected minimal path lengths in networks whose arc lengths are random variables is discussed.

Suggested Citation

  • D. R. Fulkerson, 1962. "Expected Critical Path Lengths in PERT Networks," Operations Research, INFORMS, vol. 10(6), pages 808-817, December.
  • Handle: RePEc:inm:oropre:v:10:y:1962:i:6:p:808-817
    DOI: 10.1287/opre.10.6.808
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.10.6.808
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.10.6.808?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ben-Yashar, Ruth & Khuller, Samir & Kraus, Sarit, 2001. "Optimal collective dichotomous choice under partial order constraints," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 349-364, May.
    2. Carlo Meloni & Marco Pranzo, 2020. "Expected shortfall for the makespan in activity networks under imperfect information," Flexible Services and Manufacturing Journal, Springer, vol. 32(3), pages 668-692, September.
    3. 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.
    4. Moayyad Al-Fawaeer & Abdul Sattar Al-Ali & Mousa Khaireddin, 2021. "The Impact of Changing the Expected Time and Variance Equations of the Project Activities on The Completion Time and Cost of the Project in PERT Model," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 20(2), pages 119-140, September.
    5. 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.
    6. Mihir Dash, 2017. "Extending The PERT Model For Probabilistic Activity Direct Costs," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 6(4), pages 231-236, November.
    7. 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.
    8. Moayyad Al-Fawaeer & Abdul Sattar Al-Ali & Mousa Khaireddin, 2021. "The Impact of Changing the Expected Time and Variance Equations of the Project Activities on The Completion Time and Cost of the Project in PERT Model," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 20(2), pages 1-22, September.
    9. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    10. Azaron, Amir & Fatemi Ghomi, S.M.T., 2008. "Lower bound for the mean project completion time in dynamic PERT networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 120-127, April.
    11. Mathieu, Hervé & Colin, Jean-Yves & Nakechbandi, Moustafa, 2014. "Computing Dynamic Routes in Maritime Logistic Networks," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 187-200, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    12. 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.
    13. David P. Morton & R. Kevin Wood, 1999. "Restricted-Recourse Bounds for Stochastic Linear Programming," Operations Research, INFORMS, vol. 47(6), pages 943-956, December.
    14. 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.
    15. Azaron, Amir & Fynes, Brian & Modarres, Mohammad, 2011. "Due date assignment in repetitive projects," International Journal of Production Economics, Elsevier, vol. 129(1), pages 79-85, January.
    16. 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.
    17. Raymond K. Cheung, 1998. "Iterative methods for dynamic stochastic shortest path problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 769-789, December.
    18. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:10:y:1962:i:6:p:808-817. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.