IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v198y2009i3p697-705.html
   My bibliography  Save this article

Scheduling projects with stochastic activity duration to maximize expected net present value

Author

Listed:
  • Sobel, Matthew J.
  • Szmerekovsky, Joseph G.
  • Tilson, Vera

Abstract

Although uncertainty is rife in many project management contexts, little is known about adaptively optimizing project schedules. We formulate the problem of adaptively optimizing the expected present value of a project's cash flow, and we show that it is practical to perform the optimization. The formulation includes randomness in activity durations, costs, and revenues, so the optimization leads to a recursion with a large state space even if the durations are exponentially distributed. We present an algorithm that partially exercises the "curse of dimensionality" as computational results demonstrate. Most of the paper is restricted to exponentially distributed task durations, but we sketch the adaptation of the algorithm to approximate any probability distribution of task duration.

Suggested Citation

  • Sobel, Matthew J. & Szmerekovsky, Joseph G. & Tilson, Vera, 2009. "Scheduling projects with stochastic activity duration to maximize expected net present value," European Journal of Operational Research, Elsevier, vol. 198(3), pages 697-705, November.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:3:p:697-705
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00829-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. H. Russell, 1970. "Cash Flows in Networks," Management Science, INFORMS, vol. 16(5), pages 357-373, January.
    2. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    3. Nalini Dayanand & Rema Padman, 2001. "Project Contracts and Payment Schedules: The Client's Problem," Management Science, INFORMS, vol. 47(12), pages 1654-1667, December.
    4. Zhang, Hong & Tam, C. M. & Li, Heng, 2005. "Modeling uncertain activity duration by fuzzy number and discrete-event simulation," European Journal of Operational Research, Elsevier, vol. 164(3), pages 715-729, August.
    5. 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.
    6. Herroelen, Willy S. & Van Dommelen, Patrick & Demeulemeester, Erik L., 1997. "Project network models with discounted cash flows a guided tour through recent developments," European Journal of Operational Research, Elsevier, vol. 100(1), pages 97-121, July.
    7. Elmaghraby, Salah E., 2005. "On the fallacy of averages in project risk management," European Journal of Operational Research, Elsevier, vol. 165(2), pages 307-313, September.
    8. Arnold H. Buss & Meir J. Rosenblatt, 1997. "Activity Delay in Stochastic Project Networks," Operations Research, INFORMS, vol. 45(1), pages 126-139, February.
    9. Herroelen, Willy & Leus, Roel, 2005. "Project scheduling under uncertainty: Survey and research potentials," European Journal of Operational Research, Elsevier, vol. 165(2), pages 289-306, September.
    10. Joseph G. Szmerekovsky, 2005. "The Impact of Contractor Behavior on the Client's Payment-Scheduling Problem," Management Science, INFORMS, vol. 51(4), pages 629-640, April.
    11. D. G. Malcolm & J. H. Roseboom & C. E. Clark & W. Fazar, 1959. "Application of a Technique for Research and Development Program Evaluation," Operations Research, INFORMS, vol. 7(5), pages 646-669, October.
    12. Nicholas G. Hall & Marc E. Posner, 2001. "Generating Experimental Data for Computational Testing with Machine Scheduling Applications," Operations Research, INFORMS, vol. 49(6), pages 854-865, December.
    13. V. G. Kulkarni & V. G. Adlakha, 1986. "Markov and Markov-Regenerative pert Networks," Operations Research, INFORMS, vol. 34(5), pages 769-781, October.
    14. 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.
    15. Stefano Benati, 2006. "An Optimization Model for Stochastic Project Networks with Cash Flows," Computational Management Science, Springer, vol. 3(4), pages 271-284, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Zhang, Jingwen & Elmaghraby, Salah E., 2014. "The relevance of the “alphorn of uncertainty” to the financial management of projects under uncertainty," European Journal of Operational Research, Elsevier, vol. 238(1), pages 65-76.
    2. Peymankar, Mahboobeh & Davari, Morteza & Ranjbar, Mohammad, 2021. "Maximizing the expected net present value in a project with uncertain cash flows," European Journal of Operational Research, Elsevier, vol. 294(2), pages 442-452.
    3. Illana Bendavid & Boaz Golany, 2009. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 172(1), pages 259-276, November.
    4. Yangyang Liang & Nanfang Cui & Tian Wang & Erik Demeulemeester, 2019. "Robust resource-constrained max-NPV project scheduling with stochastic activity duration," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 219-254, March.
    5. Zixuan Zhang & Michail Chronopoulos & Dimitrina S. Dimitrova & Ioannis Kyriakou, 2024. "Risk assessment and optimal scheduling of serial projects," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 709-736, September.
    6. Illana Bendavid & Boaz Golany, 2011. "Predetermined intervals for start times of activities in the stochastic project scheduling problem," Annals of Operations Research, Springer, vol. 186(1), pages 429-442, June.
    7. Bruni, Maria Elena & Hazır, Öncü, 2024. "A risk-averse distributionally robust project scheduling model to address payment delays," European Journal of Operational Research, Elsevier, vol. 318(2), pages 398-407.
    8. Stefan Creemers, 2019. "The preemptive stochastic resource-constrained project scheduling problem," Post-Print hal-02992618, HAL.
    9. Hazır, Öncü & Ulusoy, Gündüz, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," International Journal of Production Economics, Elsevier, vol. 223(C).
    10. Fatemeh Rezaei & Amir Abbas Najafi & Erik Demeulemeester & Reza Ramezanian, 2024. "A stochastic bi-objective project scheduling model under failure of activities," Annals of Operations Research, Springer, vol. 338(1), pages 453-476, July.
    11. Etgar, Ran & Gelbard, Roy & Cohen, Yuval, 2017. "Optimizing version release dates of research and development long-term processes," European Journal of Operational Research, Elsevier, vol. 259(2), pages 642-653.
    12. 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.
    13. Öncü Hazir & Gündüz Ulusoy, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," Post-Print hal-02898162, HAL.
    14. Fatemeh Azimi & Fatemeh Fathallahi, 2016. "Fuzzy Multi Objective Project Scheduling Under Inflationary Conditions," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(3), pages 337-350.
    15. Illana Bendavid & Boaz Golany, 2011. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 189(1), pages 25-42, September.
    16. Eli Gutin & Daniel Kuhn & Wolfram Wiesemann, 2015. "Interdiction Games on Markovian PERT Networks," Management Science, INFORMS, vol. 61(5), pages 999-1017, May.
    17. 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.
    18. Wenhui Zhao & Nicholas G. Hall & Zhixin Liu, 2020. "Project Evaluation and Selection with Task Failures," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 428-446, February.
    19. Maciej Nowak & Tadeusz Trzaskalik, 2022. "A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection," Annals of Operations Research, Springer, vol. 311(2), pages 1155-1181, April.
    20. Szmerekovsky, Joseph G. & Venkateshan, Prahalad & Simonson, Peter D., 2023. "Project scheduling under the threat of catastrophic disruption," European Journal of Operational Research, Elsevier, vol. 309(2), pages 784-794.
    21. Creemers, Stefan, 2019. "The preemptive stochastic resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 238-247.
    22. Hermans, Ben & Leus, Roel & Looy, Bart Van, 2023. "Deciding on scheduling, secrecy, and patenting during the new product development process: The relevance of project planning models," Omega, Elsevier, vol. 116(C).
    23. Creemers, Stefan, 2018. "Maximizing the expected net present value of a project with phase-type distributed activity durations: An efficient globally optimal solution procedure," European Journal of Operational Research, Elsevier, vol. 267(1), pages 16-22.
    24. Creemers, Stefan & De Reyck, Bert & Leus, Roel, 2015. "Project planning with alternative technologies in uncertain environments," European Journal of Operational Research, Elsevier, vol. 242(2), pages 465-476.
    25. Kerkhove, L.-P. & Vanhoucke, M., 2017. "Optimised scheduling for weather sensitive offshore construction projects," Omega, Elsevier, vol. 66(PA), pages 58-78.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wiesemann, Wolfram & Kuhn, Daniel & Rustem, Berç, 2010. "Maximizing the net present value of a project under uncertainty," European Journal of Operational Research, Elsevier, vol. 202(2), pages 356-367, April.
    2. Zhang, Jingwen & Elmaghraby, Salah E., 2014. "The relevance of the “alphorn of uncertainty” to the financial management of projects under uncertainty," European Journal of Operational Research, Elsevier, vol. 238(1), pages 65-76.
    3. Öncü Hazir & Gündüz Ulusoy, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," Post-Print hal-02898162, HAL.
    4. Creemers, Stefan, 2018. "Maximizing the expected net present value of a project with phase-type distributed activity durations: An efficient globally optimal solution procedure," European Journal of Operational Research, Elsevier, vol. 267(1), pages 16-22.
    5. Hazır, Öncü & Ulusoy, Gündüz, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," International Journal of Production Economics, Elsevier, vol. 223(C).
    6. Yangyang Liang & Nanfang Cui & Tian Wang & Erik Demeulemeester, 2019. "Robust resource-constrained max-NPV project scheduling with stochastic activity duration," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 219-254, March.
    7. Illana Bendavid & Boaz Golany, 2011. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 189(1), pages 25-42, September.
    8. Weglarz, Jan & Józefowska, Joanna & Mika, Marek & Waligóra, Grzegorz, 2011. "Project scheduling with finite or infinite number of activity processing modes - A survey," European Journal of Operational Research, Elsevier, vol. 208(3), pages 177-205, February.
    9. Zhengwen He & Nengmin Wang & Pengxiang Li, 2014. "Simulated annealing for financing cost distribution based project payment scheduling from a joint perspective," Annals of Operations Research, Springer, vol. 213(1), pages 203-220, February.
    10. Illana Bendavid & Boaz Golany, 2011. "Predetermined intervals for start times of activities in the stochastic project scheduling problem," Annals of Operations Research, Springer, vol. 186(1), pages 429-442, June.
    11. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2024. "Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies," European Journal of Operational Research, Elsevier, vol. 317(1), pages 16-24.
    12. Bruni, Maria Elena & Hazır, Öncü, 2024. "A risk-averse distributionally robust project scheduling model to address payment delays," European Journal of Operational Research, Elsevier, vol. 318(2), pages 398-407.
    13. Hermans, Ben & Leus, Roel & Looy, Bart Van, 2023. "Deciding on scheduling, secrecy, and patenting during the new product development process: The relevance of project planning models," Omega, Elsevier, vol. 116(C).
    14. Illana Bendavid & Boaz Golany, 2009. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 172(1), pages 259-276, November.
    15. Joseph G. Szmerekovsky, 2005. "The Impact of Contractor Behavior on the Client's Payment-Scheduling Problem," Management Science, INFORMS, vol. 51(4), pages 629-640, April.
    16. 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.
    17. 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.
    18. Trietsch, Dan & Mazmanyan, Lilit & Gevorgyan, Lilit & Baker, Kenneth R., 2012. "Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation," European Journal of Operational Research, Elsevier, vol. 216(2), pages 386-396.
    19. Nursel Kavlak & Gündüz Ulusoy & Funda Sivrikaya Şerifoğlu & Ş. İlker Birbil, 2009. "Client‐contractor bargaining on net present value in project scheduling with limited resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 93-112, March.
    20. Joseph G. Szmerekovsky & George L. Vairaktarakis, 2006. "Maximizing project cash availability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 272-284, June.

    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:eee:ejores:v:198:y:2009:i:3:p:697-705. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.