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Maximizing the expected net present value of a project with phase-type distributed activity durations: An efficient globally optimal solution procedure

Author

Listed:
  • Stefan Creemers

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study projects with activities that have stochastic durations that are modeled using phase-type distributions. Intermediate cash flows are incurred during the execution of the project. Upon completion of all project activities a payoff is obtained. Because activity durations are stochastic, activity starting times cannot be defined at the start of the project. Instead, we have to rely on a policy to schedule activities during the execution of the project. The optimal policy schedules activities such that the expected net present value of the project is maximized. We determine the optimal policy using a new continuous-time Markov chain and a backward stochastic dynamic program. Although the new continuous-time Markov chain allows to drastically reduce memory requirements (when compared to existing methods), it also allows activities to be preempted; an assumption that is not always desirable. We prove, however, that it is globally optimal not to preempt activities if cash flows are incurred at the start of an activity. Moreover, this proof holds regardless of the duration distribution of the activities. A computational experiment shows that we significantly outperform current state-of-the-art procedures. On average, we improve computational efficiency by a factor of 600, and reduce memory requirements by a factor of 321.

Suggested Citation

  • Stefan Creemers, 2018. "Maximizing the expected net present value of a project with phase-type distributed activity durations: An efficient globally optimal solution procedure," Post-Print hal-02572114, HAL.
  • Handle: RePEc:hal:journl:hal-02572114
    DOI: 10.1016/j.ejor.2017.11.027
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    Citations

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    Cited by:

    1. 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.
    2. Öncü Hazir & Gündüz Ulusoy, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," Post-Print hal-02898162, HAL.
    3. 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.
    4. 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.
    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).

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