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Time-cost trade-off via optimal control theory in Markov PERT networks

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  • Amir Azaron
  • Hideki Katagiri
  • Masatoshi Sakawa

Abstract

We develop a new analytical model for the time-cost trade-off problem via optimal control theory in Markov PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. Then, we construct a multi-objective optimal control problem, in which the first objective is the minimization of the total direct costs of the project, in which the direct cost of each activity is a non-decreasing function of the resources allocated to it, the second objective is the minimization of the mean of project completion time and the third objective is the minimization of the variance of project completion time. Finally, two multi-objective decision techniques, viz, goal attainment and goal programming are applied to solve this multi-objective optimal control problem and obtain the optimal resources allocated to the activities or the control vector of the problem Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    • Handle: RePEc:spr:annopr:v:150:y:2007:i:1:p:47-64:10.1007/s10479-006-0149-x
    DOI: 10.1007/s10479-006-0149-x
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    Cited by:

    1. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    2. Nelson, Richard Graham & Azaron, Amir & Aref, Samin, 2016. "The use of a GERT based method to model concurrent product development processes," European Journal of Operational Research, Elsevier, vol. 250(2), pages 566-578.
    3. Pedro Godinho & João Paulo Costa, 2020. "A stochastic model and algorithms for determining efficient time–cost tradeoffs for a project activity," Operational Research, Springer, vol. 20(1), pages 319-348, March.
    4. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    5. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2011. "Resource allocation in dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 215(3), pages 670-678, December.
    6. Marc J. Schniederjans & Dara Schniederjans & Qing Cao, 2017. "Value analysis planning with goal programming," Annals of Operations Research, Springer, vol. 251(1), pages 367-382, April.
    7. Azaron, A. & Brown, K.N. & Tarim, S.A. & Modarres, M., 2008. "A multi-objective stochastic programming approach for supply chain design considering risk," International Journal of Production Economics, Elsevier, vol. 116(1), pages 129-138, November.
    8. A. Hernández-Bastida & M. P. Fernández-Sánchez, 2019. "How adding new information modifies the estimation of the mean and the variance in PERT: a maximum entropy distribution approach," Annals of Operations Research, Springer, vol. 274(1), pages 291-308, March.
    9. Catalina García & José Pérez & Salvador Rambaud, 2010. "Proposal of a new distribution in PERT methodology," Annals of Operations Research, Springer, vol. 181(1), pages 515-538, December.

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