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Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology

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  • Illana Bendavid
  • Boaz Golany

Abstract

This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate—a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities’ durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time. (2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a “holding” cost while in the second case, we will incur a “shortage” cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications. Copyright Springer Science+Business Media, LLC 2009

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  • 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.
    • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:259-276:10.1007/s10479-009-0579-3
    DOI: 10.1007/s10479-009-0579-3
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    Cited by:

    1. Mor Kaspi & Tal Raviv, 2013. "Service-Oriented Line Planning and Timetabling for Passenger Trains," Transportation Science, INFORMS, vol. 47(3), pages 295-311, August.
    2. D. Laurie Hughes & Nripendra P. Rana & Yogesh K. Dwivedi, 2020. "Elucidation of IS project success factors: an interpretive structural modelling approach," Annals of Operations Research, Springer, vol. 285(1), pages 35-66, February.
    3. 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.
    4. Shnits, Boris & Bendavid, Illana & Marmor, Yariv N., 2020. "An appointment scheduling policy for healthcare systems with parallel servers and pre-determined quality of service," Omega, Elsevier, vol. 97(C).
    5. Stefan Creemers & Erik Demeulemeester & Stijn Vonder, 2014. "A new approach for quantitative risk analysis," Annals of Operations Research, Springer, vol. 213(1), pages 27-65, February.
    6. Illana Bendavid & Yariv N. Marmor & Boris Shnits, 2018. "Developing an optimal appointment scheduling for systems with rigid standby time under pre-determined quality of service," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 54-77, June.
    7. 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.
    8. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    9. 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.

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