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

Stefan Creemers

No 592798, Working Papers of Department of Decision Sciences and Information Management, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven

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 demonstrate, however, that it is globally optimal not to preempt activities if certain conditions are met. A computational experiment confirms this finding. The computational experiment also 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.

Keywords: Project Scheduling; Project Management; NPV maximization; SNPV; Stochastic activity durations (search for similar items in EconPapers)
Date: 2017-09
New Economics Papers: this item is included in nep-cmp and nep-ppm
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Published in FEB Research Report KBI_1718

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