The preemptive stochastic resource-constrained project scheduling problem: an efficient globally optimal solution procedure

We present a globally optimal solution procedure to tackle the preemptive stochastic resource-constrained project scheduling problem (PSRCPSP). A solution to the PSRCPSP is a policy that allows to construct a precedence- and resource-feasible schedule that minimizes the expected makespan of a project. The PSRCPSP is an extension of the stochastic resource-constrained project scheduling problem (SRCPSP) that allows activities to be interrupted. The SRCPSP and PSRCPSP both assume that activities have stochastic durations. Even though the deterministic preemptive resource-constrained project scheduling problem (PRCPSP) has received some attention in the literature, we are the first to study the PSRCPSP. We use phase-type distributions to model the stochastic activity durations, and define a new Continuous-Time Markov Chain (CTMC) that drastically reduces memory requirements when compared to the well-known CTMC of Kulkarni and Adlakha (1986). In addition, we also propose a new and efficient approach to structure the state space of the CTMC. These improvements allow us to easily outperform the current state-of-the-art in optimal project scheduling procedures, and to solve instances of the PSPLIB J90 and J120 data sets. Last but not least, if activity durations are exponentially distributed, we show that elementary policies are globally optimal for the SRCPSP and the PSRCPSP.