A CTMDP-Based Exact Method for RCPSP with Uncertain Activity Durations and Rework

Abstract

Many practical projects incorporate random rework, which leads to a stochastic project network structure. Until now, however, there have been only few works in the literature that have looked into this particular aspect of project planning and scheduling. In this paper, we consider a resource-constrained project scheduling problem (RCPSP) with exponentially distributed activity durations and two types of random rework. A mathematical model is proposed based on a continuous-time Markov decision process (CTMDP) with the objective to minimize the expected project makespan, which is further converted into an equivalent DTMDP with removing the self-transitions. In order to cope with the curse of dimensionality that comes into play upon solving large-scale instances, we examine a decomposition and parallel method that limits the memory usage. In addition, we also analyze the effect of random rework on the expected project makespan and the optimal rework strategy. Finally, a computational experiment is set up to validate the effectiveness of the proposed model and procedures.