The proactive and reactive resource-constrained project scheduling problem

Uncertainty has become an inevitable aspect of project scheduling. We study the resource-constrained project scheduling problem with stochastic durations. One of the most studied approaches to deal with stochastic durations is that of proactive and reactive scheduling. Previous researches often studied proactive and reactive scheduling rather separately and ignored the fact that proactive scheduling and reactive scheduling are closely connected. In this paper, we address this ignored aspect by formulating an integrated proactive and reactive scheduling problem with a combined cost function which includes a baseline schedule cost as well as costs of a series of reactions. We introduce solutions to this integrated problem as proactive-and-reactive policies (PR-policies). We discuss that PR-policies are more powerful and informative than their traditional counterparts (i.e., a combination of a baseline schedule and a reactive policy), provide better stability and robustness, and are more flexible when extra constraints are added to the problem. We also propose four dynamic programming based models (Models1-4) that solve the problem to optimality over different classes of PR-policies. We compare our models with each other and with a combination of a traditional proactive approach (namely, the starting time criticality heuristic) and a reactive approach (namely, the robust parallel schedule generation scheme). Computational results show that Model2 outperforms the traditional solution only when reaction costs are greater than zero. Moreover, Model3 and Model4 clearly outperform Model1 and Model2 in all settings and the traditional solution in most of the settings.