A two-stage stochastic programming model for the resource constrained project scheduling problem under uncertainty

Due to the increasing competitiveness of businesses, project planning and scheduling have become a challenging theme in the last years. In this paper, we propose a two-stage stochastic programming model for the resource constrained project scheduling problem, taking into account the stochasticity of activity durations. In this formulation, assuming that some activity duration scenarios are known, resource allocations are taken in the first stage, while scheduling decisions are postponed in the second stage. The resulting problem is a mixed integer problem with recourse, where binary variables appear in the first stage. In order to efficiently solve the problem, a decomposition algorithm is developed, based on the well-known integer L-shaped method. Detailed computational results are presented for a set of benchmark instances taken from the literature.