Critical chain based Proactive-Reactive scheduling for Resource-Constrained project scheduling under uncertainty

Project scheduling problems under both resource constraints and uncertainty have been widely studied due to their real world relevance. In this paper, we design and implement a new integrated proactive-reactive solution approach based on the critical chain method (CCM) to proactively generate a robust and reliable baseline schedule for the class of resource-constrained project scheduling problem (RCPSP) under uncertainty. A discretetime Markov decision process model is applied for the reactive scheduling phase, which embeds the look-up table method in reinforcement learning to dynamically schedule and adjust schedule reactively using the baseline schedule during project execution. The cost values in the look-up table are calculated based on the occupation of a project buffer and feeding buffers in the baseline schedule generated by the CCM. We conduct computation experiments on the benchmark instances to test our algorithm. The results show that our approach is able to obtain quality solutions efficiently, and competitive with the benchmark algorithms for small- and medium-sized instances.