Scheduling is an important problem for many applications, including manufacturing, transportation, or cloud computing. Unfortunately, most of the scheduling problems occurring in practice are intractable and, therefore, solving large industrial instances is very time-consuming. Heuristic-based dispatching methods can compute schedules in an acceptable time, but construction of a heuristic allowing for a satisfactory solution quality is a tedious process. This work introduces a method to automatically learn dispatching strategies from only a few training instances using reinforcement learning. Evaluation results obtained on real-world, large-scale instances of a resource-constrained project scheduling problem taken from the literature show that the learned dispatching heuristic generalizes to unseen instances and produces high-quality schedules within seconds. As a result, our approach significantly outperforms state-of-the-art combinatorial optimization techniques in terms of solution quality and computation time.