In context of the digitalization of railway operations, hybrid methods have become key assets for improving existing traffic control and dispatching (i.e., executing the schedule). Dispatching is characterized by continuous traffic monitoring and systematic adjustment of the schedule to the occurrence of stochastic events. Due to the complexity of this process, decision-support tools have been developed to support dispatchers in real-time. To date, available tools are applicable to simple sub-tasks within the schedule adjustment process and have limited solution quality. This project aims to investigate different combinations of hybrid methods (exact, heuristic, and machine learning) and develop practical approaches that can directly improve the schedule adjustment quality and thus enhance the railway system's capacity.