Passengers often complain about dirty trains indicating the relevance of interior cleaning of rolling stock (RS). Servicing tasks (i.e. interior and exterior cleaning and smaller technical checks) are executed on a daily basis at service locations (SLs). Currently, due to train operations during daytime, the current focus lies on night servicing. In this thesis daytime servicing is considered in order to tackle the capacity shortages at SLs. Therefore, the Rolling Stock Servicing Scheduling Problem (RS-SSP) is developed comprising a Mixed Integer Linear Programming (MILP) model. By complying with the planned timetable, the RS-SSP maximises the RS units being serviced during daytime. The RS-SSP allows RS exchanges between RS units having completed servicing and operating RS units requiring servicing. Due to this RS Exchange Concept, the number of RS units visiting the SL during daytime can be increased. Within the thesis three RS-SSP model versions have been developed: the RS-SSP Base Model and two model extensions. The RS-SSP Base Model considers trains running with a single RS unit per train and RS units to be immediately serviced when entering the SL. The first extension (RS-SSP-MU) considers multiple unit trains and the second extension (RS-SSP-MU-W) allows RS units to wait for servicing. The proposed RS-SSP models have been tested on a real-life case from the Dutch railways. The RS-SSP-MU-W yielded the most feasible and improved solutions as compared to the other two model variants. For multiple scenarios, the model was able to exchange all running RS. As a conclusion, the capacity usage at SLs can be increased by the RS-SSP by shifting the excessive workload to daytime, and thus solving the capacity shortages. As the RS-SSP model is a generic model, it may not only be applied to other railway operators, but also to other public transport companies. Further extensions on the model are suggested for an appropriate applicability on large scale.