The Train Unit Shunting Problem (TUSP) is a well studied problem within the NS (Dutch Railways). TUSP is a problem where trains have to be routed on a shunting yard such that maintenance tasks can be performed and no collisions occur. Furthermore, incoming trains have to be matched to outgoing trains, since trains of the same type can be used interchangeably. Currently, the NS uses a local-search approach to solve TUSP; however, this approach is sometimes unable to find a simple detour route when the initial route of the train is blocked by another train. This research models the TUSP as a Multi-Agent Pathfinding (MAPF) problem to solve the routing issue. We solve this model of the TUSP using Conflict-Bases Search (CBS). To achieve this, CBS is altered to work with multiple trains on the same node, to work with directed edges, and to only allow wait-moves on certain nodes. In this work, we propose two ways of routing multiple trains on the same node; CBSL, where trains are given an exact location on the track; and CBSQ, where the order in which trains enter a track is recorded with a queue. Of these two methods, the queue model was deemed best. Finally, we propose a heuristic to prefer solutions where trains are more spread out on the shunting yard. This heuristic greatly improves the runtime at a loss of optimality.