The train marshalling by a single shunting engine problem

We consider the problem of marshalling a train from a number of rail cars that are distributed throughout the classification bowl of a shunting yard. In contrast to most other contributions we do not consider marshalling based on repeated roll-ins, but marshalling by shunting engine. This is also a common process alternative at shunting yards that has not yet received much attention from the scientific community. The goal is to find the optimal route for this shunting engine that respects all constraints applicable to movements in a shunting yard. We propose a Mixed Integer Programme (MIP) under consideration of single-block trains. A block refers to rail cars that share the same destination. Then we conduct a series of numerical experiments and show that the solutions of the MIP improve by 10% on average when compared to those produced by a Real-World-Heuristic that is designed to approximate the current marshalling practice. Finally, we statistically derive relationships between selected problem instance characteristics and the expected marshalling effort that can be useful for practitioners and operators of shunting yards.