The Vehicle Positioning Problem consists in controlling the assignment of vehicles of a public transport or railway company to parking positions in a depot. The difficulty is that the parking positions are organized in queues or rows that can only be entered and left from an end. Accessing a vehicle from the middle of such a parking row would require a shunting move, which is costly and should be avoided. Assigning decent parking positions to the vehicles is a central problem in depot management and a key to the smooth operation of a public or rail transport company.

The problem appears in different versions for buses, trams, and trains. The simplest version is bus positioning; it is only about the order of vehicles in parking rows. Tram and train positioning deal with railbound traffic, in which it is more difficult to reach a certain parking position, to turn a unit around, etc. Moreover, tram and train positioning consider compositions of more than one vehicle, which might be split up or put together. While tram and commuter trains generally consist of identical vehicles, railway trains further consist of units of different types.

Vehicle positioning can be seen as one of a larger class of Stack Management Problems, in which a buffer that consists of a set of stacks receives and redistributes items, possibly subject to additional operational constraints. Other interesting problems of this type include railway and airline delay management, container stowage in harbours and ships, and high rack warehouse operation.

The primary objective in this problem is to minimize the number of shunting moves, and in most cases to avoid them completely. This is important to help companies to reduce expenses with men that must be hired to do this job and, perhaps even more important, to organize the workflow in the depot, especially in peak hours, smoothly. In particular train depots can become clogged if the parking tracks are not used properly.

We want to develop methods that can be used to optimize real-world systems. To this purpose, we must be able to deal with restrictions that are important in practice such as the availability of parking positions during a day, mileage balancing of vehicles, and track allocations on the paths towards or from a parking position in a railway parking facility. The ultimate practical goal of our project is to make a step towards the implementation of a mathematical decision support system for depot management in public and rail transport.