The vehicle positioning problem deals with the assignment of parking positions to buses, trams or trains in order to minimize the number of shunting moves and to balance vehicle mileage. This is one of the central problems in depot management. Stack management problems of this type also arise in railway and airline delay management, container stowage, high rack warehouse operation and similar applications in transport and logistics.

Combinatorial optimization provides several tools for the investigation of this problem. We propose to study the offline version of the problem using an integer programming approach, and for the online version we want to develop a novel "continuous optimization" method that aims at preventing the appearance of high-risk situations.