Rotation Planning of Locomotive and Carriage Groups with Shared Capacities

In a large railway passenger traffic network, a given set of trips or service blocks are to be serviced by equipment consisting of several groups of locomotives/carriages. The allowed groups per service block are predefined as patterns or multisets of locomotives and carriages. A given type of locomotive/carriage may occur with varying numbers in several groups. We search for a cost-minimal assignment of locomotive/carriage groups to rotations taking special restrictions into account, especially, we shall find the optimal mix of groups obeying given capacities on the level of locomotive and carriage units for each type. Our solution approach is based on a multi-layer (multi-commodity) network flow model where each layer represents a locomotive/carriage group, and the requirement of servicing each trip exactly once is modeled by cover/partitioning constraints. In this paper, we concentrate on railway specific requirements and present special techniques to model and optimize locomotive and carriage groups with shared capacities. These techniques erable us to solve large-scale practical problem instances of German Railways into optimality.