Scheduling Locomotives and Car Transfers in Freight Transport

We present a new model for a strategic locomotive scheduling problem arising at the Deutsche Bahn AG. The model is based on a multi-commodity min-cost flow formulation that is also used for public bus scheduling problems. However, several new aspects have to be additionally taken into account, such as cyclic departures of the trains, time windows on starting and arrival times, network-load dependent travel times, and a transfer of cars between trains. The model is formulated as an integer linear programming problem (ILP). The formulation is improved by preprocessing and additional cutting planes. Solutions are obtained using a randomized greedy heuristic in combination with commercial ILP solvers. Computational results are presented for several realworld test instances.