Scheduling Locomotives and Car Transfers in Freight Transport Armin F¨ ugenschuh 1 , Henning Homfeld 1 , Andreas Huck 2 , Alexander Martin 1 , and Zhi Yuan 1 1 Technische Universit¨ at Darmstadt, Arbeitsgruppe Optimierung 64289, Darmstadt, Schlossgartenstr. 7, Germany {fuegenschuh,homfeld,martin,yuan}@mathematik.tu-darmstadt.de 2 Deutsche Bahn AG, Konzernentwicklung, GSU 1 60326, Frankfurt, Stephensonstraße 1, Germany andreas.huck@bahn.de Abstract. We present a new model for a strategic locomotive schedul- ing 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 addi- tionally 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 com- mercial ILP solvers. Computational results are presented for several real- world test instances. Keywords. Railroad Freight Transport, Cyclic Vehicle Scheduling, Time Windows, Integer Linear Programming, Heuristics, Cutting Planes. 1 Introduction Deutsche Bahn AG (DB) is the largest German railway company with 216,000 employees and a turnover of 25 billion Euros in 2005. DB is active in both passenger and freight transportation. Per year, 1.8 billion passengers (72 billion passenger kilometers) and 253 million tons of goods (77 billion ton kilometers) are transported. Moreover, DB is the owner of the German railway system, where DB freight and passenger trains travel 887 million kilometers per year and external railway companies around 110 million kilometers. The overall length of the railways is 34,000 kilometers, about 4,400 freight trains and 30,000 passenger trains per day traverse this network [1,2]. All in all, DB’s network is considered as one of the most dense and most frequently used railway networks in the world. For long-term simulations and future predictions of the network load, DB developed a complex simulation tool. The entire simulation tool may be consid- ered as a chain, which decomposes into several components. To this end it is