Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.

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We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of the trains at the stations. To this end, we propose a mixed-integer programming model for feasible adaptations of the timetable draft and investigate its behaviour under different objective functions which fall into two classes: reducing the energy cost and increasing the stability of the power supply system. These tests are performed on real-world problem instances from our industry partner Deutsche Bahn AG. They show a significant potential for improvements in the existing railway timetables.

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