Christian Liebchen

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We present a new concept for optimization under uncertainty: recoverable robustness. A solution is recovery robust if it can be recovered by limited means in all likely scenarios. Specializing the general concept to linear programming we can show that recoverable robustness combines the flexibility of stochastic programming with the tractability and(More)
Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing. From a mathematical point of view, cycles in graphs have a rich structure. Cycle bases are a compact description of the set of all cycles of a graph. In this paper, we(More)
In the past, much research has been dedicated to compute optimum railway timetables. A typical objective was the minimization of passenger waiting times. But only the planned nominal waiting times were addressed, whereas delays, as they occur in daily operations, were neglected. Delays were rather treated mainly in an online-context, and solved as a(More)
In the overwhelming majority of public transportation companies, designing a periodic timetable is even nowadays largely performed manually. Software tools only support the planners in evaluating a periodic timetable, or by letting them comfortably shift sets of trips by some minutes, but they rarely use optimization methods. One of the main arguments(More)
In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization. Models for periodic timetabling are commonly based on the Periodic Event(More)