Investigating Robustness, Public Transport, Optimization, and their Interface

By investigating robustness, public transport optimization, and their interface, this dissertation contributes research to the field of mathematical optimization via the cumulation of five individual but thematically connected publications. The first two publications are concerned with designing cost-minimal public transport systems by integrating several subproblems of public transport optimization. The third publication considers passenger-convenience by integrating passenger movements at train stations into a delay management model. Publication four focuses on cutting plane techniques that are used to solve robust optimization problems and introduces speed-up techniques for these problems by approximatively solving occurring subproblems, which are induced by the cutting plane scheme. The fifth publication then combines the topics of public transport and robust optimization through formulating a robust timetabling problem in order to find delay-resistant timetables. By doing so it integrates public transport problems -as done in the first two publications . considers delay management - as in the third publication - and makes use of speed-up techniques for cutting plane algorithms for its solution algorithms -as presented in the fourth contribution.