7074 2018 eng 16:1 16:15 65 conferenceobject 0 -- -- -- We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same. 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018) 10.4230/OASIcs.ATMOS.2018.16 OpenAccess Series in Informatics (OASIcs) yes urn:nbn:de:0297-zib-69688 Ralf Borndörfer Niels Lindner Marika Karbstein Christian Liebchen Niels Lindner Mathematical Optimization Borndörfer, Ralf MODAL-RailLab MODAL-Gesamt Lindner, Niels ECMath-MI7 Applied Optimization