TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Umsteigen ohne Warten T2 - HEUREKA 2017 N2 - Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität. Y1 - 2017 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Timetabling and Passenger Routing in Public Transport T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015) N2 - The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal. KW - Passenger routing KW - Periodic timetabling KW - Public transport Y1 - 2015 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika A1 - Löbel, Fabian T1 - The Modulo Network Simplex with Integrated Passenger Routing T2 - Operations Research Proceedings 2016 N2 - Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration. Y1 - 2016 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika A1 - Lindner, Niels T1 - Separation of cycle inequalities in periodic timetabling JF - Discrete Optimization N2 - Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem in public transport. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we contribute a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. Moreover, we provide several NP-completeness results, indicating that pseudo-polynomial time is best possible. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem. Y1 - 2020 U6 - https://doi.org/10.1016/j.disopt.2019.100552 IS - 35 SP - 100552 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Separation of Cycle Inequalities for the Periodic Timetabling Problem T2 - 24th Annual European Symposium on Algorithms (ESA 2016) N2 - Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem. Y1 - 2016 U6 - https://doi.org/10.4230/LIPIcs.ESA.2016.21 VL - 57 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Passenger routing for periodic timetable optimization BT - Planning and Operations JF - Public Transport N2 - The task of periodic timetabling is to determine trip arrival and departure times in a public transport system such that travel and transfer times are minimized. This paper investigates periodic timetabling models with integrated passenger routing. We show that different routing models can have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems by integrating passenger routing. Y1 - 2016 U6 - https://doi.org/10.1007/s12469-016-0132-0 PB - Springer-Verlag Berlin Heidelberg ER - TY - JOUR A1 - Hoppmann, Heide T1 - Linienplanung und Minimale Konfigurationen JF - OR News Y1 - 2015 VL - 55 SP - 22 EP - 23 ER - TY - CHAP A1 - Hoppmann, Heide T1 - An Extended Formulation for the Line Planning Problem T2 - Operations Research Proceedings 2015 N2 - In this paper we present a novel extended formulation for the line planning problem that is based on what we call “configurations” of lines and frequencies. Configurations account for all possible options to provide a required transportation capacity on an infrastructure edge. The proposed configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, MIR, and multicover inequalities. These theoretical findings can be confirmed in computational results. Further, we show how this concept can be generalized to define configurations for subsets of edges; the generalized model implies additional inequalities from the line planning literature. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-42902-1_2 SP - 11 EP - 17 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika ED - Frigioni, Daniele ED - Stiller, Sebastian T1 - A Configuration Model for the Line Planning Problem T2 - ATMOS 2013 - 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2013 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2013.68 VL - 33 SP - 68 EP - 79 PB - Schloss Dagstuhl--Leibniz-Zentrum für Informatik ER -