Matheon-B15: Service Design in Public Transport
Service design in public transport deals with network design, line planning, timetabling, and fare planning. These problems can be dealt with using mathematical methods. We have developed such approaches in the first two Matheon funding periods. The model for timetabling is based on a periodic event scheduling problem and was applied at the Berliner Verkehrsbetrieb and at the Verkehrsbetrieb in Potsdam.
For the optimization of fares we used a discrete choice model which integrates a utility function of the passengers. Such a model can be used to compare different fare systems in respect of number of attracted passengers, profit or revenue.
The line planning model integrates line planning and passenger routing and uses a column generation approach. In a project together with the Verkehrsbetrieb in Potsdam (ViP) we used this optimization model to support the design of a new line plan for Potsdam for 2010. We could show that all requirements relevant for practice concerning the public transport company ViP can be integrated in the mathematical model.
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| line plan for Potsdam | demand with respect to prices |
A major challenge in service design optimization is the consideration of passenger behavior. The level of service decides whether passengers are attracted to this system or not. Understanding and controlling the interplay between service design and passenger behavior is therefore a main goal in service planning. We will investigate these aspects in the combinatorial context of line planning.
Organizational Details
Contact
Partners
- ViP Verkehrsbetrieb Potsdam GmbH
- City of Potsdam
- Marc Pfetsch (TU Braunschweig)
- Ramiro Torres und Luis M. Torres (EPN Quito)
- DFG Research Center Matheon "Mathematics for key technologies",
Project B3: Integrated Planning of Multi-level-/Multi-layer-Netzwerken - DFG Research Center Matheon "Mathematics for key technologies",
Project B20: Optimization of Gas Transport - DFG Research Center Matheon "Mathematics for key technologies",
Project B22: Rolling Stock Roster Planning - DFG Research Center Matheon "Mathematics for key technologies",
Project F4: Geometric Shape Optimization
Publcations
- R. Borndörfer, I. Friedow, M. Karbstein. Optimierung des Linienplans 2010 in Potsdam. Technical Report 12-04, ZIB 2012.
- R. Borndörfer, M. Karbstein. A note on Menger's Theorem for Hypergraphs. Technical Report 12-03, ZIB 2012.
- R. Borndörfer. Mathematical Optimization and Public Transportation. Habilitationthesis, TU Berlin, 2010.
- R. Meirich. Polyedrische Untersuchung eines Linienplanungsproblems. Diplomathesis, TU Berlin, 2010.
- R. Borndörfer, M. Neumann. Models for Line Planning with Transfers, Technical Report 10-11, ZIB 2010.
- R. Borndörfer, M. Neumann. Linienoptimierung- reif für die Praxis?. In Heureka '11 – Optimierung in Transport und Verkehr, M. Friedrich (ed.), Tagungsbericht, FGSV Verlag. Technical Report 10-20, ZIB 2010.
- R. Borndörfer, M. Neumann, M. Pfetsch The Steiner Connectivity Problem, Technical Report 09-07, ZIB 2009.
- R. Borndörfer, M. Neumann, M. E. Pfetsch. The Line Connectivity Problem. In Operations Research Proceedings 2008, B. Fleischmann, K. H Borgwardt, R. Klein, and A Tuma (eds), pp 557-562, Springer Verlag, 2009. Technical Report, ZIB 2008.
- R. Borndörfer, M. Neumann, M. E. Pfetsch. Models for Fare Planning in Public Transport. Technical Report, ZIB 2008.
- R. Borndörfer, M. Neumann, M. E. Pfetsch. Angebotsplanung im öffentlichen Nahverkehr. In Heureka '08 – Optimierung in Transport und Verkehr, M. Friedrich (ed.), Tagungsbericht, FGSV Verlag.
- M. Kinder. Models for Periodic Timetabling. Diplomathesis, TU Berlin, 2008.
- J. Ridder. Wegeprobleme der Graphentheorie. A-level thesis, Herder-Gymnasium Berlin, 2008.
- L. M. Torres, R. Torres, R. Borndörfer, M. E. Pfetsch. Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System. In ATMOS 2008. Technical Report, ZIB 2008.
- L. M. Torres, R. Torres, R. Borndörfer, M. E. Pfetsch. On the Line Planning Problem in Tree Networks. Technical Report, ZIB 2008.
- R. Borndörfer, C. Liebchen. When Periodic Timetables are Suboptimal. In Operations Research Proceedings 2007, J. Kalcsics and S. Nickel (eds.), pp 449-454, Springer-Verlag, 2008.
- R. Borndörfer, M. Grötschel, M. E. Pfetsch. A Column-Generation Approach to Line Planning in Public Transport. In Transportation Science 41 (1), pp. 123-132, 2007.
- M. Neumann. Fare Planning for Public Transport. In Operations Research Proceedings 2006, K.-H. Waldmann und U.-M. Stocker (eds.), pp. 61-66, Springer-Verlag (2007).
- M. Neumann. Mathematische Preisplanung im öPNV. In OR News 30, pp. 29-31, 2007.
- R. Borndörfer, M. Grötschel, M. E. Pfetsch. Public transport to the fORe. In OR/MS Today 33 (2) 2006.
- R. Borndörfer, M. Neumann, M. E. Pfetsch. Optimal Fares for Public Transport. In Operations Research Proceedings 2005, H.-D. Haasis et. al. (eds.), pp. 591-596, Springer-Verlag (2006).
- M. E. Pfetsch, R. Borndörfer. Routing in Line Planning for Public Transport. In Operations Research Proceedings 2005, H.-D. Haasis et. al. (eds.), pp. 405-410, Springer-Verlag (2006).
- R. Borndörfer, M. Neumann, M. E. Pfetsch. Fare Planning in Public Transport. Technical Report 05–20, ZIB, 2005.
- R. Borndörfer, M. Grötschel, M. E. Pfetsch. Models for Line Planning in Public Transport. In Computer-aided Systems in Public Transport (CASPT 2004), M. Hickman et al. (eds.), pp. 363-378, Springer Verlag 2008.
- A. Dix, Das statische Linienplanungsproblem Diplomathesis, TU Berlin, 2007.
- M. Neumann. Mathematische Preisplanung im ÖPNV. Diplomathesis, TU Berlin, 2005.
- R. Stephan. Polytopes Associated with Length-Restricted Directed Circuits. Diplomathesis, TU Berlin, 2005.
Awards
- Marika Karbstein "Ultimative Kalenderaufgabe 2011" (Matheon Adventskalender).
- Johanne Ridder DMV Abiturpreis Mathematik 2008.
- Marika Neumann GOR Diplomarbeitspreis 2006.
Funding
- DFG Research Center Matheon "Mathematics for key technologies: Modelling, simulation, and optimization of real-word processes."
Duration
06/2006 - 05/2014