Abstract
Timetabling is a central step in the planning of public transport and important for the quality of service. Thereby, it also faces requirements like punctuality, cost efficiency, flexibility and minimization of travel time. We show the state-of-the-art techniques and their extensions to new challenges, in particular, multi-period timetables and robustness. We conclude with a case study from the Italian Railways that shows the effectiveness of our robustness methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Borndörfer R, Hoppmann H, Karbstein M (2016) Separation of cycle inequalities for the periodic timetabling problem. In: Sankowski P, Zaroliagis CD (eds) 24th annual European symposium on algorithms, ESA. LIPIcs, vol. 57. Schloss Dagstuhl, Wadern, pp 21:1–21:13. ISBN: 978-3-95977-015-6. https://doi.org/10.4230/LIPIcs.ESA.2016.21 (cited on page 123)
Caprara A, Galli L, Toth P (2011) Solution of the train platforming problem. Transp Sci 45(2):246–257. https://doi.org/10.1287/trsc.1100.0366 (cited on pages 137, 138)
Caprara A, Galli L, Stiller S, Toth P (2014) Delayrobust event scheduling. Oper Res 62(2):274–283. https://doi.org/10.1287/opre.2014.1259 (cited on pages 132, 135)
Galli L (2011) Combinatorial and robust optimisation models and algorithms for railway applications. 4OR 9(2):215–218. https://doi.org/10.1007/s10288-010-0138-4 (cited on page 132)
Galli L, Stiller S (2010) Strong formulations for the multi-module PESP and a quadratic algorithm for graphical diophantine equation systems. In: de Berg M, Meyer U (eds) Algorithms - ESA 2010, 18th annual European symposium, Liverpool, September 6–8, 2010. Proceedings, part I. Lecture notes in computer science, vol 6346. Springer, Berlin, pp 338–349. ISBN: 978-3-642-15774-5. https://doi.org/10.1007/978-3-642-15775-2_29 (cited on pages 125, 126, 127)
Großmann P, Hölldobler S, Manthey N, Nachtigall K, Opitz J, Steinke P (2012) Solving periodic event scheduling problems with SAT. In: Jiang H, Ding W, Ali M, Wu X (eds) Proceedings of the 25th international conference on industrial engineering and other applications of applied intelligent systems. Lecture notes in computer science, vol 7345. Springer, Berlin, pp 166–175. ISBN: 978-3-642-31086-7. https://doi.org/10.1007/978-3-642-31087-4_18 (cited on page 121)
Kavitha T, Liebchen C, Mehlhorn K, Michail D, Rizzi R, Ueckerdt T, Zweig KA (2009) Cycle bases in graphs characterization, algorithms, complexity, and applications. Comput Sci Rev 3(4):199–243. https://doi.org/10.1016/j.cosrev.2009.08.001 (cited on page 122)
Liebchen C (2006) Periodic timetable optimization in public transport. PhD thesis, TU Berlin. dissertation.de. ISBN: 978-3-86624-150-3 (cited on pages 119, 121, 122)
Liebchen C, Swarat E (2008) The second Chvatal closure can yield better railway timetables. In: Fischetti M, Widmayer P (eds) Proceedings of the 8th workshop on algorithmic approaches for transportation modeling, optimization, and systems (ATMOS 2008), OASICS, vol 9. Schloss Dagstuhl, Wadern. https://doi.org/10.4230/OASIcs.ATMOS.2008.1580 (cited on page 121)
Liebchen C, Lübbecke M, Möhring R, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Springer, Berlin, pp 1–27. https://doi.org/10.1007/978-3-642-05465-5_1 (cited on pages 132)
Nachtigal K (1996) Cutting planes for a polyhedron associated with a periodic network. Technical Report, DLR (cited on page 121)
Nachtigall K (1996) Periodic network optimization with different arc frequencies. Discret Appl Math 69(1–2):1–17. https://doi.org/10.1016/0166-218X(95)00073-Z (cited on page 123)
Odijk MA (1996) A constraint generation algorithm for the construction of periodic railway timetables. Transp Res B Methodol 30(6):455–464. https://doi.org/10.1016/0191-2615(96)00005-7 (cited on pages 121, 123)
Schrijver A, Steenbeck A (1994) Dienstregelingontwikkeling voor Railned (Timetable construction for Railned). Technical Report, C.W.I. Center for Mathematics and Computer Science, Amsterdam (cited on page 121)
Serafini P, Ukovich W (1989) A mathematical model for periodic scheduling problems. SIAM J Discret Math 2(4):550–581. ISSN: 0895-4801. https://doi.org/10.1137/0402049 (cited on page 120)
Stiller S (2008) Extending concepts of reliability. PhD thesis, TU Berlin. https://doi.org/10.14279/depositonce-2093 (cited on pages 132)
UIC (2000) Timetable recovery margins to guarantee timekeeping–recovery margins. ISBN: 2-7461-0223-4 (cited on page 119)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Galli, L., Stiller, S. (2018). Modern Challenges in Timetabling. In: Borndörfer, R., Klug, T., Lamorgese, L., Mannino, C., Reuther, M., Schlechte, T. (eds) Handbook of Optimization in the Railway Industry. International Series in Operations Research & Management Science, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-319-72153-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-72153-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72152-1
Online ISBN: 978-3-319-72153-8
eBook Packages: Business and ManagementBusiness and Management (R0)