Public Transport

, Volume 9, Issue 1–2, pp 95–113 | Cite as

A comparison of performance metrics for balancing the power consumption of trains in a railway network by slight timetable adaptation

  • Andreas BärmannEmail author
  • Alexander Martin
  • Oskar Schneider
Original Paper


We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of the trains at the stations. To this end, we propose a mixed-integer programming model for feasible adaptations of the timetable draft and investigate its behaviour under different objective functions which fall into two classes: reducing the energy cost and increasing the stability of the power supply system. These tests are performed on real-world problem instances from our industry partner Deutsche Bahn AG. They show a significant potential for improvements in the existing railway timetables.


Railway timetabling Power peak reduction Mixed-integer programming 


  1. Albrecht T (2010) Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control. In: Pilo E (ed) Power supply. Energy management and catenary problems. WIT Press, LondonGoogle Scholar
  2. Amt für Statistik Berlin–Brandenburg (2016) Statistischer Bericht E IV 4–j / 13: Energie- und CO\(_2\)-Bilanz in Berlin 2013. In: Technical report, Amt für Statistik Berlin–Brandenburg.
  3. Boschetti G, Mariscotti A (2014) Optimizing the energy efficiency of electric transportation systems operation using a genetic algorithm. Int Rev Electr Eng 9(4):783–791Google Scholar
  4. Cacchiani V, Toth P (2012) Nominal and robust train timetabling problems. Eur J Oper Res 219:727–737CrossRefGoogle Scholar
  5. DB Energie GmbH (2016) Preisblatt für die Nutzung des 16,7-Hz-Bahnstromnetzes (Bahnstromnetz) gültig ab 01.01.2016.
  6. Doan VD, Watanabe S, Koseki T (2014) The design of an optimal running curve for train operation based on a novel parameterization method aiming to minimize the total energy consumption. In: Brebbia CA (ed) Computers in railways, vol XIV, pp 175–190Google Scholar
  7. E-Motion (2016) Project E-Motion: energy-efficient mobility.
  8. Feng X, Zhang H, Ding Y, Liu Z, Peng H, Xu B (2013) A review study on traction energy saving of rail transport. Discrete Dyn Nat Soc (article ID 156548). doi: 10.1155/2013/156548
  9. Fischer F, Helmberg C (2014) Dynamic graph generation for the shortest path problem in time expanded networks. Math Program A 143(1–2):257–297CrossRefGoogle Scholar
  10. Fournier D, Mulard D, Fages F (2012) Energy optimization of metro timetables: a hybrid approach. In: Proceedings of the 18th international conference on principles and practice of constraint programming, pp 8–12Google Scholar
  11. Gerhardt N, Valov B, Trost T, Degner T, Lehnert W, Rostankowski A (2011) Bahnstrom regenativ—analyse und Konzepte zur Erhöhung des Anteils der regenerativen Energie des Bahnstroms: Endbericht. In: Technical report, Fraunhofer IWES.
  12. Gong C, Zhang S, Zhang F, Jiang J, Wang X (2014) An integrated energy-efficient operation methodology for metro systems based on a real case of Shanghai metro line one. Energies 7(11):7305–7329CrossRefGoogle Scholar
  13. Gurobi Optimization, Inc (2016) Gurobi optimizer reference manual.
  14. Hasegawa D, Nicholson GL, Roberts C, Schmid F (2014) The impact of different maximum speed on journey times, energy use, headway times and the number of trains required for phase one of Britain’s high speed two line. In: Brebbia CA (ed) Computers in railways, vol XIV, pp 485–496Google Scholar
  15. Kim KM, Oh SM, Han MS (2010) A mathematical approach for reducing the maximum traction energy: the case of Korean MRT trains. In: International multiconference of engineers and computer scientists, pp 2169–2173Google Scholar
  16. Kim KM, Kim KT, Han MS (2011) A model and approaches for synchronized energy saving in timetabling. In: 9th world congress on railway researchGoogle Scholar
  17. Kimura N, Miyatake M (2014) Strategy of speed restriction allowing extended running times to minimize energy consumption and passenger disutility. In: Brebbia CA (ed) Computers in railways, vol XIV, pp 733–743Google Scholar
  18. Knörr W, Heidt C, Schacht A (2012) Aktualisierung “Daten- und Rechenmodell: Energieverbrauch und Schadstoffemissionen des motorisierten Verkehrs in Deutschland 1960–2030” (TREMOD, Version 5.3) für die Emissionsberichtserstattung 2013 (Berichtsperiode 1990–2011): Endbericht. In: Technical report, ifeu—Institut für Energie-und Umweltforschung Heidelberg GmbH.
  19. Li X, Lo HK (2014) Energy minimization in dynamic train scheduling and control for metro rail operations. Transp Res Part B Methodol 70:269–284CrossRefGoogle Scholar
  20. Li X, Chien CF, Li L, Gao Z, Yang L (2012) Energy-constraint operation strategy for high-speed railway. Int J Innov Comput Inf Control 8(10(A)):6569–6583Google Scholar
  21. Lorenz S, Hesse M, Fischer A (2012) Simulation and optimization of robot driven production systems for peak-load reduction. In: Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher AM (eds) Proceedings of the 2012 winter simulation conference, pp 2875–2886Google Scholar
  22. Miyatake M, Ko H (2010) Optimization of train speed profile for minimum energy consumption. IEEJ Trans Electr Electron Eng 5:263–269CrossRefGoogle Scholar
  23. Nelson KF, Uhan A, Zhao F, Sutherland JW (2013) Flow shop scheduling with peak power consumption constraints. Ann Oper Res 206:115–145CrossRefGoogle Scholar
  24. Peña-Alcaraz M, Fernández A, Cucala AP, Ramos A, Pecharromán RR (2011) Optimal underground timetable design based on power flow for maximizing the use of regenerative-braking energy. Proc Inst Mech Eng Part F J Rail Rapid Transit 226(4):397–408CrossRefGoogle Scholar
  25. Ragunathan AU, Wada T, Ueda K, Takahasi S (2014) Minimizing energy consumption in railways by voltage control on substations. In: Brebbia CA (ed) Computers in railways, vol XIV, pp 697–708Google Scholar
  26. Sansó B, Girard P (1997) Instantaneous power peak reduction and train scheduling desynchronization in subway systems. Transp Sci 31(4):312–323CrossRefGoogle Scholar
  27. Scheepmaker GM, Goverde RMP, Kroon LG (2017) Review of energy-efficient train control and scheduling. Eur J Oper Res 257:355–376CrossRefGoogle Scholar
  28. Statistisches Bundesamt (2016) Homepage of the Statistische Bundesamt (German Federal Statistical Office).
  29. Su S, Li X, Tang T, Gao Z (2013) A subway train timetable optimization approach based on energy-efficient operation strategy. IEEE Trans Intell Transp Syst 14(2):883–893CrossRefGoogle Scholar
  30. Wang QY, Wu P, Liang ZC, Feng XY (2014) The hierarchical real-time control of high speed trains for automatic train operation. In: Brebbia CA (ed) Computers in railways, vol XIV, pp 17–36Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Andreas Bärmann
    • 1
    Email author
  • Alexander Martin
    • 1
  • Oskar Schneider
    • 1
  1. 1.Department Mathematik, Lehrstuhl für WirtschaftsmathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

Personalised recommendations