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Introduction

  • Philine Schiewe
Chapter
  • 28 Downloads
Part of the Springer Optimization and Its Applications book series (SOIA, volume 160)

Abstract

In times of growing urban populations and increasing environmental awareness, the importance of public transport systems is increasing as well. Public transport provides an efficient way for commuting by bundling traffic flows with the same general direction, thus reducing the individual traffic and the resulting congestions in peak hours. In this chapter, we introduce the public transport problems considered in this book as well as the data sets used for the experimental evaluation.

References

  1. [AMO88]
    R. Ahuja, T. Magnanti, J. Orlin, Network Flows (1988)Google Scholar
  2. [BAE.
    R. Borndörfer, O. Arslan, Z. Elijazyfer, H. Güler, M. Renken, G. Şahin, T. Schlechte, Line planning on path networks with application to the Istanbul metrobüs, in Operations Research Proceedings 2016, pp. 235–241 (Springer, 2018)Google Scholar
  3. [BBVL17]
    S. Burggraeve, S. Bull, P. Vansteenwegen, R. Lusby, Integrating robust timetabling in line plan optimization for railway systems. Transp. Res. C Emerg. Technol. 77, 134–160 (2017)Google Scholar
  4. [BCG87]
    A. Bertossi, P. Carraresi, G. Gallo, On some matching problems arising in vehicle scheduling models. Networks 17(3), 271–281 (1987)MathSciNetzbMATHGoogle Scholar
  5. [BGJ10]
    R. Borndörfer, M. Grötschel, U. Jäger, Planning problems in public transit, in Production Factor Mathematics, pp. 95–121 (Springer, 2010)Google Scholar
  6. [BGP07]
    R. Borndörfer, M. Grötschel, M. Pfetsch, A column-generation approach to line planning in public transport. Transp. Sci. 41(1), 123–132 (2007)Google Scholar
  7. [BHK16]
    R. Borndörfer, H. Hoppmann, M. Karbstein, Separation of cycle inequalities for the periodic timetabling problem, in 24th Annual European Symposium on Algorithms (ESA 2016), vol. 57 of Leibniz International Proceedings in Informatics (LIPIcs), ed. by P. Sankowski, C. Zaroliagis, (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016), pp. 21:1–21:13Google Scholar
  8. [BHK17]
    R. Borndörfer, H. Hoppmann, M. Karbstein, Passenger routing for periodic timetable optimization. Public Transp. 9(1-2), 115–135 (2017)Google Scholar
  9. [BK09]
    S. Bunte, N. Kliewer, An overview on vehicle scheduling models. Public Transp. 1(4), 299–317 (2009)Google Scholar
  10. [BKLL18]
    R. Borndörfer, M. Karbstein, C. Liebchen, N. Lindner, A simple way to compute the number of vehicles that are required to operate a periodic timetable, in 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018), vol. 65 of OpenAccess Series in Informatics (OASIcs), ed. by R. Borndörfer, S. Storandt (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2018), pp. 16:1–16:15Google Scholar
  11. [BKZ97]
    M. Bussieck, P. Kreuzer, U. Zimmermann, Optimal lines for railway systems. Eur. J. Oper. Res. 96(1), 54–63 (1997)zbMATHGoogle Scholar
  12. [BLL04]
    M. Bussieck, T. Lindner, M. Lübbecke, A fast algorithm for near cost optimal line plans. Math. Methods Oper. Res. 59(2), 205–220 (2004)MathSciNetzbMATHGoogle Scholar
  13. [BO01]
    M. Barratt, A. Oliveira, Exploring the experiences of collaborative planning initiatives. Int. J. Phys. Distrib. Logist. Manag. 31(4), 266–289 (2001)Google Scholar
  14. [BRLL16]
    S. Bull, N. Rezanova, R. Lusby, J. Larsen, An applied optimization based method for line planning to minimize travel time. Technical report, DTU Management Engineering, 2016Google Scholar
  15. [Bus98]
    M. Bussieck, Optimal lines in public rail transport, PhD thesis, Technische Universität Braunschweig, 1998Google Scholar
  16. [BWZ97]
    M. Bussieck, T. Winter, U. Zimmermann, Discrete optimization in public rail transport. Math. Program. 79(1-3), 415–444 (1997)MathSciNetzbMATHGoogle Scholar
  17. [CHS13]
    E. Carrizosa, J. Harbering, A. Schöbel, The stop location problem with realistic traveling time, in 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, vol. 33 of OpenAccess Series in Informatics (OASIcs), ed. by D. Frigioni, S. Stiller (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2013), pp. 80–93Google Scholar
  18. [CM12]
    L. Cadarso, Á. Marín, Integration of timetable planning and rolling stock in rapid transit networks. Ann. Oper. Res. 199(1), 113–135 (2012)MathSciNetzbMATHGoogle Scholar
  19. [CvDZ98]
    M. Claessens, N. van Dijk, P. Zwaneveld, Cost optimal allocation of rail passenger lines. Eur. J. Oper. Res. 110(3), 474–489 (1998)zbMATHGoogle Scholar
  20. [CW86]
    A. Ceder, N. Wilson, Bus network design. Transp. Res. B Methodol. 20(4), 331–344 (1986)Google Scholar
  21. [DC18]
    M. Darvish, L. Coelho, Sequential versus integrated optimization: Production, location, inventory control, and distribution. Eur. J. Oper. Res. 268(1), 203–214 (2018)MathSciNetzbMATHGoogle Scholar
  22. [DH07]
    G. Desaulniers, M. Hickman, Public transit. Handbooks Oper. Res. Manag. Sci. 14, 69–127 (2007)Google Scholar
  23. [DP95]
    J. Daduna, J. Paixão, Vehicle scheduling for public mass transit - an overview. Computer-Aided Transit Scheduling (Springer, 1995), pp. 76–90Google Scholar
  24. [DRB.
    S. Dutta, N. Rangaraj, M. Belur, S. Dangayach, K. Singh, Construction of periodic timetables on a suburban rail network-case study from Mumbai, in RailLille 2017-7th International Conference on Railway Operations Modelling and Analysis, 2017Google Scholar
  25. [Ehr05]
    M. Ehrgott, Multicriteria Optimization, vol. 491 (Springer Science & Business Media, 2005)Google Scholar
  26. [FHSS17a]
    M. Friedrich, M. Hartl, A. Schiewe, A. Schöbel, Angebotsplanung im öffentlichen Verkehr - planerische und algorithmische Lösungen, in Heureka’17, 2017Google Scholar
  27. [FHSS17b]
    M. Friedrich, M. Hartl, A. Schiewe, A. Schöbel, Integrating passengers’ assignment in cost-optimal line planning, in 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017), vol. 59 of OpenAccess Series in Informatics (OASIcs), ed. by G. D’Angelo, T. Dollevoet (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017), pp. 5:1–5:16Google Scholar
  28. [FM10]
    L. Fan, C. Mumford, A metaheuristic approach to the urban transit routing problem. J. Heuristics 16(3), 353–372 (2010)zbMATHGoogle Scholar
  29. [FMR.
    M. Friedrich, M. Müller-Hannemann, R. Rückert, A. Schiewe, A. Schöbel, Robustness tests for public transport planning, in 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017), vol. 59 of OpenAccess Series in Informatics (OASIcs), ed. by G. D’Angelo, T. Dollevoet (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017), pp. 1–16Google Scholar
  30. [FMR.
    M. Friedrich, M. Müller-Hannemann, R. Rückert, A. Schiewe, A. Schöbel, Robustness as a third dimension for evaluating public transport plans, in 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018), vol. 65 of OpenAccess Series in Informatics (OASIcs), ed. by R. Borndörfer, S. Storandt (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2018), pp. 4:1–4:17Google Scholar
  31. [FOR18]
    FOR 2083: Integrated Planning For Public Transportation, Collection of open source public transport networks by DFG research unit. https://github.com/FOR2083/PublicTransportNetworks, 2018
  32. [FvdHRL18]
    J. Fonseca, E. van der Hurk, R. Roberti, A. Larsen, A matheuristic for transfer synchronization through integrated timetabling and vehicle scheduling. Transp. Res. B Methodol. 109, 128–149 (2018)Google Scholar
  33. [GGNS16]
    P. Gattermann, P. Großmann, K. Nachtigall, A. Schöbel, Integrating passengers’ routes in periodic timetabling: A SAT approach, in 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016), vol. 54 of OpenAccess Series in Informatics (OASIcs), ed. by M. Goerigk, R. Werneck (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2016), pp. 1–15Google Scholar
  34. [GH08]
    V. Guihaire, J. Hao. Transit network design and scheduling: A global review. Transp. Res. A Policy Pract. 42(10), 1251–1273 (2008)Google Scholar
  35. [GH10]
    V. Guihaire, J.-K. Hao, Transit network timetabling and vehicle assignment for regulating authorities. Comput. Ind. Eng. 59(1), 16–23 (2010)Google Scholar
  36. [GHM.
    P. Großmann, S. Hölldobler, N. Manthey, K. Nachtigall, J. Opitz, P. Steinke, Solving periodic event scheduling problems with SAT. Advanced Research in Applied Artificial Intelligence (Springer, 2012), pp. 166–175Google Scholar
  37. [GHS17]
    P. Gattermann, J. Harbering, A. Schöbel, Line pool generation. Public Transp. 9(1-2), 7–32 (2017)Google Scholar
  38. [GJ79]
    M. Garey, D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, vol. 29 (WH Freeman and Company, San Francisco, 1979)zbMATHGoogle Scholar
  39. [GL17]
    M. Goerigk, C. Liebchen, An improved algorithm for the periodic timetabling problem, in 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017), vol. 59 of OpenAccess Series in Informatics (OASIcs), ed. by G. D’Angelo, T. Dollevoet (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017), pp. 12:1–12:14Google Scholar
  40. [Goe12]
    M. Goerigk, Algorithms and concepts for robust optimization, PhD thesis, Niedersächsische Staats-und Universitätsbibliothek Göttingen, 2012Google Scholar
  41. [Goo04]
    J.-W. Goossens, Models and algorithms for railway line planning problems, PhD thesis, Universiteit Maastricht, 2004Google Scholar
  42. [GS79]
    B. Gavish, E. Shlifer, An approach for solving a class of transportation scheduling problems. Eur. J. Oper. Res. 3(2), 122–134 (1979)MathSciNetzbMATHGoogle Scholar
  43. [GS13]
    M. Goerigk, A. Schöbel, Improving the modulo simplex algorithm for large-scale periodic timetabling. Comput. Oper. Res. 40(5), 1363–1370 (2013)MathSciNetzbMATHGoogle Scholar
  44. [GS17]
    M. Goerigk, M. Schmidt, Line planning with user-optimal route choice. Eur. J. Oper. Res. 259(2), 424–436 (2017)MathSciNetzbMATHGoogle Scholar
  45. [GS18]
    L. Galli, S. Stiller, Modern challenges in timetabling. Handbook of Optimization in the Railway Industry (Springer, 2018), pp. 117–140Google Scholar
  46. [GVDHH02]
    I. Grossmann, S. Van Den Heever, I. Harjunkoski, Discrete optimization methods and their role in the integration of planning and scheduling, in AIChE Symposium Series (American Institute of Chemical Engineers, New York, 1998, 2002), pp. 150–168Google Scholar
  47. [GvHK04]
    J.-W. Goossens, S. van Hoesel, L. Kroon, A branch-and-cut approach for solving railway line-planning problems. Transp. Sci. 38(3), 379–393 (2004)Google Scholar
  48. [GvHK06]
    J.-W. Goossens, S. van Hoesel, L. Kroon, On solving multi-type railway line planning problems. Eur. J. Oper. Res. 168(2), 403–424 (2006)MathSciNetzbMATHGoogle Scholar
  49. [Har16]
    J. Harbering, Planning a public transportation system with a view towards passengers’ convenience, PhD thesis, Universität Göttingen, 2016Google Scholar
  50. [HKLV05]
    D. Huisman, L. Kroon, R. Lentink, M. Vromans, Operations research in passenger railway transportation. Statistica Neerlandica 59(4), 467–497 (2005)MathSciNetzbMATHGoogle Scholar
  51. [IRRS11]
    O. Ibarra-Rojas, Y. Rios-Solis, Integrating synchronization bus timetabling and single-depot single-type vehicle scheduling, in ORP3 Meeting, Cadiz, 2011Google Scholar
  52. [Kas10]
    M. Kaspi, Service oriented train timetabling, Master’s thesis, Tel Aviv University, 2010Google Scholar
  53. [KGN.
    M. Kümmling, P. Großmann, K. Nachtigall, J. Opitz, R. Weiß, A state-of-the-art realization of cyclic railway timetable computation. Public Transp. 7(3), 281–293 (2015)Google Scholar
  54. [KHA.
    L. Kroon, D. Huisman, E. Abbink, P.-J. Fioole, M. Fischetti, G. Maróti, A. Schrijver, A. Steenbeek, R. Ybema, The new Dutch timetable: The OR revolution. Interfaces 39(1), 6–17 (2009)Google Scholar
  55. [Kin08]
    M. Kinder, Models for periodic timetabling, Master’s thesis, Technische Universität Berlin, 2008Google Scholar
  56. [KK09]
    K. Kepaptsoglou, M. Karlaftis, Transit route network design problem. J. Transp. Eng. 135(8), 491–505 (2009)Google Scholar
  57. [KP03]
    L. Kroon, L. Peeters, A variable trip time model for cyclic railway timetabling. Transp. Sci. 37(2), 198–212 (2003)Google Scholar
  58. [KR13]
    M. Kaspi, T. Raviv, Service-oriented line planning and timetabling for passenger trains. Transp. Sci. 47(3), 295–311 (2013)Google Scholar
  59. [LHS18]
    K. Li, H. Huang, P. Schonfeld, Metro timetabling for time-varying passenger demand and congestion at stations. J. Adv. Transp. 2018, 26p. (2018)Google Scholar
  60. [LHZ18]
    K. Lu, B. Han, X. Zhou, Smart urban transit systems: From integrated framework to interdisciplinary perspective. Urban Rail Transit, 1–19 (2018)Google Scholar
  61. [Lie03]
    C. Liebchen, Finding short integral cycle bases for cyclic timetabling, in European Symposium on Algorithms (Springer, 2003), pp. 715–726Google Scholar
  62. [Lie06]
    C. Liebchen, Periodic Timetable Optimization in Public Transport, dissertation.de (Verlag im Internet, Berlin, 2006)Google Scholar
  63. [Lie08a]
    C. Liebchen, The first optimized railway timetable in practice. Transp. Sci. 42(4), 420–435 (2008)Google Scholar
  64. [Lie08b]
    C. Liebchen, Linien-, Fahrplan-, Umlauf-und Dienstplanoptimierung: Wie weit können diese bereits integriert werden?, in Heureka’08, 2008Google Scholar
  65. [Lie18]
    C. Liebchen, Nutzung graphentheoretischer Konzepte zur manuellen Erstellung effizienter Verkehrsangebote, in 26. Verkehrswissenschaftliche Tage Dresden, Germany: Technische Universität Dresden, pp. 309–332, 2018, ed. by J. Schänberger, S. NerlichGoogle Scholar
  66. [Lin00]
    T. Lindner, Train schedule optimization in public rail transport, PhD thesis, Technische Universität Braunschweig, 2000Google Scholar
  67. [LK93]
    A. Lenderink, H. Kals, The integration of process planning and machine loading in small batch part manufacturing. Robot. Comput. Integr. Manuf. 10(1-2), 89–98 (1993)Google Scholar
  68. [LLER11]
    R. Lusby, J. Larsen, M. Ehrgott, D. Ryan, Railway track allocation: models and methods. OR Spectr. 33(4), 843–883 (2011)MathSciNetzbMATHGoogle Scholar
  69. [LM07]
    C. Liebchen, R. Möhring, The modeling power of the periodic event scheduling problem: railway timetables and beyond. Algorithmic Methods for Railway Optimization (Springer, 2007), pp. 3–40Google Scholar
  70. [LP09]
    C. Liebchen, L. Peeters, Integral cycle bases for cyclic timetabling. Discret. Optim. 6(1), 98–109 (2009)MathSciNetzbMATHGoogle Scholar
  71. [LPSS18]
    M. Lübbecke, C. Puchert, P. Schiewe, A. Schöbel, Integrating line planning, timetabling and vehicle scheduling - integer programming formulation and analysis, in Proceedings of CASPT 2018, 2018Google Scholar
  72. [LPW97]
    H. Lee, V. Padmanabhan, S. Whang, Information distortion in a supply chain: The bullwhip effect. Manag. Sci. 43(4), 546–558 (1997)zbMATHGoogle Scholar
  73. [LR05]
    C. Liebchen, R. Rizzi, A greedy approach to compute a minimum cycle basis of a directed graph. Inf. Process. Lett. 94(3), 107–112 (2005)MathSciNetzbMATHGoogle Scholar
  74. [LS67]
    W. Lampkin, P. Saalmans, The design of routes, service frequencies, and schedules for a municipal bus undertaking: A case study. J. Oper. Res. Soc. 18(4), 375–397 (1967)Google Scholar
  75. [Man80]
    C. Mandl, Evaluation and optimization of urban public transportation networks. Eur. J. Oper. Res. 5(6), 396–404 (1980)MathSciNetzbMATHGoogle Scholar
  76. [Mar06]
    G. Maróti, Operations research models for railway rolling stock planning, PhD thesis, Eindhoven University of Technology, 2006Google Scholar
  77. [MASM18]
    G. Matos, L. Albino, R. Saldanha, E. Morgado, Solving periodic timetabling problems with SAT and machine learning, in Proceedings of CASPT 2018, 2018Google Scholar
  78. [MPR09]
    M. Mesquita, A. Paias, A. Respício, Branching approaches for integrated vehicle and crew scheduling. Public Transp. 1(1), 21–37 (2009)Google Scholar
  79. [MS09]
    M. Michaelis, A. Schöbel, Integrating line planning, timetabling, and vehicle scheduling: A customer-oriented approach. Public Transp. 1(3), 211–232 (2009)Google Scholar
  80. [Nac98]
    K. Nachtigall, Periodic network optimization and fixed interval timetables, PhD thesis, University of Hildesheim, 1998Google Scholar
  81. [NJ08]
    K. Nachtigall, K. Jerosch, Simultaneous network line planning and traffic assignment, in 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’08), ed. by M. Fischetti, P. Widmayer. OpenAccess Series in Informatics (OASIcs) (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2008)Google Scholar
  82. [NO08]
    K. Nachtigall, J. Opitz, Solving periodic timetable optimisation problems by modulo simplex calculations, in 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’08), ed. by M. Fischetti, P. Widmayer. OpenAccess Series in Informatics (OASIcs) (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2008)Google Scholar
  83. [NV96]
    K. Nachtigall, S. Voget, A genetic algorithm approach to periodic railway synchronization. Comput. Oper. Res. 23(5), 453–463 (1996)zbMATHGoogle Scholar
  84. [NV97]
    K. Nachtigall, S. Voget, Minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks. Eur. J. Oper. Res. 103(3), 610–627 (1997)zbMATHGoogle Scholar
  85. [NW88]
    G. Nemhauser, L. Wolsey, Integer and Combinatorial Optimization (Wiley, 1988)Google Scholar
  86. [Odi96]
    M. Odijk, A constraint generation algorithm for the construction of periodic railway timetables. Transp. Res. B Methodol. 30(6), 455–464 (1996)Google Scholar
  87. [Orl76]
    C. Orloff, Route constrained fleet scheduling. Transp. Sci. 10(2), 149–168 (1976)Google Scholar
  88. [PB87]
    J. Paixão, I. Branco, A quasi-assignment algorithm for bus scheduling. Networks 17(3), 249–269 (1987)MathSciNetzbMATHGoogle Scholar
  89. [PB06]
    M. Pfetsch, R. Borndörfer, Routing in line planning for public transport, in Operations Research Proceedings 2005 (Springer, 2006), pp. 405–410Google Scholar
  90. [Pee03]
    L. Peeters, Cyclic railway timetable optimization, PhD thesis, Erasmus University Rotterdam, 2003Google Scholar
  91. [PK01]
    L. Peeters, L. Kroon, A cycle based optimization model for the cyclic railway timetabling problem. Computer-Aided Scheduling of Public Transport (Springer, 2001), pp. 275–296Google Scholar
  92. [PLM.
    H. Petersen, A. Larsen, O. Madsen, B. Petersen, S. Ropke, The simultaneous vehicle scheduling and passenger service problem. Transp. Sci. 47(4), 603–616 (2013)Google Scholar
  93. [PS16]
    J. Pätzold, A. Schöbel, A matching approach for periodic timetabling, in 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016), vol. 54 of OpenAccess Series in Informatics (OASIcs), ed. by M. Goerigk, R. Werneck (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016), pp. 1:1–1:15Google Scholar
  94. [PSS18]
    J. Pätzold, A. Schiewe, A. Schöbel, Cost-minimal public transport planning, in 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018), vol. 65 of OpenAccess Series in Informatics (OASIcs), ed. by R. Borndörfer, S. Storandt (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2018), pp. 8:1–8:22Google Scholar
  95. [PSSS17]
    J. Pätzold, A. Schiewe, P. Schiewe, A. Schöbel, Look-ahead approaches for integrated planning in public transportation, in 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017), vol. 59 of OpenAccess Series in Informatics (OASIcs), ed. by G. D’Angelo, T. Dollevoet (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017), pp. 17:1–17:16Google Scholar
  96. [RN09]
    M. Rittner, K. Nachtigall, Simultane Liniennetz- und Fahrlagenoptimierung. Der Eisenbahningenieur, 2009Google Scholar
  97. [RS18]
    M. Reuther, T. Schlechte, Optimization of rolling stock rotations. Handbook of Optimization in the Railway Industry (Springer, 2018), pp. 213–241Google Scholar
  98. [RSAMB17]
    T. Robenek, S. Sharif Azadeh, Y. Maknoon, M. Bierlaire, Hybrid cyclicity: Combining the benefits of cyclic and non-cyclic timetables. Transp. Res. C Emerg. Technol. 75, 228–253 (2017)Google Scholar
  99. [Sah70]
    J. Saha, An algorithm for bus scheduling problems. J. Oper. Res. Soc. 21(4), 463–474 (1970)MathSciNetzbMATHGoogle Scholar
  100. [SAP.
    A. Schiewe, S. Albert, J. Pätzold, P. Schiewe, A. Schöbel, J. Schulz, LinTim: An integrated environment for mathematical public transport optimization. documentation. Technical Report 2018-08, Preprint-Reihe, Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, 2018Google Scholar
  101. [SAP.
    A. Schiewe, S. Albert, J. Pätzold, P. Schiewe, and A. Schöbel. LinTim - integrated optimization in public transportation. homepage. https://www.lintim.net, 2020
  102. [SBP74]
    L. Silman, Z. Barzily, U. Passy, Planning the route system for urban buses. Comput. Oper. Res. 1(2), 201–211 (1974)Google Scholar
  103. [Sch05a]
    D. Schmidt, Linien- und Taktfahrplanung - Ein integrierter Optimierungsansatz, Master’s thesis, Technische Universität Berlin, 2005. in GermanGoogle Scholar
  104. [Sch05b]
    S. Scholl, Customer-oriented line planning, PhD thesis, Technische Universität Kaiserslautern, 2005Google Scholar
  105. [Sch12]
    A. Schöbel, Line planning in public transportation: models and methods. OR Spectr. 34(3), 491–510 (2012)MathSciNetzbMATHGoogle Scholar
  106. [Sch14]
    M. Schmidt, Integrating Routing Decisions in Public Transportation Problems, vol. 89 of Optimization and Its Applications (Springer, 2014)Google Scholar
  107. [Sch17]
    A. Schöbel, An eigenmodel for iterative line planning, timetabling and vehicle scheduling in public transportation. Transp. Res. C Emerg. Technol. 74, 348–365 (2017)Google Scholar
  108. [SE15]
    V. Schmid, J. Ehmke, Integrated timetabling and vehicle scheduling with balanced departure times. OR Spectr. 37(4), 903–928 (2015)MathSciNetzbMATHGoogle Scholar
  109. [SG13]
    M. Siebert, M. Goerigk, An experimental comparison of periodic timetabling models. Comput. Oper. Res. 40(10), 2251–2259 (2013)MathSciNetzbMATHGoogle Scholar
  110. [Sie11]
    M. Siebert, Integration of routing and timetabling in public transportation, Master’s thesis, Georg-August-Universität Göttingen, 2011Google Scholar
  111. [Son79]
    H. Sonntag, Ein heuristisches Verfahren zum Entwurf nachfrageorientierter Linienführung im öffentlichen Personennahverkehr. Zeitschrift für Oper. Res. 23(2), B15–B31 (1979)zbMATHGoogle Scholar
  112. [SS06]
    A. Schöbel, S. Scholl, Line planning with minimal transfers, in 5th Workshop on Algorithmic Methods and Models for Optimization of Railways, vol. 6901, 2006Google Scholar
  113. [SS15a]
    M. Schmidt, A. Schöbel, The complexity of integrating passenger routing decisions in public transportation models. Networks 65(3), 228–243 (2015)MathSciNetzbMATHGoogle Scholar
  114. [SS15b]
    M. Schmidt, A. Schöbel, Timetabling with passenger routing. OR Spectr. 37(1), 75–97 (2015)MathSciNetzbMATHGoogle Scholar
  115. [SS20]
    P. Schiewe, A. Schöbel, Timetabling with integrated routing: Toward applicable approaches. Transp. Sci. (2020). AcceptedGoogle Scholar
  116. [SSS19]
    A. Schiewe, P. Schiewe, M. Schmidt, The line planning routing game. Eur. J. Oper. Res. 274(2), 560–573 (2019)MathSciNetzbMATHGoogle Scholar
  117. [SU89]
    P. Serafini, W. Ukovich, A mathematical model for periodic scheduling problems. SIAM J. Discret. Math. 2(4), 550–581 (1989)MathSciNetzbMATHGoogle Scholar
  118. [TK00]
    W. Tan, B. Khoshnevis, Integration of process planning and scheduling - a review. J. Intell. Manuf. 11(1), 51–63 (2000)Google Scholar
  119. [vdHvdAvKN08]
    A. van den Heuvel, J. van den Akker, M. van Kooten Niekerk, Integrating timetabling and vehicle scheduling in public bus transportation. Technical report, Utrecht University, 2008Google Scholar
  120. [Vig17]
    C. Viggiano, Bus network sketch planning with origin-destination travel data, PhD thesis, Massachusetts Institute of Technology, 2017Google Scholar
  121. [YHWL17]
    Y. Yue, J. Han, S. Wang, X. Liu, Integrated train timetabling and rolling stock scheduling model based on time-dependent demand for urban rail transit. Comput. Aided Civ. Inf. Eng. 32(10), 856–873 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Philine Schiewe
    • 1
  1. 1.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany

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