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Modeling and Solving the Train Timetabling Problem

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Cited by:

  1. Ji, Hangyu & Wang, Rui & Zhang, Chuntian & Yin, Jiateng & Ma, Lin & Yang, Lixing, 2024. "Optimization of train schedule with uncertain maintenance plans in high-speed railways: A stochastic programming approach," Omega, Elsevier, vol. 124(C).
  2. Scheffler, Martin & Neufeld, Janis S. & Hölscher, Michael, 2020. "An MIP-based heuristic solution approach for the locomotive assignment problem focussing on (dis-)connecting processes," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 64-80.
  3. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
  4. Zhou, Wenliang & Tian, Junli & Xue, Lijuan & Jiang, Min & Deng, Lianbo & Qin, Jin, 2017. "Multi-periodic train timetabling using a period-type-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 144-173.
  5. Yu-Jun Zheng, 2018. "Emergency Train Scheduling on Chinese High-Speed Railways," Transportation Science, INFORMS, vol. 52(5), pages 1077-1091, October.
  6. Jiateng Yin & Lixing Yang & Andrea D’Ariano & Tao Tang & Ziyou Gao, 2022. "Integrated Backup Rolling Stock Allocation and Timetable Rescheduling with Uncertain Time-Variant Passenger Demand Under Disruptive Events," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3234-3258, November.
  7. Li, Jiajie & Bai, Yun & Chen, Yao & Yang, Lingling & Wang, Qian, 2022. "A two-stage stochastic optimization model for integrated tram timetable and speed control with uncertain dwell times," Energy, Elsevier, vol. 260(C).
  8. Elio Canestrelli & Marco Corazza & Giuseppe Nadai & Raffaele Pesenti, 2017. "Managing the Ship Movements in the Port of Venice," Networks and Spatial Economics, Springer, vol. 17(3), pages 861-887, September.
  9. Lewis, R. & Thompson, J., 2015. "Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem," European Journal of Operational Research, Elsevier, vol. 240(3), pages 637-648.
  10. Zhang, Yongxiang & Peng, Qiyuan & Lu, Gongyuan & Zhong, Qingwei & Yan, Xu & Zhou, Xuesong, 2022. "Integrated line planning and train timetabling through price-based cross-resolution feedback mechanism," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 240-277.
  11. Barrena, Eva & Canca, David & Coelho, Leandro C. & Laporte, Gilbert, 2014. "Single-line rail rapid transit timetabling under dynamic passenger demand," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 134-150.
  12. Hangfei Huang & Keping Li & Paul Schonfeld, 2018. "Real-time energy-saving metro train rescheduling with primary delay identification," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-22, February.
  13. Schwerdfeger, Stefan & Otto, Alena & Boysen, Nils, 2021. "Rail platooning: Scheduling trains along a rail corridor with rapid-shunting facilities," European Journal of Operational Research, Elsevier, vol. 294(2), pages 760-778.
  14. Zhan, Shuguang & Wong, S.C. & Shang, Pan & Peng, Qiyuan & Xie, Jiemin & Lo, S.M., 2021. "Integrated railway timetable rescheduling and dynamic passenger routing during a complete blockage," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 86-123.
  15. Masoud Barah & Abbas Seifi & James Ostrowski, 2019. "Decomposing the Train-Scheduling Problem into Integer-Optimal Polytopes," Transportation Science, INFORMS, vol. 53(3), pages 763-772, May.
  16. Aliakbari, Mina & Geunes, Joseph & Ghahari, Amir & Prince, Mike, 2024. "Freight railcar-to-train assignment and departure scheduling in a railyard," European Journal of Operational Research, Elsevier, vol. 314(3), pages 950-962.
  17. Han Zheng & Junhua Chen & Zhaocha Huang & Jianhao Zhu, 2022. "Joint Optimization of Multi-Cycle Timetable Considering Supply-to-Demand Relationship and Energy Consumption for Rail Express," Mathematics, MDPI, vol. 10(21), pages 1-29, November.
  18. Cacchiani, Valentina & Caprara, Alberto & Toth, Paolo, 2010. "Scheduling extra freight trains on railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 215-231, February.
  19. Juan Mesa & Francisco Ortega & Miguel Pozo, 2014. "Locating optimal timetables and vehicle schedules in a transit line," Annals of Operations Research, Springer, vol. 222(1), pages 439-455, November.
  20. Yin, Jiateng & Wang, Miao & D’Ariano, Andrea & Zhang, Jinlei & Yang, Lixing, 2023. "Synchronization of train timetables in an urban rail network: A bi-objective optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
  21. Xiaoming Xu & Keping Li & Lixing Yang & Ziyou Gao, 2019. "An efficient train scheduling algorithm on a single-track railway system," Journal of Scheduling, Springer, vol. 22(1), pages 85-105, February.
  22. Zhang, Yongxiang & D'Ariano, Andrea & He, Bisheng & Peng, Qiyuan, 2019. "Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 237-278.
  23. Harrod, Steven & Schlechte, Thomas, 2013. "A direct comparison of physical block occupancy versus timed block occupancy in train timetabling formulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 54(C), pages 50-66.
  24. Zhang, Qin & Lusby, Richard Martin & Shang, Pan & Zhu, Xiaoning, 2022. "A heuristic approach to integrate train timetabling, platforming, and railway network maintenance scheduling decisions," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 210-238.
  25. Pellegrini, Paola & Rodriguez, Joaquin, 2013. "Single European Sky and Single European Railway Area: A system level analysis of air and rail transportation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 57(C), pages 64-86.
  26. Blanco, Víctor & Conde, Eduardo & Hinojosa, Yolanda & Puerto, Justo, 2020. "An optimization model for line planning and timetabling in automated urban metro subway networks. A case study," Omega, Elsevier, vol. 92(C).
  27. Ansarilari, Zahra & Bodur, Merve & Shalaby, Amer, 2024. "A novel model for transfer synchronization in transit networks and a Lagrangian-based heuristic solution method," European Journal of Operational Research, Elsevier, vol. 317(1), pages 76-91.
  28. Kang, Liujiang & Zhu, Xiaoning & Sun, Huijun & Puchinger, Jakob & Ruthmair, Mario & Hu, Bin, 2016. "Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 17-36.
  29. Louwerse, Ilse & Huisman, Dennis, 2014. "Adjusting a railway timetable in case of partial or complete blockades," European Journal of Operational Research, Elsevier, vol. 235(3), pages 583-593.
  30. Xueqiao Yu & Maoxiang Lang & Wenhui Zhang & Shiqi Li & Mingyue Zhang & Xiao Yu, 2019. "An Empirical Study on the Comprehensive Optimization Method of a Train Diagram of the China High Speed Railway Express," Sustainability, MDPI, vol. 11(7), pages 1-30, April.
  31. Xu, Xiaoming & Li, Chung-Lun & Xu, Zhou, 2021. "Train timetabling with stop-skipping, passenger flow, and platform choice considerations," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 52-74.
  32. Yin, Jiateng & D’Ariano, Andrea & Wang, Yihui & Yang, Lixing & Tang, Tao, 2021. "Timetable coordination in a rail transit network with time-dependent passenger demand," European Journal of Operational Research, Elsevier, vol. 295(1), pages 183-202.
  33. Wang, Dian & D’Ariano, Andrea & Zhao, Jun & Zhong, Qingwei & Peng, Qiyuan, 2022. "Integrated rolling stock deadhead routing and timetabling in urban rail transit lines," European Journal of Operational Research, Elsevier, vol. 298(2), pages 526-559.
  34. Yan, Fei & Goverde, Rob M.P., 2019. "Combined line planning and train timetabling for strongly heterogeneous railway lines with direct connections," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 20-46.
  35. Cacchiani, Valentina & Furini, Fabio & Kidd, Martin Philip, 2016. "Approaches to a real-world Train Timetabling Problem in a railway node," Omega, Elsevier, vol. 58(C), pages 97-110.
  36. Zhang, Chuntian & Gao, Yuan & Yang, Lixing & Gao, Ziyou & Qi, Jianguo, 2020. "Joint optimization of train scheduling and maintenance planning in a railway network: A heuristic algorithm using Lagrangian relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 64-92.
  37. Martin-Iradi, Bernardo & Ropke, Stefan, 2022. "A column-generation-based matheuristic for periodic and symmetric train timetabling with integrated passenger routing," European Journal of Operational Research, Elsevier, vol. 297(2), pages 511-531.
  38. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
  39. Huang, Yeran & Yang, Lixing & Tang, Tao & Gao, Ziyou & Cao, Fang, 2017. "Joint train scheduling optimization with service quality and energy efficiency in urban rail transit networks," Energy, Elsevier, vol. 138(C), pages 1124-1147.
  40. E. Ursavas & Stuart X. Zhu, 2018. "Integrated Passenger and Freight Train Planning on Shared-Use Corridors," Service Science, INFORMS, vol. 52(6), pages 1376-1390, December.
  41. Tian, Xiaopeng & Niu, Huimin, 2020. "Optimization of demand-oriented train timetables under overtaking operations: A surrogate-dual-variable column generation for eliminating indivisibility," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 143-173.
  42. Min, Yun-Hong & Park, Myoung-Ju & Hong, Sung-Pil & Hong, Soon-Heum, 2011. "An appraisal of a column-generation-based algorithm for centralized train-conflict resolution on a metropolitan railway network," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 409-429, February.
  43. Robenek, Tomáš & Maknoon, Yousef & Azadeh, Shadi Sharif & Chen, Jianghang & Bierlaire, Michel, 2016. "Passenger centric train timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 107-126.
  44. Zhang, Di & Gao, Yuan & Yang, Lixing & Cui, Lixin, 2024. "Timetable synchronization of the last several trains at night in an urban rail transit network," European Journal of Operational Research, Elsevier, vol. 313(2), pages 494-512.
  45. Wang, Dian & D’Ariano, Andrea & Zhao, Jun & Zhan, Shuguang & Peng, Qiyuan, 2024. "Joint rolling stock rotation planning and depot deadhead scheduling in complicated urban rail transit lines," European Journal of Operational Research, Elsevier, vol. 314(2), pages 665-684.
  46. Coviello, Nicola, 2015. "Modelling periodic operations on single track lines: Timetable design and stability evaluation," Research in Transportation Economics, Elsevier, vol. 54(C), pages 2-14.
  47. Robenek, Tomáš & Azadeh, Shadi Sharif & Maknoon, Yousef & de Lapparent, Matthieu & Bierlaire, Michel, 2018. "Train timetable design under elastic passenger demand," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 19-38.
  48. Zhan, Shuguang & Kroon, Leo G. & Veelenturf, Lucas P. & Wagenaar, Joris C., 2015. "Real-time high-speed train rescheduling in case of a complete blockage," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 182-201.
  49. Valentina Cacchiani & Alberto Caprara & Matteo Fischetti, 2012. "A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling," Transportation Science, INFORMS, vol. 46(1), pages 124-133, February.
  50. Mo, Pengli & D’Ariano, Andrea & Yang, Lixing & Veelenturf, Lucas P. & Gao, Ziyou, 2021. "An exact method for the integrated optimization of subway lines operation strategies with asymmetric passenger demand and operating costs," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 283-321.
  51. Li, Jing-Quan & Song, Myoung Kyun & Li, Meng & Zhang, Wei-Bin & Miller, Mark, 2009. "Evaluation of Cost-Effective Planning and Design Options for Bus Rapid Transit in Dedicated Bus Lanes," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3g62m787, Institute of Transportation Studies, UC Berkeley.
  52. Laurent Daudet & Frédéric Meunier, 2020. "Minimizing the waiting time for a one-way shuttle service," Journal of Scheduling, Springer, vol. 23(1), pages 95-115, February.
  53. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2018. "The two-train separation problem on non-level track—driving strategies that minimize total required tractive energy subject to prescribed section clearance times," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 135-167.
  54. Bodenstein, Christian & Schryen, Guido & Neumann, Dirk, 2012. "Energy-aware workload management models for operation cost reduction in data centers," European Journal of Operational Research, Elsevier, vol. 222(1), pages 157-167.
  55. Maria Fleischer Fauske & Carlo Mannino & Paolo Ventura, 2020. "Generalized Periodic Vehicle Routing and Maritime Surveillance," Transportation Science, INFORMS, vol. 54(1), pages 164-183, January.
  56. Shi, Jungang & Yang, Lixing & Yang, Jing & Gao, Ziyou, 2018. "Service-oriented train timetabling with collaborative passenger flow control on an oversaturated metro line: An integer linear optimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 26-59.
  57. Wenliang Zhou & Xiaorong You & Wenzhuang Fan, 2020. "A Mixed Integer Linear Programming Method for Simultaneous Multi-Periodic Train Timetabling and Routing on a High-Speed Rail Network," Sustainability, MDPI, vol. 12(3), pages 1-34, February.
  58. Endong Zhu & Teodor Gabriel Crainic & Michel Gendreau, 2014. "Scheduled Service Network Design for Freight Rail Transportation," Operations Research, INFORMS, vol. 62(2), pages 383-400, April.
  59. Lee, Yusin & Chen, Chuen-Yih, 2009. "A heuristic for the train pathing and timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 837-851, September.
  60. Chow, Andy H.F. & Pavlides, Aris, 2018. "Cost functions and multi-objective timetabling of mixed train services," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 335-356.
  61. Zhou, Wenliang & Teng, Hualiang, 2016. "Simultaneous passenger train routing and timetabling using an efficient train-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 409-439.
  62. Zhang, Yongxiang & Peng, Qiyuan & Yao, Yu & Zhang, Xin & Zhou, Xuesong, 2019. "Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 344-379.
  63. Jonas Harbering, 2017. "Delay resistant line planning with a view towards passenger transfers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 467-496, October.
  64. Leonardo Lamorgese & Carlo Mannino, 2015. "An Exact Decomposition Approach for the Real-Time Train Dispatching Problem," Operations Research, INFORMS, vol. 63(1), pages 48-64, February.
  65. Talebian, Ahmadreza & Zou, Bo, 2015. "Integrated modeling of high performance passenger and freight train planning on shared-use corridors in the US," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 114-140.
  66. Gao, Yuan & Kroon, Leo & Yang, Lixing & Gao, Ziyou, 2018. "Three-stage optimization method for the problem of scheduling additional trains on a high-speed rail corridor," Omega, Elsevier, vol. 80(C), pages 175-191.
  67. Zhang, Chuntian & Gao, Yuan & Yang, Lixing & Kumar, Uday & Gao, Ziyou, 2019. "Integrated optimization of train scheduling and maintenance planning on high-speed railway corridors," Omega, Elsevier, vol. 87(C), pages 86-104.
  68. Zhi-Chun Li & William Lam & S. Wong & A. Sumalee, 2010. "An activity-based approach for scheduling multimodal transit services," Transportation, Springer, vol. 37(5), pages 751-774, September.
  69. Jiang, Feng & Cacchiani, Valentina & Toth, Paolo, 2017. "Train timetabling by skip-stop planning in highly congested lines," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 149-174.
  70. Reisch, Julian & Großmann, Peter & Pöhle, Daniel & Kliewer, Natalia, 2021. "Conflict resolving – A local search algorithm for solving large scale conflict graphs in freight railway timetabling," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1143-1154.
  71. Kang, Liujiang & Li, Hao & Sun, Huijun & Wu, Jianjun & Cao, Zhiguang & Buhigiro, Nsabimana, 2021. "First train timetabling and bus service bridging in intermodal bus-and-train transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 443-462.
  72. Meng, Lingyun & Zhou, Xuesong, 2014. "Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 208-234.
  73. Steven Harrod, 2011. "Modeling Network Transition Constraints with Hypergraphs," Transportation Science, INFORMS, vol. 45(1), pages 81-97, February.
  74. Leutwiler, Florin & Corman, Francesco, 2022. "A logic-based Benders decomposition for microscopic railway timetable planning," European Journal of Operational Research, Elsevier, vol. 303(2), pages 525-540.
  75. Carlo Mannino & Alessandro Mascis, 2009. "Optimal Real-Time Traffic Control in Metro Stations," Operations Research, INFORMS, vol. 57(4), pages 1026-1039, August.
  76. Zhengwen Liao, 2023. "Rescheduling Out-of-Gauge Trains with Speed Restrictions and Temporal Blockades on the Opposite-Direction Track," Mathematics, MDPI, vol. 11(12), pages 1-26, June.
  77. Zhan, Shuguang & Wang, Pengling & Wong, S.C. & Lo, S.M., 2022. "Energy-efficient high-speed train rescheduling during a major disruption," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
  78. Xia, Jun & Wang, Kai & Wang, Shuaian, 2019. "Drone scheduling to monitor vessels in emission control areas," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 174-196.
  79. Bettinelli, Andrea & Santini, Alberto & Vigo, Daniele, 2017. "A real-time conflict solution algorithm for the train rescheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 237-265.
  80. Kroon, L.G. & Huisman, D. & Maróti, G., 2007. "Railway timetabling from an operations research," Econometric Institute Research Papers EI 2007-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  81. Juraj Čamaj & Eva Brumerčíková & Michal Petr Hranický, 2020. "Information System and Technology Optimization as a Tool for Ensuring the Competitiveness of a Railway Undertaking—Case Study," Sustainability, MDPI, vol. 12(21), pages 1-23, October.
  82. Mina Aliakbari & Joseph Geunes, 2022. "Multiple Train Repositioning Operations in a Railyard Network," SN Operations Research Forum, Springer, vol. 3(4), pages 1-31, December.
  83. Luis Cadarso & Ángel Marín, 2012. "Integration of timetable planning and rolling stock in rapid transit networks," Annals of Operations Research, Springer, vol. 199(1), pages 113-135, October.
  84. Jiateng Yin & Lixing Yang & Xuesong Zhou & Tao Tang & Ziyou Gao, 2019. "Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 297-320, June.
  85. Ralf Borndörfer & Berkan Erol & Thomas Graffagnino & Thomas Schlechte & Elmar Swarat, 2014. "Optimizing the Simplon railway corridor," Annals of Operations Research, Springer, vol. 218(1), pages 93-106, July.
  86. Kang, Liujiang & Meng, Qiang, 2017. "Two-phase decomposition method for the last train departure time choice in subway networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 568-582.
  87. Xiao, Jie & Pachl, Joern & Lin, Boliang & Wang, Jiaxi, 2018. "Solving the block-to-train assignment problem using the heuristic approach based on the genetic algorithm and tabu search," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 148-171.
  88. Christian Liebchen, 2008. "The First Optimized Railway Timetable in Practice," Transportation Science, INFORMS, vol. 42(4), pages 420-435, November.
  89. Li, Feng & Sheu, Jiuh-Biing & Gao, Zi-You, 2014. "Deadlock analysis, prevention and train optimal travel mechanism in single-track railway system," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 385-414.
  90. Xu, Xiaoming & Li, Keping & Yang, Lixing, 2015. "Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 364-384.
  91. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
  92. Meng, Lingyun & Zhou, Xuesong, 2019. "An integrated train service plan optimization model with variable demand: A team-based scheduling approach with dual cost information in a layered network," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 1-28.
  93. Matteo Fischetti & Domenico Salvagnin & Arrigo Zanette, 2009. "Fast Approaches to Improve the Robustness of a Railway Timetable," Transportation Science, INFORMS, vol. 43(3), pages 321-335, August.
  94. D'Ariano, Andrea & Pacciarelli, Dario & Pranzo, Marco, 2007. "A branch and bound algorithm for scheduling trains in a railway network," European Journal of Operational Research, Elsevier, vol. 183(2), pages 643-657, December.
  95. Chaoda Xie & Xifu Wang & Daisuke Fukuda, 2020. "On the Pricing of Urban Rail Transit with Track Sharing Freight Service," Sustainability, MDPI, vol. 12(7), pages 1-29, April.
  96. Liang, Jinpeng & Zang, Guangzhi & Liu, Haitao & Zheng, Jianfeng & Gao, Ziyou, 2023. "Reducing passenger waiting time in oversaturated metro lines with passenger flow control policy," Omega, Elsevier, vol. 117(C).
  97. Huang, Yeran & Mannino, Carlo & Yang, Lixing & Tang, Tao, 2020. "Coupling time-indexed and big-M formulations for real-time train scheduling during metro service disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 38-61.
  98. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
  99. Cacchiani, Valentina & Qi, Jianguo & Yang, Lixing, 2020. "Robust optimization models for integrated train stop planning and timetabling with passenger demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 1-29.
  100. Mu, Shi & Dessouky, Maged, 2011. "Scheduling freight trains traveling on complex networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1103-1123, August.
  101. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
  102. Zhou, Leishan & Tong, Lu (Carol) & Chen, Junhua & Tang, Jinjin & Zhou, Xuesong, 2017. "Joint optimization of high-speed train timetables and speed profiles: A unified modeling approach using space-time-speed grid networks," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 157-181.
  103. Wenliang Zhou & Sha Li & Jing Kang & Yu Huang, 2022. "Capacity-Oriented Train Scheduling of High-Speed Railway Considering the Operation and Maintenance of Rolling Stock," Mathematics, MDPI, vol. 10(10), pages 1-30, May.
  104. Shi Qiang Liu & Erhan Kozan, 2011. "Scheduling Trains with Priorities: A No-Wait Blocking Parallel-Machine Job-Shop Scheduling Model," Transportation Science, INFORMS, vol. 45(2), pages 175-198, May.
  105. Zhang, Chuntian & Gao, Yuan & Cacchiani, Valentina & Yang, Lixing & Gao, Ziyou, 2023. "Train rescheduling for large-scale disruptions in a large-scale railway network," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
  106. Gedik, Ridvan & Medal, Hugh & Rainwater, Chase & Pohl, Ed A. & Mason, Scott J., 2014. "Vulnerability assessment and re-routing of freight trains under disruptions: A coal supply chain network application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 45-57.
  107. Xu, Xiaoming & Li, Chung-Lun & Xu, Zhou, 2018. "Integrated train timetabling and locomotive assignment," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 573-593.
  108. Li, Wenqing & Ni, Shaoquan, 2022. "Train timetabling with the general learning environment and multi-agent deep reinforcement learning," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 230-251.
  109. Shi, Jungang & Yang, Jing & Yang, Lixing & Tao, Lefeng & Qiang, Shengjie & Di, Zhen & Guo, Junhua, 2023. "Safety-oriented train timetabling and stop planning with time-varying and elastic demand on overcrowded commuter metro lines," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
  110. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2017. "Bi-objective programming approach for solving the metro timetable optimization problem with dwell time uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 22-37.
  111. Sartor, Giorgio & Mannino, Carlo & Nygreen, Thomas & Bach, Lukas, 2023. "A MILP model for quasi-periodic strategic train timetabling," Omega, Elsevier, vol. 116(C).
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