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A fast algorithm for near cost optimal line plans

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  • Michael R. Bussieck
  • Thomas Lindner
  • Marco E. Lübbecke

Abstract

We consider the design of line plans in public transport at a minimal total cost. Both, linear and nonlinear integer programming are adequate and intuitive modeling approaches for this problem. We present a heuristic variable fixing procedure which builds on problem knowledge from both techniques. We derive and compare lower bounds from different linearizations in order to assess the quality of our solutions. The involved integer linear programs are strengthened by means of problem specific valid inequalities. Computational results with practical data from the Dutch Railways indicate that our algorithm gives excellent solutions within minutes of computation time. Copyright Springer-Verlag 2004

Suggested Citation

  • Michael R. Bussieck & Thomas Lindner & Marco E. Lübbecke, 2004. "A fast algorithm for near cost optimal line plans," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 205-220, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:205-220
    DOI: 10.1007/s001860300332
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    Citations

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    Cited by:

    1. Schiewe, Alexander & Schiewe, Philine & Schmidt, Marie, 2019. "The line planning routing game," European Journal of Operational Research, Elsevier, vol. 274(2), pages 560-573.
    2. 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.
    3. Canca, David & Andrade-Pineda, José Luis & De los Santos, Alicia & Calle, Marcos, 2018. "The Railway Rapid Transit frequency setting problem with speed-dependent operation costs," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 494-519.
    4. Xin Zhang & Lei Nie & Xin Wu & Yu Ke, 2020. "How to Optimize Train Stops under Diverse Passenger Demand: a New Line Planning Method for Large-Scale High-Speed Rail Networks," Networks and Spatial Economics, Springer, vol. 20(4), pages 963-988, December.
    5. Canca, David & Barrena, Eva & De-Los-Santos, Alicia & Andrade-Pineda, José Luis, 2016. "Setting lines frequency and capacity in dense railway rapid transit networks with simultaneous passenger assignment," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 251-267.
    6. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Peng, Qiyuan, 2024. "Integrating train service route design with passenger flow allocation for an urban rail transit line," European Journal of Operational Research, Elsevier, vol. 313(1), pages 146-170.
    7. David Canca & Belén Navarro-Carmona & Gabriel Villa & Alejandro Zarzo, 2023. "A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem," Mathematics, MDPI, vol. 11(19), pages 1-36, October.
    8. Mathias Michaelis & Anita Schöbel, 2009. "Integrating line planning, timetabling, and vehicle scheduling: a customer-oriented heuristic," Public Transport, Springer, vol. 1(3), pages 211-232, August.
    9. 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.
    10. Guan, J.F. & Yang, Hai & Wirasinghe, S.C., 2006. "Simultaneous optimization of transit line configuration and passenger line assignment," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 885-902, December.
    11. Hamid, Faiz & Agarwal, Yogesh K., 2024. "Train stop scheduling problem: An exact approach using valid inequalities and polar duality," European Journal of Operational Research, Elsevier, vol. 313(1), pages 207-224.
    12. Wenliang Zhou & Yujun Huang & Naijie Chai & Bo Li & Xiang Li, 2022. "A Line Planning Optimization Model for High-Speed Railway Network Merging Newly-Built Railway Lines," Mathematics, MDPI, vol. 10(17), pages 1-34, September.
    13. Ralf Borndörfer & Martin Grötschel & Marc E. Pfetsch, 2007. "A Column-Generation Approach to Line Planning in Public Transport," Transportation Science, INFORMS, vol. 41(1), pages 123-132, February.
    14. Masing, Berenike & Lindner, Niels & Borndörfer, Ralf, 2022. "The price of symmetric line plans in the Parametric City," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 419-443.
    15. Jin Qin & Xiqiong Li & Kang Yang & Guangming Xu, 2022. "Joint Optimization of Ticket Pricing Strategy and Train Stop Plan for High-Speed Railway: A Case Study," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    16. Jinfei Wu & Xinghua Shan & Jingxia Sun & Shengyuan Weng & Shuo Zhao, 2023. "Daily Line Planning Optimization for High-Speed Railway Lines," Sustainability, MDPI, vol. 15(4), pages 1-20, February.
    17. Fu, Huiling & Nie, Lei & Meng, Lingyun & Sperry, Benjamin R. & He, Zhenhuan, 2015. "A hierarchical line planning approach for a large-scale high speed rail network: The China case," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 61-83.
    18. Gattermann, P. & Schiewe, A. & Schmidt, M.E., 2014. "The line planning routing game," ERIM Report Series Research in Management ERS-2014-017-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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