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The line planning routing game

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  • Schiewe, Alexander
  • Schiewe, Philine
  • Schmidt, Marie

Abstract

In this paper, we take a novel perspective on line planning in public transportation: We interpret line planning as a game where the passengers are players who aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. We discuss the relation among equilibria of this game and line planning solutions found by optimization approaches. Furthermore, we investigate the algorithmic viability of our approach as a solution method for line planning problems, using a best-response algorithm to find equilibria. We investigate under which conditions a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm.

Suggested Citation

  • Schiewe, Alexander & Schiewe, Philine & Schmidt, Marie, 2019. "The line planning routing game," European Journal of Operational Research, Elsevier, vol. 274(2), pages 560-573.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:2:p:560-573
    DOI: 10.1016/j.ejor.2018.10.023
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    1. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    2. Goerigk, Marc & Schmidt, Marie, 2017. "Line planning with user-optimal route choice," European Journal of Operational Research, Elsevier, vol. 259(2), pages 424-436.
    3. Szeto, W.Y. & Wu, Yongzhong, 2011. "A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong," European Journal of Operational Research, Elsevier, vol. 209(2), pages 141-155, March.
    4. Anita Schöbel & Silvia Schwarze, 2013. "Finding delay-resistant line concepts using a game-theoretic approach," Netnomics, Springer, vol. 14(3), pages 95-117, November.
    5. Schmöcker, Jan-Dirk & Fonzone, Achille & Shimamoto, Hiroshi & Kurauchi, Fumitaka & Bell, Michael G.H., 2011. "Frequency-based transit assignment considering seat capacities," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 392-408, February.
    6. Bussieck, Michael R. & Kreuzer, Peter & Zimmermann, Uwe T., 1997. "Optimal lines for railway systems," European Journal of Operational Research, Elsevier, vol. 96(1), pages 54-63, January.
    7. Goossens, Jan-Willem & van Hoesel, Stan & Kroon, Leo, 2006. "On solving multi-type railway line planning problems," European Journal of Operational Research, Elsevier, vol. 168(2), pages 403-424, January.
    8. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    9. Mandl, Christoph E., 1980. "Evaluation and optimization of urban public transportation networks," European Journal of Operational Research, Elsevier, vol. 5(6), pages 396-404, December.
    10. Marie E. Schmidt, 2014. "Integrating Routing Decisions in Public Transportation Problems," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-9566-6, December.
    11. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    12. Nisan,Noam & Roughgarden,Tim & Tardos,Eva & Vazirani,Vijay V. (ed.), 2007. "Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9780521872829, January.
    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. 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.
    15. 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.
    16. Laporte, Gilbert & Mesa, Juan A. & Perea, Federico, 2010. "A game theoretic framework for the robust railway transit network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 447-459, May.
    17. Silvia Schwarze, 2009. "Path Player Games," Springer Optimization and Its Applications, Springer, number 978-0-387-77928-7, December.
    18. Jan-Willem Goossens & Stan van Hoesel & Leo Kroon, 2004. "A Branch-and-Cut Approach for Solving Railway Line-Planning Problems," Transportation Science, INFORMS, vol. 38(3), pages 379-393, August.
    19. David Canca & Alicia De-Los-Santos & Gilbert Laporte & Juan A. Mesa, 2016. "A general rapid network design, line planning and fleet investment integrated model," Annals of Operations Research, Springer, vol. 246(1), pages 127-144, November.
    20. Claessens, M. T. & van Dijk, N. M. & Zwaneveld, P. J., 1998. "Cost optimal allocation of rail passenger lines," European Journal of Operational Research, Elsevier, vol. 110(3), pages 474-489, November.
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