Annals of Operations Research

, Volume 246, Issue 1–2, pp 127–144 | Cite as

A general rapid network design, line planning and fleet investment integrated model

  • David Canca
  • Alicia De-Los-SantosEmail author
  • Gilbert Laporte
  • Juan A. Mesa


Traditionally, network design and line planning have been studied as two different phases in the planning process of public transportation. At the strategic level approaches dealing with the network design problem minimize travel time or maximize trip coverage, whereas at the tactical level, in the case of line planning, most models minimize cost or the number of transfers. The main novelty of this paper is the integration of the strategic and tactical phases of the rapid transit planning process. Specifically, a mathematical programming model that simultaneously determines the infrastructure network, line planning, train capacity of each line, fleet investment and personnel planning is defined. Moreover, the demand is assumed to be elastic and, therefore it is split into the rapid transit network and a competing mode according to a generalized cost. A rigorous analysis for the calibration of the different concepts that appear as consequence of the integration of phases is presented. Our approach maximizes the total profit of the network by achieving a balance between the maximum trip coverage and the minimum total cost associated to the network. Numerical results taking into account data based on real-world instances are presented.


Network design Line planning Rolling stock Costs 



This research work was partially supported Ministerio de Economía y Competitividad (Spain)/FEDER under grant MTM2012-37048, by Junta de Andalucía (Spain)/FEDER under excellence projects P09-TEP-5022 and P10-FQM-5849 and by the Canadian Natural Sciences and Engineering Research Council under grant 39682-10. We are also grateful to RENFE (Spanish railway services operator) and Fundación de los Ferrocarriles Españoles for providing data and information relevant to the calibration of the model. Thanks are due to the referees for their valuable comments.


  1. Alfieri, A., Groot, R., Kroon, L., & Schrijver, A. (2006). Efficient circulation of railway rolling stock. Transportation Science, 40(3), 378–391.CrossRefGoogle Scholar
  2. Bussieck, M. R., Winter, T., & Zimmermann, U. T. (1997). Discrete optimization in public rail transport. Mathematical Programming, 79(1–3), 415–444.Google Scholar
  3. Ceder, A. (2007). Public transit planning and operation: Theory, modelling, and practice. Oxford: Elsevier, Butterworth-Heinemann.Google Scholar
  4. Chang, Y. H., Yeh, C. H., & Shen, C. C. (2000). A multiobjective model for passenger train services planning: Application to taiwan’s high-speed rail line. Transportation Research Part B: Methodological, 34(2), 91–106.CrossRefGoogle Scholar
  5. Claessens, M. T., van Dijk, N. M., & Zwaneveld, P. J. (1998). Cost optimal allocation of rail passenger lines. European Journal of Operational Research, 110(3), 474–489.CrossRefGoogle Scholar
  6. Cordeau, J.-F., Soumis, F., & Desrosiers, J. (2000). A Benders decomposition approach for the locomotive and car assignment problem. Transportation Science, 34(2), 133–149.CrossRefGoogle Scholar
  7. Cordeau, J. F., Toth, P., & Vigo, D. (1998). A survey of optimization models for train routing and scheduling. Transportation Science, 32(4), 380–404.CrossRefGoogle Scholar
  8. Drud, A. S. (1997). Interactions between nonlinear programming and modeling systems. Mathematical Programming, 79(1–3), 99–123.Google Scholar
  9. Feifei, Q. (2012). Remodeling in-vehicle crowding cost functions for public transit: Linear or non-linear? In Transportation Research Board 91th annual meeting, Washington, D.C.Google Scholar
  10. García, A., & Martín, M. P. (2012). Diseño de los vehículos ferroviarios para la mejora de su eficiencia energética. In Monografías ElecRail (Vol. 6). Fundación de los Ferrocarriles Españoles.Google Scholar
  11. García, R., Garzón-Astolfi, A., Marín, A., Mesa, J. A., & Ortega, F. A. (2006). Analysis of the parameters of transfers in rapid transit network design. In L. G. Kroon & R. H. Möhring (Eds.), 5th workshop on algorithmic methods and models for optimization of railways, Schloss Dagstuhl, Germany.Google Scholar
  12. Gendreau, M., Laporte, G., & Mesa, J. A. (1995). Locating rapid transit lines. Journal of Advanced Transportation, 29(2), 145–162.CrossRefGoogle Scholar
  13. Goossens, J.-W., van Hoesel, S., & Kroon, L. (2006). On solving multi-type railway line planning problems. European Journal of Operational Research, 168(2), 403–424.CrossRefGoogle Scholar
  14. Guihaire, V., & Hao, J. K. (2008). Transit network design and scheduling: A global review. Transportation Research Part A: Policy and Practice, 42(10), 1251–1273.Google Scholar
  15. Kepaptsoglou, K., & Karlaftis, M. (2009). Transit route network design problem: Review. Journal of Transportation Engineering, 135(8), 491–505.CrossRefGoogle Scholar
  16. Laporte, G., Marín, A., Mesa, J. A., & Ortega, F. A. (2007). An integrated methodology for the rapid transit network design problem. In F. Geraets, L. G. Kroon, A. Schoebel, D. Wagner, & C. D. Zaroliagis (Eds.), Algorithmic methods for railway optimization volume 4359 of Lecture notes in computer science (pp. 187–199). Springer.Google Scholar
  17. Laporte, G., Marín, A., Mesa, J. A., & Perea, F. (2012). Designing robust rapid transit networks with alternative routes. Journal of Advanced Transportation, 45(1), 54–65.CrossRefGoogle Scholar
  18. Laporte, G., Mesa, J. A., & Perea, F. (2010). A game theoretic framework for the robust railway transit network design problem. Transportation Research Part B: Methodological, 44(4), 447–459.CrossRefGoogle Scholar
  19. Li, Z.-C., Lam, W. H. K., Wong, S. C., & Sumalee, A. (2011). Design of a rail transit line for profit maximization in a linear transportation corridor. Transportation Research Part E: Logistics and Transportation Review, 48(1), 50–70.CrossRefGoogle Scholar
  20. Liebchen, C., & Möhring, R. (2007). The modeling power of the periodic event scheduling problem: Railway timetables and beyond. In F. Geraets, L. Kroon, A. Schoebel, D. Wagner, & C. D. Zaroliagis (Eds.), Algorithmic methods for railway optimization, volume 4359 of Lecture notes in computer science (pp. 3–40). Berlin, Heidelberg: Springer.Google Scholar
  21. Marín, A. (2007). An extension to rapid transit network design problem. TOP, 15(2), 231–241.CrossRefGoogle Scholar
  22. Marín, A., & García-Ródenas, R. (2009). Location of infrastructure in urban railway networks. Computers and Operations Research, 36(5), 1461–1477.CrossRefGoogle Scholar
  23. Marín, A., Mesa, J. A., & Perea, F. (2009). Integrating robust railway network design and line planning under failures. In R. K. Ahuja (Ed.), Robust and online large-scale optimization, volume 5868 of Lecture notes in computer science (pp. 273–292). Springer.Google Scholar
  24. Ortúzar, J. D., & Willumsem, L. G. (1990). Modelling transport. Chichester: Wiley.Google Scholar
  25. Raja, S. C., Banu, S. A. W., & Venkatesh, P. (2012). Congestion management using gams/conopt solver. In IEEE international conference on advances in engineering, science and management (ICAESM), 2012 (pp. 72–78), Nagapattinam, Tamil Nadu, India, March 30–31, 2012. IEEE.Google Scholar
  26. Ranjbari, A., Shairat Mohaymany, A., & Mahdi Amipour, S. M. (2011). The necessity of elastic demand consideration. Transit network design. Applied Mechanics and Materials, 97–98, 1117–1122.Google Scholar
  27. Schöbel, A. (2011). Line planning in public transportation: Models and methods. OR Spectrum, 34(3), 491–510.CrossRefGoogle Scholar
  28. Van Nes, R. (2002). Design of multimodal transport networks: A hierarchical approach. Ph.D. thesis, Delf University of Technology, TRAIL Netherlands Research School for TRAnsport, Infrastructure and Logistics.Google Scholar
  29. Van Nes, R., & Bovy, P. H. L. (2000). Importance of objectives in urban transit-network design. Transportation Research Record: Journal of the Transportation Research Board, 1735, 25–34.CrossRefGoogle Scholar
  30. Vuchic, V. R. (2005). Urban transit operations, planning and economics. New Jersey: Wiley.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • David Canca
    • 1
  • Alicia De-Los-Santos
    • 2
    Email author
  • Gilbert Laporte
    • 3
  • Juan A. Mesa
    • 2
  1. 1.Department of Industrial Engineering and Management Science IUniversity of SevilleSevilleSpain
  2. 2.Department of Applied Mathematics IIUniversity of SevilleSevilleSpain
  3. 3.Canada Research Chair in Distribution ManagementHEC MontréalMontrealCanada

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