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Integration of timetable planning and rolling stock in rapid transit networks


The aim of this paper is to propose an integrated planning model to adequate the offered capacity and system frequencies to attend the increased passenger demand and traffic congestion around urban and suburban areas. The railway capacity is studied in line planning, however, these planned frequencies were obtained without accounting for rolling stock flows through the rapid transit network.

In order to provide the problem more freedom to decide rolling stock flows and therefore better adjusting these flows to passenger demand, a new integrated model is proposed, where frequencies are readjusted. Then, the railway timetable and rolling stock assignment are also calculated, where shunting operations are taken into account. These operations may sometimes malfunction, causing localized incidents that could propagate throughout the entire network due to cascading effects. This type of operations will be penalized with the goal of selectively avoiding them and ameliorating their high malfunction probabilities. Swapping operations will also be ensured using homogeneous rolling stock material and ensuring parkings in strategic stations.

We illustrate our model using computational experiments drawn from RENFE (the main Spanish operator of suburban passenger trains) in Madrid, Spain. The results show that through this integrated approach a greater robustness degree can be obtained.

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  • Alfieri, A., Groot, R., Kroon, L. G., & Schrijver, A. (2006). Efficient circulation of railway rolling stock. Transportation Science, 40, 378–391.

    Article  Google Scholar 

  • Brännlund, U., Lindberg, P. O., Nou, A., & Nilsson, J. E. (1998). Railway timetabling using Lagrangian relaxation. Transportation Science, 32, 358–369.

    Article  Google Scholar 

  • Ben-Khedher, N., Kintanar, J., Queille, C., & Stripling, W. (1998). Schedule optimization at SNCF: from conception to day of departure. Interfaces, 28, 6–23.

    Article  Google Scholar 

  • Cacchiani, V., Caprara, A., & Toth, P. (2010). Scheduling extra freight trains on railway networks. Transportation Research. Part B: Methodological, 44(2), 215–231.

    Article  Google Scholar 

  • Cadarso, L., & Marín, A. (2011). Robust rolling stock in rapid transit networks. Computers & Operations Research, 38(8), 1131–1142.

    Article  Google Scholar 

  • Caprara, A., Fischetti, M., & Toth, P. (2002). Modeling and solving the train timetabling problem. Operations Research, 50, 851–861.

    Article  Google Scholar 

  • Caprara, A., Monaci, M., Toth, P., & Guida, P. L. (2006). A Lagrangian heuristic approach to real-world train timetabling problems. Discrete Applied Mathematics, 154, 738–753.

    Article  Google Scholar 

  • Caprara, A., Kroon, L., Monaci, M., Peeters, M., & Toth, P. (2007). Passenger railway optimization. In C. Barnhart & G. Laporte (Eds.), Handbook in operations research and management science (vol. 14). Elsevier: Amsterdam.

    Google Scholar 

  • Carraresi, P., Malucelli, F., & Pallottino, S. (1996). Regional mass transit assignment with resource constraints. Transportation Research. Part B: Methodological, 30(2), 81–98.

    Article  Google Scholar 

  • Cordeau, J. F., Soumis, F., & Desrosiers, J. (2000). A Benders decomposition approach for the locomotive and car assignment problem. Transportation Science, 34, 133–149.

    Article  Google Scholar 

  • Cordeau, J. F., Desaulniers, G., Lingaya, N., Soumis, F., & Desrosiers, J. (2001). Simultaneous locomotive and car assignment at VIA Rail Canada. Transportation Research. Part B: Methodological, 35, 767–787.

    Article  Google Scholar 

  • Fioole, P. J., Kroon, L. G., Maróti, G., & Schrijver, A. (2006). A rolling stock circulation model for combining and splitting of passenger trains. European Journal of Operational Research, 174(2), 1281–1297.

    Article  Google Scholar 

  • Kroon, L. G., & Peeters, L. W. P. (2003). A variable trip time model for cyclic railway timetabling. Transportation Science, 37, 198–212.

    Article  Google Scholar 

  • Liebchen, C., & Möhring, R. H. (2008). The modeling power of the periodic event scheduling problem: railway timetables—and beyond. In Lecture notes in economics and mathematical systems: Vol. 600 (II). Computer-aided Systems in Public Transport (pp. 117–150).

    Chapter  Google Scholar 

  • Maróti, G. (2006). Operations research models for railway rolling stock planning. PhD thesis, Eindhoven, Technische Universiteit Eindhoven.

  • Mellouli, T., & Suhl, L. (2007). Rotation planning of locomotive and carriage groups with shared capacities. In F. Geraets, L. G. Kroon, A. Schöbel, D. Wagner, & C. Zaroliagis (Eds.), Algorithmic methods for railway optimization. Berlin: Springer.

    Google Scholar 

  • Nachtingall, K. (1996). Periodic network optimization with different arc frequencies. Discrete Applied Mathematics, 69, 1–17.

    Article  Google Scholar 

  • Nachtingall, K., & Voget, S. (1997). Minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks. European Journal of Operational Research, 103, 610–627.

    Article  Google Scholar 

  • Serafini, P., & Ukovich, W. (1989). A mathematical model for periodic event scheduling problems. SIAM Journal on Discrete Mathematics, 2, 550–581.

    Article  Google Scholar 

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Correspondence to Ángel Marín.

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Cadarso, L., Marín, Á. Integration of timetable planning and rolling stock in rapid transit networks. Ann Oper Res 199, 113–135 (2012).

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  • Timetable
  • Rolling sock
  • Integration
  • Rapid transit
  • Robustness