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A constraint generation algorithm for the construction of periodic railway timetables

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  • Odijk, Michiel A.
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    Abstract

    This paper addresses the problem of constructing periodic timetables for train operations. We use a mathematical model consisting of periodic time window constraints by means of which arrival and departure times can be related pairwise on a clock, rather than on a linear time axis. Constructing a timetable, then, means solving a set of such constraints. This problem is known to be hard, i.e. it is NP-complete. We describe a new algorithm to solve the problem based on constraint generation and work out a real-life example. It appears that, for problem instances of modest, yet non-trivial, size, the algorithm performs very well, which opens a way to thorough performance analysis of railway systems by studying a large number of possible future timetables.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 30 (1996)
    Issue (Month): 6 (December)
    Pages: 455-464

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    Handle: RePEc:eee:transb:v:30:y:1996:i:6:p:455-464

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    1. Gertsbakh, Ilya & Serafini, Paolo, 1991. "Periodic transportation schedules with flexible departure times : An interactive approach based on the periodic event scheduling problem and the deficit function approach," European Journal of Operational Research, Elsevier, Elsevier, vol. 50(3), pages 298-309, February.
    2. Serafini, Paolo & Ukovich, Walter, 1989. "A mathematical model for the fixed-time traffic control problem," European Journal of Operational Research, Elsevier, Elsevier, vol. 42(2), pages 152-165, September.
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    Cited by:
    1. Huisman, D. & Kroon, L.G. & Lentink, R.M. & Vromans, M.J.C.M., 2005. "Operations Research in Passenger Railway Transportation," ERIM Report Series Research in Management, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasm ERS-2005-023-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.
    2. Cordone, Roberto & Redaelli, Francesco, 2011. "Optimizing the demand captured by a railway system with a regular timetable," Transportation Research Part B: Methodological, Elsevier, Elsevier, vol. 45(2), pages 430-446, February.
    3. Carey, Malachy & Crawford, Ivan, 2007. "Scheduling trains on a network of busy complex stations," Transportation Research Part B: Methodological, Elsevier, Elsevier, vol. 41(2), pages 159-178, February.
    4. Thomas Lindner & Uwe Zimmermann, 2005. "Cost optimal periodic train scheduling," Computational Statistics, Springer, Springer, vol. 62(2), pages 281-295, November.
    5. Carey, Malachy & Carville, Sinead, 2003. "Scheduling and platforming trains at busy complex stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(3), pages 195-224, March.
    6. Chakroborty, Partha & Vikram, Durgesh, 2008. "Optimum assignment of trains to platforms under partial schedule compliance," Transportation Research Part B: Methodological, Elsevier, Elsevier, vol. 42(2), pages 169-184, February.
    7. Kroon, L.G. & Peeters, L.W.P. & Wagenaar, J.C. & Zuidwijk, R.A., 2012. "Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling," ERIM Report Series Research in Management, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasm ERS-2012-008-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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