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A constraint generation algorithm for the construction of periodic railway timetables

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  • Odijk, Michiel A.

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.

Suggested Citation

  • Odijk, Michiel A., 1996. "A constraint generation algorithm for the construction of periodic railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 30(6), pages 455-464, December.
    • Handle: RePEc:eee:transb:v:30:y:1996:i:6:p:455-464
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    References listed on IDEAS

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    1. Serafini, Paolo & Ukovich, Walter, 1989. "A mathematical model for the fixed-time traffic control problem," European Journal of Operational Research, Elsevier, vol. 42(2), pages 152-165, September.
    2. 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, vol. 50(3), pages 298-309, February.
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