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A branch and bound algorithm for scheduling trains in a railway network. (English) Zbl 1179.90135
Summary: The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.

90B35 Deterministic scheduling theory in operations research
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Full Text: DOI
[1] Adenso-Dı´az, B.; Oliva González, M.; González-Torre, P., On-line timetable rescheduling in regional train services, Transportation research part B, 33, 387-398, (1999)
[2] Brännlund, U.; Lindberg, P.O.; Nöu, A.; Nilsson, J.E., Railway timetabling using Lagrangian relaxation, Transportation science, 32, 358-369, (1998) · Zbl 1004.90035
[3] Caprara, A.; Fischetti, M.; Toth, P., Modeling and solving the train timetabling problem, Operations research, 50, 851-861, (2002) · Zbl 1163.90482
[4] Carlier, J., The one-machine sequencing problem, European journal of operational research, 11, 42-47, (1982) · Zbl 0482.90045
[5] Carlier, J.; Pinson, E., An algorithm for solving the job-shop problem, Management science, 35, 2, 164-176, (1989) · Zbl 0677.90036
[6] Carlier, J.; Pinson, E., Adjustment of heads and tails for the job-shop problem, European journal of operational research, 78, 146-161, (1994) · Zbl 0812.90063
[7] Cordeau, J.F.; Toth, P.; Vigo, D., A survey of optimization models for train routing and scheduling, Transportation science, 32, 4, 380-420, (1998) · Zbl 0987.90507
[8] Dessouky, M.M.; Lu, Q.; Zhao, J.; Leachman, R.C., An exact solution procedure to determine the optimal dispatching times for complex rail networks, IIE transaction, 38, 2, 141-152, (2006)
[9] Dorfman, M.J.; Medanic, J., Scheduling trains on a railway network using a discrete event model of railway traffic, Transportation research part B, 38, 81-98, (2004)
[10] Fay, A., A fuzzy knowledge-based system for railway traffic control, Engineering application of artificial intelligence, 13, 719-729, (2000)
[11] R. Hemelrijk, J. Kruijer, D.K. de Vries, Schiphol tunnel 2007. Description of the situation, Internal report, Holland Railconsult, Utrecht, The Netherlands, 2003.
[12] Higgins, A.; Kozan, E.; Ferreira, L., Optimal scheduling of trains on a single line track, Transportation research part B, 30, 147-161, (1996)
[13] Higgins, A.; Kozan, E., Heuristic techniques for single line train scheduling, Journal of heuristics, 3, 43-62, (1997) · Zbl 1071.90535
[14] J.R. Jackson, Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Science Research Project, University of California, Los Angeles, USA, 1955.
[15] Jovanovic, D.; Harker, P.T., Tactical scheduling of train operations: the SCAN I system, Transportation science, 25, 46-64, (1991)
[16] Kauppi, A.; Wikstrm, J.; Sandblad, B.; Andersson, A.W., Future train traffic control: control by re-planning, Cognition technology and work, 8, 1, 50-56, (2006)
[17] Kraft, E., A branch and bound procedure for optimal train dispatching, Journal of the transportation research forum, 28, 3, 263-276, (1987)
[18] Mascis, A.; Pacciarelli, D., Job shop scheduling with blocking and no-wait constraints, European journal of operational research, 143, 3, 498-517, (2002) · Zbl 1082.90528
[19] Nie, L.; Hansen, I.A., System analysis of train operations and track occupancy at railway stations, European journal of transport and infrastructure research, 5, 1, 31-54, (2005)
[20] E. Oliveira, B.M. Smith, A Job-Shop Scheduling Model for the Single-Track Railway Scheduling Problem, School of Computing Research Report 2000.21, University of Leeds, England, 2000.
[21] Pachl, J., Railway operation and control mountlake terrace, (2002), VTD Rail Publishing
[22] L. Ping, N. Axin, J. Limin, W. Fuzhang, Study on intelligent train dispatching, in: Proceedings of IEEE Intelligent Transportation Systems Conference, Oakland, USA, 25-29 August 2001.
[23] Şahin, İ., Railway traffic control and train scheduling based on inter-train conflict management, Transportation research part B, 33, 511-534, (1999)
[24] A.A.M. Schaafsma, Dynamic traffic management – innovative solution for the Schiphol bottleneck 2007, in: Proceedings of the First International Seminar on Railway Operations Modelling and Analysis, Delft, The Netherlands, 8-10 June 2005.
[25] Szpigel, B., Optimal train scheduling on a single track railway, (), 343-352
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