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A Lagrangian heuristic algorithm for a real-world train timetabling problem. (English) Zbl 1120.90324
Summary: The train timetabling problem (TTP) aims at determining an optimal timetable for a set of trains which does not violate track capacities and satisfies some operational constraints. In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following issues: $\bullet$ Manual block signaling for managing a train on a track segment between two consecutive stations. $\bullet$ Station capacities, i.e., maximum number of trains that can be present in a station at the same time. $\bullet$ Prescribed timetable for a subset of the trains, which is imposed when some of the trains are already scheduled on the railway line and additional trains are to be inserted. $\bullet$ Maintenance operations that keep a track segment occupied for a given period. We show how to incorporate these additional constraints into a mathematical model for a basic version of the problem, and into the resulting Lagrangian heuristic. Computational results on real-world instances from Rete Ferroviaria Italiana (RFI), the Italian railway infrastructure management company, are presented.

MSC:
90B35Scheduling theory, deterministic
90C59Approximation methods and heuristics
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References:
[1] Brännlund, U.; Lindberg, P. O.; Nöu, A.; Nilsson, J. E.: Allocation of scarce track capacity using Lagrangian relaxation. Transportation sci. 32, 358-369 (1998) · Zbl 1004.90035
[2] Cai, X.; Goh, C. J.: A fast heuristic for the train scheduling problem. Comput. oper. Res. 21, 499-510 (1994) · Zbl 0799.90068
[3] Caprara, A.; Fischetti, M.; Toth, P.: Modeling and solving the train timetabling problem. Oper. res. 50, 851-861 (2002) · Zbl 1163.90482
[4] Carey, M.; Lockwood, D.: A model, algorithms and strategy for train pathing. J. oper. Res. soc. 46, 988-1005 (1995) · Zbl 0832.90068
[5] Escudero, L. F.; Guignard, M.; Malik, K.: A Lagrangian relax and cut approach for the sequential ordering with precedence constraints. Ann. oper. Res. 50, 219-237 (1994) · Zbl 0833.90068
[6] Fisher, M.: Optimal solution of vehicle routing problems using minimum k-trees. Oper. res. 42, 626-642 (1994) · Zbl 0815.90066
[7] Higgings, A.; Kozan, E.; Ferreira, L.: Heuristic techniques for single line train scheduling. J. heuristics 3, 43-62 (1997) · Zbl 1071.90535
[8] Jovanovic, D.; Harker, P. T.: Tactical scheduling of rail operationsthe SCAN I system. Transportation sci. 25, 46-64 (1991)
[9] Lindner, T.; Zimmermann, U. T.: Cost-oriented train scheduling. Eighth international conference on computer aided scheduling of public transport (CASPT 2000) (June 2000)
[10] E. Oliveira, B.M. Smith, A job-shop scheduling model for the single-track railway scheduling problem, Technical Report 2000.21, School of Computing Research Report, University of Leeds, 2000.
[11] L.W.P. Peeters, Cyclic railway timetable optimization, Ph.D. Thesis, Erasmus Research Institute of Management, Erasmus University Rotterdam, 2003.
[12] L.W.P. Peeters, L.G. Kroon, A cycle based optimization model for the cyclic railway timetabling problem, in: J. Daduna, S. Voss (Eds.), Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems, vol. 505, Springer, Berlin, 2001, pp. 275 -- 296. · Zbl 0989.90521
[13] A. Schrijver, A. Steenbeek, Timetable construction for railned, Technical Report, CWI, Amsterdam, 1994 (in Dutch).
[14] Szpigel, B.: Optimal train scheduling on a single track railway. Or’72, 343-351 (1973)