Modeling and solving the train timetabling problem

Operations Research

Volumn 50, Issue 5, 2002, Pages

  Caprara, Alberto ^a   Fischetti, Matteo ^a   Toth, Paolo ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Heuristics; Programming algorithms: Lagrangian relaxation; Railway; Transportation: train timetabling

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; HEURISTIC PROGRAMMING; LAGRANGE MULTIPLIERS; LINEAR PROGRAMMING; PROBLEM SOLVING;

TRAIN TIMETABLING PROBLEM;

SCHEDULING;

EID: 0036759198     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.50.5.851.362     Document Type: Article

References (20)

1. Brännlund, U., P.O. Lindberg, A. Nöu, J.E. Nilsson. 1998. Railway timetabling using Lagrangian relaxation. Transportation Sci. 32 358-369.
2. Cai, X., C.J. Goh. 1994. A fast heuristic for the train scheduling problem. Comput. Open Res. 21 499-510.
3. Caprara, A., M. Fischetti, P. Toth. 1999. A heuristic method for the set covering problem. Open. Res. 47 730-743.
4. Carey, M., D. Lockwood. 1995. A model, algorithms and strategy for train pathing. J. Open Res. Soc. 46 988-1005.
5. Carr, R.D., G. Lancia, S. Istrail. 2000. Branch-and-cut algorithms for independent set problems: Integrality gap and an application to protein structure alignment. SAND Report SAND2000-2171, Sandia National Laboratories. Available at 〈http://infoserve.sandia.gov/sand_doc/2000/002171.pdf〉.
6. Escudero, L.E., M. Guignard, K. Malik. 1994. A Lagrangian relax and cut approach for the sequential ordering with precedence constraints. Ann. Open. Res. 50 219-237.
7. Fisher, M. 1994. Optimal solution of vehicle routing problems using minimum k-trees. Oper. Res. 42 626-642.
8. Garey, M.R., D.S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco, CA.
9. Grötschel, M., L. Lovász, A. Schrijver. 1988. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin, Germany.
10. Harker, P.T., S. Hong. 1994. Pricing of track time in railroad operations: An internal market approach. Transportation Res. 28-B 197-212.
11. Held, M., R.M. Karp. 1971. The traveling salesman problem and minimum spanning trees: Part II. Math. Programming 1 6-25.
12. Higgings, A., E. Kozan, L. Ferreira. 1997. Heuristic techniques for single line train scheduling. J. Heuristics 3 43-62.
13. Jovanovic, D., P.T. Harker. 1991. Tactical scheduling of rail operations: The SCAN I system. Transportation Sci. 25 46-64.
14. Kann, V., A. Panconesi. 1997. Hardness of approximation. Annotated Bibliographies in Combinatorial Optimization. M. Dell'Amico, F. Maffioli, S. Martello, eds. J. Wiley and Sons, Chichester, U.K., 13-30.
15. Lindner, T., U.T. Zimmermann. 2000. Cost-oriented train scheduling. 8th Internat. Conference on Computer Aided Scheduling of Public Transport (CASPT 2000). Berlin, June.
16. Peeters, L.W.P., L.G. Kroon. 2000. A cycle based optimization model for the cyclic railway timetabling problem. 8th Internat. Conference on Computer Aided Scheduling of Public Transport (CASPT 2000). Berlin, June.
17. Petersen, E.R., R. Merchant. 1981. Scheduling of trains in a linear railway system. INFOR 19 246-258.
18. Reinert, K., H.-P. Lenhof, P. Mutzel, K. Mehlhom, J.D. Kececioglou. 1996. A branch-and-cut algorithm for multiple sequence alignment. Research Report MPI-I-96-1-028, Max-Planck-Institut für Informatik. Available at 〈http://data.mpi-sb.mpg.de/internet/reports.nsf〉.
19. Schrijver, A., A. Steenbeek. 1994. Timetable construction for Railned. Technical report, CWI, Amsterdam, The Netherlands (in Dutch).
20. Szpigel, B. 1973 Optimal train scheduling on a single track railway. M. Ross, ed. OR'72. North-Holland, Amsterdam, The Netherlands, 343-351.