Abstract
We consider a problem faced by train companies: How can trains be assigned to satisfy scheduled routes in a cost efficient way? Currently, many railway companies create solutions by hand, a timeconsuming task which is too slow for interaction with the schedule creators. Further, it is difficult to measure how efficient the manual solutions are. We consider several variants of the problem. For some, we give efficient methods to solve them optimally, while for others, we prove hardness results and propose approximation algorithms.
Work partially supported by the Swiss Federal Office for Education and Science under the Human Potential Programme of the European Union under contract no. HPRN-CT-1999-00104 (AMORE).
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References
P. Alimonti and V. Kann. Hardness of approximating problems on cubic graphs. In Proc. 3rd Italian Conference on Algorithms and Complexity, LNCS 1203, pages 288–298, Berlin, 1997. Springer-Verlag.
A. Bertossi, P. Carraresi, and G. Gallo. On some matching problems arising in vehicle scheduling models. Networks, 17:271–281, 1987.
P. Brucker, J.L. Hurink, and T. Rolfes. Routing of railway carriages: A case study. Memorandum No. 1498, University of Twente, Fac. of Mathematical Sciences, 1999.
M.R. Bussieck, T. Winter, and U.T. Zimmermann. Discrete optimization in public rail transport. Mathematical Programming, 79:415–444, 1997.
G. Carpaneto, M. Dell’Amico, M. Fischetti, and P. Toth. A branch and bound algorithm for the multiple depot vehicle scheduling problem. Networks, 19:531–548, 1989.
P. Crescenzi and L. Trevisan. On approximation scheme preserving reducibility and its applications. In Proc. 14th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 880, pages 330–341, Berlin, 1994. Springer-Verlag.
G. Dantzig and D. Fulkerson. Minimizing the number of tankers to meet a fixed schedule. Nav. Res. Logistics Q., 1:217–222, 1954.
J. Desrosiers, Y. Dumas, M.M. Solomon, and F. Soumis. Time Constrained Routing and Scheduling. Elsevier, 1995.
T. Erlebach, M. Gantenbein, D. Hürlimann, G. Neyer, A. Pagourtzis, P. Penna, K. Schlude, K. Steinhöfel, D.S. Taylor, and P. Widmayer. On the complexity of train assignment problems. Technical report, Swiss Federal Institute of Technology Zürich (ETH), 2001. Available at http://www.inf.ethz.ch/.
R. Freling, J.M.P. Paixão, and A.P.M. Wagelmans. Models and algorithms for vehicle scheduling. Report 9562/A, Econometric Institute, Erasmus University Rotterdam, 1999.
A. Löbel. Optimal vehicle scheduling in public transit. PhD thesis, TU Berlin, 1998.
C. Papadimitriou and M. Yannakakis. Optimization, approximization and complexity classes. Journal of Computer and System Sciences, 43:425–440, 1991.
C. Ribeiro and F. Soumis. A column generation approach to the multiple-depot vehicle scheduling problem. Operations Research, 42(1):41–52, 1994.
A. Schrijver. Minimum circulation of railway stock. CWI Quarterly, 6(3):205–217, 1993.
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Erlebach, T. et al. (2001). On the Complexity of Train Assignment Problems. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_34
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DOI: https://doi.org/10.1007/3-540-45678-3_34
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