Locomotive Assignment Using Train Delays
The locomotive assignment problem is to provide at minimum cost sufficient motive power to pull all the trains of a timetabled schedule. Optimization methods for large scale problems are based on multi-commodity flow models with additional restrictions, solved on a rolling horizon. Branch-and-bound strategies are used to find integer solutions. When there is an insufficient number of locomotives, some companies rent additional units while others prefer to postpone train departures. In this paper, we propose a method that finds a feasible solution by delaying the departure of some trains, according to their types. The numerical results using data from the company CN North America show that with a total of about 38 hours of delay time, all the train requirements could be satisfied for a one-week planning problem involving 1988 train segments. When the train requirements are satisfied, the cost penalties associated with undercovering are significantly reduced, and consequently, the integrality gap is decreased. In our numerical experiments, this gap decreases by 2% on average.
KeywordsPenalty Cost Delay Cost Rolling Horizon Augmented Network Train Delay
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- Ahuja, R.K./Magnanti, T.L./Orlin, J.B. (1993): Network flows: theory, algorithms, and applications. (Prentice Hall) Englewood Cliffs, New Jersey.Google Scholar
- Benders, J.F. (1962): Partitioning procedures for solving mixed variables programming problems. in: Numerische Mathematik 4, 238–252.Google Scholar
- Booler, J.M. (1980): The solution of railway locomotive scheduling problem. in: Journal of Operational Research Society 31, 943–948.Google Scholar
- Cordeau, J.-F./Toth, P./Vigo, D. (1998): A survey of optimization models for train routing and scheduling. Les Cahiers de GERAD, Ecole des Hautes Etudes Commerciales, Montréal, Canada. In preparation.Google Scholar
- Fischetti, M./Toth, P. (1989): An additive bounding procedure for combinatorial optimization problems. in: Operations Research 37, 319–328.Google Scholar
- Florian, M./Bushell, G./Ferland, J./Guérin, G./Nastansky, L. (1976): The engine scheduling problem in a railway network. in: INFOR 14, 121–138.Google Scholar
- Forbes, M.A./Holt, J.N./Watts, A.M. (1991): Exact solution of locomotive scheduling problems. in: Journal of Operational Research Society 42, 825–831.Google Scholar
- Ribeiro, C./Soumis, F. (1994): A column generation approach to the multiple depot vehicle scheduling problem. in: Operations Research 42, 41–52.Google Scholar
- Wren, A. (1972): Bus scheduling: an interactive computer method. in: Transportation Planning and Technology 1, 115–122.Google Scholar
- Wright, M.B. (1989): Applying stochastic algorithms to a locomotive scheduling problem. in: Journal of Operational Research Society 40, 187–192.Google Scholar
- Ziarati, K. (1997): Affectation des locomotives aux trains. Ph.D. dissertation, École Polytechnique de Montréal, Montréal, Canada. In French.Google Scholar
- Ziarati, K./Soumis, F./Desrosiers, J./Gélinas, S./Saintonge, A. (1997): Locomotive assignment with heterogeneous consist at CN North America. in: European Journal of Operational Research 97, 281–292.Google Scholar