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Experimental Validation of an Enhanced System Synthesis Approach Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Modelling and Solving a Train Path Assignment Model

Authors : Karl Nachtigall, Jens Opitz

Published in: Operations Research Proceedings 2014

Publisher: Springer International Publishing

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Abstract

We introduce a binary linear model for solving the train path assignment problem. For each train request a train path has to be constructed from a set of predefined path parts within a time-space network. For each possible path we use a binary decision variable to indicate, whether the path is used by the train request. Track and halting capacity constraints are taken into account. We discuss different objective functions, like maximizing revenue or maximizing total train path quality. The problem is solved by using column generation within a branch and price approach. This paper gives some modeling and implementation details and presents computational results from real world instances.

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Footnotes
1
The requirements for a request may be easily extended; e.g. intermediate stops and a desired time of arrival can be included into the model.
 
Literature
1.
Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelbergh, M.W.P., Vance, P.H.: Branch-and-price: column generation for solving huge integer programs. Oper. Res. 316–329 (1998)
2.
Feil, M., Poehle, D.: Why does a railway infrastructure company need an optimized train path assignment for industrialized timetabling?. In: Proceedings of International Conference on Operations Research, Aachen (2014) to appear
3.
Jacob, R., Barrett, C., Marathe, M.: Formal language constrained path problems. SIAM J. Comput. 30(3), 809–837 (2001)
4.
Padberg, M., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large- scale traveling salesman problems. 33, 60–71 (1991)
5.
Poehle, D., Feil, M.: What are new insights using optimized train paths assignment for the development of railway infrastructure?. In: Proceedings of International Conference on Operations Research, Aachen (2014) to appear
Metadata
Title
Modelling and Solving a Train Path Assignment Model
Authors
Karl Nachtigall
Jens Opitz
Copyright Year
2016
Book
Operations Research Proceedings 2014

Print ISBN: 978-3-319-28695-2

Electronic ISBN: 978-3-319-28697-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-28697-6_59