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Mathematical Problems in Engineering
Volume 2015, Article ID 289072, 12 pages
Research Article

A Branch and Bound Algorithm and Iterative Reordering Strategies for Inserting Additional Trains in Real Time: A Case Study in Germany

1Institute of Railway Systems Engineering and Traffic Safety, Technical University of Braunschweig, Pockelsstrasse 3, 38106 Braunschweig, Germany
2School of Transportation Engineering, Tongji University, 4800 Caoan Road, Shanghai 201804, China

Received 6 June 2014; Revised 1 September 2014; Accepted 2 September 2014

Academic Editor: Huimin Niu

Copyright © 2015 Yuyan Tan and Zhibin Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With the aim of supporting the process of adapting railway infrastructure and future traffic needs, we have developed a method to insert additional trains efficiently to an existing timetable without introducing large consecutive delays to scheduled trains. In this work, the problem is characterized as a job-shop scheduling problem. In order to meet the limited time requirement and minimize deviations to the existing timetable, the modification that consists of retiming or reordering trains is implemented if and only if it potentially leads to a better solution. With these issues in mind, the problem of adding train paths is decomposed into two subproblems. One is finding the optimal insertion for a fixed order timetable and the other is reordering trains. The two subproblems are solved iteratively until no improvement is possible within a time limit of computation. An innovative branch and bound algorithm and iterative reordering strategy are proposed to solve this problem in real time. Unoccupied capacities are utilized as primary resources for additional trains and the transfer connections for passengers can be guaranteed in the new timetable. From numerical investigations, the proposed framework and associated techniques are tested and shown to be effective.