High-Speed Train Network Routing with Column Generation

This paper is based on an award-winning rail scheduling project. It examines a high-speed train routing problem in which the trains are operated on a large network with sparse stations. The relatively long distance between train stations makes it unlikely to get a backup train unit in time when an operating train is out of service because of the need for maintenance. Therefore, regular maintenance is carefully incorporated into the base routing plan and is strictly enforced. An integrated path-based routing model is proposed here to design train routes and scheduling optimally. The objective is to cover the published trains and timetable with the least cost without violating operational rules and maintenance requirements. The scheduling for each operational cycle needs to be completed in a timely manner and be implementable in practice. A heuristic is proposed to solve the problem in a column generation framework. Numerical tests are conducted with operational data from the French National Railways. The test not only shows a significant cost savings but also indicates its efficiency in real-world applications.