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Train delays have a great impact on the schedule of high-speed railways including overall efficiency and the quality of the travel service of the passengers. Therefore, the development of an approach to recover a schedule via timely and rapid operation adjustments must be investigated. In this paper, a complete final real-time adjustment scheme is proposed for the train dispatcher of a railway enterprise for delayed trains. A train operation process model based on the Max-Plus algebra method is proposed. Six operation adjustment strategies are analyzed including section acceleration, operation based on the original timetable, dwell time reduction, increase in overtaking, reduction in overtaking, and train postponement. An approximate model is then built based on the minimum number of delayed trains considering the constraints of the adjustment strategies and the feasible adjusted schemes can be quickly obtained without any record specific time data and constraints. The set of feasible solutions of the approximate model is then regarded as the importation of the second model. In addition, the second model is an optimization model for operation adjustment with the least average delay time of each train at each station by updating the state matrixes of the train operation process model. The algorithms are designed for these models, and this approach can reduce the computation time. Finally, the timetable of the Beijing-Shanghai high-speed railway is considered as the actual case for analysis. Thus, the method was proven feasible for operation adjustment of delayed trains.

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