In western China, railway lines are sparse, and there is a large fluctuation in transport demand under different transportation scenarios, which yields severe difficulties in setting up a signaling system and making a train timetable. To meet the fluctuating transport demand effectively and provide efficient train services in the changing multimodal transportation market, a new Chinese train control system based on flexible minimum headway time (FCTCS) is introduced and going to be implemented. Considering that the cost of implementing signaling systems corresponding to different minimum headway times varies significantly, it is necessary to find an optimal minimum headway time and design its corresponding train timetable. In this paper, we propose a mixed integer linear programming model for selecting an optimal minimum headway time, with which a satisfactory train timetable is generated with the consideration of symmetry transport demand. The objective function is to maximize the total profit of train operation. We further develop genetic algorithm with an integer and binary coding method for searching for the solution. Finally, a set of numerical tests based on a railway line in a sparse railway network in western China is used to demonstrate the validity and effectiveness of the proposed model.

In train rescheduling, the arrival and departure times of trains at stations are normally constrained by many operations rules that must be respected. Therefore, different methods were proposed to describe train operations for preventing train conflicts, especially concerning the safety headways. This paper develops a virtual resource-based method in place of the commonly used big-M method and ‘either-or’ constraints for reformulating the safety headway of opposing trains arriving at the same station on a single-track rail. This new formulation can provide an efficient decomposition mechanism by decomposing the original complex problem into several single train-based subproblems. A resource-oriented mixed-integer linear programming model based on a time-space network is developed to minimize the total train delay time with cumulative flow variables used to describe time-space resources occupation. We also present a set of numerical experiments based on a single-track railway line in China to evaluate the validity of the proposed method.