A virtual resource-based method for formulating the safety headway of opposing trains arriving at the same station on a single-track railway line

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.