Emergency Train Scheduling on Chinese High-Speed Railways

China has recently developed a large-scale high-speed railway (HSR) network that not only revolutionizes the perception of long-haul transport but also fundamentally improves the emergency response capability of the country. This gives rise to a problem of scheduling a set of emergency trains within the predefined HSR timetable. According to different degrees of disturbance of the timetable, this paper identifies three kinds of solutions, named, ideal, quasi-ideal, and feasible solutions, to the problem. We define a “headroom” function for computing the maximum number of emergency trains that can be inserted between two adjacent regular trains without any disturbance, from which a linear algorithm for finding ideal solutions is derived. By identifying the scope of changes to each regular train, quasi-ideal and feasible solutions can be found based on the ideal solutions on a set of alternative timetables. Numerical experiments demonstrate that our method is very efficient for supporting near-immediate emergency responses. We have used the solution method to evaluate the emergency capacity of most HSR lines in China. In particular, we successfully applied the method to schedule emergency trains in the rescue operation of the 2015 Tianjin chemical explosion.