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 eme...