A MIP-based timetable rescheduling formulation and algorithm minimizing further inconvenience to passengers

This paper presents a timetable rescheduling algorithm based on Mixed Integer Programming (MIP) formulation when train traffic is disrupted. We minimize further inconvenience to passengers instead of consecutive delays caused by the disruption, since loss of time and satisfaction of the passengers are considered implicitly and insufficiently in the latter optimization. We presume that inconvenience of traveling by train consists of the traveling time on board, the waiting time at platforms and the number of transfers. Hence, the objective function is calculated on the positive difference between the inconvenience which each passenger suffers on his/her route in a rescheduled timetable and that in a planned timetable. The inconvenience-minimized rescheduling is often achieved at the cost of further train delays. Some trains dwell longer at a station to wait for extra passengers to come or to keep a connection, for instance. In the MIP model, train operation, each passenger's behavior and the amount inconvenience are simultaneously expressed by a system of integer linear inequalities. As countermeasures against the disruption, changes of train types and rolling stock operation schedules at termini as well as changes of departing order of trains and assignment of a track to trains in stations are performed. We also consider capacities of a line between adjacent stations as well as those of a track in stations. We have conducted numerical experiments using actual data and have obtained better rescheduled timetables in terms of customer satisfaction within practical time in proper solution space.