Optimizing last trains timetable in the urban rail network: social welfare and synchronization

Last train timetable design is to coordinate last train services from different lines in an urban rail network for maximizing the number of transfers. It is a challenging operational research problem to balance the competing demand of two decision agents: that of the government agencies to provide the best social services with minimal government subsidy, and that of the train operating companies to minimize operating costs. A bi-level programming model is formulated for the last train timetabling problem, in which the upper level is to maximize the social service efficiency, and the lower level is to minimize the revenue loss for the operating companies. To solve this problem, a genetic algorithm combined with an active-set approach is developed. We report the optimization results on real-world cases of the Beijing subway network. The results show that the optimized last train timetable can significantly improve the transfer coordination.