Scheduling synchronization in urban rail transit networks: Trade-offs between transfer passenger and last train operation

The scheduling synchronization problem in this paper is to obtain an optimal schedule by optimizing running time, departure time, dwell time and arrival time of the last train in urban rail transit networks. Operators are often faced with multiple conflicting requirements simultaneously such as high passenger’s service quality and less cost, smooth transfer events and less passenger’s travel time, and high accessibility and less operation time. Thus, researchers in this industry concentrate on utilizing operations and management decisions to solve the scheduling problem while balancing the service trade-offs. In this paper, we formulate a mixed integer programming approach for the last train schedule planning, and passengers benefit from smoother transfer in the form of maximizing the transfer synchronization events, while operators simultaneously can benefit with lower operation costs by minimizing the worst big difference between last trains. We propose an improved non-dominated sorting approach embedded in a genetic algorithm to obtain close-to-optimal solutions in a much shorter time for a sophisticated, real-world and large-scale Beijing subway network. Results demonstrate that significant service performance gains (76.33% for Just-missed, 32.01% for successful transfer, 15.39% for non-equity for last trains and 45.25% for variance indicators, etc.), which indicate the effectiveness of the proposed modeling framework and solution algorithm. The operator formulates an efficient schedule for the actual operation of the urban rail transit network by the proposed application method, and it also would be applicable to solving schedule problems among a large-scale network in other industries.