Integrated optimization of train stop planning and ticket pricing with equity concerns of passengers for high-speed railways

Ticket pricing, which is critical to increasing the revenue for high-speed railways, is typically optimized with a given train stop plan. However, the passenger distributions are restricted by fixed train stop plans, and the optimal ticket price scheme may not be achieved. Therefore, a mixed-integer linear programming model is proposed to optimize collaboratively train stop planning and ticket pricing in this study. The objective is to maximize the total ticket revenue, while the total number of train stops is limited to guarantee service quality. Furthermore, equity concerns of passengers are addressed by ensuring that passengers have equitable travel costs and opportunities to access high-speed railways. Finally, numerical experiments are conducted on a hypothetical railway line and the Zhengzhou-Xi'an high-speed railway corridor to demonstrate the application of the proposed approach. The computational results indicate that the proposed method can increase the total ticket revenue by 27% through adding 14 train stops and formulating a new ticket price scheme compared to the traditional method. In addition, the equity performance can be kept at a level of 1.5.