Social equity-based timetabling and ticket pricing for high-speed railways

High-speed railways are expanding rapidly over the world, providing fast, convenient, and comfortable transport. It is therefore important to ensure that people are not excluded from high-speed railway use due to relatively high ticket prices. We aim to develop a railway timetable according to passenger requirements that explicitly considers social equity by applying variable ticket prices to trains. Specifically, we want to optimize ticket prices for trains operating during off-peak hours to improve accessibility for low-income passengers to improve social justice. A mixed integer linear programming model is formulated to solve our problem. In this timetabling-based model, we not only minimize the total general travel cost from a passenger perspective but also ensure that the revenue of the train company is no less than a specified value and that social equity is maintained at a specific level. To do this, we consider the social equity constraint and the minimum revenue requirement constraint, in addition to the traditional passenger-centric (-oriented) train timetabling-related constraints. Finally, we test our model on both a hypothetical high-speed railway network and the Guangzhou–Nanning and Guangzhou–Guilin high-speed railway network in China. The results demonstrate that the proposed optimization framework can provide a convenient timetable for passengers, adequate revenue for train companies and enhance social equity to meet government targets.