Equity-aware optimisation of train capacity allocation and pricing in railway systems

Travel equity across income groups is an important indicator of railway passenger service reliability. However, conventional capacity allocation and pricing strategies priorities operator profits, often overlooking equity. This study proposes an integrated equity-aware optimization framework for capacity allocation and pricing. A user equilibrium model captures heterogeneous travel choices across differentiated service classes and income groups, while the Rawlsian max–min fairness criterion quantifies equity. A mixed-integer nonlinear programming (MINLP) model jointly optimizes carriage configuration, seat allocation, and pricing across multiple service classes and OD pairs. We reduce model complexity through linearization techniques and demonstrate the effectiveness of the proposed approach using a small illustrative example and a case study of the Wuhan–Guangzhou high-speed rail corridor in China. Results show that the approach reduces the risk of travel opportunity loss for low-income passengers, improves equity in capacity allocation among groups, and achieves mutually beneficial outcomes for operators and passengers.