Objective Tianjin Rail Transit is about to enter the mature operational stage of its development. The current fare scheme has been in use since it was approved by the Tianjin Municipal Development and Reform Commission in 2006. The existing fare scheme can no longer meet the sustainable development needs of enterprises; therefore, it is necessary to study a fare formulation scheme for this mature operational stage.

Method A bi-level programming model is adopted to construct a fare solution model for Tianjin Rail Transit in its mature operational stage. The upper-level model programming establishes a function aiming to maximize enterprise profit, using government price caps as constraint conditions. The lower-level programming establishes a function aiming to minimize passengers' generalized travel costs, using public transit travel volume as constraint conditions. A heuristic algorithm based on sensitivity analysis is utilized to solve for the equilibrium fare. A method combining RP （revealed preference） and SP （stated preference） surveys is adopted to conduct an analysis of passenger sensitivity to fare increases and to demonstrate the implementability of the formulated fare scheme. Tianjin Rail Transit Line 10 is selected as a case study for empirical analysis.

Result & Conclusion  Compared to the current fare scheme, the equilibrium fare of Tianjin Rail Transit Line 10 in its mature operational stage is increased by 1.5 yuan. The enterprise's annual revenue can increase by 8.37 million yuan, the number of stations required for a fare upgrade is reduced by one station, and the passenger loss rate is 19.6%. These research results are fundamentally consistent with existing survey conclusions. In such fare equilibrium, the passenger sensitivity is relatively low, indicating that the proposed fare scheme possesses implementability.