Profit Maximization Model with Fare Structures and Subsidy Constraints for Urban Rail Transit

This paper analyzes government subsidies based on the service design (i.e., headway) and fare structures of an urban rail transit system while considering necessary financial support from the government. To capture the interactions among the operator performance, government subsidies, and passengers in an urban rail transit system, a profit maximization model with nonnegative profit constraint is formulated to determine the optimal fare and headway solutions. Then, the social welfare that results from the operator profit maximization model is analyzed. Finally, a numerical example from Changsha, China, is employed to verify the feasibility of the proposed model. The major results consist of optimized solutions for decision variables, i.e., the fares and train headways, as well as subsidies to the operator. The fare elasticity factor under two fare structures significantly affects fares and demand. As the fare elasticity factor increases, the social welfare gradually decreases and a deficit occurs at low fares and demand, while subsidies rise from 0 to ¥24658.00 and ¥38089.16 under the flat fare and distance-based fare structures.