Cooperative Optimization for Public Transit and Ride-Hailing Services Incorporated with Mode Loyalty and Heterogeneity

Accompanied by the rise in ride-hailing (RH) market share, its competition with conventional public transit (PT) has become increasingly pronounced. Consequently, administrators have been placing greater emphasis on how to enhance system revenue and service efficiency through effective fare coordination between the two modes. This study aims to propose a bilevel cooperative pricing model between the PT and RH operators. The upper-level model represents the cooperative decision-making between the two operators, aiming to maximize their joint revenue under the target PT share and accessibility constraint. The lower-level model describes travelers’ mode and route choices using a dogit–nested weibit–path size weibit (DNW–PSW) model, which explicitly captures mode heterogeneity, traveler loyalty, and route overlap. The proposed model is applied to diverse travel scenarios. The results show that, in most scenarios, cooperative pricing can increase the revenue of both PT and RH modes while ensuring the PT share and travel accessibility.