Optimizing multi-modal travel with ride-sourcing services: a bi-level modeling approach with a credit-based charge-reward scheme

• This study investigates a CCR scheme design problem that incorporates ride-sourcing services. • A three-layer time-expanded network is developed to depict the daily mode choice of travelers. • The CCR scheme design problem is formulated as a bi-level optimization problem. • A momentum method with random perturbation is proposed to solve the combined equilibrium with route-specific cost. Given the rapid growth of ride-sourcing services, integrating them effectively into multi-modal traffic management systems is imperative to alleviate congestion and pollution pressures. This study advances the existing Credit-Charge-Reward (CCR) mechanism by incorporating ride-sourcing services into a multi-modal framework, incentivizing travelers toward greener transportation modes through integrated pricing and rewarding. We construct a bi-level optimization model to capture the interplay between the ride-sourcing market equilibrium and travelers’ periodic mode choice with CCR implementation. To model the multi-day mode choices of heterogeneous travelers, we propose an enhanced multi-layer time-expanded network at the lower level that ensures daily ride-sourcing market equilibrium while minimizing total travel costs of all travelers. Based on the mode choice pattern, the government’s optimal decision on the CCR scheme is derived from the upper-level model constrained by revenue neutrality and Pareto improvement. We tailor an efficient algorithm to address the route-specific costs inherent in the time-expanded network and the model’s non-convexity issue. The numerical experiments confirm the efficacy of the ride-sourcing-integrated CCR scheme in curbing carbon emissions and mitigating traffic congestion, implementing our designed CCR scheme reduced carbon emissions by 10% to 35% and decreased average daily road travel time by 10% to 28%, providing key implications for real-world traffic management.