Abstract This paper studies the optimal spatial pricing for a ride-sourcing platform subject to a congestion charge. The platform determines the ride prices over the transportation network to maximize its profit, while the regulatory agency imposes the congestion charge to reduce traffic congestion in the urban core. A network economic equilibrium model is proposed to capture the intimate interactions among passenger demand, driver supply, passenger and driver waiting times, platform pricing, vehicle repositioning and flow balance over the transportation network. The overall optimal pricing problem is cast as a non-convex program. An algorithm is proposed to approximately compute its optimal solution, and a tight upper bound is established to evaluate its performance loss with respect to the globally optimal solution. Using the proposed model, we compare the impacts of three forms of congestion charge: (a) a one-directional cordon charge on ride-sourcing vehicles that enter the congestion area; (b) a bi-directional cordon charge on ride-sourcing vehicles that enter or exit the congestion area; (c) a trip-based congestion charge on all ride-sourcing trips. We show that the one-directional congestion charge not only reduces the ride-sourcing traffic in the congestion area, but also reduces the travel cost outside the congestion zone and benefits passengers in these underserved areas. We establish that in all congestion charge schemes the largest share of the tax burden is carried by the platforms, as opposed to passengers and drivers. We further show that compared to other congestion charges, the one-directional cordon charge is more effective in congestion mitigation: to achieve the same congestion-mitigation target, it imposes a smaller cost on passengers, drivers, and the platform. On the other hand, compared with the other charges, the trip-based congestion charge is more effective in revenue-raising: to raise the same tax revenue, it leads to a smaller loss to passengers, drivers, and the platform. We validate these results through realistic numerical studies for San Francisco.

Highlights • The optimal spatial pricing strategies are derived for the ride-sourcing platforms. • Empty vehicle relocation and interceptions during relocation are considered. • One-directional cordon price limits congestion in the urban core and reduces travel costs in the suburb. • One-directional cordon price is more effective in congestion mitigation. • Trip-based congestion charge is more effective in revenue-raising.