Optimal Spatial Pricing for an On-demand Ride-sourcing Service Platform

This paper investigates a long-term optimal spatial pricing strategy for a ride-sourcing platform that serves a particular (possibly populated) area with profit-driven service providers (i.e., drivers) and time- and price- sensitive customers. By observing that oftentimes, the pricing strategy is anisotropic and spatially dependent, and both the supply and request rates are endogenous, we build an analytical bi-level optimization model. In the upper-level formulation, the ride-sourcing platform aims to set up the spatially heterogeneous pricing strategy to maximize its total profit. While in the lower level, we solve the trip distribution model that characterizes the optimal flow rates among zones given the travel demand rate at each zone. We prove that when the platform seeks to expand its business, the optimal number of participating drivers and their optimal wages will be influenced not only by the pricing strategy but also by the levels of service of the service zones. Our further investigation shows that the profit at a particular zone can be also influenced by the potential customers' service requests from the other zones. Finally, we use the real-world data provided by DiDi Chuxing to numerically validate our theoretical results.