Real-Time Spatial–Intertemporal Pricing and Relocation in a Ride-Hailing Network: Near-Optimal Policies and the Value of Dynamic Pricing.

The article addresses the spatial–intertemporal dynamic pricing problem faced by a ride-hailing firm managing a fixed fleet of servers (drivers) serving price-sensitive customers over a network with nonstationary and stochastic demand and nonnegligible travel times. It analyzes static pricing policies, showing their inherent limitations with a revenue loss lower bound on the order of \(n^{-1/2}\) as system scale \(n\) grows, and proposes a static price control (SPC) policy that nearly attains this bound. The authors then develop a novel dynamic pricing policy called the arc-balancing control (ABC) policy, which adaptively adjusts prices in batches to correct demand variability, achieving a significantly improved revenue loss on the order of \(n^{-2/3}\). Extensive numerical studies using synthetic data and real-world New York City taxi data confirm the theoretical advantages of dynamic pricing, notably that revenue gains primarily stem from serving more customers rather than raising prices. The framework is further extended to jointly optimize pricing and server relocation decisions via the joint relocation and arc-balancing control (R-ABC) policy, which maintains the same asymptotic performance order. The study highlights the importance of transient (nonsteady-state) analysis and intertemporal pricing adjustments in urban ride-hailing systems, and suggests directions for future research including strategic driver behavior and uncertain travel times.