Real-time spatial-intertemporal dynamic pricing for balancing supply and demand in a ride-hailing network: near-optimal policies and the value of dynamic pricing

Motivated by the growth of ride-hailing services in urban areas, we study a (tactical) real-time spatial–intertemporal dynamic pricing problem where a firm uses a pool of homogeneous servers (e.g., a fleet of taxis) to serve price-sensitive customers (i.e., a rider requesting a trip from an origin to a destination) within a finite horizon (e.g., a day). We consider a revenue maximization problem in a model that captures the stochastic and nonstationary nature of demands, and the nonnegligible travel time from one location to another location. We first show that the relative revenue loss of any static pricing policy is at least in the order of n−1/2 in a large system regime where the demand arrival rate and the number of servers scale linearly with n, which highlights the limitation of static pricing control. We also propose a static pricing control with a matching performance (up to a multiplicative logarithmic term). Next, we develop a novel state-dependent dynamic pricing control with a reduced relative revenue loss of order n−2/3. The key idea is to dynamically adjust the prices in a way that reduces the impact of past “errors” on the balance of future distributions of servers and customers across the network. Our extensive numerical studies using both a synthetic data set and a real data set from the New York City Taxi and Limousine Commission, confirm our theoretical findings and highlight the benefit of dynamic pricing over static pricing, especially when dealing with nonstationary demands. Interestingly, we also observe that the revenue improvement under our proposed policy primarily comes from an increase in the number of customers served instead of from an increase in the average prices compared with the static pricing policy. This suggests that dynamic pricing can be potentially used to simultaneously increase both revenue and the number of customers served (i.e., service level). Finally, as an extension, we discuss how to generalize the proposed policy to a setting where the firm can also actively relocate some of the available servers to different locations in the network in addition to implementing dynamic pricing