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

Abstract

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 non-stationary nature of demands, and the non-negligible travel time from one location to another location. We first show that the relative revenue loss of any static pricing control 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 synthetic and real data set from Manhattan Yellow Taxi confirm our theoretical findings and highlight the benefit of dynamic pricing over static pricing, especially when dealing with non-stationary demands. Interestingly, we also observe that the revenue improvement under our proposed control primarily comes from an increase in the number of customers served instead of from an increase in the average prices compared to the static pricing control. 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 control 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.