Real-Time Spatial-Intertemporal Dynamic Pricing for Balancing Supply and Demand in a Ride-Hailing Network

Motivated by the growth of ride-hailing services in urban areas, we study a (tactical) real-time spatial-inter-temporal dynamic pricing problem where a firm uses a pool of homogeneous servers (e.g., a fleet of taxis) in a network to serve price-sensitive customers who request a service (i.e., a trip from an origin to a destination) over a finite planning horizon (e.g., a day). We consider a model that captures the stochastic and non-stationary pattern of demand arrivals as well as the friction to match servers with customers caused by the spatial and inter-temporal features of the trips, which take non-negligible travel time from one location to another location in the network. We propose a static pricing heuristic and two dynamic pricing heuristics (a node-based pricing, where the same adjustment is applied to all trips originating at the same location, and an arc-based pricing, where the adjustment is specific to each origin-destination pair) that vary in the level of flexibility in price adjustments. We show that all three heuristics are asymptotically optimal in the setting with a large number of demand and supply, but have different optimality gaps relative to the optimal control. Our analysis shed light on the value of dynamic pricing and the extent to which it depends on how the travel time of a trip compares to the length of the horizon. We also conduct extensive numerical studies using both synthetic and real data set from Manhattan Yellow Taxi. The results confirm our theoretical findings and highlight the benefit of inter-temporal feature of dynamic pricing when dealing with non-stationary demand. Interestingly, we also observe that the revenue improvement under our arc-based pricing heuristic over the static pricing heuristic comes primarily from the increase in the number of customers served instead of from the increase in the average prices. This provides an interesting insight that certain forms of dynamic pricing can be used to not only increase revenue but also the number of customers served (i.e., service level), which is undoubtedly one of the most important goals of an urban transportation system