Optimal pricing and vehicle allocation in local ride-sharing markets with user heterogeneity

A ride-sharing platform (RSP) typically provides both solo and pooled ride services to passengers. Passengers opting for pooled rides pay a lower fare but generally experience longer travel times. Pooled ride services gain from improving occupancy per car, thereby serving more passengers, but this comes at the cost of a lower profit margin per passenger compared to solo ride services. We develop a stochastic queueing model to characterize the user equilibrium in a local on-demand market for solo and pooled ride services. In this model, passengers have heterogeneous values of time (VOTs), and drivers operate as independent agents. We find that in equilibrium, the VOT threshold value regulated by the set trip fares for solo and pooled ride services determines passengers’ travel mode choices. Specifically, passengers with lower VOTs than the threshold value choose to pool, while the others choose to ride alone. Built upon the user equilibrium, we then design customized optimal pricing and vehicle allocation strategies to maximize the total expected revenue of the RSP. This approach adapts the revenue-maximizing pricing and vehicle allocation strategies to a specific local ride-sharing market. It achieves this customization by considering factors such as users’ VOTs, supply and demand levels, spatial distances, and prevailing traffic conditions. Numerical results demonstrate that, in situations of high demand but limited supply, our proposed optimal pricing and vehicle allocation strategy effectively maximizes the total expected revenue of the RSP in the presence of spatial–temporal variations in ride-sharing demand. In such scenarios, solo ride prices are set at higher levels, and a majority of idle vehicles are allocated to solo passengers. Conversely, when demand is low but supply is sufficient, combining the optimal pricing strategy with a proportional vehicle allocation strategy also nearly maximizes the total expected revenue. In this case, the optimal vehicle allocation strategy is deemed non-critical due to the surplus supply. Solo ride prices are adjusted differently than those in high-demand situations to incentivize solo ride selection while discouraging pooled rides, ultimately resulting in the highest total expected revenue.