Dynamic Matching for Real-Time Ride Sharing

In a ride-sharing system, arriving customers must be matched with available drivers. These decisions affect the overall number of customers matched, because they impact whether future available drivers will be close to the locations of arriving customers. A common policy used in practice is the closest driver policy, which offers an arriving customer the closest driver. This is an attractive policy because it is simple and easy to implement. However, we expect that parameter-based policies can achieve better performance. We propose matching policies based on a continuous linear program (CLP) that accounts for (i) the differing arrival rates of customers and drivers in different areas of the city, (ii) how long customers are willing to wait for driver pickup, (iii) how long drivers are willing to wait for a customer, and (iv) the time-varying nature of all the aforementioned parameters. We prove asymptotic optimality of a forward-looking CLP-based policy in a large market regime and of a myopic linear program–based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates and parameters are time homogeneous, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers under mild conditions.