Dynamic Matching for Real-Time Ridesharing
Abstract: In a ridesharing system such as Uber or Lyft, arriving customers must be matched with available drivers. These decisions affect the overall number of customers matched, because they impact whether or not future available drivers will be close to the locations of arriving customers. A common policy used in practice is the closest driver (CD) policy that 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 to base the matching decisions on the solution to 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 pick-up, and (iii) 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. We leverage that result to also prove the asymptotic optimality of a myopic LP-based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers when parameters are time homogeneous under very mild conditions. We conduct simulation experiments to test the performances of the CD, the LP-based, and the CLP-based matching policies.
Based on a paper written with Erhun Ozkan (Marshall School of Business, USC).