Optimizing flexible one-to-two matching in ride-hailing systems with boundedly rational users

This study investigates a flexible one-to-two matching problem in ride-hailing systems. In the ride-hailing platform, dedicated drivers are assigned to serve a single request (one-to-one matching) or two requests (one-to-two matching). We aim to examine the en-route matching problem, i.e., an in-transit driver who is currently serving riders may be informed to pick up co-riders traveling in the same direction. We consider boundedly rational users who accept ride-shares at reasonable travel costs. To encourage riders to join one-to-two matching, we propose an incentive scheme under which riders who experience detour time in one-to-two matching will be charged at a discounted rate. To make en-route decisions quickly, we propose a rolling horizon approach. The flexible one-to-two matching problem is formulated as a multi-stage integer program with the objective of maximizing the system-wide profit. We derive the upper bound on detour time for riders, based on which we develop an efficient algorithm to determine cost-feasible ride-shares. We also develop a neighborhood searching method to identify the locations that are close to a driver. Exploiting the historical trip data of New York taxis, we investigate the matching patterns and provide strategies to benefit the users and the platform when the ride-hailing program is introduced into the existing road network. The numerical experiments reveal that our proposed incentive scheme for one-to-two matching problems can increase both ridership and profit. Furthermore, the productivity and the compensation of dedicated drivers are also improved.