Discretization-Free Particle-Based Taxi Dispatch Methods With Network Flow Decomposition

The increasing popularity of on-demand ride-hailing services has introduced research problems, including those related to fleet management. Many existing fleet management approaches discretize a spatiotemporal distribution to reduce the problem complexity. Although spatial discretization greatly simplifies the problems, this approximation results in a suboptimal solution. To address this limitation, we present a novel spatial discretization-free, particle-based formulation of fleet management. Our model requires only temporal discretization. The nodes in our spatiotemporal network model represent the positions of the fleet and ride requests over the time horizon. Under this representation, a taxi dispatch problem can be solved by the minimum-cost maximum-flow (MCMF) algorithm. We show some structural properties that disclose a type of monotonicity by applying the MCMF algorithm to our problem. The obtained dispatch solution maximizes the number of served requests from these structural properties at least at the most current time step, regardless of the demand prediction quality. Moreover, these properties enable the decomposition of the MCMF algorithm without sacrificing optimality, and the decomposed multistage maximum-flow algorithm is significantly faster than the MCMF algorithm. Furthermore, we propose an efficient method that alleviates the dearth of input data for service providers who lack sufficient computing power to calculate substantial travel time information. We demonstrate the performance of our method by using data collected in New York City, USA. Our simulation studies indicate that a service provider can fulfill 74–85% of the ride requests within 2 minutes.