Dynamic Dispatch and Centralized Relocation of Cars in Ride-Hailing Platforms

We consider a ride-hailing platform that seeks to maximize its profit by dynamically dispatching cars to pick up customers and centrally relocating cars from one area to another. We model the ride-hailing platform as a closed stochastic processing network. Because the problem appears intractable, we resort to an approximate analysis in the heavy-traffic regime and consider the resulting Brownian control problem. This problem is simplified considerably and reduced to a lower-dimensional singular control problem called the workload formulation. We develop a novel algorithm to solve the workload problem numerically. We apply this algorithm to the workload problem derived from the New York City taxi data set. The solution helps us derive a dynamic control policy for the New York City application. In doing so, we prescribe the ride-hailing platform to first solve an offline linear program, whose optimal solution can be interpreted as the optimal static control policy. This solution helps partition the areas of the city into pools of areas. The platform only uses the information on the fraction of cars in the various pools, which reduces the state space dimension significantly, making the problem computationally tractable. When the distribution of cars among the pools is balanced, the platform follows the optimal static control policy. Otherwise, the platform intervenes to move the system to a more balanced state by either dropping demand or using a dispatch or relocation activity that is not used under the optimal static control policy. We demonstrate the effectiveness of the proposed dynamic control policy for the New York City application using a simulation study.