  Large-scale ride-sharing systems combine real-time dispatching and routing
optimization over a rolling time horizon with a model predictive control (MPC)
component that relocates idle vehicles to anticipate the demand. The MPC
optimization operates over a longer time horizon to compensate for the inherent
myopic nature of the real-time dispatching. These longer time horizons are
beneficial for the quality of relocation decisions but increase computational
complexity. Consequently, the ride-sharing operators are often forced to use a
relatively short time horizon. To address this computational challenge, this
paper proposes a hybrid approach that combines machine learning and
optimization. The machine-learning component learns the optimal solution to the
MPC on the aggregated level to overcome the sparsity and high-dimensionality of
the solution. The optimization component transforms the machine-learning
prediction back to the original granularity through a tractable transportation
model. As a consequence, the original NP-hard MPC problem is reduced to a
polynomial time prediction and optimization, which allows the ride-sharing
operators to consider a longer time horizon. Experimental results show that the
hybrid approach achieves significantly better service quality than the MPC
optimization in terms of average rider waiting time, due to its ability to
model a longer horizon.
