Data-driven robust optimization for contextual vehicle rebalancing in on-demand ride services under demand uncertainty

The rebalancing of idle vehicles is critical to mitigating the supply-demand imbalance in on -demand ride services. Motivated by a ride service platform, this paper investigates a short-term vehicle rebalancing problem under demand uncertainty in the presence of contextual data. We deploy a novel data-driven robust optimization approach that takes a direct path from "Data"to "Decision"instead of the predict-then-optimize paradigm and leverages the prediction problem structure to seamlessly integrate demand predictions with optimization models. We further develop a risk-based uncertainty set to evaluate how well uncertain demand is estimated from contextual data by prediction models, and discuss the classes of prediction models that are highly compatible with robust optimization models. Based on the convex analysis and duality theory, we reformulate the original models into equivalent Mixed Integer Second Order Cone Programmings (MISOCPs) that are solvable via state-of-the-art commercial solvers. To solve large-scale instances, we utilize the affine decision rule technique to derive polynomial-sized reformulations. Extensive experiments are conducted on the instances based on a real-world on-demand ride service in Chengdu. The computational experiments demonstrate the promising performance of our rebalancing strategies and solution approaches.