Matching Riders to Drivers Under Uncertain Wait Times in Ride-Hailing Systems: A Robust Optimization Approach with Box Uncertainty

The advent of ride-hailing systems has revolutionized urban mobility, yet efficient vehicle assignment remains challenging due to inherent uncertainties in passenger waiting times. This study addresses the ride-hailing matching problem under uncertain wait times, proposing a robust optimization model with a box uncertainty set to mitigate the impact of variability in service delivery. We first contextualize the problem by examining the evolution of transportation systems, emphasizing how ride-hailing services complicate traditional matching paradigms. Existing approaches often fail to account for real-world unpredictability, leading to suboptimal assignments. To bridge this gap, we formulate a data-driven robust optimization framework that bounds waiting time fluctuations within a box uncertainty set, ensuring reliable performance under worst-case scenarios. Using simulation data from Manhattan taxi trips, we compare our robust model against deterministic benchmarks, demonstrating its superiority in reducing average waiting times and enhancing system reliability, even under high uncertainty. Our results highlight the practical viability of robust optimization for ride-hailing platforms operating in dynamic environments.