Robust minimum fleet problem for autonomous and human-driven vehicles in on-demand ride services considering mixed operation zones

In this paper, we envision an emerging Mixed Operation Zone (MOZ) where both autonomous vehicles (AVs) and human-driven vehicles (HVs) are present for on-demand ride services. This paper aims to size and operate a fleet of AVs and HVs in the presence of MOZs and to investigate the impact of MOZs on on-demand ride services. Considering the demand uncertainty, we propose a demand-oriented robust minimum fleet problem (RMFP) and employ a two-stage robust optimization (RO) to model the decision-making. Fluctuant demand is bounded by distribution-free uncertainty sets. For the convenience of solving RO models, we reformulate the second-stage recourse problem with an equivalent mathematical programming formulation. A tailored column-and-constraint generation algorithm is developed to solve the RMFP exactly. The algorithm is proved to converge in a finite number of iterations. Extensive experiments are conducted on the instances based on a real-world on-demand ride service in Chengdu. The developed algorithm performs better than the state-of-the-art Benders decomposition approach. Numerical results imply huge potential benefits from MOZs on improving service performance for ride service platforms.