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.

在本文中，我们设想了一个新兴的混合操作区 (MOZ)，其中自动驾驶汽车 (AV) 和人类驾驶汽车 (HV) 都可用于按需乘车服务。本文旨在在有 MOZ 的情况下确定和运营一组 AV 和 HV，并调查 MOZ 对按需乘车服务的影响。考虑到需求的不确定性，我们提出了面向需求的鲁棒最小车队问题（RMFP），并采用两阶段鲁棒优化（RO）对决策进行建模。波动的需求受到无分布的不确定性集的限制。为了方便求解 RO 模型，我们用等效的数学规划公式重新表述了第二阶段的追索问题。开发了一种定制的列和约束生成算法来精确求解 RMFP。该算法被证明在有限次数的迭代中收敛。对基于成都真实世界按需乘车服务的实例进行了大量实验。开发的算法比最先进的 Benders 分解方法性能更好。数值结果表明 MOZ 在提高乘车服务平台的服务性能方面具有巨大的潜在好处。