The burden of first-mile connection to public transit stations is a key barrier that discourages riders from taking public transportation. Public transit agencies typically operate a modest fleet of vehicles to provide first-mile services due to the high operating costs, thus failing to adequately meet the first-mile travel demands, especially during peak hours. At the same time, private cars are underutilized and have a lot of idle time. With the emergence of self-driving vehicles, new opportunities for addressing the current dilemma arise, such as integrating idle private self-driving vehicles to provide first-mile services, which is beneficial for public transportation agencies to provide high-quality services at low costs. This study investigates the first-mile ridesharing problem in which public transit agencies utilize idle privately-owned autonomous vehicles to dynamically inflate their fleet. This problem is more challenging in decision-making than conventional first-mile problems, as it involves decisions on heterogeneous fleet scheduling, vehicle routing, and time scheduling, all while taking into account the service quality for riders. To address this problem, an arc-based mixed-integer linear programming (MILP) model and a trip-based set-partitioning model are developed, both aiming to minimize total operational costs. To identify promising trips, we propose a tailored labeling algorithm with a novel dominance rule, along with a time window shift algorithm to determine the best schedule. To yield high-quality solutions in a short computation time, a tailored column-generation matheuristic algorithm is introduced. A branch-and-price exact algorithm and an adaptive large neighborhood search algorithm are developed to assess the matheuristic algorithm. Numerical experiments are conducted to demonstrate the effectiveness and applicability of the proposed models and algorithms. Experiments also show that this kind of ridesharing service can provide low-cost and high-quality services for the first-mile problem.

中文翻译：

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一种列生成数学方法，用于优化公有和私有自动驾驶车辆的第一英里乘车共享服务

与公共交通站的第一英里连接的负担是阻碍乘客乘坐公共交通的主要障碍。由于运营成本高昂，公共交通机构通常只运营少量车辆来提供首英里服务，因此无法充分满足首英里出行需求，尤其是在高峰时段。与此同时，私家车利用率不足，闲置时间较多。随着自动驾驶汽车的出现，解决当前困境的新机会出现，例如整合闲置私人自动驾驶车辆提供首英里服务，这有利于公共交通机构以低成本提供高质量服务。本研究调查了第一英里的乘车共享问题，其中公共交通机构利用闲置的私人自动驾驶车辆来动态扩充其车队。该问题比传统的首英里问题更具决策挑战性，因为它涉及异构车队调度、车辆路线和时间安排的决策，同时还要考虑乘客的服务质量。为了解决这个问题，开发了基于弧的混合整数线性规划（MILP）模型和基于行程的集合划分模型，两者都旨在最小化总运营成本。为了识别有希望的旅行，我们提出了一种具有新颖的主导规则的定制标记算法，以及时间窗口移位算法来确定最佳时间表。为了在短时间内产生高质量的解决方案，引入了定制的列生成数学算法。开发了分支和价格精确算法和自适应大邻域搜索算法来评估数学算法。进行数值实验来证明所提出的模型和算法的有效性和适用性。实验还表明，这种拼车服务可以为第一英里问题提供低成本、高质量的服务。