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• Adoption model for carsharing membership under gradual extension of service area. • Consideration of "dual mode": Free-floating and station-based service. • Population size and points of interest in the old and newly served areas are considered as determining factors. • Further, adoption dynamics consider follower-effects and initial information spread. • Case study based on 70 month data from Montreal, Canada. Carsharing operators (CSOs) are adapting their service over time to meet changing demands and grow their market share. Service areas are enlarged and, in some cities, "dual-mode settings" evolve, incorporating free-floating carsharing (FFcs) as a new service alongside existing station-based carsharing (SBcs). This paper proposes a methodology to discuss adoption dynamics in such a context, specifically focusing on the impact of existing services and service extensions on the adoption of the new service. We propose a framework, comprising of two parts: a potential market assessment and an adoption model. The potential market assessment focuses on establishing the relationships between the local population, carsharing memberships and Points of Interest (POIs) within the given service area. The adoption model then describes the likelihood of consumers adopting the FFcs service. By combining these two models, the effects of service extensions can be assessed. We evaluate the framework using a nearly six year dataset from Communauto, Montreal. The first 35 months of data are set as training data, while the subsequent 33 months are used for validation of predictive performance. Results demonstrate that the proposed model accurately predicts adoption dynamics. Prior experience of SBcs and initial information spread are found to be key parameters for demand prediction determining early adoption peaks and, due to follower effects, also impact long-term demand. Additionally, we quantify the importance of covering residential areas and points of interests in the service area, highlighting the synergy effects of service area expansions. [ABSTRACT FROM AUTHOR]

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. • The first-mile ridesharing problem with public and private autonomous vehicles is introduced. • Passengers' requirements for service quality, such as the latest arrival time and the maximum ride time, are considered. • An arc-based mixed-integer programming model and a trip-based set-partitioning model are proposed. • A branch-and-price algorithm and a tailored column-generation matheuristic algorithm are designed. • A tailored labeling algorithm with a novel dominance rule and a time schedule algorithm for routes are proposed. [ABSTRACT FROM AUTHOR]