A continuous approximation model for the optimal design of mixed free-floating and station-based car-sharing systems

•Mixed car-sharing: station-based and free-floating layers working simultaneously.•Optimal design for each city context: vehicle fleet, parking, and repositioning.•Possibility of considering electrical vehicles not implying additional restrictions.•Part of the demand unserved if the system is to be economically sustainable.•Mixed systems will generally perform better. One-way car-sharing systems have become a popular urban transportation mode in many cities worldwide. First pilot implementations were originally station-based, so that trips needed to be station-to-station. This configuration created implementation difficulties in many cities and higher infrastructure costs for operating agencies. The appearance of free-floating on-street systems eased these limitations and implied an important growth of car-sharing implementations. In spite of these, free-floating systems are not free of planning and operative difficulties, which if not addressed carefully, might imply the economical unsustainability of the system. The idea of mixed systems, where a free-floating system and a station-based system complement each other, is new. The objective is to exploit the potentialities of both designs, while limiting their respective drawbacks. This paper presents a parsimonious model from which to derive the optimal strategical design variables for mixed car-sharing systems (i.e. the vehicle fleet size, the number of stations and the required intensity of rebalancing operations). This requires an integrated view of the system, allowing the optimization of the trade-off between the costs incurred by the operating agency and the level of service offered to users. The approach is based on the modelling technique of continuous approximations, which requires strong simplifications but allows obtaining very clear trade-offs and insights. The model has been applied to a case study taking the parameters from the city of Barcelona. Results prove the profitability of mixed car-sharing systems, which in particular contexts, is higher than that of pure free-floating or pure station-based systems on their own. Furthermore, if electrical cars are used, results show that battery recharging will not imply an active restriction to the system configuration. In conclusion, the proposed modeling approach represents a tool for the strategic design of car-sharing systems in the planning phase and provides guidelines for their adequate development, contributing to a more sustainable urban mo