A continuous approximation model for the optimal design of public bike-sharing systems

During the last decade, public bike-sharing systems have gained momentum and popularity. Many cities worldwide have put their trust in bike-sharing to promote bicycle use and move towards more sustainable mobility. This paper presents a parsimonious model from which to derive the optimal strategical design variables for bike-sharing systems (i.e. the number of bicycles, 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 validated using data from Bicing in Barcelona, and the results prove, for example, the existence of economies of scale in bike-sharing systems. Also, station-based and free-floating system configurations are compared, showing that free-floating systems achieve a better average level of service for the same agency costs. In spite of this, the performance of free-floating systems will tend to deteriorate in the absence of a strong regulation. Furthermore, if electrical bikes are used, results show that battery recharging will not imply an active restriction in station-based configurations. In conclusion, the proposed modeling approach represents a tool for strategic design in the planning phase and provides a better understanding of bike-sharing systems.