User satisfaction based model for resource allocation in bike-sharing systems

Over the past decade, the number of ongoing bike-sharing programs has remarkably risen. In this framework, operators need appropriate methodologies to support them in optimizing the allocation of their resources to globally enhance the bike-sharing program, even without massive and costly interventions on the existing configuration of the system. In this paper, we propose an optimization model able to determine how to employ a given budget to enhancing a bike-sharing system, maximizing the global user satisfaction. During the day, each bicycle station has a certain number of bikes that fluctuates according to the travel demand; it happens, however, that for certain time slots, the station is full or empty. Then, we propose to consider as key performance indicators the zero-vehicle time and the full-port time, that reflected respectively the duration of vehicle shortage and parking stall unavailability in the stations. Both these indicators, together with the lost users of the system, need to be kept to a minimum if the final aim is maximizing the customer satisfaction, i.e. not forcing the user to use other stations or turn/shift to other travel modes. We have analyzed the historical usage patterns of the bike-sharing stations, smoothing their trends (by wavelets), and operated a preliminary spatio-temporal clustering. Our model verifies the necessity of adding or removing racks to each station, setting at the same time the optimal number of bikes to allocate in them, and decide the eventual realization of further stations. Then, an application, both on a small test and a real-size network, is presented, together with a sensitivity analysis.