Bike-sharing systems: User dissatisfaction in the presence of unusable bicycles

In bike-sharing systems, at any given moment, a certain share of the bicycle fleet is unusable. This phenomenon may significantly affect the quality of service provided to the users. However, to date this matter has not received any attention in the literature. In this article, the users' quality of service is modeled in terms of their satisfaction from the system. We measure user dissatisfaction using a weighted sum of the expected shortages of bicycles and lockers at a single station. The shortages are evaluated as a function of the initial inventory of usable and unusable bicycles at the station. We analyze the convexity of the resulting bivariate function and propose an accurate method for fitting a convex polyhedral function to it. The fitted polyhedral function can later be used in linear optimization models for operational and strategic decision making in bike-sharing systems. Our numerical results demonstrate the significant effect of the presence of unusable bicycles on the level of user dissatisfaction. This emphasizes the need to have accurate real-time information regarding bicycle usability.