The multi-vehicle stochastic-dynamic inventory routing problem for bike sharing systems

We address the operational management of station-based bike sharing systems (BSSs). In BSSs, users can spontaneously rent and return bikes at any stations in the system. Demand is driven by commuter, shopping, and leisure activities. This demand constitutes a regular pattern of bike usage over the course of the day but also shows a significant short-term uncertainty. Due to the heterogeneity and the uncertainty in demand, stations may run out of bikes or congest during the day. At empty stations, no rental demand can be served. At full stations, no return demand can be served. To avoid unsatisfied demand, providers dynamically relocate bikes between stations in reaction of current shortages or congestion, but also in anticipation of potential future demand. For this real-time decision problem, we present a method that anticipates potential future demands based on historical observations and that coordinates the fleet of vehicles accordingly. We apply our method for two case studies based on real-world data of the BSSs in Minneapolis and San Francisco. We show that our policy outperforms benchmark policies from the literature. Moreover, we analyze how the interplay between anticipation and coordination is essential for the successful operational management of BSSs. Finally, we reveal that the value of coordination and anticipation based on the demand-structure of the BSS under consideration.