A two-stage stochastic programming model for bike-sharing systems with rebalancing

We study the problem of determining the target inventory level of stations in a bike-sharing system, when bikes can be rebalanced later during the day. We propose a two-stage stochastic programming formulation, where the target inventory decisions are made at the first stage, while the recourse decisions, related to rebalancing, are made at the second stage. In the literature, the problem of determining the target inventory levels is solved without taking into account the rebalancing problem, or these two problems are solved sequentially. We prove that more efficient bike-sharing systems can be obtained by integrating these two problems. Moreover, we show that our methodology provides better results than the deterministic formulation, and consider an effective matheuristic, based on the solution of the deterministic problem, to solve the stochastic program. Finally, we compare the solutions obtained by our approach with the actual allocation of bikes in the real bike-sharing system of the city of San Francisco. The results show the effectiveness of our approach also in a realistic setting.