Optimal inventory management of a bike-sharing station

Bike-sharing systems allow people to rent a bicycle at one of many automatic rental stations scattered around a city, use them for a short journey, and return them at any other station in that city. A crucial factor in the success of such a system is its ability to meet the fluctuating demand for both bicycles and vacant lockers at each station. In order to meet the demand, the inventory of each station must be reviewed regularly. This article introduces an inventory model suited for the management of bike rental stations and a numerical solution method used to solve it. Moreover, a structural result about the convexity of the model is proved. The method may be applicable for other closed-loop inventory systems. An extensive numerical study based on real-life data is presented to demonstrate its effectiveness and efficiency.