Optimizing the Location of Virtual Stations in Free-Floating Bike-Sharing Systems with the User Demand during Morning and Evening Rush Hours

In recent years, free-floating bike-sharing systems (FFBSSs) have been considerably developed in China. As there is no requirement to construct bike stations, this system can substantially reduce the cost when compared to the traditional bike-sharing systems. However, FFBSSs have also become a critical cause of parking disorder, especially during the morning and evening rush hours. To address this issue, the local governments stipulated that FFBSSs are required to deploy virtual stations near public transit stations and major establishments. Therefore, the location assignment of virtual stations is sufficiently considered in the FFBSSs, which is required to solve the parking disorder and satisfy the user demand, simultaneously. The purpose of this study is to optimize the location assignment of virtual stations that can meet the growing demand of users by analyzing the usage data of their shared bikes. This optimization problem is generally formulated as a mixed-integer linear programming (MILP) model to maximize the user demand. As an alternative solution, this article proposes a clustering algorithm, which can solve this problem in real time. The experimental results demonstrate that the MILP model and the proposed method are superior to the K-means method. Our method not only provides a solution for maximizing the user demand but also gives an optimized design scheme of the FFBSSs that represents the characteristics of virtual stations.