In the past few years, station-free bike sharing systems (SFBSSs) have been adopted in many cities worldwide. Different from conventional station-based bike sharing systems (SBBSSs) that rely upon fixed bike stations, SFBSSs allow users the flexibility to locate a bike nearby and park it at any appropriate site after use. With no fixed bike stations, the spatial extent/scale used to evaluate bike shortage/surplus in an SFBSS has been rather arbitrary in existing studies. On the one hand, a balanced status using large areas may contain multiple local bike shortage/surplus sites, leading to a less effective rebalancing design. On the other hand, an imbalance evaluation conducted in small areas may not be meaningful or necessary, while significantly increasing the computational complexity. In this study, we examine the impacts of analysis scale on the SFBSS imbalance evaluation and the associated rebalancing design. In particular, we develop a spatial optimization model to strategically optimize bike rebalancing in an SFBSS. We also propose a region decomposition method to solve large-sized bike rebalancing problems that are constructed based on fine analysis scales. We apply the approach to study the SFBSS in downtown Beijing. The empirical study shows that imbalance evaluation results and optimal rebalancing design can vary substantially with analysis scale. According to the optimal rebalancing results, bike repositioning tends to take place among neighboring areas. Based on the empirical study, we would recommend 800 m and 100/200 m as the suitable scale for designing operator-based and user-based rebalancing plans, respectively. Computational results show that the region decomposition method can be used to solve problems that cannot be handled by existing commercial optimization software. This study provides important insights into effective bike-share rebalancing strategies and urban bike transportation planning.
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