Bicycles become popular again in the transportation system because they could serve as useful tools for convenient, economical, and environmentally friendly short-trips. In the traditional public bicycle system, customers need to reach a fixed public bicycle station before they can rent a public bicycle. However, the current station-free bicycle-sharing systems can allow customers to borrow or return shared bicycles, which would be distributed almost anywhere. Such new systems bring new optimisation problems for bicycle management. The authors study a placement optimisation problem that highlights the distribution characteristics of shared bicycles, aiming to minimise the total walking distance of customers. The proposed model is a 0–1 mix-integer non-linear programme. To solve the model, they propose a bi-level solving framework. The upper-level model optimises the locations of supply stations. The lower-level model optimises the number of bikes assigned to each demand site. A test based on the campus of Tsinghua University is employed to validate the proposed model. The optimal location suggested by their model is significantly different from the location suggested by models that ignore the distributed feature. Their model performs better in terms of reducing the total walking distance.

中文翻译：

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一维分布假设下无站台自行车共享的布局优化

自行车在交通运输系统中再次变得流行，因为它们可以作为方便，经济和环保的短途旅行的有用工具。在传统的公共自行车系统中，客户需要先到达固定的公共自行车站，然后才能租用公共自行车。但是，当前的无站共享自行车系统可以使客户借用或归还共享自行车，这些自行车几乎可以分配到任何地方。这样的新系统给自行车管理带来了新的优化问题。作者研究了一个布局优化问题，该问题突出了共享自行车的分布特征，旨在最大程度地减少客户的总步行距离。提出的模型是一个0–1混合整数非线性程序。为了解决该模型，他们提出了一个双层解决框架。上层模型优化了补给站的位置。下层模型优化了分配给每个需求点的自行车数量。该模型以清华大学校园为基础进行了测试。他们的模型建议的最佳位置与忽略分布式特征的模型建议的位置明显不同。他们的模型在减少总步行距离方面表现更好。