This paper studies the problem of deploying electric bicycle (e-bike) sharing stations and determining their capacities, i.e. the number of shared e-bikes and charging piles, considering travelers’ responses to the charging demands and different deployment schemes. Given a one-way station-based setting, we propose an e-bike sharing network where the generalized trip cost is measured as the sum of the delay cost at stations and the travel time en-route. To estimate the trip costs, we modeled the pick-up and drop-off e-bikes at each sharing station as two different queues affected by e-bikes’ charging demands, and described the traffic flow of shared e-bike on each route based on Greenshield’s model. Further, the e-bike sharing station deployment problem was then formulated as a bi-level programming model, taking into account the government’s and individual travelers’ profits. The uniqueness of solution was proved. For the purpose of solution approach, this bi-level model was then reformulated into a single-level mixed-integer programming model, and a hybrid particle swarm optimization algorithm was proposed to solve the single-level model. Numerical experiments were presented to demonstrate the validity of the proposed model and solution technique. More importantly, through numerical experiments, further insights for designing an e-bike sharing system were examined and discussed: 1) sharing stations are bottlenecks in the e-bike sharing network, since the charging activities cause travelers large delay costs; 2) a well-designed quick-charging technology and reservation policy could be incorporated into e-bike sharing systems to reduce system costs; 3) the proposed hybrid particle swarm optimization algorithm shows good solution quality and convergence performance.

中文翻译：

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电动自行车共享站的最佳部署：模型制定和解决技术

本文研究了部署电动自行车（e-bike）共享站并确定其容量（即共享电动自行车和充电桩的数量）的问题，其中考虑了旅行者对充电需求的反应和不同的部署方案。给定基于单站的设置，我们提出了一种电动自行车共享网络，其中广义的出行成本是站点的延误成本与行进时间的总和。为了估算出行成本，我们将每个共享站点的上下车电动自行车建模为受电动自行车充电需求影响的两个不同的队列，并基于每个路线描述了共享电动自行车的交通流量在Greenshield的模型上。此外，然后将电动自行车共享站部署问题表述为双层编程模型，考虑到政府和个人旅行者的利润。证明了解决方案的唯一性。出于求解方法的目的，将该双层模型重新构造为单级混合整数规划模型，并提出了一种混合粒子群优化算法来求解该单级模型。通过数值实验证明了所提模型和求解技术的有效性。更重要的是，通过数值实验，对设计电动自行车共享系统的进一步见解进行了讨论和讨论：1）共享站点是电动自行车共享网络中的瓶颈，因为充电活动会导致旅行者产生大量的延误成本；2）可以将精心设计的快速充电技术和预订政策纳入电动自行车共享系统中，以降低系统成本；