In the bike-sharing system, inspired by the problem proposed by O’Mahony and Shmoys (AAAI 2015), we present a new model called the balanced center problem with matching constraints. Given a network containing the same number of two types of points, supply points and demand points, we aim to allocate (supply) centers for supply points, and (demand) centers for demand points. The supply centers should be perfectly matched with the demand centers, within an allowed distance. The goal is to minimize the maximum distance from each supply (or demand) point to its closest supply (or demand) centers.

中文翻译：

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自行车再平衡：如何在k中心问题中找到平衡匹配？

在自行车共享系统中，受到 O'Mahony 和 Shmoys 提出的问题（AAAI 2015）的启发，我们提出了一种新模型，称为带有匹配约束的平衡中心问题。给定一个包含相同数量的两种类型点（供应点和需求点）的网络，我们的目标是为供应点分配（供应）中心，为需求点分配（需求）中心。供应中心与需求中心应在允许的距离内完美匹配。目标是最小化每个供应（或需求）点与其最近的供应（或需求）中心的最大距离。