We consider an online car-sharing problem between two locations with advance bookings. Each customer submits a pair of requests, where each request specifies the pick-up time and the pick-up location: one request from A to B, and the other request from B to A, not necessary in this order. The scheduler aims to maximize the number of satisfied customers, where the schedule has to decide whether or not to accept a request pair immediately at the time when the request pair is submitted. This problem is called OnlineTransfersForCommuting. We present lower bounds on the competitive ratio for this problem with both fixed booking times and variable booking times, and propose two algorithms, greedy algorithm and balanced greedy algorithm, that achieve the best possible competitive ratios.

我们考虑了两个地点之间的在线汽车共享问题，需要提前预订。每个客户提交一对请求，其中每个请求都指定了接送时间和接送位置：一个请求从A到B，另一个请求从B到A，此顺序不是必需的。调度程序旨在最大化满足客户的数量，其中调度程序必须在提交请求对时决定是否立即接受请求对。此问题称为OnlineTransfersForCommuting。对于固定预订时间和可变预订时间这两个问题，我们都给出了竞争比率的下限，并提出了两种算法，即贪心算法和平衡贪婪算法，它们可以实现最佳的竞争比率。