Online Scheduling of Car-Sharing Request Pairs between Two Locations with Advance Bookings

We consider an online car-sharing problem with advance bookings, in which users (customers) submit their ride requests, and the scheduler aims to maximize the number of satisfied users. For the setting with two locations A and B, every user has a pair of requests where each request specifies the pickup time, the drop-off time, the pick-up location, and the drop-off location: one request from A to B, and one request from B to A, not necessary in this order. The schedule has to decide whether or not to accept a pair of requests immediately at the time when the request pairs are submitted. We present lower bounds on the competitive ratio for this problem and propose a greedy algorithm that achieves the best possible competitive ratio.