The ubiquity of information and communication technology (ICT) and application of global positioning system (GPS) enabled cell phones provide new opportunities to implement ride-sharing in many ride-hailing platforms, where matching proposals with multiple riders are established on very short notice. In this paper, the travelers joining in the ridesharing are assumed to be homogeneous in terms of having their own vehicles. When they have announced their travel requests, the ride-sharing platform will check whether they can be picked up by any other travelers. If failed, they will drive by themselves and become a driver who would like to pick up other passengers in the system. To solve this problem, the ride-matching problem is formulated as a set-partitioning problem and a so-called ordered greedy (OG) method is presented to get the approximately optimum under the large-scale circumstance. The results of simulation examples prove that the proposed method can achieve a reasonable matching result through Cplex within a few seconds but at most 3.8％ worse than the exact optimum. Furthermore, several interesting results are also found via simulating generated data and the real-world data of Chengdu in China. In simulation experiments, with a higher level of demand density, the easiest place to find a ride is not in the center but a ring close by it, which is determined by traffic flows, OD distance and vehicles' utilization. As a contrast, the optimal strategy for participants to be a rider is going to other specific regions rather than staying in the city center in real-world experiments.