Considering that ride-sourcing platforms pay taxi drivers the same rate as private car drivers or charge a commission on taxi orders to open the platform, this study examines the opening strategy selection of ride-sourcing platforms. By analyzing the four cases of non-opening, opening ride-sourcing order, opening taxi order, and mixed opening, the profit models for ride-sourcing platforms are constructed by using operational optimization methods, respectively. The optimal decisions for all scenarios are obtained by maximizing platform profits. The results show that all four strategies may be optimal, and the total number of potential private ride-sourcing drivers in the market and the coverage of taxi market play a key role in the selection of platform opening strategies. Platform opening does not always increase the overall profits of taxis and social welfare. Under the strategy of opening taxi order, there is a specific value of the number of taxis that maximizes the total profits of taxis and social welfare.