The first-mile problem, which refers to the design of transport services that connect passengers to their nearby transit station, has attracted growing attention in recent years. In this paper we consider first-mile ride-sharing services and study the problem of optimally determining the fleet size and assigning vehicles to transport requests. We formulate the problem as a mixed-integer program and present a number of numerical experiments based on a small-scale system to analyse different configurations of the service, namely with and without fleet control (FC). Result shows that a configuration with FC is superior in terms of profits while service rates can be higher in a configuration without FC, depending on the revenue-sharing mechanism.