Given a set of transport requests to a transit station and a set of homogeneous vehicle, both geographically dispersed in a business area, the First-Mile Ride-Sharing Problem (FMRSP) consists of finding least cost vehicle routes to transport passengers to the station by shared rides. In this paper we formulate the problem as a mathematical optimization problem and study the effectiveness of preventive movements of idle vehicles (i.e., rebalancing) in order to anticipate future demand. That is, we identify promising rebalancing locations based on historical data and give the model incentives to assign vehicles to such location. We then assess the effectiveness of such movements by simulating online usage of the mathematical model in a rolling-horizon framework. The results show that rebalancing is consistently preferable both in terms of profits and service rate. Particularly, in operating contexts where the station is not centrally located, rebalancing movements increase both profits and service rates by around 30% on average.