In one-way station-based shared mobility systems, where system users share vehicles for making trips between vehicle stations, the accumulation of one-way trips inevitably causes vehicle imbalances between stations. To correct these imbalances, we focus on the effective use of linear control policies for calculating online vehicle relocations from a history of user trips. Our scenario-based optimization model for computing linear control policies is formulated as a linear optimization problem. Computational results using a real-world dataset demonstrate that our method provides high relocation performance with short online computation times.