Multi-story mechanical parking facilities are becoming popular in crowded cities, as they are spatially efficient. When many cars are waiting to enter or to leave, it is important to schedule the movement of two rail-mounted automated carriers on each floor so that the makespan is minimized. We consider the problem of finding an optimal schedule when an ordered set of car placing and car removing is given. We propose an exact algorithm based on dynamic programming, and approximate algorithms using metaheuristics.