Group elevator scheduling is important for transportation efficiency in mid-rise and high-rise buildings, and incessant efforts have been made to improve the service efficiency of elevators. Although these efforts have achieved performance improvements, the performance limit remains an open issue. This paper tries to address that goal by estimating the optimal performance of group elevator scheduling with complete knowledge of future traffic information. A two-level minimization formulation is presented, with passenger-to-car at the high level, and single car dispatching at the low level. The low level is formulated as a passenger-to-trip assignment problem by using a concept trip to facilitate the description of single car dispatching strategies. In view of the difficulty to obtain the absolute optimal performance, our goal turns into its upper and lower bounds. The upper bound is obtained by finding a good feasible solution to this problem. The lower bound is obtained by finding the lower bound for a newly constructed problem whose optimal performance is less than or equal to that of the original problem. Numerical results demonstrate the effectiveness and the scalability of our method