In a new system of container terminal, its yard is divided into buffer area and stack area in order to separate ship loading/unloading and yard operations. Such a system then necessitates the shift operations between buffer areas and stack areas; import containers are moved from buffer area to stack area and export containers are moved from stack area to buffer area by two RMGs which travel on the same rails. As a result of analyzing the movements of two RMGs, which may interfere each other, we have reduced the scheduling problem of shift operations into two graph theoretical problems, paring problem and sequencing problem, where the paring problem is the maximum weight matching problem with degree constraints and the sequencing problem is a problem of seeking a shortest path that visits a given number of nodes, both of which have been studied in operations research. Furthermore, to deal with multilayer stacks of containers, the scheduling period is decomposed into overlapping subperiods, to which the above scheduling algorithm is applied. The resulting algorithm shows good performance in both quality of solutions and computational speed, and will be in operation in a real system of container terminal from April 1996.