To improve the ship operation in automated container terminals, it is important to schedule different types of handling equipment to operate synchronously. For example, a vehicle with container receiving and lifting capabilities is used to transport containers from a storage yard to a vessel and vice versa, while a triple quay crane (QC) can handle up to three 40-ft containers simultaneously. This paper discusses the manner in which vehicles should be assigned to containers to support such multi-lifts of QCs by using information about the locations and times of deliveries. A mixed-integer programming model is introduced to optimally assign delivery tasks to vehicles. This model considers the constraint imposed by the limited buffer space under each QC. A procedure for converting buffer-space constraints into time window constraints and a heuristic algorithmfor overcoming the excessive computational time required for solving the mathematical model are suggested. A numerical experiment is conducted to compare the objective values and computational times of the heuristic algorithm with those of the optimizing method to evaluate the performance of the heuristic algorithm.