We concentrate on the construction of a logistics system applied for the allocation and scheduling of the berths and quay cranes in container terminals in this paper, especially the automated container terminals. The above optimization problems can be integrated as the berth allocation, quay crane assignment and scheduling problem (BACASP). The berth allocation problem called BAP, the quay crane assignment problem called QCAP, and the quay crane scheduling problem called QCSP, constitute the integrated problem. Therefore, a mathematical model is designed with two stages. The berth allocation problem is combined with the quay crane assignment problem called BACAP is defined as the first-step subproblem, while the quay crane scheduling problem is set as the second-stage subproblem. After that, a quantum-behavior heuristic algorithm named quantum-behavior ant colony optimization algorithm (QACA) is designed to compute, which combines the concept of quantum computing and the ant colony optimization algorithm (ACA). Finally, a series of experimental studies is executed to demonstrate the performance of the proposed model and the algorithm.