The four-way-shuttle-based storage and retrieval system is a recent innovative intelligent vertical warehousing system that has been widely applied in manufacturing and e-commerce environments due to its high flexibility and density. As a complex multi-device cooperative operational system, this system features the parallel operation of multiple elevators and four-way shuttles. During large-scale-batch inbound operations, the quality of scheduling solutions for inbound-operation equipment significantly impacts the system’s efficiency and performance. In this paper, a detailed analysis of the inbound-operation process in the system is conducted, taking into consideration the motion characteristics of both the elevators and four-way shuttles. Furthermore, we establish operational time constraints that account for equipment acceleration and deceleration characteristics and introduce a flexible flow-shop-scheduling model to address the scheduling problem in the system. Additionally, we propose an improved genetic algorithm based on double-layer encoding to solve this problem. Comparative experiments with a traditional genetic algorithm and ant-colony algorithm demonstrate the superior efficiency and accuracy of our approach. Finally, the effectiveness of the proposed algorithm is validated through comparisons with large-scale practical experiments.