Automated storage and retrieval systems (AS/RS) have become essential to modern warehousing and logistics, offering enhanced efficiency, accuracy, and flexibility. These systems depend on the smooth coordination of multiple components. In systems that require vertical coordination, the interaction between vertically moving elements—such as lifts—plays a critical role in overall performance. This section focuses on a shuttle-based AS/RS that features two independent lifts sharing a single vertical mast. These lifts operate simultaneously to fulfill retrieval tasks but are constrained by the fact that they cannot pass each other. This limitation adds complexity to the scheduling of retrieval requests, requiring careful coordination. Each request is completed through the combined efforts of a lift and a shuttle, making it essential to optimize both the sequence of retrievals and the assignment of each request to a specific lift in order to minimize total retrieval time (makespan).