Multi-Robot Scheduling of Storage Systems

Compact storage systems are essential in modern warehouses, particularly for handling large volumes or products requiring refrigeration. A key example is deep-lane storage, which includes automated shuttle-based systems and rail-mounted cranes in automated deep-lane systems. These are widely applied in bulk storage and finished goods warehouses, where high-density storage and operational efficiency are vital. In shuttle-based deep-lane storage systems, tasks are distributed between automated shuttles and forklifts. The shuttles manage the movement of loads within storage lanes, while forklifts handle both the horizontal and vertical movement of goods. Due to the high cost of shuttles, their number is often smaller than the number of storage lanes, meaning forklifts are required to transfer shuttles between lanes. This research addresses the problem of sequencing shuttle transfers and retrieval requests to minimize the total makespan, given a set of retrieval requests and a limited number of shuttles. A mathematical model is developed for this NP-hard problem. A two-stage heuristic is proposed to compute near-optimal solutions. Numerical results show that this approach significantly reduces the makespan compared to more straightforward heuristics commonly used in practice and the literature. Additionally, the proposed method can be employed to determine the optimal size of the shuttle fleet.