Scheduling shuttles in deep-lane shuttle-based storage systems

Deep-lane shuttle-based storage systems with forklifts are widely used in bulk storage and finished-goods warehouses that require dense storage paired with high operational efficiency. In such a system, automated shuttles take care of the movements of loads within the storage lanes, and forklifts take care of the horizontal and vertical movements of loads. Since shuttles are expensive, the number of shuttles in the system is typically smaller than the number of storage lanes, so shuttle transfers are required with the help of the forklift. This paper focuses on optimizing the schedule: Given a set of retrieval requests and shuttles, how can the shuttle transfer sequence and the retrieval request sequence be arranged to minimize the makespan? A mathematical model is formulated. Since the problem is NP-hard, an efficient two-stage heuristic is proposed to compute near-optimal solutions. This study’s numerical results show that the two-stage heuristic can provide high-quality solutions in reasonable time. Compared to straightforward heuristics used in practice and in the literature, the makespan can be reduced considerably. The proposed two-stage heuristic can also be used to decide the optimal shuttle fleet size.