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.

深巷穿梭叉车仓储系统广泛应用于需要密集存储和高运营效率的散装仓库和成品仓库。在这样的系统中，自动穿梭车负责货物在存储通道内的移动，叉车负责货物的水平和垂直移动。由于穿梭车价格昂贵，系统中穿梭车的数量通常少于存储通道的数量，因此需要借助叉车进行穿梭车转移。本文着重于优化调度：给定一组检索请求和班车，如何安排班车传输序列和检索请求序列以最小化完工时间？制定了一个数学模型。由于问题是 NP-hard，提出了一种有效的两阶段启发式来计算接近最优的解决方案。本研究的数值结果表明，两阶段启发式可以在合理的时间内提供高质量的解决方案。与实践和文献中使用的直截了当的启发式方法相比，完工时间可以大大缩短。所提出的两阶段启发式也可用于确定最佳穿梭机队规模。