Optimal dimensions for multi-deep storage systems under class-based storage policies

Multi-deep automated storage and retrieval systems (AS/RSs) have seen many implementations in warehouses due to their high floor space utilization. However, the rack size, which will fundamentally affect the operating efficiency of the storage and retrieval machine in the system, should be optimized analytically. While extensive studies have been made to analyze the system performance and optimize operating policies for single-deep and double-deep AS/RSs by travel-time models. No analytical models are available for multi-deep AS/RSs. To fill this gap, we develop travel-time models for this system, considering the random storage policy and two class-based storage policies in a multi-deep AS/RS: the one that zoning only on picking face and the one that zoning on both picking face and the depth direction. Based on the travel-time models, we derive the formulation of the optimal system size, to minimize the expected travel time of S/R machine. Simulation models are built to validate the analytical models and the results show that the maximum relative error between analytical result and simulation result is 4.3%. Numerical experiments are conducted to find the optimal size of a multi-deep AS/RS and compare the performance of these storage policies. The results show that class-based storage policy always outperform the random storage policy in terms of expected travel time, and the class-based storage policy that zoning on both picking face and the depth direction may not be better than that only zoning on the picking face, while it may be harder to handle in the system.