Storage Assignment Optimization in a Multi-tier Shuttle Warehousing System

The current mathematical models for the storage assignment problem are generally established based on the traveling salesman problem(TSP), which has been widely applied in the conventional automated storage and retrieval system(AS/RS). However, the previous mathematical models in conventional AS/RS do not match multi-tier shuttle warehousing systems(MSWS) because the characteristics of parallel retrieval in multiple tiers and progressive vertical movement destroy the foundation of TSP. In this study, a two-stage open queuing network model in which shuttles and a lift are regarded as servers at different stages is proposed to analyze system performance in the terms of shuttle waiting period (SWP) and lift idle period (LIP) during transaction cycle time. A mean arrival time difference matrix for pairwise stock keeping units(SKUs) is presented to determine the mean waiting time and queue length to optimize the storage assignment problem on the basis of SKU correlation. The decomposition method is applied to analyze the interactions among outbound task time, SWP, and LIP. The ant colony clustering algorithm is designed to determine storage partitions using clustering items. In addition, goods are assigned for storage according to the rearranging permutation and the combination of storage partitions in a 2D plane. This combination is derived based on the analysis results of the queuing network model and on three basic principles. The storage assignment method and its entire optimization algorithm method as applied in a MSWS are verified through a practical engineering project conducted in the tobacco industry. The applying results show that the total SWP and LIP can be reduced effectively to improve the utilization rates of all devices and to increase the throughput of the distribution center.