Optimal Storage Rack Design for a 3-Dimensional Compact As/Rs

In this paper, we consider a newly-designed compact three-dimensional automated storage and retrieval system (AS/RS). The system consists of an automated crane taking care of movements in the horizontal and vertical direction. A gravity conveying mechanism takes care of the depth movement. Our research objective is to analyze the system performance and optimally dimension of the system. We estimate the crane's expected travel time for single-command cycles. From the expected travel time, we calculate the optimal ratio between three dimensions that minimizes the travel time for a random storage strategy. In addition, we derive an approximate closed-form travel time expression for dual command cycles. Finally, we illustrate the findings of the study by a practical example