In this paper, we consider a newly-designed 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. The aim of the research was to facilitate the problem of optimal design and performance evaluation of the system. We estimate the craneâ€™s expected travel time for single command cycles. From the expected travel time, we calculate the optimal ratio between three dimensions that minimize the travel time for a random storage strategy. Finally, we illustrate the findings of the study by a practical example.