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 the pallets' movements in the horizontal and vertical direction. A gravity or powered conveying mechanism takes care of the pallets' depth movement in the rack. Our research objective is to analyze the system performance and optimally dimension the system. For single-command cycles, the crane's expected retrieval travel time is the same for gravity and powered conveyors; we give a closed-form expression. 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 travel time expression for dual command cycles for the system with powered and gravity conveyors, respectively, and use it to optimize the system dimensions. Finally, we illustrate the findings of the study by a practical example.