Dual cycle time modelling and design optimisation for the bidirectional flow-rack AS/RS

This article discusses the problem of evaluating performance and optimising the design of Automated Storage/Retrieval Systems (AS/RS) in a steady state, with a focus on the dual cycle in the bidirectional flow-rack (BFR) AS/RS. To accomplish this, two well-known approaches (discrete and continuous) are utilised to model the dual cycle time. The developed models reveal that the system is near optimal when designed to be square in time. Furthermore, the continuous models are shown to be relatively accurate compared to the discrete counterparts, with discrepancies under 6%. Subsequently, the optimal dimensions of the system are identified through design optimisation aimed at minimising the cycle time. The findings indicate the optimal depth decreases as load rate increases, while optimal height and length follow a cubic root function of system volume. Approximate formulas are derived, allowing for direct calculation of optimal dimensions based on the system size and its load rate. Finally, the article evaluates the system's overall performance by calculating its throughput, providing a tool to estimate capacity. These findings provide an essential tool for optimising the system's performance in a steady state during the upstream design and installation phase, prior to making significant investments.