An approach for a performance calculation of shuttle-based storage and retrieval systems with multiple-deep storage

This paper presents a method to determine the performance of shuttle-based storage and retrieval systems (SBS/RS) with tier captive single-aisle shuttles and multiple-deep storage. The basis of this calculation method is a continuous-time open queueing system with limited capacity. The cycle times of lifts and shuttles, determined by a spatial value approach, can be directly used in the presented method with their time distributions. To take the multiple storage into account, a probability-based approach is applied. The invented approach is validated by a comparison with a discrete event simulation. A European material handling provider had given the data used in this comparison. Finally, an example is presented to outline how this calculation model can be used for designing SBS/RS which fulfil the predefined requirements. The result of this example is that with an increase of the storage depth to a certain value, the throughput increases and the cost decreases up to the same storage depth.