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

Abstract

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 probabilitybased 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. Keywords Automated warehouse • Shuttle-based storage and retrieval system • Multiple-deep storage • Analytical and numerical modeling • Performance analysis (2020) 107:859-873

An approach for performance evaluation of SBS/RS with shuttle vehicles serving multiple tiers of multiple-deep storage rack

“…The shortcoming of these approaches is that they evaluate waiting times between lifts and shuttles. On the basis of that approach, the time to retrieve one tote from the system can be calculated, but it is not possible to evaluate the throughput of the whole system [4].…”

“…In Eder [3], the transition to a time-continuous and spatially discrete approach is effectuated. The latest publication of Eder [4] uses also this open-queueing model with limited capacity and extends the model to multiple-deep storage systems.…”

“…With the exceptions of Lerher [20], Eder et al [5], Manzini et al [30], Tappia et al [35], and Eder [4], all publications mentioned in this paper only discuss singledeep racks. These papers use a probability-based approach to take storage depth into account.…”

“…This literature overview shows that there are a number of publications with different queueing approaches discussing single-and multiple-deep SBS/RS. Eder [3,4] approaches the system closest to its real behavior. The queueing system presented in that investigation is time-continuous, with a spatially discrete evaluation of lift interarrival times and shuttle service times, corresponding well to reality.…”

“…What also can be seen is that there is no literature addressing the field of a sorting factor to optimize the cycles within the system. In the present paper, the main idea of Eder et al's [4] approach is used and advanced. The main changes are (1) an extension of the single-tier serving shuttle to a shuttle that serves multiple tiers and (2) the inclusion of a sorting factor to account for the fact that the pallets can be sorted into retrieval batches to avoid re-storage processes.…”