Model of a multiple-deep automated vehicles storage and retrieval system following the combination of Depth-First storage and Depth-First relocation strategies

This paper studies a multiple-deep automated vehicles storage and retrieval system (AVS/RS) rack following a Depth-First storage and a Depth-First relocation strategy. We propose an analytical model based on a novel approach that utilises the Markov chain stochastic steady-state model. To verify the analytical model, a numerical simulation is developed. We also derive an empirical model using first- and second-order polynomial functions that are accurately fitted with regression equations and examined with MAPE and RMSE prediction accuracy measurements from a large-scale simulation study. The empirical model enables a straightforward calculation of the expected number of location movements of shuttle carriers and the attached satellite vehicles from which the AVS/RS throughput performance can be calculated. We present threefold and sixfold deep AVS/RS case study scenarios with an equal number of storage locations and estimate the cycle times. The evaluation of the case study results reveals that the analytical and empirical models achieve less than 2% error in the case of a dual command cycle time prediction compared to the simulation results. This proves that our approach allows an accurate estimation of multiple-depth AVS/RS throughput performance.