Travel time model for multi-deep automated storage and retrieval system with a homogeneous allocation structure

This paper presents a travel time model for multi-deep AS/RS, which determines the average travel times during a single command storage or retrieval and a dual command cycle. The model can determine the relocation probability, the number of expected relocations and the travel times in storage channels itself exactly dependingon the stock filling level. The travel time model assumes random storage policies. Travel time determination is trivial for single-deep AS/RS, because no relocation necessity applies and it gets more complicated with an increasing depth of the storage racks. The deeper goods can be stored, the more goods can potentially be stored in front of each other in one storage channel. This leads to relocation operations of blocking goods and causes higher total travel times. The higher the stock filling level, the higher is the relocation probability and the number of necessary relocations. The calculation of relocation probabilities in this work is based on a homogeneous storage good allocation structure which leads to a symmetrical location of storage goods and enables an easy modelling of travel times. This paper presents a travel time model with a continuous storage rack approximation of a multi-deep AS/RS in closed- form expression. Furthermore, the storage channel allocation probabilities are mathematically proven. The relocation probability for storage operations and retrieval operations are the same. Finally, the derived travel time models and relocation probabilities are verified by simulation.