Mathematical modeling of the average retrieval time for flow-rack automated storage and retrieval systems

In the present paper, a particular type of Automated Storage and Retrieval Systems (AS/RS), known as flow-rack AS/RS, is studied. The flow-rack AS/RS consists of a multi-deep rack, and two machines; the first one is used for storage operations and the second one for retrieval operations. This paper aims to develop an analytical model for the average retrieval time of a machine operating under random storage conditions. This analytical model, which depends on the variety of items stored in the system and on their proportions, certainly represents a functional relation between the physical parameters (length, width and depth) of the flow-rack AS/RS. This model is useful for the performance evaluation and design of the flow-rack AS/RS. This analytic model was validated by simulation and was found to be highly accurate.