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

Abstract

Automated storage/retrieval systems (AS/RS) are computer-controlled automated material handling systems, widely used in industry and warehousing systems. They have interesting advantages, the majors of which are a high throughput, efficient use of space and improvement of safety. All the disadvantages of AS/RS are related to economic factors such as high initial investments and difficulty to change layout. This implies the importance of careful design of the AS/RS by taking into account all constraints. The latter may be linked either to the AS/RS dimensions or to products. The evaluation of average travel time that the S/R machine takes to store and retrieve a product is necessary for an optimal design. The present paper is devoted to a particular configuration of AS/RS said flow-rack AS/RS. The flow-rack AS/RS consists of only one deep rack and two machines; the first is used for storing operations and the second for retrieval operations. Our aim is to model mathematically the average travel time of the retrieval machine under random storage. The mathematical model proposed hereunder is certainly function of the physical parameters of the flow-rack AS/RS such as length, width, depth, etc.; but it is also function of the variety of products stored in the system and of their proportions. The mathematical model could be useful for performance evaluation and for design considerations of the flow-rack AS/RS in real world applications. The validation of the model is done by simulation.