Relative pre-positioning of storage/retrieval machines in automated storage/retrieval system to minimize expected system response time

This paper is focused on the control problem of determining the dwell point of an idle storage/retrieval (S/R) machine in an automated S/R system to improve the overall system service level as measured by the turnaround time of requests to the system. The emphasis of the paper is on the minimization of the expected response time over all retrieval and storage requests executed by the system. The model presented is developed under the operating condition that each machine serves several dedicated aisles of the system. The aisles are assumed to exist in the same region of the automated storage/retrieval system (AS/RS) and thus form a valid order S/R zone. A solution algorithm for determining the optimal dwell point location is developed. The paper assumes a dynamic environment where orders arrive over time and are to be serviced by the S/R machine. A dwell point or strategic point to pre-position the machine is to be determined whenever the machine becomes idle in anticipation of an incoming service request. A numerical example is provided to demonstrate how the technique can be used in an actual production setting to improve the overall order turnaround time.