Note. Optimal storage assignment policies for automated storage and retrieval systems with stochastic demands

In existing AS/RS research, storage assignment policies are evaluated based on the probability that item type j will be stored (and subsequently retrieved). This note applies the turnover-based and class-based assignment policies of Hausman et al. (1976) to a stochastic environment by identifying the kth pallet of item type j: Frequently demanded pallets are stored close to the input/output point and rarely demanded pallets are stored at the end of the storage rack. We consider a discrete storage rack and a continuous storage rack. For the continuous rack case, we develop an expression for expected one-way travel time given uniform and exponentially distributed demand. We show that the turnover-based policy applied to the stochastic environment is optimal(it minimizes one-way travel time) and that both the turnover-based and class-based assignment policies applied in the stochastic environment reduce expected storage/retrieval time compared with random assignment. These savings can be directly translated into increased throughput capacity for existing systems and can be used to improve the design of proposed systems.