Modeling the effect of imperfect staggering in product inflow using queuing theory: revisiting block stacking layout

Conventional approaches to layout design of block stacked warehouses assume perfect staggering of product inflow leading to perfect sharing of space among products. Since such an assumption is seldom true, we argue that warehouses designed using the conventional approach may result in choking situations with large quantities of inventory waiting outside the storage areas. On the other hand, liberal space allocation such as in dedicated policy might lead to under-utilization of space. In this paper, we take a fresh look at the block stacked layout problem, modeling the effect of imperfectly staggered product arrivals using queuing theory. Analytical expressions are derived for arrival time and processing time coefficients of variation using warehouse parameters and design variables. Further, we develop a bi-objective optimization model to minimize both the space cost and waiting time. Our approach provides design options over a total space cost-waiting time trade-off frontier as opposed to singular design points given by conventional approaches. Computational experiments are conducted to derive further insights into the design of block stacked warehouses.