Managing Replenishment and Clearance of Perishables: Last-In,First-Out (LIFO) Issuing Policy and Age-Sensitive Demand

Abstract

In supermarkets, customers choose the unit(s) they purchase, which leads to inventory being sold in a last-in, first-out (LIFO) order for perishable products. Furthermore, for such products, the demand for inventory may depend on its age since customers may choose to walk away if the freshest available inventory is too old for them. Despite the widespread occurrence of LIFO-based inventory systems, few studies have analyzed them. In this study, we contribute by developing insights on joint replenishment and clearance policy for a perishable product with a general, finite lifetime using a periodic review model such that the inventory is sold in a LIFO order and demand is age-dependent. The model seeks to optimize two decisions every period: how much of fresh inventory to order and how much of existing inventory to clear. A key objective of the model is to understand the effect of age-dependence of demand on the optimal replenishment and clearance policy. We find that the optimal clearance policy for all but the oldest inventory is a multiindex policy such that between any pair of adjacent indexes, either no inventory is cleared or all the inventory is cleared till the lower index. For the oldest inventory, we show that the optimal policy may have multiple forms depending on how sensitive demand is to inventory’s age. This is a notable result in inventory theory since parameters usually affect only the policy value(s) and not the policy structure. Since the optimal policy has a complex structure in general, which makes it difficult to compute, we develop an efficient heuristic to compute the replenishment and clearance quantities. The heuristic underperforms the optimal policy by $\sim$ 0.92% on average.