Optimal Replenishment and Clearance Policy for a Perishable Product with LIFO Issuing Policy and Age-Dependent Demand

We study joint replenishment and clearance policy for a perishable product with a general, finite lifetime using a periodic review model over a finite horizon such that the inventory is sold in a last-in, first-out (LIFO) manner. Further, 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. The model seeks to optimize two decisions every period: how much of fresh inventory to order and how much of existing inventory to clear. The 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 policy when demand depends on age may diverge substantially from the optimal policy when demand is independent of age, though there exists a sufficient condition under which the structure of the optimal policy becomes identical in both scenarios for all units newer than a threshold age. Further, we show that the structure of the optimal policy for the inventory with one-period remaining lifetime may both simplify and complicate in terms of the number of indexes compared to when demand is independent of age. For the same set of results, we streamline a few arguments for the existing results that are derived assuming demand is independent of age. Finally, we briefly discuss an extension in which clearance is not possible