Managing Perishable Inventories in Retailing: Replenishment, Clearance Sales, and Segregation

We study joint replenishment and clearance sales of perishable goods under a general finite lifetime and a last-in-first-out (LIFO) issuing rule, a problem common in retailing. We show that the optimal policies can be characterized by two thresholds for each age group of inventory: a lower one and a higher one. For an age group of inventory with a remaining lifetime of two periods or longer, clearance sales may take place when its inventory level is above its higher threshold. There is no clearance sale if its inventory level is below its lower threshold and the inventory levels in all the fresher age groups are also below their corresponding lower thresholds. The optimal policy for the age group of inventory with a one-period remaining lifetime is different. Clearance sales may occur if its inventory level is above its higher threshold or below its lower threshold. The phenomenon that a clearance sale happens when the inventory is low is driven by the need to segregate the newest inventory from the oldest inventory and is unique to the LIFO issuing rule. The optimal policy requires a full inventory record of every age group and its computation is challenging. We consider two myopic heuristics that require only partial information. The first requires only the information about the total inventory and the second requires the information about the total inventory as well as the information about the inventory with a one-period remaining lifetime. Our numerical studies show that the second outperforms the first significantly and its performance is consistently very close to that of the optimal policy.