Managing Perishable Inventory Systems with Age-differentiated Demand

We consider a periodic-review perishable inventory system with multiple demand classes, each characterized by a different lost-sales cost and a least freshness requirement. Demands of different classes in the same period can be correlated, while demands across periods are independent but not necessarily identical. In each period, the firm jointly makes the decisions regarding inventory issuing, rationing, production/ordering, and disposal. The objective is to minimize the total discounted expected cost over the entire planning horizon including linear ordering cost, inventory holding/lost-sales cost, expiration cost and disposal cost. By establishing new properties of multimodularity, we are able to explore some monotonicity and bounded sensitivity properties of the optimal policies and show that the optimal inventory issuing policy follows the first-in-first-out (FIFO) rule. The optimality analysis enables us to propose a novel heuristic, called adaptive approximation approach, which can be recursively calculated through a single-dimension dynamic program. Numerical studies demonstrate that our proposed approximation approach is nearly optimal with the average optimality gap 0.30% and significantly outperforms existing heuristics studied in the literature. Another important observation from numerical studies is that ignoring customers' freshness requirements can lead to a significant increase in total costs. Our heuristic idea can also be applied to the setting with the last-in-first-out (LIFO) issuing rule and still performs rather well.