Managing Perishable Inventory Systems with Positive Lead Times: Inventory Position vs. Projected Inventory Level

We study periodic review perishable inventory systems with a fixed product lifetime, positive replenishment lead times, and a general issuance policy under the average cost criterion. The optimal replenishment policy for such systems is notoriously complex and computationally intractable because of the curse of dimensionality. To address this challenge, we propose a class of projected inventory level (PIL) policies, which maintain a constant expected on-hand inventory level, and compare them with conventional base-stock (BS) policies that maintain a constant inventory position. For both backlogging and lost-sales systems, we show that the best PIL policy is asymptotically optimal with large unit penalty costs for a broad class of unbounded demand distributions. When demand is bounded and the unit penalty cost is sufficiently large, we prove that the best BS policy is optimal under first-in-first-out issuance, whereas the best PIL policy is optimal under last-in-first-out issuance (under certain conditions). Furthermore, we show that both policies are asymptotically optimal as the demand population size grows large, and their optimality gaps diminish exponentially fast in backlogging systems under a broad range of issuance policies. To facilitate computation, we introduce a class of approximate PIL (APIL) policies and extend most theoretical results for PIL to the APIL policy. Numerical results show that both PIL and APIL policies perform very close to optimal and significantly outperform BS policies. This paper was accepted by Jeannette Song, operations management. Funding: X. Gong and H. Yin were partially supported by the National Natural Science Foundation of China [Grant 72425008] and the Hong Kong Research Grants Council General Research Fund [Grant CUHK14500120]. J. Bu was partially supported by the Hong Kong Research Grants Council General Research Fund [Grant PolyU15504525]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03801 .