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 due to 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 (FIFO) issuance, whereas the best PIL policy is optimal under last-in-first-out (LIFO) 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.

The full paper is available at https://ssrn.com/abstract=4638265.