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

Abstract

We consider 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 these systems is notoriously complex and intractable due to the curse of dimensionality. We  propose a  class of projected inventory level (PIL) policies that maintain a constant expected on-hand inventory level at the time of each order arrival. For both backlogging and lost-sales systems, we prove that the best PIL policy is asymptotically optimal with large unit penalty cost under a broad class of unbounded demand distributions. When demand is bounded,  it can underperform the best base-stock policy (which maintains a constant inventory position) under FIFO (i.e., first-in-first-out) issuance policy while arbitrarily outperforming the latter under LIFO (i.e., last-in-first-out) issuance policy. We further prove that it is asymptotically optimal with large demand population sizes and its optimality gap decays exponentially fast in the backlogging system under a large class of issuance policies. To facilitate computation, we  also propose a class of approximate PIL  (APIL) policies and extend most of our results for the PIL policy to the APIL policy. Our numerical results show that both policies perform close to optimal and significantly better than the base-stock policy.

Keywords: perishable inventory, lead times, inventory issuance, inventory position, projected inventory level, asymptotic analysis