Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

We consider a classic periodic-review perishable inventory system with a fixed product lifetime and zero replenishment lead time under a first-in-first-out issuance policy. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty and outdating cost. The optimal policy for this system is notoriously complex and intractable due to the curse of dimensionality. Hence, various heuristic replenishment policies have been proposed in the literature, including the base-stock policy which raises the total on-hand inventory level to a constant at each review epoch. While extensive numerical studies have shown near-optimal performances of such base-stock policies, the results on their theoretical performances are very limited. In this paper, we construct a simple heuristic base-stock policy, and show that the optimality gap between its long-run average cost and that of the optimal replenishment policy converges to zero when any one of lifetime, demand population size, unit penalty cost, or unit outdating cost goes to infinity. Moreover, the convergence rate is exponentially fast in the lifetime and demand population size. We also characterize the convergence rate and the asymptotic long-run average cost in the unit penalty cost for several classes of demand distributions. Further, we extend some of our results to a class of base-stock policies, the system under a last-in-first-out issuance policy, and a backlogging system with positive lead time. Finally, we provide an extensive numerical study to demonstrate the performances of different base-stock policies in three different systems