On Ordering Perishable Inventory when Both Demand and Lifetime are Random

We consider the problem of ordering perishable inventory when there is uncertainty in both the demand and the lifetime of the product. Under the assumption that units outdate in the same order in which they enter inventory, it is shown that the structure of the optimal policy is essentially the same as in the case where the lifetime is deterministic. An explicit expression for the expected outdating of any order is derived. Two different bounds on the expected outdating are then used to construct two critical number approximations. Computations for a discrete version of the problem are performed to compare the expected costs of both approximations with the optimal. One approximation appeared to give slightly better results and produced an expected cost generally within a fraction of a percent of the optimal for the cases tested.