A Markovian Model for a Perishable Product Inventory

The rate of outdating of a perishable product (such as blood) and the age distribution of the inventory are analyzed. It is assumed that after each period's demand, the inventory is replenished with fresh product, up to a constant level. The age distribution is treated as a finite Markov chain. Expected outdating is shown to be convex in the inventory level. Upper and lower bounds for the expected outdating are obtained for the case of general demand distribution. Better and easily computable bounds and approximate distribution are found for the Poisson demand case.