Inventory Depletion Management with Stochastic Field Life Functions

Most inventory depletion analysis has been concerned with the case of a deterministic field life function. Since it is rarely the case that the exact field life function of a stock of items would be known, it is more reasonable to treat the case where the field life of an item is a random variable, X(S), which depends only on the age, S, of the item upon issuance. In this stochastic case, it is shown that the policy of issuing the oldest item first (FIFO) is optimal provided E[X(S)] - aS + b where 0 \geqq a > - 1, b > 0, i.e., where the items have a linearly decreasing mean value function, and where some additional, but behaviorally not restrictive, assumptions are made.