Inventory Depletion Management with Stochastic Field Life Functions

Abstract

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 ≧ 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.