Actuarial valuation of perishable inventory systems

Abstract

The aim of this article is to derive the income and cost functionals required to determine the actuarial value of certain types of perishable inventory system. In the basic model, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The price of an item depends on its shelf age. For an actuarial valuation, it is important to know the distribution of the total value of the items in the system and the expected (discounted) total income and cost generated by the system when in steady state. All of these functionals are determined explicitly. As extensions of the original model, we also deal with the case of batch arrivals and general renewal interdemand times; in both cases, closed-form solutions are obtained.