Perishable inventories with random input: a unifying survey with extensions

Abstract

This paper is devoted to the theory of perishable inventory systems. In such systems items arrive and stay ‘on the shelf’ until they are either taken by a demand or become outdated. Our aim is to survey, extend and enrich the probabilistic analysis of a large class of such systems. A unifying principle is to consider the so-called virtual outdating process $$\textbf{V}$$ V , where V(t) is the time that would pass from t until the next outdating if no new demands arrived after t. The steady-state density of $$\textbf{V}$$ V is determined for a wide range of perishable inventory systems. Key performance measures like the rate of outdatings, the rate of unsatisfied demands and the distribution of the number of items on the shelf are subsequently expressed in that density. Some of the main ingredients of our analysis are level crossing theory and the observation that the $$\textbf{V}$$ V process can be interpreted as the workload process of a specific single server queueing system.