A compound Poisson EOQ model for perishable items with intermittent high and low demand periods

We consider a stochastic EOQ-type model, with demand operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases according to different compound Poisson processes during the periods of high demand and of low demand. The inventory level is refilled to level q when level 0 is hit or when an expiration date is reached, whichever comes first. We determine various performance measures of interest, like the distribution of the time until refill, the expected amount of discarded material and of material held (inventory), and the expected values of various kinds of shortages. For a given cost/revenue structure, we can thus determine the long-run average profit.