A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates

We consider a stochastic fluid EOQ-type model with demand rates 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 linearly at rate β_H during the periods of high demand, and at rate β_L < β_H at periods of low demand. Refilling of the inventory level to level q is required when the first of two events takes place: Either the buffer level reaches zero, or the buffer content becomes outdated. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period.

We determine the steady-state distribution of the inventory level, as well as other quantities of interest such as the distribution of the time until a refill is required. Finally, for a given cost/revenue structure, we determine the long-run average profit, and we consider the problem of choosing q such that the profit is optimized.