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 that operate 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 a during the periods of high demand, and at rate b < a at periods 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 the steady-state distribution of the inventory level, as well as other quantities of interest like the distribution of the time between successive refills. 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. ∗EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, HG 9.14, P.O. Box 513, 5600 MB Eindhoven, The Netherlands ([email protected]) †Department of Statistics, University of Haifa, Haifa 31905 Israel ([email protected]) ‡Binghamton University, Department of Mathematical Sciences, Binghamton, NY 13902-6000, USA ([email protected])