A fluid EOQ model with a two-state random environment

Abstract

We study a stochastic fluid EOQ-type model operating in a Markovian random environment of alternating good and bad periods determining the demand rate. We deal with the classical problem of ``when to place an order'' and ``how big it should be,'' leading to the trade-off between the setup cost and the holding cost. The key functionals are the steady-state mean of the content level, the expected cycle length (which is the time between two large orders), and the expected number of orders in a cycle. These performance measures are derived in closed form by using the level crossing approach in an intricate way. We also present numerical examples and carry out a sensitivity analysis.