An infinite horizon inventory model with periodic order commitment

This paper studies an infinite horizon inventory model of a buyer with a periodic order commitment. The commitment requires the buyer to purchase at least a certain fixed amount on a periodic basis. There is no extra adjustment cost should the buyer decide to order more than the basic amount. We consider general discrete demand distributions. We formulate a Markov chain to represent the behavior of the inventory system. Stimulated by the solution approach to the classical GI/M/1 queue, we derive the steady-state results and obtain the exact closed-form cost function. Numerical examples are provided.