Determining the fill rate for a periodic review inventory policy with capacitated replenishments, lost sales and zero lead time

In this paper we consider a periodic review order-up-to inventory system with capacitated replenishments, lost sales and zero lead time. We consider discrete demand. It is shown that the initial stock levels of the different review periods form a Markov chain and we determine the transition matrix. Furthermore we study for what probability mass functions of the review period demand the Markov chain has a unique stationary distribution. Finally, we present a method to determine the fill rate.