<p>This article discusses a continuous review stochastic inventory system with postponed demands. Assume that demand time points form a Poisson process, and their demand is immediately satisfied whenever inventory level is positive. Demands that occur during stock-out periods enter a pool of infinite size. The pooled customer is selected one-by-one when the on-hand inventory is positive and no order is pending. The inter-selection times of customers from the pool follow exponential distribution. The inventory is replenished from the outside supplier with flexible reorder point, and the lead times for the order are exponential distribution. We formulating this model as a Markov decision problem. We derive an optimal threshold replenishment policy under the discounted cost criterion. To demonstrate the outcome, we provide a few numerical examples.</p>