The exact fill rate in a periodic review base stock system under normally distributed demand

In this paper, we consider a periodic review order-up-to-level (or base stock) inventory control system under normally distributed demand. For such circumstances, an expression for the exact fill rate (fraction of demand satisfied without backordering) has been available in the literature, but has not been widely known, let alone used by practitioners. In this paper, we redevelop the expression and contrast our derivation with the earlier published one. The paper has two purposes. First, we hope that the reappearance of the exact result in this journal will lead to its wider adoption. Second, showing two contrasting approaches to obtaining the same result may be useful for both research and pedagogical purposes.