For the familiar (R,s,S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock. Best-known are the approximations derived from renewal theory, holding under specific conditions; in particular, S−s should be reasonably large. Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued shape parameter, while lead time is constant. These exact results allow a check of the renewal theory based approximations. In addition, an extremely fast simulation program was written, obviously holding for general shape parameter values.
