Exact fill rates for (<Emphasis Type="Italic">R,s, S</Emphasis>) inventory control with gamma distributed demand |
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Authors: | J J A Moors L W G Strijbosch |
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Institution: | 1.Center for Economic Research, Tilburg University,Tilburg,The Netherlands |
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Abstract: | For the familiar (R, s, S) inventory control system only approximate expressions exist for the fill rate, ie 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. |
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