Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

J.J.A. Moors, L.W.G. Strijbosch

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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 by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.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 parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages20
Publication statusPublished - 2001

Publication series

NameCentER Discussion Paper


  • demand
  • inventory control
  • simulation


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