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Exact fill rates for (R, s, S) inventory control with gamma distributed demand

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Author Info
Moors, J.J.A.
Strijbosch, L.W.G. (Tilburg University, Center for Economic Research)

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Abstract

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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 32.

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Date of creation: 2001
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Handle: RePEc:dgr:kubcen:200132

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C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research

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  1. Strijbosch, L.W.G. & Moors, J.J.A., 2003. "Modified normal demand distributions in (R,S)-inventory models," Discussion Paper 76, Tilburg University, Center for Economic Research. [Downloadable!]
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