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

J.J.A. Moors · Leo W. G. Strijbosch

43 citations0/0 files storedJournal of the Operational Research Society

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Supply Chain and Inventory Management Reliability and Maintenance Optimization Advanced Queuing Theory Analysis

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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References

1975The Gamma Distribution and Inventory Control 1998Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint 1984Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service level constraints 1981Effect of service-levels on order-points or order-levels in inventory models 1978Methods for Determining the Re-order Point of an (s, S) Ordering Policy when a Service Level is Specified 1990Power Approximation for Computing (s, S) Policies Using Service Level

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