# On computing optimal (*Q*,*r*) replenishment policies under quantity discounts

The all-units and incremental discount cases

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## Abstract

This article studies the classical reorder quantity, order point (*Q*,*r*) continuous review stochastic inventory model with Poisson arrivals and a fixed lead time. This model has been extensively studied in the literature and its use in practice is widespread. This work extends previous research in this area by providing efficient algorithms for the computation of the optimal (*Q* ^{∗},*r* ^{∗}) values when there is a multi-breakpoint discount pricing structure.

### Keywords

Inventory Production Lot sizing Backorders Quantity discounts## Notes

### Acknowledgements

The authors would like to thank Professor Flora Spieksma, Mathematics Institute, University of Leiden, the Netherlands, for many useful comments. Research partially supported by Rutgers Business School Research Committee.

### References

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