Annals of Operations Research

, Volume 200, Issue 1, pp 279–298 | Cite as

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

The all-units and incremental discount cases
Article

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

  1. Benton, W. C., & Park, S. W. (1996). A classification of literature on determining the lot size under quantity discounts. European Journal of Operational Research, 92, 219–238. CrossRefGoogle Scholar
  2. Federgruen, A., & Zheng, Y. S. (1992). An efficient algorithm for finding an optimal (r,Q) policy in continuous review stochastic inventory systems. Operations Research, 40, 808–813. CrossRefGoogle Scholar
  3. Feller, W. (1968). An introduction to probability theory and its applications (Vol. 1). New York: Wiley. Google Scholar
  4. Gallego, G., & Katircioglu, K. (2007). Inventory management under highly uncertain demand. Operations Research Letters 35, 281–289. CrossRefGoogle Scholar
  5. Galliher, H., Morse, P., & Simmond, M. (1959). Dynamics of two classes of continuous-review inventory systems. Operations Research, 7, 362–384. CrossRefGoogle Scholar
  6. Hadley, G., & Whitin, T. M. (1963). Analysis of inventory systems. Englewood Cliffs: Prentice Hall International. Google Scholar
  7. Munson, C. L., & Hu, J. (2010). Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision. European Journal of Operational Research, 201, 581–592. CrossRefGoogle Scholar
  8. Papachristos, S., & Skouri, K. (2003). An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, 83, 247–256. CrossRefGoogle Scholar
  9. Rubalskiy, G. (1972). Calculation of optimum parameters in an inventory control problem. Journal of Computer & Systems Sciences International, 10, 182–187. Google Scholar
  10. Sahin, I. (1979). On the stationary analysis of continuous review (s,S) inventory systems with constant lead times. Operations Research, 27(4), 717–729. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Management Science and Information SystemsRutgers Business School, Newark and New BrunswickNewarkUSA
  2. 2.Mathematisch InstituutUniversiteit LeidenLeidenNetherlands

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