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

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  • Michael Katehakis
  • Laurens Smit

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Michael Katehakis & Laurens Smit, 2012. "On computing optimal (Q,r) replenishment policies under quantity discounts," Annals of Operations Research, Springer, vol. 200(1), pages 279-298, November.
    • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:279-298:10.1007/s10479-012-1071-z
    DOI: 10.1007/s10479-012-1071-z
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    References listed on IDEAS

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    1. H. P. Galliher & Philip M. Morse & M. Simond, 1959. "Dynamics of Two Classes of Continuous-Review Inventory Systems," Operations Research, INFORMS, vol. 7(3), pages 362-384, June.
    2. Papachristos, S. & Skouri, K., 2003. "An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 83(3), pages 247-256, March.
    3. Benton, W. C. & Park, Seungwook, 1996. "A classification of literature on determining the lot size under quantity discounts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 219-238, July.
    4. Munson, C.L. & Hu, J., 2010. "Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision," European Journal of Operational Research, Elsevier, vol. 201(2), pages 581-592, March.
    5. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    6. Izzet Sahin, 1979. "On the Stationary Analysis of Continuous Review ( s , S ) Inventory Systems with Constant Lead Times," Operations Research, INFORMS, vol. 27(4), pages 717-729, August.
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    Cited by:

    1. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
    2. Yong Zhang & Xingyu Yang & Weiguo Zhang & Weiwei Chen, 2020. "Online ordering rules for the multi-period newsvendor problem with quantity discounts," Annals of Operations Research, Springer, vol. 288(1), pages 495-524, May.
    3. Kartikeya Puranam & Michael Katehakis, 2014. "On optimal bidding and inventory control in sequential procurement auctions: the multi period case," Annals of Operations Research, Springer, vol. 217(1), pages 447-462, June.
    4. Eugene A. Feinberg & Yan Liang, 2022. "On the optimality equation for average cost Markov decision processes and its validity for inventory control," Annals of Operations Research, Springer, vol. 317(2), pages 569-586, October.
    5. Wen Chen & Adam J. Fleischhacker & Michael N. Katehakis, 2015. "Dynamic pricing in a dual‐market environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 531-549, October.
    6. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    7. Wen Chen & Burcu Tan, 2022. "Dynamic procurement from multiple suppliers with random capacities," Annals of Operations Research, Springer, vol. 317(2), pages 509-536, October.
    8. Apostolos Burnetas & Odysseas Kanavetas, 2018. "Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 676-698, December.
    9. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    10. Vicky Ching Gu & Bin Zhou & Qing Cao & Jeffery Adams, 2021. "Exploring the relationship between supplier development, big data analytics capability, and firm performance," Annals of Operations Research, Springer, vol. 302(1), pages 151-172, July.
    11. Arda Yenipazarli, 2015. "A road map to new product success: warranty, advertisement and price," Annals of Operations Research, Springer, vol. 226(1), pages 669-694, March.
    12. Lina Johansson & Fredrik Olsson, 2017. "Quantifying sustainable control of inventory systems with non-linear backorder costs," Annals of Operations Research, Springer, vol. 259(1), pages 217-239, December.

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