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Inventory policies with quantized ordering

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  • Yu‐Sheng Zheng
  • Fangruo Chen

Abstract

This article studies (nQ, r) inventory policies, under which the order quantity is restricted to be an integer multiple of a base lot size Q. Both Q and r are decision variables. Assuming the one‐period expected holding and backorder cost function is unimodal, we develop an efficient algorithm to compute the optimal Q and r. The algorithm is facilitated by simple observations about the cost function and by tight upper bounds on the optimal Q. The total number of elementary operations required by the algorithm is linear in these upper bounds. By using the algorithm, we compare the performance of the optimal (nQ, r) policy with that of the optimal (s, S) policy through a numerical study, and our results show that the difference between them is small. Further analysis of the model shows that the cost performance of an (nQ, r) policy is insensitive to the choice of Q. These results establish that (nQ, r) models are potentially useful in many settings where quantized ordering is beneficial.

Suggested Citation

  • Yu‐Sheng Zheng & Fangruo Chen, 1992. "Inventory policies with quantized ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 285-305, April.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:3:p:285-305
    DOI: 10.1002/1520-6750(199204)39:33.0.CO;2-T
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    References listed on IDEAS

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    Cited by:

    1. Frank Chen & Tong Wang & Tommy Xu, 2005. "Integrated Inventory Replenishment and Temporal Shipment Consolidation: A Comparison of Quantity-Based and Time-Based Models," Annals of Operations Research, Springer, vol. 135(1), pages 197-210, March.
    2. Agrawal, Narendra & Smith, Stephen A., 2019. "Optimal inventory management using retail prepacks," European Journal of Operational Research, Elsevier, vol. 274(2), pages 531-544.
    3. Osman Alp & Woonghee Tim Huh & Tarkan Tan, 2014. "Inventory Control with Multiple Setup Costs," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 89-103, February.
    4. Stanislaw Bylka, 1997. "Strong turnpike policies in the single‐item capacitated lot‐sizing problem with periodical dynamic parameter," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 775-790, December.
    5. Thomas Wensing & Michael G. Sternbeck & Heinrich Kuhn, 2018. "Optimizing case-pack sizes in the bricks-and-mortar retail trade," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 913-944, October.
    6. Esmail Mohebbi & Morton J.M. Posner, 1998. "A continuous‐review inventory system with lost sales and variable lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 259-278, April.
    7. Ruud Heuts & Jan de Klein, 1995. "An (s, q) inventory model with stochastic and interrelated lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 839-859, August.
    8. Sean X. Zhou & Chaolin Yang, 2016. "Continuous-Review ( R, nQ ) Policies for Inventory Systems with Dual Delivery Modes," Operations Research, INFORMS, vol. 64(6), pages 1302-1319, December.
    9. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    10. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    11. Ying Wei, 2020. "Optimizing constant pricing and inventory decisions for a periodic review system with batch ordering," Annals of Operations Research, Springer, vol. 291(1), pages 939-957, August.

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