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The dynamic lot size model with quantity discount

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  • Awi Federgruen
  • Chung‐Yee Lee

Abstract

This article treats the dynamic lot size model with quantity discount in purchase price. We study the problem with two different cost structures: the all‐units‐discount cost structure and the incremental‐discount cost structure. We solve the problem under both discount cost structures by dynamic programming algorithms of complexity O(T3) and O(T2),respectively, with T the number of periods in the planning horizon.

Suggested Citation

  • Awi Federgruen & Chung‐Yee Lee, 1990. "The dynamic lot size model with quantity discount," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 707-713, October.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:5:p:707-713
    DOI: 10.1002/1520-6750(199010)37:53.0.CO;2-5
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    References listed on IDEAS

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    1. S. K. Goyal, 1987. "Note---Comment on: A Generalized Quantity Discount Pricing Model to Increase Supplier's Profits," Management Science, INFORMS, vol. 33(12), pages 1635-1636, December.
    2. James P. Monahan, 1984. "A Quantity Discount Pricing Model to Increase Vendor Profits," Management Science, INFORMS, vol. 30(6), pages 720-726, June.
    3. Hau L. Lee & Meir J. Rosenblatt, 1986. "A Generalized Quantity Discount Pricing Model to Increase Supplier's Profits," Management Science, INFORMS, vol. 32(9), pages 1177-1185, September.
    4. repec:inm:ormnsc:v:30:y:1984:i:12:p:1524-1539(2 is not listed on IDEAS
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    1. Kirschstein, Thomas & Meisel, Frank, 2019. "A multi-period multi-commodity lot-sizing problem with supplier selection, storage selection and discounts for the process industry," European Journal of Operational Research, Elsevier, vol. 279(2), pages 393-406.
    2. Chia‐Shin Chung & Sin‐Hoon Hum & Omer Kirca, 2000. "An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 686-695, December.
    3. Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Shen & David Simchi-Levi, 2002. "On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures," Operations Research, INFORMS, vol. 50(6), pages 1058-1067, December.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    5. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.
    6. Chung‐Lun Li & Jinwen Ou & Vernon N. Hsu, 2012. "Dynamic lot sizing with all‐units discount and resales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 230-243, April.
    7. Awi Federgruen & Min Wang, 2015. "Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs," Operations Research, INFORMS, vol. 63(3), pages 701-715, June.
    8. Leon Yang Chu & Vernon Ning Hsu & Zuo‐Jun Max Shen, 2005. "An economic lot‐sizing problem with perishable inventory and economies of scale costs: Approximation solutions and worst case analysis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 536-548, September.
    9. Rita Vachani, 1992. "Performance of heuristics for the uncapacitated lot‐size problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 801-813, October.
    10. Aria Shahsavar & Nima Zoraghi & Babak Abbasi, 2018. "Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects," Operational Research, Springer, vol. 18(2), pages 315-342, July.
    11. Jiefeng Xu & Leonard L. Lu, 1998. "The dynamic lot size model with quantity discount: Counterexamples and correction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(4), pages 419-422, June.
    12. Esra Koca & Hande Yaman & M. Selim Aktürk, 2014. "Lot Sizing with Piecewise Concave Production Costs," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 767-779, November.

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