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An economic lot‐sizing problem with perishable inventory and economies of scale costs: Approximation solutions and worst case analysis

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  • Leon Yang Chu
  • Vernon Ning Hsu
  • Zuo‐Jun Max Shen

Abstract

The costs of many economic activities such as production, purchasing, distribution, and inventory exhibit economies of scale under which the average unit cost decreases as the total volume of the activity increases. In this paper, we consider an economic lot‐sizing problem with general economies of scale cost functions. Our model is applicable to both nonperishable and perishable products. For perishable products, the deterioration rate and inventory carrying cost in each period depend on the age of the inventory. Realizing that the problem is NP‐hard, we analyze the effectiveness of easily implementable policies. We show that the cost of the best Consecutive‐Cover‐Ordering (CCO) policy, which can be found in polynomial time, is guaranteed to be no more than (4$\sqrt{2}$ + 5)/7 ≈ 1.52 times the optimal cost. In addition, if the ordering cost function does not change from period to period, the cost of the best CCO policy is no more than 1.5 times the optimal cost. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

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  • 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.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:6:p:536-548
    DOI: 10.1002/nav.20096
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    References listed on IDEAS

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    1. Steven A. Lippman, 1969. "Optimal Inventory Policy with Multiple Set-Up Costs," Management Science, INFORMS, vol. 16(1), pages 118-138, September.
    2. 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.
    3. 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.
    4. 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.
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    6. Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    7. Peter E. Earl, 1995. "Microeconomics for Business and Marketing," Books, Edward Elgar Publishing, number 159.
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    Cited by:

    1. Feng Xue & Qiumin Li, 2024. "Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    2. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    3. Zuo‐Jun Max Shen & Jia Shu & David Simchi‐Levi & Chung‐Piaw Teo & Jiawei Zhang, 2009. "Approximation algorithms for general one‐warehouse multi‐retailer systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(7), pages 642-658, October.
    4. Li‐Ming Chen & Amar Sapra, 2021. "Inventory renewal for a perishable product: Economies of scale and age‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 359-377, April.

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