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A note on "The Economic Lot Sizing Problem with Inventory Bounds"

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  • Onal, M.
  • van den Heuvel, W.J.
  • Liu, T.

Abstract

In a recent paper, Liu (2008) considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O(n^2) algorithm for the general problem, and an O(n) algorithm for the special case with non-speculative motives. We show that neither of the algorithms provides an optimal solution in general. Furthermore, we propose a fix for the former algorithm that maintains the O(n^2) complexity.

Suggested Citation

  • Onal, M. & van den Heuvel, W.J. & Liu, T., 2012. "A note on "The Economic Lot Sizing Problem with Inventory Bounds"," Econometric Institute Research Papers EI 2012-04, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:32133
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    References listed on IDEAS

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    1. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    2. Stephen F. Love, 1973. "Bounded Production and Inventory Models with Piecewise Concave Costs," Management Science, INFORMS, vol. 20(3), pages 313-318, November.
    3. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    4. Liu, Tieming, 2008. "Economic lot sizing problem with inventory bounds," European Journal of Operational Research, Elsevier, vol. 185(1), pages 204-215, February.
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    Cited by:

    1. Fan, Jie & Wang, Guoqing, 2018. "Joint optimization of dynamic lot and warehouse sizing problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 849-854.
    2. José M. Gutiérrez & Beatriz Abdul-Jalbar & Joaquín Sicilia & Inmaculada Rodríguez-Martín, 2021. "Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure," Mathematics, MDPI, vol. 9(6), pages 1-21, March.
    3. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    4. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    5. Ayse Akbalik & Bernard Penz & Christophe Rapine, 2015. "Capacitated lot sizing problems with inventory bounds," Annals of Operations Research, Springer, vol. 229(1), pages 1-18, June.

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