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The dynamic lot‐sizing model with backlogging: A simple o(n log n) algorithm and minimal forecast horizon procedure

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  • Awi Federgruen
  • Michal Tzur

Abstract

We develop a simple O(n log n) solution method for the standard lot‐sizing model with backlogging and a study horizon of n periods. Production costs are fixed plus linear and holding and backlogging costs are linear with general time‐dependent parameters. The algorithm has linear [O(n)] time complexity for several important subclasses of the general model. We show how a slight adaptation of the algorithm can be used for the detection of a minimal forecast horizon and associated planning horizon. The adapted algorithm continues to have complexity O(n log n) or O(n) for the above‐mentioned subclasses of the general model. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Awi Federgruen & Michal Tzur, 1993. "The dynamic lot‐sizing model with backlogging: A simple o(n log n) algorithm and minimal forecast horizon procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 459-478, June.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:4:p:459-478
    DOI: 10.1002/1520-6750(199306)40:43.0.CO;2-8
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    References listed on IDEAS

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    1. Ioannis Ganas & Sotirios Papachristos, 2005. "The Single-Product Lot-Sizing Problem with Constant Parameters and Backlogging: Exact Results, a New Solution, and All Parameter Stability Regions," Operations Research, INFORMS, vol. 53(1), pages 170-176, February.
    2. Akartunalı, Kerem & Dauzère-Pérès, Stéphane, 2022. "Dynamic lot sizing with stochastic demand timing," European Journal of Operational Research, Elsevier, vol. 302(1), pages 221-229.
    3. Yongpei Guan & Andrew J. Miller, 2008. "Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 56(5), pages 1172-1183, October.
    4. Awi Federgruen & Michal Tzur, 1996. "Detection of minimal forecast horizons in dynamic programs with multiple indicators of the future," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 169-189, March.

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