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Forecast horizons for the discounted dynamic lot‐size problem allowing speculative motive

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  • James C. Bean
  • Robert L. Smith
  • Candace A. Yano

Abstract

This article considers the dynamic lot‐size problem under discounting, allowing speculative motive for holding inventory. A variable rolling‐horizon procedure is presented, which, under certain regularity conditions, is guaranteed to generate an infinite‐horizon optimal‐production plan. We also discuss a fixed rolling‐horizon procedure which provides a production plan that achieves an infinite‐horizon cost within a user‐specified tolerance ϵ of optimality. The fixed‐horizon length T* needed in this procedure is given in terms of a closed‐form formula that is independent of specific forecasted demands. We also present computational results for problems with a range of cost parameters and demand characteristics.

Suggested Citation

  • James C. Bean & Robert L. Smith & Candace A. Yano, 1987. "Forecast horizons for the discounted dynamic lot‐size problem allowing speculative motive," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 761-774, December.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:6:p:761-774
    DOI: 10.1002/1520-6750(198712)34:63.0.CO;2-X
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    References listed on IDEAS

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    1. Edward Zabel, 1964. "Some Generalizations of an Inventory Planning Horizon Theorem," Management Science, INFORMS, vol. 10(3), pages 465-471, April.
    2. James C. Bean & Robert L. Smith, 1984. "Conditions for the Existence of Planning Horizons," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 391-401, August.
    3. Willard I. Zangwill, 1968. "Minimum Concave Cost Flows in Certain Networks," Management Science, INFORMS, vol. 14(7), pages 429-450, March.
    4. Joseph D. Blackburn & Howard Kunreuther, 1974. "Planning Horizons for the Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 21(3), pages 251-255, November.
    5. Gary D. Eppen & F. J. Gould & B. Peter Pashigian, 1969. "Extensions of the Planning Horizon Theorem in the Dynamic Lot Size Model," Management Science, INFORMS, vol. 15(5), pages 268-277, January.
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    1. 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.

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