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A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs

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  • Alain Bensoussan
  • Jean‐Marie Proth
  • Maurice Queyranne

Abstract

We consider a single‐product, discrete‐time production/inventory‐control problem with nonstationary concave nondecreasing costs. Given a forecast horizon K, the problem is to find a decision horizon. We specialize to piecewise linear costs a general approach whereby a problem with horizon K + 1 and arbitrary final demand is parametrically solved. The resulting algorithm is polynomial in the input size.

Suggested Citation

  • Alain Bensoussan & Jean‐Marie Proth & Maurice Queyranne, 1991. "A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 729-742, October.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:5:p:729-742
    DOI: 10.1002/1520-6750(199110)38:53.0.CO;2-U
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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.
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    Cited by:

    1. Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
    2. 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.
    3. Bylka, Stanislaw, 2005. "Turnpike policies for periodic review inventory model with emergency orders," International Journal of Production Economics, Elsevier, vol. 93(1), pages 357-373, January.
    4. Stanislaw Bylka, 1997. "Strong turnpike policies in the single‐item capacitated lot‐sizing problem with periodical dynamic parameter," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 775-790, December.
    5. 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.
    6. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    7. Awi Federgruen & Michal Tzur, 1999. "Time‐partitioning heuristics: Application to one warehouse, multiitem, multiretailer lot‐sizing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 463-486, August.

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