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Fast Solution and Detection of Minimal Forecast Horizons in Dynamic Programs with a Single Indicator of the Future: Applications to Dynamic Lot-Sizing Models

Author

Listed:
  • Awi Federgruen

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Michal Tzur

    (Department of Industrial Engineering, Tel Aviv University, Tel Aviv, Israel)

Abstract

In most dynamic planning problems, one observes that an optimal decision at any given stage depends on limited information, i.e., information pertaining to a limited set of adjacent or nearby stages. This holds in particular for planning problems over time, where an optimal decision in a given period depends on information related to a limited future time horizon, a so-called forecast horizon, only. In this paper we identify a general class of dynamic programs in which an efficient forward algorithm can be designed to solve the problem and to identify minimal forecast horizons. Such a procedure specifies necessary and sufficient conditions for a stage to arise as a forecast horizon. This class of dynamic programs includes the single-item dynamic lot-sizing model with general concave costs, both with and without backlogging, to which special attention is given.

Suggested Citation

  • Awi Federgruen & Michal Tzur, 1995. "Fast Solution and Detection of Minimal Forecast Horizons in Dynamic Programs with a Single Indicator of the Future: Applications to Dynamic Lot-Sizing Models," Management Science, INFORMS, vol. 41(5), pages 874-893, May.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:5:p:874-893
    DOI: 10.1287/mnsc.41.5.874
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    Citations

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    Cited by:

    1. Kimms, A, 1998. "Stability Measures for Rolling Schedules with Applications to Capacity Expansion Planning, Master Production Scheduling, and Lot Sizing," Omega, Elsevier, vol. 26(3), pages 355-366, June.
    2. Milind Dawande & Srinagesh Gavirneni & Sanjeewa Naranpanawe & Suresh Sethi, 2007. "Forecast Horizons for a Class of Dynamic Lot-Size Problems Under Discrete Future Demand," Operations Research, INFORMS, vol. 55(4), pages 688-702, August.
    3. Fuying Jing & Zirui Lan, 2017. "Forecast horizon of multi-item dynamic lot size model with perishable inventory," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-15, November.
    4. Kimms, Alf, 1996. "Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 418, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    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. Archis Ghate & Robert L. Smith, 2013. "A Linear Programming Approach to Nonstationary Infinite-Horizon Markov Decision Processes," Operations Research, INFORMS, vol. 61(2), pages 413-425, April.
    7. Drexl, Andreas & Kimms, Alf, 1996. "Lot sizing and scheduling: Survey and extensions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 421, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.
    9. Shen Hong & Deng Qiang & Lao Rebecca & Wu Simon, 2016. "A Case Study of Inventory Management in a Manufacturing Company in China," Nang Yan Business Journal, Sciendo, vol. 5(1), pages 20-40, December.
    10. 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.

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