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Minimal Forecast Horizons and a New Planning Procedure for the General Dynamic Lot Sizing Model: Nervousness Revisited

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Michal Tzur

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

We show for the general dynamic lot sizing model how minimal forecast horizons may be detected by a slight adaptation of an earlier O ( n log n ) or O ( n ) forward solution method for the model. A detailed numerical study indicates that minimal forecast horizons tend to be small, that is, include a small number of orders. We describe a new planning approach to ensure stability of the lot sizing decisions over an initial interval of time or stability horizon in those (relatively rare) cases where no planning horizon is detected or where the stability horizon extends beyond the planning horizon. To this end, we develop a heuristic, but full horizon-based adaptation of the optimal lot sizing schedule, designed to minimize an upper bound for the worst-case optimality gap under the desired stability conditions. We also show how the basic horizon length n may be chosen to guarantee any prespecified positive optimality gap.

Suggested Citation

  • Awi Federgruen & Michal Tzur, 1994. "Minimal Forecast Horizons and a New Planning Procedure for the General Dynamic Lot Sizing Model: Nervousness Revisited," Operations Research, INFORMS, vol. 42(3), pages 456-468, June.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:3:p:456-468
    DOI: 10.1287/opre.42.3.456
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    Cited by:

    1. Hartmut Stadtler & Malte Meistering, 2019. "Model formulations for the capacitated lot-sizing problem with service-level constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 1025-1056, December.
    2. Marshall Fisher & Kamalini Ramdas & Yu-Sheng Zheng, 2001. "Ending Inventory Valuation in Multiperiod Production Scheduling," Management Science, INFORMS, vol. 47(5), pages 679-692, May.
    3. 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.
    4. 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.
    5. Charles, Mehdi & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Mazhoud, Issam, 2022. "Motivations and analysis of the capacitated lot-sizing problem with setup times and minimum and maximum ending inventories," European Journal of Operational Research, Elsevier, vol. 302(1), pages 203-220.
    6. Wilco van den Heuvel & Albert P.M. Wagelmans, 2002. "A Note on Ending Inventory Valuation in Multiperiod Production Scheduling," Tinbergen Institute Discussion Papers 02-067/4, Tinbergen Institute.
    7. 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.
    8. Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
    9. G. Rius-Sorolla & J. Maheut & S. Estellés-Miguel & J. P. García-Sabater, 2021. "Operations planning test bed under rolling horizons, multiproduct, multiechelon, multiprocess for capacitated production planning modelling with strokes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1289-1315, December.
    10. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    11. 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.
    12. 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.
    13. Archis Ghate & Robert L. Smith, 2009. "Optimal Backlogging Over an Infinite Horizon Under Time-Varying Convex Production and Inventory Costs," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 362-368, June.
    14. Aarts, E. H. L. & Reijnhoudt, M. F. & Stehouwer, H. P. & Wessels, J., 2000. "A novel decomposition approach for on-line lot-sizing," European Journal of Operational Research, Elsevier, vol. 122(2), pages 339-353, April.
    15. 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.
    16. Cuisinier, Étienne & Lemaire, Pierre & Penz, Bernard & Ruby, Alain & Bourasseau, Cyril, 2022. "New rolling horizon optimization approaches to balance short-term and long-term decisions: An application to energy planning," Energy, Elsevier, vol. 245(C).
    17. Herbon, Avi & Khmelnitsky, Eugene & Maimon, Oded, 2004. "Effective information horizon length in measuring off-line performance of stochastic dynamic systems," European Journal of Operational Research, Elsevier, vol. 157(3), pages 688-703, September.
    18. 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.
    19. 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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