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Existence of Forecast Horizons in Undiscounted Discrete-Time Lot Size Models

Author

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  • Suresh Chand

    (Purdue University, West Lafayette, Indiana)

  • Suresh P. Sethi

    (University of Toronto, Toronto, Canada)

  • Jean-Marie Proth

    (INRIA, Nancy, France)

Abstract

We are concerned with a discrete-time undiscounted dynamic lot size model in which demand and cost parameters are constant for an initial few periods. As our main result, we obtain an upper bound on the number of these periods which guarantees the optimality of the Economic Order Quantity (EOQ) as the size of the production lot to be produced in the first period. The upper bound is given and the optimality holds for every problem with an horizon not less than the upper bound and for the infinite horizon problem. The data beyond the upper bound are allowed to be specified arbitrarily. In the context of forecast horizon theory, we obtain conditions for a finite forecast horizon to exist in the undiscounted dynamic lot size model. Furthermore, existence results for forecast horizons in an undiscounted optimization problem are obtained for the first time in this paper.

Suggested Citation

  • Suresh Chand & Suresh P. Sethi & Jean-Marie Proth, 1990. "Existence of Forecast Horizons in Undiscounted Discrete-Time Lot Size Models," Operations Research, INFORMS, vol. 38(5), pages 884-892, October.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:5:p:884-892
    DOI: 10.1287/opre.38.5.884
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    Citations

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    Cited by:

    1. 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.
    2. Glomb, Lukas & Liers, Frauke & Rösel, Florian, 2022. "A rolling-horizon approach for multi-period optimization," European Journal of Operational Research, Elsevier, vol. 300(1), pages 189-206.
    3. Lodi, Andrea & Vigo, Daniele & Zannoni, Cinzia, 2000. "Exact and heuristic algorithms for data sets reconstruction," European Journal of Operational Research, Elsevier, vol. 124(1), pages 139-150, July.
    4. 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.
    5. Ganas, Ioannis S. & Papachristos, Sotirios, 1997. "Analytical evaluation of heuristics performance for the single-level lot-sizing problem for products with constant demand," International Journal of Production Economics, Elsevier, vol. 48(2), pages 129-139, January.
    6. Bylka, S.Stanislaw & Rempala, Ryszarda, 2004. "Heuristics for impulse replenishment with continuous periodic demand," International Journal of Production Economics, Elsevier, vol. 88(2), pages 183-190, March.
    7. Balakrishnan, Jaydeep & Hung Cheng, Chun, 2009. "The dynamic plant layout problem: Incorporating rolling horizons and forecast uncertainty," Omega, Elsevier, vol. 37(1), pages 165-177, February.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.
    14. Robert L. Smith & Rachel Q. Zhang, 1998. "Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs," Management Science, INFORMS, vol. 44(9), pages 1313-1320, September.
    15. Dawande, Milind & Gavirneni, Srinagesh & Naranpanawe, Sanjeewa & Sethi, Suresh P., 2009. "Discrete forecast horizons for two-product variants of the dynamic lot-size problem," International Journal of Production Economics, Elsevier, vol. 120(2), pages 430-436, August.
    16. 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.
    17. S. Bylka & S. Sethi & G. Sorger, 1992. "Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 487-507, June.

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