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Planning Horizons for Production Smoothing with Deterministic Demands

Author

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  • Howard C. Kunreuther

    (University of Pennsylvania)

  • Thomas E. Morton

    (University of Chicago and Carnegie Mellon University)

Abstract

In Part I of this paper, we develop an algorithm for finding planning horizons for the deterministic production smoothing problem when all demand must be met from regular production, under rather general assumptions for the production, production smoothing, and holding cost functions. (In Part II, planning horizons will be developed when the model is extended to include backlogging and overtime.) The techniques developed here are essentially forward-looking and marginal-cost-balancing in nature, rather than total-cost-minimizing and backward-looking such as dynamic programming, or total-cost-minimizing and omni-looking in nature such as linear programming. The fact that the planning horizon theorems do not depend on having discount rates less than one illustrates that the approach developed here is fundamentally different from ordinary infinite horizon dynamic programming techniques. The algorithm is "user oriented" in the sense that only a small amount of forecasting work and computation ordinarily must be done to determine the horizon; the nature of the algorithm also makes the exact dependence of the horizon on the forecast clear for sensitivity analysis. Firms facing a seasonal demand pattern will often find that the horizon occurs within the first several periods after the peak period if there is a sufficient enough drop in demand afterwards. This result complements the findings of Modigliani and Hohn and provides insight into the nature of the optimal policy for stochastic planning problems.

Suggested Citation

  • Howard C. Kunreuther & Thomas E. Morton, 1973. "Planning Horizons for Production Smoothing with Deterministic Demands," Management Science, INFORMS, vol. 20(1), pages 110-125, September.
  • Handle: RePEc:inm:ormnsc:v:20:y:1973:i:1:p:110-125
    DOI: 10.1287/mnsc.20.1.110
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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. Molinder, Anders, 1995. "Application of calculus of variations to a continuous time aggregate production model," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 273-280, October.
    3. 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.
    4. 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.
    5. Nuthall, Peter L., 1980. "A Survey of Methods for Determining A Planning Horizon," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 48(01), pages 1-15, April.
    6. 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.
    7. 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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