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.
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