A Note on the Bergstrom-Smith Multi-Item Production Planning Model

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Abstract
This note demonstrates that the model proposed by Bergstrom and Smith (B & S) for deterministic multi-item production planning can, with some reinterpretation, be used to solve two related stochastic multi-item production planning problems. Specifically, the benefits of individual item-by-item treatment and diminishing marginal revenue contained in the B & S model can be obtained when future sales are (i) stochastic and uncontrollable, or (ii) stochastic but with the mean value under the control of the firm. We demonstrate that under both of these situations the certainty-equivalence property holds, thereby reducing the two stochastic problems to two related deterministic problems.

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