The traditional or textbook approach for finding an s, S inventory policy is to take a demand distribution as given and then find a reorder point s and order up to point S that are optimal for this demand distribution. In reality, the demand distribution may have been obtained by fitting it to some historical demand stream. In contrast, the deterministic s, S inventory problem is to directly determine the s, S pair that would have been optimal for the original demand stream, bypassing the distribution fitting step. The deterministic s, S inventory problem thus chooses parameters s and S which minimize setup, holding and backorder costs when the corresponding s, S policy is implemented over n periods with known demands d1, d2,', dn. Our contributions are two: a a polynomial time algorithm for finding an optimal s, S for the deterministic problem, and b an empirical comparison of the two approaches. In b we compare the long term average costs of the two approaches as a function of the amount of data available, distributional assumptions, and order lead time.

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