Analysis of the Deterministic (s, S) Inventory Problem

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,..., d_n. 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.