Analysis of the Deterministic (s, S) Inventory Problem

Ananth V. Iyer · Linus E. Schrage

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Supply Chain and Inventory Management Management and Optimization Techniques Optimization and Search Problems

Abstract

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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References

2004Dynamic Version of the Economic Lot Size Model 1951Optimal Inventory Policy 2005The Optimality of (S,s) Policies in the Dynamic Inventory Problem 1959Bayes Solutions of the Statistical Inventory Problem 1979The Power Approximation for Computing (s, S) Inventory Policies 1960Some remarks on bayes solutions to the inventory problem 1989Introductory Management Science 1986Scarf's State Reduction Method, Flexibility, and a Dependent Demand Inventory Model

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