The Existence of The Environment-Dependent Optimal (s,S) Policy

概要

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Inventory systems are often subject to randomly changing exogenous environment-conditions that affect the demand for the product, the supply, and the cost structure. This paper analyzes a single product, periodic review inventory model with uncertain demand in a random environment. The demand distribution and cost parameters depend on environmental fluctuations which is assumed to follows a discrete-time Markov chain. To minimize the total discounted expected cost (fixed ordering, ordering, holding, and shortage costs), we formulate the model as a dynamic programming problem. For the finite-horizon model, we prove that the objective function is convex and that the structure of the optimal policy is characterized by two environmental-dependent critical numbers for the initial inventory level at each period. Expressions for solving the critical numbers and the optimal planned ordering are obtained. We further show that the solution for the finite-horizon model converges to that of the infinite-horizon model.
名古屋商科大学の論文
2004-07-01