Vanishing Discount Approach Versus Stationary Distribution Approach
In Part III, we derived the structure of the optimal policy to minimize the long-run average cost by using the vanishing discount method. In the classical inventory literature, a stationary distribution approach is often used to minimize the long-run average cost. In this approach, the stationary distribution of the inventory levels is obtained for a specific class of policies, the best policy in this class is found, and then it is proven that this policy is average optimal. In this chapter, we review the stationary distribution approach in solving the simpler problem of an inventory model with i.i.d demands, and then show how the results of this analysis relate to those obtained by the vanishing discount approach.
KeywordsInventory Model Markov Decision Process Average Cost Demand Distribution Renewal Function
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