Probabilistic Dynamic Programming For Inventory Problems

Stockout cost is the cost that happen when the demand is greater thanrnthe inventory. It may be either back order cost or lost sale cost. Generallyrninventory problems has many features and cases. I formulate a probabilis-rntic dynamic programming model to study problems over the nite planningrnhorizon. This paper presents with the scope of stochastic dynamic program-rnming.Mainly two models are discussed the rst model is single period modelrnand the second model is multi-stage model. Unfortunately, dynamic pro-rngramming designed for multi-period problems not for single period but Irndiscussed Christmas inventory problem or newsboy problem within single-rnperiod model.rnIn chapter 1 we will discuss de nition of probabilistic or stochastic dy-rnnamic programming with illustrative example, historical background in short.rnIn chapter 2 some preliminary concepts and de nitions are included. Sincernthis concepts are used for chapter four specially. In chapter 3 and 4 thernmain work of the paper with to models single-period model on chapter 3rnand multi-stage or multi-period model in chapter 4. Finally conclusion andrnrecommendation are in the last chapter. At the end a numerical example isrnincluded to illustrate how the model applied.

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