Probabilistic Dynamic Programming for Inventory Problems

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Addis Ababa University


Stockout cost is the cost that happen when the demand is greater than the inventory. It may be either back order cost or lost sale cost. Generally inventory problems has many features and cases. I formulate a probabilis- tic dynamic programming model to study problems over the nite planning horizon. This paper presents with the scope of stochastic dynamic program- ming.Mainly two models are discussed the rst model is single period model and the second model is multi-stage model. Unfortunately, dynamic pro- gramming designed for multi-period problems not for single period but I discussed Christmas inventory problem or newsboy problem within single- period model. In chapter 1 we will discuss de nition of probabilistic or stochastic dy- namic programming with illustrative example, historical background in short. In chapter 2 some preliminary concepts and de nitions are included. Since this concepts are used for chapter four specially. In chapter 3 and 4 the main work of the paper with to models single-period model on chapter 3 and multi-stage or multi-period model in chapter 4. Finally conclusion and recommendation are in the last chapter. At the end a numerical example is included to illustrate how the model applied.



Expected Value, Inventory, Items, Poisson, Probabilistic, Stochastic, Stockout, Uncertainty