Probabilistic Dynamic Programming for Inventory Problems
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Date
2020-09-05
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Addis Ababa University
Abstract
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.
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Keywords
Expected Value, Inventory, Items, Poisson, Probabilistic, Stochastic, Stockout, Uncertainty