Stochastic Dynamic Programming - Discrete Modeling and Optimization - Lecture Slides, Slides of Discrete Structures and Graph Theory

Download Stochastic Dynamic Programming - Discrete Modeling and Optimization - Lecture Slides and more Slides Discrete Structures and Graph Theory in PDF only on Docsity!

Dynamic Programming

In this handout

• Stochastic Dynamic Programming

Probabilistic Dynamic Programming

So far we have assumed that a specification of the

current state and current decision is enough to

determine with certainty the state we will end up

in the next stage.

However, in many practical situations there might

be some external factors, like stochastic demand

for a product, that might affect the resulting state

in the next stage.

Thus, it is more realistic to assume that there is a

probability distribution for what the next state will

be. In this case the model is known as

probabilistic dynamic programming.

The basic structure for Probabilistic

Dynamic Programming

Inventory problem with random demands

• 3 production periods
• No inventory at the beginning
• Can produce at most 3 units in each period
• Can keep at most 2 units in inventory
• Set-up cost for each period is 5

The demand is not known in advance. It is given by a

probability distribution (see next slide).

Period 1 2 3

Unit cost 3 5 4