Dynamic Programming 2 .pptx - Dynamic Programming...

Dynamic Programming

Introduction
• Dynamic Programming is a modeling framework that is generally used for optimization
• problems involving sequential decision processes. In these dynamical problems,
• decisions are made for a planning horizon, which is divided into periods or stages, and
•
a decison at one stage influences the outcome and the decisions of all the flollowing
•
stages.
•
This optimization technique was developed by R. Bellman in 1950 (USA). It consists of
•
decomposing a problem into subproblems or stages that can be easily solved.
•
In this course we consider only: Discrete, finite horizon and deterministic dynamic
programming.

Dynamic Programming formulations
• Many applications are reduced to finding the shortest (or the longest) path between
two nodes of a graph.
The shortest route problem in a network
Consider the following example. Joe Cougar needs to travel from Nashville to Los
Angeles. In order to minimize his total travel cost, he decided to spend each night at
a friend's house living in each of the following cities: Kansas City, Omaha, Dallas, San