# Dynamic Programming 2 .pptx - Dynamic Programming...

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Dynamic Programming
IntroductionDynamic Programming is a modeling framework that is generally used for optimizationproblems involving sequential decision processes. In these dynamical problems,decisions are made for a planning horizon, which is divided into periods or stages, anda decison at one stage influences the outcome and the decisions of all the flollowingstages.This optimization technique was developed by R. Bellman in 1950 (USA). It consists ofdecomposing a problem into subproblems or stages that can be easily solved.In this course we consider only:Discrete, finite horizon and deterministicdynamicprogramming.
Dynamic Programming formulationsMany applications are reduced to finding the shortest (or the longest) path betweentwo nodes of a graph.The shortest route problem in a networkConsider the following example. Joe Cougar needs to travel from Nashville to LosAngeles. In order to minimize his total travel cost, he decided to spend each night ata friend's house living in each of the following cities: Kansas City, Omaha, Dallas, San
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Shortest path problem, Bellman equation

Unformatted text preview: Antonio and Denver. Joe knows that after one day of driving he can reach Kansas City,Omaha or Dallas and after 2 days he can arrive at San Antonio or Denver. Finally, after 3 days he can be at Los Angeles. Joe has to decide at which cities he should stay in order to minimize the total distance traveled. The corresponding network is shown on the following figure. A network example General form of a dynamic program Forward formulation • We begin by finding the shortest route from the origin city to each of the cities of stage 2. Then, we use this information to find the shortest path from the origin city to each of the cities of stage 3. This information is then used to find the shortest path from the origin city to the destination city. The idea is to solve, at each iteration, an easy problem which helps to solve a more complex problem. Forward recursion: Forward recursion: Forward recursion: General Forward formulation...
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