Lecture2 - Introduction to Mathematical Programming IE406...

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Introduction to Mathematical Programming IE406 Lecture 2 Dr. Ted Ralphs
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IE406 Lecture 2 1 Reading for This Lecture Primary Reading Bertsimas 1.1-1.2, 1.4-1.5 Supplementary Reading Bertsimas 1.3 Operations Research Methods and Models Model Building in Mathematical Programming
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IE406 Lecture 2 2 Review from Last Time Recall that a mathematical model consists of: Decision variables (with domains) Constraints (functions of the variables with domains) Objective Function (maximize or minimize) Parameters and Data The general form of a mathematical programming model is: min or max f ( x 1 , . . . , x n ) s.t. g i ( x 1 , . . . , x n ) = b i ( x 1 , . . . , x n ) X where X may be a discrete set.
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IE406 Lecture 2 3 Example of a Mathematical Program: The Diet Problem Goal : Choose the cheapest menu satisfying nutritional requirements. What is the input data ? What is the formulation in words?
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IE406 Lecture 2 4 Critique of the Model What are the possible problems with this model?
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IE406 Lecture 2 5 A Little History George Dantzig is considered to be the father of linear programming. The diet problem was one of the first applications of linear programming.
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