Lecture2 - Introduction to Mathematical Programming IE406...

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Unformatted text preview: Introduction to Mathematical Programming IE406 Lecture 2 Dr. Ted Ralphs 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 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. 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? IE406 Lecture 2 4 Critique of the Model What are the possible problems with this model? IE406 Lecture 2 5 A Little History • George Dantzig is considered to be the father of linear programming....
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This note was uploaded on 08/06/2008 for the course IE 406 taught by Professor Ralphs during the Fall '08 term at Lehigh University .

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Lecture2 - Introduction to Mathematical Programming IE406...

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