Lecture1

Lecture1 - Integer Programming IE418 Lecture 1 Dr. Ted...

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Integer Programming IE418 Lecture 1 Dr. Ted Ralphs
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IE418 Lecture 1 1 Reading for This Lecture Wolsey, Chapter 1 N&W Sections I.1.1-I.1.4
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IE418 Lecture 1 2 What is a model? mod · el : A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics . –American Heritage Dictionary of the English Language Two types of models Concrete Abstract Mathematical models Are abstract models Describe the mathematical relationships among elements in a system.
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IE418 Lecture 1 3 Systems Modeling In ISE, we are mainly concerned with modeling systems . What is a system? sys · tem : A functionally related group of elements, especially: The human body regarded as a functional physiological unit. An organism as a whole, especially with regard to its vital processes or functions. A group of physiologically or anatomically complementary organs or parts: the nervous system; the skeletal system. A group of interacting mechanical or electrical components. A network of structures and channels, as for communication, travel, or distribution. A network of related computer software, hardware, and data transmission devices.
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IE418 Lecture 1 4 Why do we model systems? The exercise of building a model can provide insight. It’s possible to do things with models that we can’t do with “the real thing.” Analyzing models can help us decide on a course of action.
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IE418 Lecture 1 5 Examples of Standard Model Types Simulation Models Probability Models Economic Models Biological Models Mathematical Programming Models
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IE418 Lecture 1 6 Mathematical Programming Models What does mathematical programming mean? Programming here means “planning.” Literally, these are “mathematical models for planning.” Also called optimization models . The essential element is the existence of an objective . Some categories of mathematical programs (see the NEOS Guide). Linear Non-linear Integer Stochastic
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7 Forming a Math Programming Model Decision variables Constraints Objective Function Parameters and Data The general form of a math programming model is: min or max f ( x 1 , . . . , x n ) s.t. g
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Lecture1 - Integer Programming IE418 Lecture 1 Dr. Ted...

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