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Lecture22 - Introduction to Mathematical Programming IE406...

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Introduction to Mathematical Programming IE406 Lecture 22 Dr. Ted Ralphs
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IE406 Lecture 22 1 Reading for This Lecture Bertsimas Sections 10.2, 10.3, 11.1, 11.2
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IE406 Lecture 22 2 Solving Linear Programs in Practice The practice of linear and integer programming is as much art as science . There are many tradeoffs and considerations in developing and solving a model for a complex system. Developing a Model For large, complex systems, there may be a large number of possible models. Real systems have many, many constraints. Timing considerations will determine how many constraints can realistically be modeled. It is important to limit the number of constraints and variables as much as possible.
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IE406 Lecture 22 3 Developing a Set of Variables It is easy to develop models with far too many variables . The variables should represent independent decisions that need to be made. If the value of a variable can be inferred from the values of other variables, it can sometimes be eliminated. Exception : complex cost structures. Examples Inventory Models Fixed Charge Network Flow Models Additional variables can mean additional linking constraints . If the number of variables in the model is still large, consider column generation or try alternative pricing rules.
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IE406 Lecture 22 4 Developing a Set of Constraints The number of constraints determines the size of the basis , which in turn affects the efficiency of the simplex algorithm (and others).
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