lecture14 - PPP General Modeling Tricks A Final PPP Example...

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Unformatted text preview: PPP General Modeling Tricks A Final PPP Example IE426: Optimization Models and Applications: Lecture 14 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University October 19, 2006 Jeff Linderoth IE426:Lecture 14 PPP General Modeling Tricks A Final PPP Example Background Variable Upper Bounds Variable Lower Bounds Homework #3 Handed Out (and Posted) It is long! . Start it Now! You have 12 days to complete. It is due 10/31. It will be counted double the first two homeworks. Jeff Linderoth IE426:Lecture 14 PPP General Modeling Tricks A Final PPP Example Background Variable Upper Bounds Variable Lower Bounds The Slide of Tricks = 1 j N a j x j b j N a j x j + M M + b j N a j x j b = 1 j N a j x j- ( m- ) b + = 1 j N a j x j b j N a j x j + m m + b j N a j x j b = 1 j N a j x j- ( M + ) b- Jeff Linderoth IE426:Lecture 14 PPP General Modeling Tricks A Final PPP Example Background Variable Upper Bounds Variable Lower Bounds More Tricks The first tricks we learned (for variable upper bound and variable lower bound) can be derived from these general tricks. x > = 1 x M = 1 x m x m Jeff Linderoth IE426:Lecture 14 PPP General Modeling Tricks A Final PPP Example Background Variable Upper Bounds Variable Lower Bounds Cool Things You Can Now Do Either this or this must hold Create indicators 1 , 2 , then 1 + 2 1 At least one constraint should hold i M i 1 k out of n constraints must hold i M i k If x , then y y x Jeff Linderoth IE426:Lecture 14 PPP General Modeling Tricks A Final PPP Example Background Variable Upper Bounds Variable Lower Bounds Modeling Nonlinear integer 0-1 variables One final quick trick you may find useful. Its not really on the slide of Trix....
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This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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lecture14 - PPP General Modeling Tricks A Final PPP Example...

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