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lecture11 - Soft Constraints Goal Programming Flow Models...

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Soft Constraints Goal Programming Flow Models IE426: Optimization Models and Applications: Lecture 11 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University October 5, 2006 Jeff Linderoth IE426:Lecture 11 Soft Constraints Goal Programming Flow Models Review Got MILP? Mixed Integer Linear Program minimize c T x subject to Ax b x 0 x j Z j I N. Jeff Linderoth IE426:Lecture 11 Soft Constraints Goal Programming Flow Models Review IP Stuff Many people would just call this “integer programming” (IP). (Assumed linear unless expressly stated otherwise) Mixed integer programming Only some of the variables have integer restrictions ( I N ) Pure integer programming ( I = N ) All variables have integer restrictions 0-1 integer programming All integer restricted variables also have bounds of 0 and 1 . B n def = The set of all n -dimensional (0,1) (binary) vectors. (Or maybe { 0 , 1 } n ) Jeff Linderoth IE426:Lecture 11 Soft Constraints Goal Programming Flow Models Review Why Integer Programming? 1 Indivisible quantities If x represents the number of airplanes to build Best to use IP if x will be small. It is not worth the extra burden of IP if x is the number of chickens in Arkansas. 2 Decision variable x ∈ { 0 , 1 } represents a “yes” or “no” decision. We can impose logical connections between these decisions (often using linear constraints). We’ll do lots of examples of this Jeff Linderoth IE426:Lecture 11
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Soft Constraints Goal Programming Flow Models SmallVille Multiple Objectives Weighted Goal Programming Hierarchical Goal Programming How We Solve Integer Programs IP models can be very much more difficult to solve than LP models. I’m not kidding IP models can be very much more difficult to solve than LP mod- els. It is important that you have a handle on... 1 How to build a problem that is likely to be solved – Proper formulation is important!
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