lecture17 - Quadratic Assignment Examples Financial...

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Quadratic Assignment Examples Financial Modeling IE426: Optimization Models and Applications: Lecture 17 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University October 31, 2006 Jeff Linderoth IE426:Lecture 17 Quadratic Assignment Examples Financial Modeling Review 1 Questions on the Homework? 2 Questions on Modeling using the Bag of Trix? 3 Let’s do some examples... 4 Class over at 5:30 today. Jeff Linderoth IE426:Lecture 17 Quadratic Assignment Examples Financial Modeling Background Model The Trick Let’s Make Some Moola Sets/Parameters N : “Universe” of stocks that we might be able to buy. B : Budget α i , i N : Expected return of stock i b i , i N : Benchmark holding of stock i h i : Initial holding of stock i Decision Variables x i : Final holding of stock i Jeff Linderoth IE426:Lecture 17 Quadratic Assignment Examples Financial Modeling Background Model The Trick Things We Will Model 1 Turnover 2 Transaction costs 3 Benchmark Tracking 4 Hold only k stocks 5 Minimum transactions 6 Industry/Sector constraints 7 Exotic “Business Rules” Jeff Linderoth IE426:Lecture 17
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Quadratic Assignment Examples Financial Modeling Nonconvex Region YAE Nonconvex regions Suppose I wanted to optimize a function such that I was in exactly one of these three regions? Region I x 2 3 x 1 + x 2 4 Region II - x 1 + x 2 0 3 x 1 - x 2 8 Region III x 2 1 x 1 5 Jeff Linderoth IE426:Lecture 17 Quadratic Assignment Examples Financial Modeling Nonconvex Region YAE How To Do It This means that it would have to be in region I, or in region II, or in region III δ I = 1 x 2 3 AND x 1 + x 2 4 δ I = 1 x 2 3 , δ = 1 x 1 + x 2 4 δ II = 1 ⇒ - x 1 + x 2 0 AND 3 x 1 - x 2 8 δ III = 1 x 2 1 AND x 1 5 δ I + δ II + δ III 1 Jeff Linderoth IE426:Lecture 17 Quadratic Assignment Examples
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