Midterm2011review

Midterm2011review - MS&E 211 Midterm Review 2011-2012 L&Y...

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MS&E 211 Midterm Review 2011-2012 L&Y: Chapters 1-4, Chapter 6.1-6.4, 6.8
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MS&E 211 LP Models Know how to recognize an LP in verbose or matrix form; standard or otherwise; max or min Know how to set up an LP problem Understand how to make various conversions between different types of LPs (max/min; < , > , =; > , free; |abs. value|; etc.)
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MS&E 211 LP Modeling Modeling Process Understand the problem Collect information and data Identify and define the decision variables formulate the objective function Isolate and formulate the constraints
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World Cup Portfolio Management Portfolio Management for World Cup Assets Five securities in a market for open trading at fixed prices and pay- offs, share limit on investment and short is not allowed We d like to decide how many shares to purchase to maximize the pay-off when the game is realized. Security Price Share Limit q Argentina Brazil Italy Germany France 1 $0.75 10 $1 $1 $1 2 $0.35 5 $1 3 $0.40 10 $1 $1 $1 4 $0.95 10 $1 $1 $1 $1 5 $0.75 5 $1 $1
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Portfolio Optimization Model free : , 0 , 5 , 10 , 10 , 5 , 10 0 0 0 0 0 . . 75 . 95 . 4 . 35 . 75 . 5 4 3 2 1 3 5 4 2 4 3 1 5 4 1 4 3 1 5 4 3 2 1 s x x x x x x x s x x x s x x x s x x x s x x x s t s x x x x x s Max j x: shares purchased for each security; s: worst-case return
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Portfolio Optimization Model N j x N j q x S i x a s t s x s Max j j j j j ij j j j 0 0 . .
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The Geometry of LPs Understand the geometrical interpretation of LPs and associated intuition Plot a feasible region in 2D Plot the optimal iso-profit lines Relate how the Simplex Method moves from corner point to adjacent corner point in improving direction Understand the geographical interpretation of the various LP terms – (e.g. active constraints, basic variables, multiple optima, infeasibility, unbounded-ness,, etc.)
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MS&E 211 Theory of Linear Programming An LP problem falls in one of three cases: Problem is infeasible: Feasible region is empty. Problem is unbounded: Feasible region is unbounded towards the optimizing direction. Problem is feasible and bounded: then there exists an optimal point; an optimal point is on the boundary of the feasible region; and there is always at least one optimal corner point (if the feasible region has a corner point). When the problem is feasible and bounded, There may be a unique optimal point or multiple optimizers (alternative optimizers, adjacent or not). If a corner point is not “worse” than all its neighbor corners, then it is optimal.
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Algebraic Interpretation of LPs Understand why we emphasize basic solutions and basic feasible solutions (corner points). Understand the equivalent (canonical) form of the LP and where it came from Understand what the different elements of this form mean: reduced cost coefficients, shadow prices, canonical constraint matrix, RHS Know when to terminate Know its relation with dual
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The Canonical Form of the LP
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This note was uploaded on 01/16/2012 for the course MS&E 211 at Stanford.

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Midterm2011review - MS&E 211 Midterm Review 2011-2012 L&Y...

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