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Review211midterm2007

Review211midterm2007 - MS&E 211 Midterm Review 2007-2008...

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MS&E 211 Yinyu Ye MS&E 211 Midterm Review 2007-2008
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MS&E 211 Yinyu Ye Midterm Review 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 Understand how to make various conversions between different types of LPs (max/min; < , > , =; > , free; |abs. value|; etc.)
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MS&E 211 Yinyu Ye Midterm Review 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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MS&E 211 Yinyu Ye Midterm Review Max-Flow on a Capacitated Network ( Thousands of Gallons Per Hour ) 2 4 3 5 1 6 6 0 4 0 0 3 0 1 0 6 0 0 0 0 2 2 6 4
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MS&E 211 Yinyu Ye 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 selling 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 π 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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MS&E 211 Yinyu Ye 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 - - - - - - - - - - - - - - - - - -
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MS&E 211 Yinyu Ye 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 2200 2200 2200 - - 0 0 . . π
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MS&E 211 Yinyu Ye 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 Yinyu Ye Midterm Review 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 optima (alternative optima). If a corner point is not “worse” than all its neighbor corners, then it is optimal.
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MS&E 211 Yinyu Ye Algebraic Interpretation of LPs Understand why we emphasize basic solutions and basic feasible solutions (corner points).
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