Zahra_Mohaghegh_March 4

Zahra_Mohaghegh_March 4 - Engineering Management Systems...

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1 Engineering Management & Systems Engineering The George Washington University EMSE 102 EMSE 102 - - 202 202 Survey of Operations Research Methods Survey of Operations Research Methods Zahra Mohaghegh [email protected] Post-Doctoral Research Associate Center For Risk and Reliability University of Maryland March 4, 2008

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2 Engineering Management & Systems Engineering The George Washington University Sensitivity Analysis Sensitivity Analysis (Cont.) (Cont.)
3 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Graphical Sensitivity Analysis ± Shadow Prices ± Some Important formula ± Sensitivity Analysis ± Duality ± LINDO examples

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4 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Graphical Sensitivity Analysis ± Shadow Prices ± Some Important formula ± Sensitivity Analysis ± Duality ± LINDO examples
5 Engineering Management & Systems Engineering The George Washington University A Graphical Introduction to Sensitivity A Graphical Introduction to Sensitivity Analysis Analysis ± Sensitivity analysis is concerned with how changes in an LP’s parameters affect the optimal solution. ± The optimal solution to the Giapetto problem was z = 180, x 1 = 20, x 2 = 60 (Point B in the figure to the right) and it has x 1 , x 2 , and s 3 (the slack variable for the demand constraint) as basic variables. ± How would changes in the problem’s objective function coefficients or the constraint’s right-hand sides change this optimal solution?

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6 Engineering Management & Systems Engineering The George Washington University ± If the isoprofit line is flatter than the carpentry constraint, Point A(0,80) is optimal. ± Point B(20,60) is optimal if the isoprofit line is steeper than the carpentry constraint but flatter than the finishing constraint. ± Point C(40,20) is optimal if the slope of the isoprofit line is steeper than the slope of the finishing constraint. X1 X2 20 40 50 60 80 2 0 4 6 8 1 finishing constraint Slope = -2 carpentry constraint Slope = -1 demand constraint Feasible Region A D Isoprofit line z = 120 Slope = -3/2 C B Giapetto Problem
7 Engineering Management & Systems Engineering The George Washington University ± Changing the objective function coefficient : ± The current bases remain optimal as long as the current optimal solution is the last point in the feasible region to make contact with isoprofit lines , as we move in the direction of increasing z (for a max problem) ± If the current basis remains optimal , then the values of the decision variables remain unchanged, but the optimal z- value may change. X1 X2 20 40 50 60 80 2 0 4 6 8 1 finishing constraint Slope = -2 carpentry constraint Slope = -1 demand constraint Feasible Region A D Isoprofit line z = 120 Slope = -3/2 C B Giapetto Problem

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8 Engineering Management & Systems Engineering The George Washington University X1 X2 20 40 50 60 80 2 0 4 6 8 1 finishing constraint, b1 = 100 carpentry constraint demand constraint Feasible Region A D Isoprofit line z = 120 C B finishing constraint, b1 = 120 finishing constraint, b1 = 80 ±
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Zahra_Mohaghegh_March 4 - Engineering Management Systems...

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