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# 331-07 - Chapter 4 Linear Programming Sensitivity Analysis...

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Chapter 4: Linear Programming Sensitivity Analysis

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What if there is uncertainty about one or more data values in an LP model? Sensitivity analysis allows us to determine how “sensitive” the optimal solution is to changes in data values. Then, we will have more confidence in implementing the recommended solution.
Sensitivity Analysis Includes analyzing the effect of changes in: 1. An Objective Function Coefficient (OFC) 2. A Right Hand Side (RHS) value of a constraint Unless stated otherwise, we consider one change in  Unless stated otherwise, we consider one change in  data at a time data at a time

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Graphical Sensitivity Analysis Example: Flair Furniture Problem Max 7T + 5C (profit) subject to the constraints: 3T + 4C < 2400 (carpentry hours) 2T + 1C < 1000 (painting hours) C < 450 (maximum # chairs) T > 100 (minimum # tables) T, C > 0 (nonnegativity)
Objective Function Coefficient (OFC) Changes What if the profit contribution for tables changes from \$7 to \$8 per table? 8 Max 7 T + 5 C (profit) Clearly profit goes up, but would we want to make more tables and less chairs? (i.e., does the optimal solution change?) X

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0 100 200 300 400 500 T C 500 400 300 200 100 0 Original optimal Solution (T=320, C=360) - still optimal Feasible Region Original Objective Function 7T + 5 C = \$4040 Revised Objective Function 8T + 5 C = \$4360 So, the solution remains the same, but profit increases
C 1000 600 450 0 Feasible Region 0 100 500 800 T What if the OFC became higher? Or lower? 11T + 5C = \$5500 Optimal Solution (T=500, C=0) 3T + 5C = \$2850 Optimal Solution (T=200, C=450) Both have new optimal corner points

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Characteristics of OFC Changes There is no effect on the feasible region The slope of the profit line changes If the slope changes enough, a different corner point will become optimal There is a range (i.e. wiggle room ) for each OFC where the current optimal corner point remains optimal, and the new objective function value can be calculated. Excel Solver calculates the OFC range automatically in the “Sensitivity Report” page.
Right Hand Side (RHS) Changes What if the number of painting hours available changed from 1000 to 1300?

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