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PowerPointCh03 - Project Management Huntingdon College...

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Project Management Huntingdon College School of Business
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Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of Solution Introduction to Sensitivity Analysis Graphical Sensitivity Analysis Sensitivity Analysis: Computer Solution Simultaneous Changes
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In the previous chapter we discussed: objective function value values of the decision variables reduced costs slack/surplus In this chapter we will discuss: changes in the coefficients of the objective function changes in the right-hand side value of a constraint Introduction to Sensitivity Analysis
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Introduction to Sensitivity Analysis Sensitivity analysis (or post-optimality analysis) is used to determine how the optimal solution is affected by changes, within specified ranges, in: the objective function coefficients the right-hand side (RHS) values Sensitivity analysis is important to a manager who must operate in a dynamic environment with imprecise estimates of the coefficients. Sensitivity analysis allows a manager to ask certain what-if questions about the problem.
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Example 1 LP Formulation Max     5 Max     5 x x 1  + 7  + 7 x x 2 s.t.           s.t.           x x 1                           < <    6    6                             2 2 x x 1  + 3  + 3 x x 2       < <   19   19                                 x x 1  +     +    x x 2       < <    8    8                                         x x 1 x x 2       > >   0   0
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Example 1 Graphical Solution 2 2 x x 1  + 3  + 3 x x 2       < <  19   19        x x 2 x x 1 x x 1  +   +  x x 2       < <   8   8 Max  5 x 1  +  7x 2 x x 1     < <   6   6 Optimal Solution: Optimal Solution:             x x 1  = 5,    = 5,   x x 2  = 3  = 3 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 1     1         2     2         3     3         4     4         5     5         6     6         7     7         8     8         9    9        10 10
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Objective Function Coefficients Let us consider how changes in the objective function coefficients might affect the optimal solution. The range of optimality for each coefficient provides the range of values over which the current solution will remain optimal. Managers should focus on those objective coefficients that have a narrow range of optimality and coefficients near the endpoints of the range.
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Example 1 Changing Slope of Objective Function x x 1 Feasible Feasible Region Region 1 2 3 4 5       x x 2 Coincides with Coincides with x x 1  +   +  x x 2       < <   8   8 constraint line constraint line 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 1     1         2     2         3     3         4     4    
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