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**Unformatted text preview: **Project Management Huntingdon College School of Business Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of Solution • Introduction to Sensitivity Analysis • Graphical Sensitivity Analysis • Sensitivity Analysis: Computer Solution • Simultaneous Changes • 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 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. 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 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 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. 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...

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