LP Sensitivity Analysis Master 1

LP Sensitivity Analysis Master 1 - 1 Linear Programming...

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Unformatted text preview: 1 Linear Programming Sensitivity Analysis 2 Reminders § Read Chapter 4 § No class on Monday, September 5, because of Labor Day. § Help session Tuesday, September 6, from 6 to 8 pm. § Homework § Due in Julie’s Office (519 Krannert) by 2:30 pm Wednesday September 7th. § Be sure to include the name of your partner on the homework and the section you are both in. § Quiz Monday September 12. § Closed book, closed notes § May use 8.5x11 double sided formula sheet § Calculator and ruler allowed § Covers material on HW 1. 3 Sensitivity Analysis: Post-optimality Analysis § Many of the input parameters are only estimates and need to be refined if the model output is “sensitive” to small changes in these parameters. § Possible future changes in a dynamic problem environment need to be easily analyzed without resolving the model. § When certain parameters in the model represent managerial policy decisions, post-optimality analysis provides guidance to management about the impact of altering these policies. 4 Sensitivity Analysis § Sensitivity analysis is to determine how the optimal solution and optimal objective value are affected by changes in the model input data (parameters). § We investigate some possible change of • objective function coefficient • right-hand side (RHS) of constraint to see how it influences the optimal solution and optimal objective value. 5 Changes of Objective Function Coefficients § If an objective function coefficient changes, as long as the changed coefficient is not too far from the original coefficient, the optimal solution is still optimal for the changed model. § In other words, as long as the changed coefficient is located in some range (interval) that contains the original coefficient, the optimal solution remains optimal for the new model. § For each objective function coefficient, the range of numbers for the coefficient over which the optimal solution will remain optimal is called the range of optimality . 6 Example 1: Catch-Big Problem § LP model: Max 5 x1 + 7 x2 s.t. x1 < 6 2x1 + 3x2 < 19 x1 + x2 < 8 x1, x2 > § Optimal solution: x1 = 5 , x2 = 3 . § Optimal objective value: 46 7 Example 1: Graphical Solution x2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 2x1 + 3x2 < 19 x1 x1 + x2 < 8 objective function line x1 < 6 optimal x1 = 5, x2 = 3 8 Example 1: Effect of Changing Objective Coefficients § Changing slope of objective function 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x1 Feasible Region 1 2 3 x2 Changing a coefficient in the objective function changes the slope of the objective function line....
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LP Sensitivity Analysis Master 1 - 1 Linear Programming...

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