LP Sensitivity Analysis

# LP Sensitivity Analysis - Linear Programming Sensitivity...

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1 Linear Programming Sensitivity Analysis

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2 Reminders § Read Chapter 4 § Help Session Tuesday, 6 - 8 p.m. Rawls 2070 § Homework § Due in Marta’s Office (507 Krannert) by 3:00 pm Wednesday. § You may turn it in to me at the end of class if you desire. § Be sure to include the name of your partner on the homework and the section you are both in. § Quiz next Monday § Closed book, closed notes § May use 8.5x11 double sided formula sheet § Calculator and ruler allowed § Covers material on HW 1.
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4 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.
5 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.

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6 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 .
7 Example 1: Catch-Big Problem § LP model: Max 5 x1 + 7 x2 s.t. x1 < 6 2x1 + 3x2 < 19 x1 + x2 < 8 x1, x2 > 0 § Optimal solution: x1 = 5 , x2 = 3 . § Optimal objective value: 46

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8 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 x 1 x1 + x2 < 8 objective function line x1 < 6 optimal x1 = 5, x2 = 3
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 x 1 Feasible Region 1 2 3 x 2 Changing a coefficient in the objective function changes the slope of the objective function line. The slope of a line

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## This note was uploaded on 01/31/2011 for the course MGMT 306 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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LP Sensitivity Analysis - Linear Programming Sensitivity...

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