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lect15 - happens at the corners of this function 3 Example...

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ISE 536–Fall03: Linear Programming and Extensions October 27, 2003 Lecture 15: Sensitivity Analysis, Continued Lecturer: Fernando Ord´ o˜nez 1 Global Dependence on b Let P ( b ) = { x | Ax = b, x 0 } , define the set S = { b | P ( b ) = ∅} , and for every b S define the function F ( b ) = min c t x s . t . Ax = b x 0 Proposition 1. Function F ( b ) is a convex function proof: First that S is convex To show that F ( b ) is convex, consider the dual. 2 Global Dependence on c Consider the function G ( c ) = min c t x s . t . Ax = b x 0 1

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similar to what is done for the dependence on b , we consider all the extreme points of the feasible solution: x 1 , . . . , x M , then G ( c ) = min { c t x 1 , . . . , c t x M } Therefore it is a piecewise linear concave function.
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Unformatted text preview: happens at the corners of this function? 3 Example Suppose that the ﬁnishing hours increase by 6 (hiring overtime) in the furniture example. What is the eﬀect on the proﬁt? What is the allowable increase? How does g ( θ ) look like outside the range [-4 , 4]. .. formulate the dual! Therefore 320 = g (4) ≤ g (6) ≤ g (0) + 6 * 10 = 340. How about if the proﬁt from tables increases from \$30 to \$40? (allowable increase is 5). 2...
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lect15 - happens at the corners of this function 3 Example...

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