IOE510+Lecture+02+22+10+Mon

# IOE510+Lecture+02+22+10+Mon - IOE 510 Linear Programming I...

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1 IOE 510 Linear Programming I Monday February 22, 2010 Professor Amy Cohn

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2 Announcements Graded exams to be handed back at end of class Discussion of TSP homework problem
3 Re-cap from Last Time Working through steps of the simplex method Proof of optimality

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4 Revised Simplex Method
5 A Modified Approach – The Simplex Method 1) Start at a BFS 2) Check all non-basic variables for a corresponding improving direction (i.e. negative reduced cost) 3) If we don’t find any, stop – optimal 4) If we do find one, begin moving in that direction 5) If we can move forever, stop – the problem is unbounded 6) If we reach a new constraint, we have found a new BFS – return to step 2

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6 Constructing Direction Vectors Ad = A B d B + A N d N + A j d j = A B d B + A j = 0 Also, A B is invertible and thus d B = -A B -1 A j
7 Is d an Improving Direction? What is the cost of x + d p ? c(x + d p ) = cx + cd p cx + cd p < cx => cd p < 0 cd p = c p d p p + c B d p B + c N d p N = c p - c B A B -1 A p We call this the reduced cost of non-basic variable x p

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## This note was uploaded on 04/11/2010 for the course IOE 510 taught by Professor Staff during the Fall '08 term at University of Michigan.

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IOE510+Lecture+02+22+10+Mon - IOE 510 Linear Programming I...

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