Set_3_revised_simplex

# Set_3_revised_simplex - Dr. Maddah ENMG 500 Engineering...

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1 ( ) 1 11 12 1 1 2 21 22 2 2 1 2 3 1 2 max s.t. where c , , , , , , , n n n n m m mn m Z a a a b a a a b c c c A a a a b = = = = = = cx Ax b x 0 x x c x b x K L K M K K K K M K max s.t. B B N N B N Z = + + = c x c x Bx Nx b x 0 Dr. Maddah ENMG 500 Engineering Management I 11/03/09 Simplex method in matrix form (revised simplex method) h A LP with n decision variables and m constraints can be written as h Alternatively, the LP can be written as where the subscripts “B” and “N” denote basic and nonbasic variables respectively. h For example, 1 2 1 2 1 2 1 2 1 1 2 1 2 2 1 2 max 2 3 max 2 3 s.t. 50 s.t. 50 2 30 2 30 , 0 Z x x Z x x x x x x S x x x x S x x = + = + + + + = + + + = 1 2 1 2 , , , 0 x x S S (1)

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2 1 1 1 1 max ( ) s.t. B B N N B N Z B = + = c B b c B N c x x B Nx b x 0 Then, at O(0,0), 1 1 2 2 50 , , (2,3), (0,0), 30 1 0 1 1 , 0 1 2 1 B N N B S x S x N = = = = = = = x x c c b B h Solving for x B in (1) gives ( ) 1 1 1 B N B N N = = = Bx b Nx x B b Nx B b B Nx h The LP can then be rewritten as h Recall that each iteration of the simplex method allows a
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## This note was uploaded on 12/23/2010 for the course ENMG 500 taught by Professor Drbacelmaddah during the Fall '09 term at American University of Beirut.

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Set_3_revised_simplex - Dr. Maddah ENMG 500 Engineering...

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