6417c05 - THE REVISED SIMPLEX ALGORITHM CONTENTS Linear...

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1 THE REVISED SIMPLEX ALGORITHM CONTENTS Linear Program in Matrix Notation Dictionary in Matrix Notation Simplex Algorithm in Matrix Notation
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2 Matrix Notation Maximize j=1,n c j x j subject to j=1,n a ij x j b i for all i = 1, 2, …, m x j 0 for all j = 1, 2, … , n Add the slack variables: x n+i = b i - j=1,n a ij x j for all i = 1, 2, …, m Problem in the matrix notation: Maximize cx subject to Ax = b x 0
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3 Matrix Notation Maximize cx subject to Ax = b x 0 where a 11 a 12 ….. a 1n 1 a 21 a 22 ….. a 2n 1 A = : : : : : : : : a m1 a m2 a mn 1 b 1 b 2 b = : : b m x 1 x 2 : : x = x n X n+1 : : X n+m c 1 c 2 : : c = c n 0 : : 0
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4 The Primal Simplex Algorithm B : The set of indices corresponding to basic variables N : The set of indices corresponding to nonbasic variables x B x = x N The linear program in the matrix form : Minimize ξ = c B x B + c N x N subject to Bx B + N x N = b x B 0, x N 0 c B c = c N A = B N
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5 The Primal Simplex Algorithm (contd.) Constraint Matrix : Bx B + N x N = b or Bx B = b - Nx N Let x B define a dictionary, then
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This note was uploaded on 08/27/2011 for the course ESI 6417 taught by Professor Siriphonglawphongpanich during the Spring '07 term at University of Florida.

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6417c05 - THE REVISED SIMPLEX ALGORITHM CONTENTS Linear...

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