Revsimp - 4 y = c B A-1 B =(6-2 c =(0-5-34-19-7-9-6 2 pivot x 10 in A 10 = A-1 B A 10 =-1 1 pivot x 9 out B =(2 10 1 A-1 B = 0 1 0-1 1 1 1 0 0 b =

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ORIE 330/5300 Optimization Fall 2011 Professor Bland Example of the Revised Simplex Method (with the explicit basis inverse) Reference: BHM Appendix B. Note that where we use the notation A B ,A B - 1 BHM use B,B - 1 . Maximize 4 x 1 +2 x 2 + x 3 - 2 x 4 + x 5 - x 6 + x 7 s.t. x 1 + x 3 +5 x 4 +3 x 5 +2 x 6 +2 x 7 + x 8 = 1 x 2 + x 3 +4 x 4 +4 x 5 - x 6 + x 7 + x 9 = 1 x 1 - x 2 - x 4 - x 5 +3 x 6 + x 7 + x 10 = 0 x 1 ,...,x 10 0 Initial basis B = (8 , 9 , 10) A - 1 B = I 3 b = 1 1 0 c B = ( c 8 ,c 9 ,c 10 ) = (0 , 0 , 0) y = c B A - 1 B = (0 , 0 , 0) , c = c pivot x 1 in A 1 = A - 1 B A 1 = A 1 = 1 0 1 pivot x 10 out B = (8 , 9 , 1); A - 1 B = 1 0 - 1 0 1 0 0 0 1 , b = 1 1 0 c B = (0 , 0 , 4) y = c B A - 1 B = (0 , 0 , 4) c = c - yA = (0 , 6 , 1 , 2 , 5 , - 13 , - 3 , 0 , 0 , - 4) pivot x 2 in A 2 = A - 1 B A 2 = 1 1 - 1 pivot x 8 or x 9 out
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B = (2 , 9 , 1) A - 1 B = 1 0 - 1 - 1 1 1 1 0 0 b = 1 0 1 c B = (2 , 0 ,
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Unformatted text preview: 4) y = c B A-1 B = (6 , ,-2) c = (0 , ,-5 ,-34 ,-19 ,-7 ,-9 ,-6 , , +2) pivot x 10 in A 10 = A-1 B A 10 =-1 1 pivot x 9 out B = (2 , 10 , 1) A-1 B = 0 1 0-1 1 1 1 0 0 b = 1 1 c B = (2 , , 4) y = c B A-1 B = (4 , 2 , 0) c = (0 , ,-5 ,-30 ,-19 ,-7 ,-9 ,-4 ,-2 , 0). optimal...
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Revsimp - 4 y = c B A-1 B =(6-2 c =(0-5-34-19-7-9-6 2 pivot x 10 in A 10 = A-1 B A 10 =-1 1 pivot x 9 out B =(2 10 1 A-1 B = 0 1 0-1 1 1 1 0 0 b =

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