Lecture09 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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Unformatted text preview: IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 9 Date: 21 October 2007 1 2 [A|b] Tableau form of Simplex • Consider 3 . . m i n     x b A x x c z t s z T . . m i n   x b A x t s x c T Tableau form of Simplex 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . z 1 1 1 1 1 1 1 1 1 m m n m j m i i n i j i n j n j n j b a a a b a a a b a a a c c c R H S x x x    Tableau form of Simplex Given B, the same tableau can be partitioned as: 5 1 x z b A c R H S  1 R H S b N B c c x x z N B N B   Tableau form of Simplex • Now consider 6 , . . m i n       N B N B N T N B T B x x b N x B x x c x c z t s z b B N x B x B N B 1 1 ) (     b B N x B Ix N B 1 1     N B N x B b B x 1 1     Tableau form of Simplex Now we have: 7 , . . m i n 1 1         N B N B N T N B T B x x b B N x B Ix x c x c z t s z N B N x B b B x 1 1     ) ( 1 1       N T N N T B x c N x B b B c z b B c x c N B c z T B N T N T B 1 1 ) (      Tableau form of Simplex Thus Is equivalent to 8 1 R H S b N B-c-c x x z N B N B 1 R H S 1 1 1 1 b B N B I x b B c N B c c x x z B T B T B N N B       N c  N r Tableau form of Simplex m mp m B r rp r B p B T B p p T B p b u x b u x b u x b B c c u c RHS x z ... ... . ... . ... . ... ... . ... . ... . ... ... ... 1 ... ... ) ( ) ( 1 1 ) 1 ( 1   9 Consider where b B b 1   p p A B u 1   enters Pivot column Pivot row leaves Tableau form of Simplex m mp m B r rp r B p B T B p p T B p b u x...
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This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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Lecture09 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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