Lecture 20110311

Lecture 20110311 - IMSE2008 Operational Research Techniques...

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IMSE2008 Operational Research Techniques Lecture 03/11 Simplex Method ensitivity Analysis Sensitivity Analysis Miao Song Dept of Industrial & Manufacturing Systems Engineering
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eview of Previous Lecture Review of Previous Lecture Formalizing Simplex Method Min Ratio Rule Degeneracy ultiple Optima Multiple Optima 3/11/2011 2
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genda Agenda Simplex Method Obtaining an initial bfs g The two-phase simplex method he big- method The big M method Sensitivity Analysis 3/11/2011 3
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hase 1 LP Phase 1 LP Is the Phase 1 LP feasible? Is the Phase 1 LP unbounded? oes there exist an optimal bfs for the Phase 1 LP? Does there exist an optimal bfs for the Phase 1 LP? If the original problem is feasible, what is the optimal bfs the Phase 1 LP? to the Phase 1 LP? If the original problem is infeasible, what is the optimal bfs to the Phase 1 LP? How to obtain an optimal bfs to the Phase 1 LP? min – 2x 1 –3x 2 –x 3 min w = y 1 + y 2 s.t .x 1 + x 2 + x 3 = 2 x 1 + 2x 2 + 3x 3 = 4 x x 0 s.t 1 + x 2 + x 3 + y 1 = 2 x 1 + 2x 2 + 3x 3 + y 2 = 4 x x 0 3/11/2011 4 x 1 , x 2 , x 3 x 1 , x 2 , x 3
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hase 1 Tableau min w = y 1 + y 2 s.t. x + x + x + y = 2 Phase 1 Tableau 1 2 3 y 1 x 1 + 2x 2 + 3x 3 + y 2 = 4 x 1 , x 2 , x 3 0 x 1 x 2 x 3 y 1 y 2 0 00011 2 11110 4 12301 x 1 x 2 x 3 y 1 y 2 -2 -1 -1 -1 0 1 R1 – R2 2 4 x 1 x 2 x 3 y 1 y 2 -6 -2 -3 -4 0 0 R1 – R3 3/11/2011 5 2 4
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hase 1 Tableau min w = y 1 + y 2 s.t. x + x + x + y = 2 Phase 1 Tableau 1 2 3 y 1 x 1 + 2x 2 + 3x 3 + y 2 = 4 x 1 , x 2 , x 3 0 x 1 x 2 x 3 y 1 y 2 -6 -2 -3 -4 0 0 2 11110 4 12301 x 1 x 2 x 3 y 1 y 2 -6 -2 -3 -4 0 0 R3 – R2 2 2 012 - 1 1 x 1 x 2 x 3 y 1 y 2 -2 0- 1 - 22 0 R1 + 2R2 3/11/2011 6 2 2 - 1 1
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hase 1 Tableau min w = y 1 + y 2 s.t. x + x + x + y = 2 Phase 1 Tableau 1 2 3 y 1 x 1 + 2x 2 + 3x 3 + y 2 = 4 x 1 , x 2 , x 3 0 x 1 x 2 x 3 y 1 y 2 -2 0- 1 - 22 0 2 11110 2 012 - 1 1 x 1 x 2 x 3 y 1 y 2 -2 1 - 0 R3/2 2 1 0 0.5 1 -0.5 0.5 x 1 x 2 x 3 y 1 y 2 -2 1 - 0 R2 – R3 3/11/2011 7 1 1 0.5 0 1.5 -0.5 1 0 0.5 1 -0.5 0.5
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hase 1 Tableau min w = y 1 + y 2 s.t. x + x + x + y = 2 Phase 1 Tableau 1 2 3 y 1 x 1 + 2x 2 + 3x 3 + y 2 = 4 x 1 , x 2 , x 3 0 x 1 x 2 x 3 y 1 y 2 -2 0- 1 - 22 0 1 1 0.5 0 1.5 -0.5 1 0 0.5 1 -0.5 0.5 x 1 x 2 x 3 y 1 y 2 0 00011
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Lecture 20110311 - IMSE2008 Operational Research Techniques...

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