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picture1_Slides Simplex Dual


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File: Slides Simplex Dual
simplex method and reduced costs duality and marginal costs frederic giroire fg simplex 1 17 simplex method and reduced costs strong duality theorem fg simplex 2 17 simplex reminder start ...

icon picture PDF Filetype PDF | Posted on 29 Jan 2023 | 2 years ago
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         Simplex Method and Reduced Costs,
                Duality and Marginal Costs
                             Frédéric Giroire
  FG                                                         Simplex 1/17
      ** Simplex Method and Reduced Costs, Strong Duality Theorem **
  FG                                                              Simplex 2/17
                               Simplex - Reminder
       Start with a problem written under the standard form.
                   Maximize     5x    + 4x       + 3x
                                   1         2          3
                   Subject to :
                                2x    + 3x       + x ≤ 5
                                   1         2          3
                                4x    + x + 2x ≤ 11
                                   1         2          3
                                3x    + 4x       + 2x      ≤ 8
                                   1         2          3
                                                    x1,x2,x3     ≥ 0.
  FG                                                                           Simplex 3/17
                               Simplex - Reminder
       Write the Dictionary:
                       x4  = 5 − 2x1 − 3x2 −                     x3
                       x5  = 11 − 4x1 −               x2  − 2x3
                       x6  = 8 − 3x1 − 4x2 − 2x3
                        z  =              5x1   + 4x2 + 3x3.
       Basic variables: x4,x5,x6, variables on the left.
       Non-basic variable: x ,x ,x , variables on the right.
                              1  2   3
       Adictionary is feasible if a feasible solution is obtained by setting all
       non-basic variables to 0.
  FG                                                                           Simplex 4/17
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...Simplex method and reduced costs duality marginal frederic giroire fg strong theorem reminder start with a problem written under the standard form maximize x subject to write dictionary z basic variables on left non variable right adictionary is feasible if solution obtained by setting all...

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