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單純形表
鎖定
單純形表簡介
對線性規劃的標準型:
min
s.t.
記一個基礎可行解的基為 B ,A 其餘的列為 N ,
相應地,記
。有
當
全部大於等於零時,已經是最優基。對基 B ,以下的表稱為單純形表:
0 (基變量判別數) | (非基變量判別數) | |
(基礎可行解基變量值) | (基變量對於的單位矩陣) | (非基變量對應的約束矩陣) |
單純形表舉例
設有線性規劃問題如下:
min
s.t.
其對應的單純形表為:
max | 0 | 0 | 0 | 0 | 0 | -1 | -1 | RHS |
x₁ | x₂ | x₃ | x₄ | x₅ | x₆ | x₇ | ||
x₆ | 1 | 2 | 1 | -1 | 0 | 1 | 0 | 3 |
x₇ | 2 | -1 | 3 | 0 | -1 | 0 | 1 | 4 |
檢驗數σ𝚓 | 3 | 1 | 4 | -1 | -1 | 0 | 0 | |
x₆ | 1/3 | 7/3 | 0 | -1 | 1/3 | 1 | -1/3 | 5/3 |
x₃ | 2/3 | -1/3 | 1 | 0 | -1/3 | 0 | 1/3 | 4/3 |
檢驗數σ𝚓 | 1/3 | 7/3 | 0 | -1 | 1/3 | 0 | -4/3 | |
x₂ | 1/7 | 1 | 0 | -3/7 | 1/7 | 3/7 | -1/7 | 5/7 |
x₃ | 5/7 | 0 | 1 | -1/7 | -2/7 | 1/7 | 2/7 | 11/7 |
檢驗數σ𝚓 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | |
x₂ | 1/7 | 1 | 0 | -3/7 | 1/7 | 3/7 | -1/7 | 5/7 |
x₃ | 5/7 | 0 | 1 | -1/7 | -2/7 | 1/7 | 2/7 | 11/7 |
檢驗數σ𝚓 | 0 | 0 | 0 | 0 | 0 | -1 | -1 |