Compléments sur l`algorithme du simplexe

M
max
BX=b
X≥0
z=q·X,
b≥0−1
B
eq·Y=MPm
i=1 yieq=M(1, . . . , 1) ∈M1,m(R)
Y=t(y1, . . . , ym)≥0yii= 1, . . . , m m ≥0M
yi
max
BX+Y=b
X,Y ≥0ez=q·X−M
m
X
i=1
yi,
e
Be B=B
Idm
ez=q·X−MPm
i=1 yiM
Y6= 0 Y= 0 X=ˆ Xˆ X
Y
X
X= 0 Y=b≥0
Y Y = 0
M
z=−2x1+ 5x2+ 3x3−4x4
s.l.c.
8
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:
4x1+ 2x2−x3≤ −5
x1+ 4x2+x4= 7
8x1−7x2≥10
x1, x2, x3, x4≥0
y

X(b, Ik)θmax = 0
X(b, Ik+1) = X(b, Ik)
Ik+i=Ikk i
z= 2x1+ 3x2−x3−12x4
s.l.c.
8
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:
−2x1−9x2+x3+ 9x4+x5= 0
1
3x1+x2−1 3x3−2x4+x6= 0
x1, x2, x3, x4, x5, x6≥0
.
I0={5,6}I1={2,5}
I2={1,2}I3={1,4}I4={3,4}I5={3,6}I6={5,6}=I0
z= 100x1+ 10x2+x3
s.l.c.
8
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:
x1≤1
20x1+x2≤100
200x1+ 20x2+x3≤10000
x1, x2, x3≥0
.
exp N N
n L
N N
80
exp N
N6
N3,5