
Dantzig-Wolfe Decomposition 197
a =
q
1
2
e
1
=
L
1
v
1
2
e
1
=
1 1
152.89068985
80.44534492
1
0
=
233.33603477
1
0
.
Step 4: Bd = −a and so d =
−8.37842506e − 14
−1
0
.
Step 5: α =min
n
−
4.30885443e−15
−8.37842506e−14
, −
1
−1
o
= 0.05142798 and so λ
1
2
= α.
Step 6: x
B
=
µ
1
1
λ
1
1
λ
2
1
=
4.30885443e − 15
1
1
+(0.05142798)
−8.37842506e − 14
−1
0
=
0
0.94857202
1
so µ
1
1
leaves the basis and λ
1
2
enters the basis and the
updated basic variable set is
x
B
=
λ
1
2
λ
1
1
λ
2
1
=
0.05142798
0.94857202
1
.
Step 7: Column a enters the basis and the column (1, 0, 0)
T
associated
with µ
1
1
leaves the basis, and so
B =
233.33603477 0 0
1 1 0
0 0 1
.
Go to Step 1.
Iteration 3
Step 1: f
B
=
f
1
2
f
1
1