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Introduction to Linear Optimization and Extensions with MATLAB®
book

Introduction to Linear Optimization and Extensions with MATLAB®

by Roy H. Kwon
September 2013
Intermediate to advanced content levelIntermediate to advanced
362 pages
8h 44m
English
CRC Press
Content preview from Introduction to Linear Optimization and Extensions with MATLAB®
The Simplex Method 115
The basic variables are then
x
B
= B
1
b =
x
3
x
4
x
1
=
ε
1
2ε
3
5 + ε
2
ε
3
15 + ε
3
where
B =
1 0 2
0 1 1
0 0 1
, so the reduced costs are
r
2
= 1 (0, 0, 1)
1 0 2
0 1 1
0 0 1
1
1
1
0
= 1
and r
5
= 1 (in general, if a variable left the basis in the previous iteration,
then it will not enter the basis in the next iteration), so x
2
is selected to enter
the basis. Then,
d
2
=
B
1
N
2
e
2
=
1 0 2
0 1 1
0 0 1
1
1
1
0
0
1
=
1
1
0
0
1
.
The minimum ratio test gives
α = min{
ε
1
2ε
3
1
,
5+ε
2
ε
3
1
} = ε
1
2ε
3
(why?),
so x
3
leaves the basis. Then,
x
2
=
ε
1
2ε
3
5 + ε
2
ε
3
15 + ε
3
0
0
+ (ε
1
2ε
3
)
1
1
0
0
1
=
0
5 ε
1
+ ε
2
+ ε
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Publisher Resources

ISBN: 9781439862636