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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®
Linear Optimization under Uncertainty 307
The optimal solution is x
3
=
x
1
x
2
=
66.8276
53.1724
and θ
3
= 7849.
Step 2: Not necessary.
Step 3: Solve recourse sub-problems given x
3
.
For ξ(1), the recourse problem is
minimize 12y
1
14y
2
subject to 3y
1
+ 5y
2
2004.8000
y
1
+ 0.625y
2
531.7328
y
1
500
y
2
100
y
1
0, y
2
0.
The optimal objective value is w
1
= 7030.7000 and solution y
1
=
469.2238
100
and π
T
1
=
0 12 0 6.5
.
For ξ(2), the recourse problem is
minimize 14y
1
16y
2
subject to 3y
1
+ 5y
2
2004.8000
y
1
+ 0.625y
2
531.7328
y
1
300
y
2
300
y
1
0, y
2
0.
The optimal objective value is w
2
= 7735.5 and solution y
2
=
300
220.9657
and π
T
2
=
3.2 0 4.4 0
.
Now e
3
= 0.4π
T
1
h
1
+ 0.6π
T
2
h
2
= 0.4(650) + 0.6(1320) = 1052 and
E
3
= 0.4π
T
1
T + 0.6π
T
2
T =
57.6 48
.
Then, w
2
= e
3
E
3
x
3
= 1052
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Publisher Resources

ISBN: 9781439862636