IE 534 Linear Programming
Lecture 21: Sensitivity Analysis
Lizhi Wang
October 22, 2012
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
1 / 30

Outline
1
Motivation
2
Gusek for sensitivity analysis
3
Four cases of sensitivity analysis
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
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All models are wrong
“Essentially, all models are wrong, but some are useful.”
– George Box
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
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Sensitivity analysis
Sensitivity analysis is concerned with how changes in parameters
affect the optimal solution.
How do changes in data affect LP optimal solution?
What data uncertainty is the optimal solution most sensitive to?
How much would you pay for additional resources?
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
4 / 30

Review: the TCP problem
x
1
: barrels of Saudi Arabia crude refined per day (in thousand)
x
2
: barrels of Venezuela crude refined per day (in thousand)
minimize
ζ
= 20
x
1
+ 15
x
2
(daily cost)
subject to
0
.
3
x
1
+ 0
.
4
x
2
≥
2
(gasoline requirement)
0
.
4
x
1
+ 0
.
2
x
2
≥
1
.
5
(jet fuel requirement)
0
.
2
x
1
+ 0
.
3
x
2
≥
0
.
5
(lubricants requirement)
x
1
≤
9
(Saudi availability)
x
2
≤
6
(Venezuela availability)
x
1
, x
2
≥
0
.
(non-negativity)
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
5 / 30

Sensitivity of the TCP problem
(1)
What if
20
is changed to
15
?
min
20
x
1
+ 15
x
2
s
.
t
.
0
.
3
x
1
+ 0
.
4
x
2
≥
2
0
.
4
x
1
+ 0
.
2
x
2
≥
1
.
5
0
.
2
x
1
+ 0
.
3
x
2
≥
0
.
5
x
1
≤
9
x
2
≤
6
x
1
, x
2
≥
0
.
x
*
1
= 2
, x
*
2
= 3
.
5
, ζ
*
=
92
.
5
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
6 / 30

Sensitivity of the TCP problem
(1)What if20is changed to15? Same
5
Lizhi Wang ([email protected])
IE 534 Linear Programming
October 22, 2012
7 / 30

Sensitivity of the TCP problem

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