November 12, 2003
Lecture 19: Bender’s Decomposition
Lecturer: Fernando Ord´o˜nez
1
Motivation: Stochastic Programming
An electric utility company faces the problem of satisfying demand at minimum cost. In
the case of a thermal plant and a hydro plant, satisfying the demand over the next two
periods can be written as:
min 3
x
1
+ 3
x
2
x
1
+
h
1
≥
10
x
2
+
h
2
≥
12
h
1
≤
5
h
2
≤
V
2
V
2
+
h
1
= 5 +
r
x
i
, h
i
≥
0
Note that this is a production and inventory problem.
Suppose
 2nd period demand can be 15 or 10 each with prob. 1/2
 2nd period thermal cost can be 1 or 5 each with prob. 1/2
 rain can be
r
= 0 or
r
= 10 each with prob. 1/2
Question: What is the best strategy to satisfy 1st period demand taking into account this
uncertainty?
scenario
prob.
2nd demand
thermal cost
rain
best strategy
1
0.125
15
5
0
save water,
x
1
high
2
0.125
10
3
10
use water,
x
1
low
.
.
.
.
.
.
1
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 Spring '05
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 Operations Research, C Programming, Optimization, Trigraph, xt Bi wk

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