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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '05
 YY
 Operations Research, C Programming, Optimization, Trigraph, xt Bi wk

Click to edit the document details