IE 495 – Stochastic Programming
Problem Set #1
Due Date: February 3, 2003
Do any four of the following ﬁve problems. If you are working in pairs,
do all ﬁve problems. You are allowed to examine outside sources, but you
must cite any references that you use. Please don’t discuss the problems with
other members of the class (other than your partner, if you are working with
one).
1 Random Linear Programs and the Distri
bution Problem
Recall the random linear program that we saw in class:
minimize
x
1
+
x
2
subject to
ω
1
x
1
+
x
2
≥
7
ω
2
x
1
+
x
2
≥
4
x
1
≥
0
x
2
≥
0
with
ω
1
∼ U
[1
,
4] and
ω
2
∼ U
[1
/
3
,
1].
Let
•
(
x
*
1
(
ω
)
,x
*
2
(
ω
)) be the optimal solution for a given value of
ω
= (
ω
1
,ω
2
).
•
v
*
(
ω
) =
x
*
1
(
ω
) +
x
*
2
(
ω
) be the optimal objective function value.
1.1 Problem
Calculate
x
*
1
(
ω
)
,x
*
2
(
ω
)
,
and
v
*
(
ω
) for all
ω
∈
Ω = [1
,
4]
×
[1
/
3
,
1].
1.2 Problem
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 Spring '08
 Linderoth
 Derivative, Continuous function, Louveaux

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