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MIE376 Mathematical Programming
Lecture Notes
Daniel Frances
2011
4
or
Max
Σ
(90P
1
i
+ 80
i
P
2
i
)
µ
i
+
Σ
(70Q
1
i
+ 60Q
2
i
)
λ
i
Σ
(8P
1
i
+ 6P
2
i
)
µ
i
+
Σ
(7Q
1
i
+ 5
i
Q
2
i
)
λ
i
+ s
1
= 80;
Σµ
i
=1
Σλ
i
= 1
µ
i
,
λ
i
, s
1
≥ 0
Note that since we are assuming that ALL the potential offers are known in advance, therefore the
variables in this new LP are the linear combination coefficients
µ
i
, and
λ
e
as well as the slack iron s1.
It is at this point that we start to see a hint of the same phenomenon as column generation.
The potential offers are the equivalent of the Cut Types, whereas
µ
i
and
λ
i
. perform the same role as the
number of each of the cuttypes to be selected.
DantzigWolfe Iterations
Before we start we always need to be able to refer to the master coordinator problem
Max
Σ
(90P
1
i
+ 80
i
P
2
i
)
µ
i
+
Σ
(70Q
1
i
+ 60Q
2
i
)
λ
i
Σ
(8P
1
i
+ 6P
2
i
)
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 Spring '11
 Daniel

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