<s>
Dantzig	B-Algorithm
–	I-Algorithm
Wolfe	I-Algorithm
decomposition	I-Algorithm
is	O
an	O
algorithm	O
for	O
solving	O
linear	B-Algorithm
programming	I-Algorithm
problems	I-Algorithm
with	O
special	O
structure	O
.	O
</s>
<s>
Many	O
texts	O
on	O
linear	B-Algorithm
programming	I-Algorithm
have	O
sections	O
dedicated	O
to	O
discussing	O
this	O
decomposition	B-Application
algorithm	I-Application
.	O
</s>
<s>
Dantzig	B-Algorithm
–	I-Algorithm
Wolfe	I-Algorithm
decomposition	I-Algorithm
relies	O
on	O
delayed	B-Algorithm
column	I-Algorithm
generation	I-Algorithm
for	O
improving	O
the	O
tractability	O
of	O
large-scale	O
linear	B-Algorithm
programs	I-Algorithm
.	O
</s>
<s>
For	O
most	O
linear	B-Algorithm
programs	I-Algorithm
solved	O
via	O
the	O
revised	O
simplex	B-Algorithm
algorithm	I-Algorithm
,	O
at	O
each	O
step	O
,	O
most	O
columns	O
(	O
variables	O
)	O
are	O
not	O
in	O
the	O
basis	O
.	O
</s>
<s>
In	O
order	O
to	O
use	O
Dantzig	B-Algorithm
–	I-Algorithm
Wolfe	I-Algorithm
decomposition	I-Algorithm
,	O
the	O
constraint	O
matrix	O
of	O
the	O
linear	B-Algorithm
program	I-Algorithm
must	O
have	O
a	O
specific	O
form	O
.	O
</s>
<s>
The	O
master	O
program	O
then	O
requests	O
additional	O
solutions	O
from	O
the	O
subproblem	O
such	O
that	O
the	O
overall	O
objective	O
to	O
the	O
original	O
linear	B-Algorithm
program	I-Algorithm
is	O
improved	O
.	O
</s>
<s>
While	O
there	O
are	O
several	O
variations	O
regarding	O
implementation	O
,	O
the	O
Dantzig	B-Algorithm
–	I-Algorithm
Wolfe	I-Algorithm
decomposition	I-Algorithm
algorithm	O
can	O
be	O
briefly	O
described	O
as	O
follows	O
:	O
</s>
<s>
Master	O
program	O
performs	O
x	O
iterations	O
of	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
,	O
where	O
x	O
is	O
the	O
number	O
of	O
columns	O
incorporated	O
.	O
</s>
<s>
There	O
are	O
examples	O
of	O
the	O
implementation	O
of	O
Dantzig	B-Algorithm
–	I-Algorithm
Wolfe	I-Algorithm
decomposition	I-Algorithm
available	O
in	O
the	O
closed	B-Application
source	I-Application
AMPL	B-Language
and	O
GAMS	B-Application
mathematical	O
modeling	O
software	O
.	O
</s>
<s>
There	O
are	O
general	O
,	O
parallel	O
,	O
and	O
fast	O
implementations	O
available	O
as	O
open-source	B-Application
software	I-Application
,	O
including	O
some	O
provided	O
by	O
JuMP	O
and	O
the	B-Application
GNU	I-Application
Linear	I-Application
Programming	I-Application
Kit	I-Application
.	O
</s>
