<s>
In	O
operations	O
research	O
,	O
the	O
Big	B-Algorithm
M	I-Algorithm
method	I-Algorithm
is	O
a	O
method	O
of	O
solving	O
linear	B-Algorithm
programming	I-Algorithm
problems	I-Algorithm
using	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
Big	B-Algorithm
M	I-Algorithm
method	I-Algorithm
extends	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
to	O
problems	O
that	O
contain	O
"	O
greater-than	O
"	O
constraints	O
.	O
</s>
<s>
The	O
simplex	B-Algorithm
algorithm	I-Algorithm
is	O
the	O
original	O
and	O
still	O
one	O
of	O
the	O
most	O
widely	O
used	O
methods	O
for	O
solving	O
linear	O
maximization	O
problems	O
.	O
</s>
<s>
The	O
Big	B-Algorithm
M	I-Algorithm
method	I-Algorithm
introduces	O
surplus	O
and	O
artificial	O
variables	O
to	O
convert	O
all	O
inequalities	O
into	O
that	O
form	O
.	O
</s>
<s>
For	O
less-than	O
or	O
equal	O
constraints	O
,	O
introduce	O
slack	B-Algorithm
variables	I-Algorithm
si	O
so	O
that	O
all	O
constraints	O
are	O
equalities	O
.	O
</s>
<s>
Solve	O
the	O
problem	O
using	O
the	O
usual	O
simplex	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Then	O
row	B-Algorithm
reductions	I-Algorithm
are	O
applied	O
to	O
gain	O
a	O
final	O
solution	O
.	O
</s>
<s>
When	O
used	O
in	O
the	O
objective	O
function	O
,	O
the	O
Big	B-Algorithm
M	I-Algorithm
method	I-Algorithm
sometimes	O
refers	O
to	O
formulations	O
of	O
linear	B-Algorithm
optimization	I-Algorithm
problems	O
in	O
which	O
violations	O
of	O
a	O
constraint	O
or	O
set	O
of	O
constraints	O
are	O
associated	O
with	O
a	O
large	O
positive	O
penalty	O
constant	O
,	O
M	O
.	O
</s>
