<s>
MPS	B-Algorithm
(	O
Mathematical	O
Programming	O
System	O
)	O
is	O
a	O
file	O
format	O
for	O
presenting	O
and	O
archiving	O
linear	B-Algorithm
programming	I-Algorithm
(	O
LP	O
)	O
and	O
mixed	O
integer	O
programming	O
problems	O
.	O
</s>
<s>
The	O
format	O
was	O
named	O
after	O
an	O
early	O
IBM	O
LP	O
product	O
and	O
has	O
emerged	O
as	O
a	O
de	O
facto	O
standard	O
ASCII	B-Protocol
medium	O
among	O
most	O
of	O
the	O
commercial	O
LP	O
solvers	O
.	O
</s>
<s>
Essentially	O
all	O
commercial	O
LP	O
solvers	O
accept	O
this	O
format	O
,	O
and	O
it	O
is	O
also	O
accepted	O
by	O
the	O
open-source	O
COIN-OR	B-Application
system	O
.	O
</s>
<s>
Other	O
software	O
may	O
require	O
a	O
customized	O
reader	O
routine	O
in	O
order	O
to	O
read	O
MPS	B-Algorithm
files	O
.	O
</s>
<s>
However	O
,	O
with	O
the	O
acceptance	O
of	O
algebraic	B-Application
modeling	I-Application
languages	I-Application
MPS	B-Algorithm
usage	O
has	O
declined	O
.	O
</s>
<s>
For	O
example	O
,	O
according	O
to	O
the	O
NEOS	O
server	O
statistics	O
in	O
January	O
2011	O
less	O
than	O
1%	O
of	O
submissions	O
were	O
in	O
MPS	B-Algorithm
form	O
compared	O
to	O
59.4	O
%	O
of	O
AMPL	B-Language
and	O
29.7	O
%	O
of	O
GAMS	B-Application
submissions	O
.	O
</s>
<s>
MPS	B-Algorithm
is	O
column-oriented	O
(	O
as	O
opposed	O
to	O
entering	O
the	O
model	O
as	O
equations	O
)	O
,	O
and	O
all	O
model	O
components	O
(	O
variables	O
,	O
rows	O
,	O
etc	O
.	O
)	O
</s>
<s>
MPS	B-Algorithm
is	O
an	O
old	O
format	O
,	O
so	O
it	O
is	O
set	O
up	O
for	O
punch	O
cards	O
:	O
Fields	O
start	O
in	O
column	O
2	O
,	O
5	O
,	O
15	O
,	O
25	O
,	O
40	O
and	O
50	O
.	O
</s>
<s>
Sections	O
of	O
an	O
MPS	B-Algorithm
file	O
are	O
marked	O
by	O
so-called	O
header	O
cards	O
,	O
which	O
are	O
distinguished	O
by	O
their	O
starting	O
in	O
column	O
1	O
.	O
</s>
<s>
Although	O
it	O
is	O
typical	O
to	O
use	O
upper-case	O
throughout	O
the	O
file	O
for	O
historical	O
reasons	O
,	O
many	O
MPS-readers	O
will	O
accept	O
mixed-case	O
for	O
anything	O
except	O
the	O
header	O
cards	O
,	O
and	O
some	O
allow	O
mixed-case	O
anywhere	O
.	O
</s>
<s>
Here	O
is	O
a	O
little	O
sample	O
model	O
written	O
in	O
MPS	B-Algorithm
format	O
(	O
explained	O
in	O
more	O
detail	O
below	O
)	O
:	O
</s>
<s>
Strangely	O
,	O
nothing	O
in	O
MPS	B-Algorithm
format	O
specifies	O
the	O
direction	O
of	O
optimization	O
,	O
and	O
there	O
is	O
no	O
standard	O
"	O
default	O
"	O
direction	O
;	O
some	O
LP	O
solvers	O
will	O
maximize	O
if	O
not	O
instructed	O
otherwise	O
,	O
others	O
will	O
minimize	O
,	O
and	O
still	O
others	O
put	O
safety	O
first	O
and	O
have	O
no	O
default	O
and	O
require	O
a	O
selection	O
somewhere	O
in	O
a	O
control	O
program	O
or	O
by	O
a	O
calling	O
parameter	O
.	O
</s>
<s>
Some	O
programs	O
support	O
specifying	O
minimization/maximization	O
within	O
the	O
MPS	B-Algorithm
file	O
.	O
</s>
<s>
A	O
few	O
special	O
cases	O
of	O
the	O
MPS	B-Algorithm
standard	O
are	O
not	O
consistently	O
handled	O
by	O
implementations	O
.	O
</s>
<s>
MPS	B-Algorithm
has	O
many	O
limitations	O
.	O
</s>
<s>
One	O
of	O
the	O
alternatives	O
to	O
MPS	B-Algorithm
that	O
does	O
not	O
have	O
its	O
limitations	O
and	O
is	O
supported	O
by	O
most	O
solvers	O
is	O
the	O
nl	B-Application
file	I-Application
format	I-Application
.	O
</s>
<s>
Many	O
LP	O
products	O
include	O
extensions	O
to	O
the	O
MPS	B-Algorithm
format	O
.	O
</s>
<s>
The	O
free	O
format	O
MPS	B-Algorithm
allows	O
for	O
long	O
names	O
and	O
more	O
accurate	O
data	O
by	O
allowing	O
fields	O
to	O
exceed	O
the	O
columns	O
defined	O
by	O
the	O
original	O
standard	O
,	O
and	O
apply	O
whitespaces	O
as	O
separators	O
instead	O
of	O
fixed	O
column	O
positions	O
(	O
note	O
that	O
this	O
makes	O
some	O
MPS	B-Algorithm
files	O
that	O
included	O
whitespaces	O
as	O
part	O
of	O
names	O
to	O
be	O
no	O
longer	O
valid	O
)	O
.	O
</s>
<s>
Some	O
extensions	O
include	O
adding	O
new	O
kind	O
of	O
data	O
to	O
the	O
MPS	B-Algorithm
file	O
(	O
e.g.	O
</s>
<s>
SMPS	O
is	O
a	O
specialized	O
extension	O
,	O
designed	O
to	O
represent	O
stochastic	B-Algorithm
programming	I-Algorithm
problem	O
instances	O
,	O
in	O
use	O
especially	O
in	O
research	O
environments	O
.	O
</s>
