<s>
In	O
mathematical	O
optimization	O
,	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
(	O
also	O
known	O
as	O
Bland	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
Bland	O
's	O
anti-cycling	O
rule	O
or	O
Bland	O
's	O
pivot	O
rule	O
)	O
is	O
an	O
algorithmic	O
refinement	O
of	O
the	O
simplex	B-Algorithm
method	I-Algorithm
for	O
linear	B-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
With	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
,	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
solves	O
feasible	O
linear	B-Algorithm
optimization	I-Algorithm
problems	O
without	O
cycling	O
.	O
</s>
<s>
The	O
original	O
simplex	B-Algorithm
algorithm	I-Algorithm
starts	O
with	O
an	O
arbitrary	O
basic	B-Algorithm
feasible	I-Algorithm
solution	I-Algorithm
,	O
and	O
then	O
changes	O
the	O
basis	O
in	O
order	O
to	O
decrease	O
the	O
minimization	O
target	O
and	O
find	O
an	O
optimal	O
solution	O
.	O
</s>
<s>
However	O
,	O
there	O
are	O
examples	O
of	O
degenerate	O
linear	B-Algorithm
programs	I-Algorithm
,	O
on	O
which	O
the	O
original	O
simplex	B-Algorithm
algorithm	I-Algorithm
cycles	O
forever	O
.	O
</s>
<s>
It	O
gets	O
stuck	O
at	O
a	O
basic	B-Algorithm
feasible	I-Algorithm
solution	I-Algorithm
(	O
a	O
corner	O
of	O
the	O
feasible	O
polytope	O
)	O
and	O
changes	O
bases	O
in	O
a	O
cyclic	O
way	O
without	O
decreasing	O
the	O
minimization	O
target	O
.	O
</s>
<s>
Such	O
cycles	O
are	O
avoided	O
by	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
for	O
choosing	O
a	O
column	O
to	O
enter	O
and	O
a	O
column	O
to	O
leave	O
the	O
basis	O
.	O
</s>
<s>
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
was	O
developed	O
by	O
Robert	O
G	O
.	O
Bland	O
,	O
now	O
an	O
Emeritus	O
Professor	O
of	O
operations	O
research	O
at	O
Cornell	O
University	O
,	O
while	O
he	O
was	O
a	O
research	O
fellow	O
at	O
the	O
Center	O
for	O
Operations	O
Research	O
and	O
Econometrics	O
in	O
Belgium	O
.	O
</s>
<s>
One	O
uses	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
during	O
an	O
iteration	O
of	O
the	O
simplex	B-Algorithm
method	I-Algorithm
to	O
decide	O
first	O
what	O
column	O
(	O
known	O
as	O
the	O
entering	O
variable	O
)	O
and	O
then	O
row	O
(	O
known	O
as	O
the	O
leaving	O
variable	O
)	O
in	O
the	O
tableau	O
to	O
pivot	O
on	O
.	O
</s>
<s>
It	O
can	O
be	O
formally	O
proved	O
that	O
,	O
with	O
Bland	O
's	O
selection	O
rule	O
,	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
never	O
cycles	O
,	O
so	O
it	O
is	O
guaranteed	O
to	O
terminate	O
in	O
a	O
bounded	O
time	O
.	O
</s>
<s>
In	O
the	O
abstract	O
setting	O
of	O
oriented	O
matroids	O
,	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
cycles	O
on	O
some	O
examples	O
.	O
</s>
<s>
A	O
restricted	O
class	O
of	O
oriented	O
matroids	O
on	O
which	O
Bland	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
avoids	O
cycling	O
has	O
been	O
termed	O
"	O
Bland	O
oriented	O
matroids	O
"	O
by	O
Jack	O
Edmonds	O
.	O
</s>
<s>
Another	O
pivoting	O
rule	O
,	O
the	O
criss-cross	B-Algorithm
algorithm	I-Algorithm
,	O
avoids	O
cycles	O
on	O
all	O
oriented-matroid	O
linear-programs	O
.	O
</s>
