<s>
In	O
linear	B-Algorithm
programming	I-Algorithm
,	O
reduced	B-Algorithm
cost	I-Algorithm
,	O
or	O
opportunity	O
cost	O
,	O
is	O
the	O
amount	O
by	O
which	O
an	O
objective	O
function	O
coefficient	O
would	O
have	O
to	O
improve	O
(	O
so	O
increase	O
for	O
maximization	O
problem	O
,	O
decrease	O
for	O
minimization	O
problem	O
)	O
before	O
it	O
would	O
be	O
possible	O
for	O
a	O
corresponding	O
variable	O
to	O
assume	O
a	O
positive	O
value	O
in	O
the	O
optimal	O
solution	O
.	O
</s>
<s>
Given	O
a	O
system	O
minimize	O
subject	O
to	O
,	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
vector	O
can	O
be	O
computed	O
as	O
,	O
where	O
is	O
the	O
dual	O
cost	O
vector	O
.	O
</s>
<s>
It	O
follows	O
directly	O
that	O
for	O
a	O
minimization	O
problem	O
,	O
any	O
non-basic	O
variables	O
at	O
their	O
lower	O
bounds	O
with	O
strictly	O
negative	O
reduced	B-Algorithm
costs	I-Algorithm
are	O
eligible	O
to	O
enter	O
that	O
basis	O
,	O
while	O
any	O
basic	O
variables	O
must	O
have	O
a	O
reduced	B-Algorithm
cost	I-Algorithm
that	O
is	O
exactly	O
0	O
.	O
</s>
<s>
For	O
a	O
maximization	O
problem	O
,	O
the	O
non-basic	O
variables	O
at	O
their	O
lower	O
bounds	O
that	O
are	O
eligible	O
for	O
entering	O
the	O
basis	O
have	O
a	O
strictly	O
positive	O
reduced	B-Algorithm
cost	I-Algorithm
.	O
</s>
<s>
For	O
the	O
case	O
where	O
x	O
and	O
y	O
are	O
optimal	O
,	O
the	O
reduced	B-Algorithm
costs	I-Algorithm
can	O
help	O
explain	O
why	O
variables	O
attain	O
the	O
value	O
they	O
do	O
.	O
</s>
<s>
For	O
each	O
variable	O
,	O
the	O
corresponding	O
sum	O
of	O
that	O
stuff	O
gives	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
show	O
which	O
constraints	O
forces	O
the	O
variable	O
up	O
and	O
down	O
.	O
</s>
<s>
In	O
principle	O
,	O
a	O
good	O
pivot	O
strategy	O
would	O
be	O
to	O
select	O
whichever	O
variable	O
has	O
the	O
greatest	O
reduced	B-Algorithm
cost	I-Algorithm
.	O
</s>
<s>
The	O
Devex	B-Algorithm
algorithm	I-Algorithm
attempts	O
to	O
overcome	O
the	O
latter	O
problem	O
by	O
estimating	O
the	O
reduced	B-Algorithm
costs	I-Algorithm
rather	O
than	O
calculating	O
them	O
at	O
every	O
pivot	O
step	O
,	O
exploiting	O
that	O
a	O
pivot	O
step	O
might	O
not	O
alter	O
the	O
reduced	B-Algorithm
costs	I-Algorithm
of	O
all	O
variables	O
dramatically	O
.	O
</s>
<s>
"	O
Associated	O
with	O
each	O
variable	O
is	O
a	O
reduced	B-Algorithm
cost	I-Algorithm
value	O
.	O
</s>
<s>
However	O
,	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
value	O
is	O
only	O
non-zero	O
when	O
the	O
optimal	O
value	O
of	O
a	O
variable	O
is	O
zero	O
.	O
</s>
<s>
A	O
somewhat	O
intuitive	O
way	O
to	O
think	O
about	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
variable	O
is	O
to	O
think	O
of	O
it	O
as	O
indicating	O
how	O
much	O
the	O
cost	O
of	O
the	O
activity	O
represented	O
by	O
the	O
variable	O
must	O
be	O
reduced	O
before	O
any	O
of	O
that	O
activity	O
will	O
be	O
done	O
.	O
</s>
<s>
...	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
value	O
indicates	O
how	O
much	O
the	O
objective	O
function	O
coefficient	O
on	O
the	O
corresponding	O
variable	O
must	O
be	O
improved	O
before	O
the	O
value	O
of	O
the	O
variable	O
will	O
be	O
positive	O
in	O
the	O
optimal	O
solution	O
.	O
</s>
<s>
So	O
,	O
in	O
the	O
case	O
of	O
a	O
cost-minimization	O
problem	O
,	O
where	O
the	O
objective	O
function	O
coefficients	O
represent	O
the	O
per-unit	O
cost	O
of	O
the	O
activities	O
represented	O
by	O
the	O
variables	O
,	O
the	O
"	O
reduced	B-Algorithm
cost	I-Algorithm
"	O
coefficients	O
indicate	O
how	O
much	O
each	O
cost	O
coefficient	O
would	O
have	O
to	O
be	O
reduced	O
before	O
the	O
activity	O
represented	O
by	O
the	O
corresponding	O
variable	O
would	O
be	O
cost-effective	O
.	O
</s>
<s>
The	O
reduced	B-Algorithm
cost	I-Algorithm
value	O
indicates	O
how	O
much	O
the	O
profitability	O
of	O
the	O
activity	O
would	O
have	O
to	O
be	O
increased	O
in	O
order	O
for	O
the	O
activity	O
to	O
occur	O
in	O
the	O
optimal	O
solution	O
.	O
</s>
<s>
If	O
the	O
optimal	O
value	O
of	O
a	O
variable	O
is	O
positive	O
(	O
not	O
zero	O
)	O
,	O
then	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
is	O
always	O
zero	O
.	O
</s>
<s>
If	O
the	O
optimal	O
value	O
of	O
a	O
variable	O
is	O
zero	O
and	O
the	O
reduced	B-Algorithm
cost	I-Algorithm
corresponding	O
to	O
the	O
variable	O
is	O
also	O
zero	O
,	O
then	O
there	O
is	O
at	O
least	O
one	O
other	O
corner	O
that	O
is	O
also	O
in	O
the	O
optimal	O
solution	O
.	O
</s>
