<s>
Flow-shop	B-Algorithm
scheduling	I-Algorithm
is	O
an	O
optimization	O
problem	O
in	O
computer	B-General_Concept
science	I-General_Concept
and	O
operations	O
research	O
.	O
</s>
<s>
It	O
is	O
a	O
variant	O
of	O
optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
In	O
a	O
general	O
job-scheduling	O
problem	O
,	O
we	O
are	O
given	O
n	O
jobs	O
J1	O
,	O
J2	O
,...,	O
Jn	O
of	O
varying	O
processing	O
times	O
,	O
which	O
need	O
to	O
be	O
scheduled	O
on	O
m	O
machines	O
with	O
varying	O
processing	O
power	O
,	O
while	O
trying	O
to	O
minimize	O
the	O
makespan	B-Algorithm
–	O
the	O
total	O
length	O
of	O
the	O
schedule	O
(	O
that	O
is	O
,	O
when	O
all	O
the	O
jobs	O
have	O
finished	O
processing	O
)	O
.	O
</s>
<s>
In	O
the	O
specific	O
variant	O
known	O
as	O
flow-shop	B-Algorithm
scheduling	I-Algorithm
,	O
each	O
job	O
contains	O
exactly	O
m	O
operations	O
.	O
</s>
<s>
Flow-shop	B-Algorithm
scheduling	I-Algorithm
is	O
a	O
special	O
case	O
of	O
job-shop	B-Algorithm
scheduling	I-Algorithm
where	O
there	O
is	O
strict	O
order	O
of	O
all	O
operations	O
to	O
be	O
performed	O
on	O
all	O
jobs	O
.	O
</s>
<s>
Flow-shop	B-Algorithm
scheduling	I-Algorithm
may	O
apply	O
as	O
well	O
to	O
production	O
facilities	O
as	O
to	O
computing	O
designs	O
.	O
</s>
<s>
A	O
special	O
type	O
of	O
flow-shop	B-Algorithm
scheduling	I-Algorithm
problem	O
is	O
the	O
permutation	O
flow-shop	B-Algorithm
scheduling	I-Algorithm
problem	O
in	O
which	O
the	O
processing	O
order	O
of	O
the	O
jobs	O
on	O
the	O
resources	O
is	O
the	O
same	O
for	O
each	O
subsequent	O
step	O
of	O
processing	O
.	O
</s>
<s>
In	O
the	O
standard	O
three-field	B-Algorithm
notation	I-Algorithm
for	I-Algorithm
optimal-job-scheduling	I-Algorithm
problems	I-Algorithm
,	O
the	O
flow-shop	O
variant	O
is	O
denoted	O
by	O
F	O
in	O
the	O
first	O
field	O
.	O
</s>
<s>
the	O
one	O
with	O
the	O
shortest	O
possible	O
total	O
job	O
execution	O
makespan	B-Algorithm
.	O
</s>
<s>
The	O
proposed	O
methods	O
to	O
solve	O
flow-shop-scheduling	O
problems	O
can	O
be	O
classified	O
as	O
exact	B-Algorithm
algorithm	I-Algorithm
such	O
as	O
branch	B-Algorithm
and	I-Algorithm
bound	I-Algorithm
and	O
heuristic	B-Algorithm
algorithm	I-Algorithm
such	O
as	O
genetic	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
It	O
is	O
required	O
to	O
schedule	O
n	O
jobs	O
on	O
machines	O
so	O
as	O
to	O
minimize	O
makespan	B-Algorithm
.	O
</s>
