<s>
Open-shop	B-Algorithm
scheduling	I-Algorithm
or	O
open-shop	B-Algorithm
scheduling	I-Algorithm
problem	O
(	O
OSSP	O
)	O
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
open-shop	B-Algorithm
scheduling	I-Algorithm
,	O
each	O
job	O
consists	O
of	O
a	O
set	O
of	O
operations	O
O1	O
,	O
O2	O
,...,	O
On	O
which	O
need	O
to	O
be	O
processed	O
in	O
an	O
arbitrary	O
order	O
.	O
</s>
<s>
In	O
the	O
standard	O
three-field	B-Algorithm
notation	I-Algorithm
for	I-Algorithm
optimal	I-Algorithm
job-scheduling	I-Algorithm
problems	I-Algorithm
,	O
the	O
open-shop	O
variant	O
is	O
denoted	O
by	O
O	O
in	O
the	O
first	O
field	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
problem	O
denoted	O
by	O
"	O
O3||	O
"	O
is	O
a	O
3-machines	O
job-shop	B-Algorithm
problem	I-Algorithm
with	O
unit	O
processing	O
times	O
,	O
where	O
the	O
goal	O
is	O
to	O
minimize	O
the	O
maximum	O
completion	O
time	O
.	O
</s>
<s>
The	O
input	O
to	O
the	O
open-shop	B-Algorithm
scheduling	I-Algorithm
problem	O
consists	O
of	O
a	O
set	O
of	O
n	O
jobs	O
,	O
another	O
set	O
of	O
m	O
workstations	O
,	O
and	O
a	O
two-dimensional	O
table	O
of	O
the	O
amount	O
of	O
time	O
each	O
job	O
should	O
spend	O
at	O
each	O
workstation	O
(	O
possibly	O
zero	O
)	O
.	O
</s>
<s>
However	O
,	O
unlike	O
the	O
job-shop	B-Algorithm
problem	I-Algorithm
,	O
the	O
order	O
in	O
which	O
the	O
processing	O
steps	O
happen	O
can	O
vary	O
freely	O
.	O
</s>
<s>
The	O
usual	O
measure	O
of	O
quality	O
of	O
a	O
solution	O
is	O
its	O
makespan	B-Algorithm
,	O
the	O
amount	O
of	O
time	O
from	O
the	O
start	O
of	O
the	O
schedule	O
(	O
the	O
first	O
assignment	O
of	O
a	O
job	O
to	O
a	O
workstation	O
)	O
to	O
its	O
end	O
(	O
the	O
finishing	O
time	O
of	O
the	O
last	O
job	O
at	O
the	O
last	O
workstation	O
)	O
.	O
</s>
<s>
The	O
open-shop	B-Algorithm
scheduling	I-Algorithm
problem	O
can	O
be	O
solved	O
in	O
polynomial	O
time	O
for	O
instances	O
that	O
have	O
only	O
two	O
workstations	O
or	O
only	O
two	O
jobs	O
.	O
</s>
<s>
For	O
three	O
or	O
more	O
workstations	O
,	O
or	O
three	O
or	O
more	O
jobs	O
,	O
with	O
varying	O
processing	O
times	O
,	O
open-shop	B-Algorithm
scheduling	I-Algorithm
is	O
NP-hard	O
.	O
</s>
<s>
Job-shop	B-Algorithm
scheduling	I-Algorithm
is	O
a	O
similar	O
problem	O
but	O
with	O
a	O
yet	O
additional	O
constraint	O
the	O
operations	O
must	O
be	O
done	O
in	O
a	O
specific	O
order	O
.	O
</s>
<s>
Flow-shop	B-Algorithm
scheduling	I-Algorithm
is	O
a	O
job-shop	B-Algorithm
scheduling	I-Algorithm
but	O
with	O
an	O
additional	O
flow	O
constraint	O
each	O
operation	O
must	O
be	O
done	O
on	O
a	O
specific	O
machine	O
.	O
</s>
