<s>
Optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
is	O
a	O
class	O
of	O
optimization	O
problems	O
related	O
to	O
scheduling	O
.	O
</s>
<s>
The	O
inputs	O
to	O
such	O
problems	O
are	O
a	O
list	O
of	O
jobs	B-General_Concept
(	O
also	O
called	O
processes	O
or	O
tasks	O
)	O
and	O
a	O
list	O
of	O
machines	O
(	O
also	O
called	O
processors	O
or	O
workers	O
)	O
.	O
</s>
<s>
The	O
required	O
output	O
is	O
a	O
schedule	O
–	O
an	O
assignment	O
of	O
jobs	B-General_Concept
to	O
machines	O
.	O
</s>
<s>
In	O
the	O
literature	O
,	O
problems	O
of	O
optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
are	O
often	O
called	O
machine	O
scheduling	O
,	O
processor	O
scheduling	O
,	O
multiprocessor	B-Algorithm
scheduling	I-Algorithm
,	O
or	O
just	O
scheduling	O
.	O
</s>
<s>
There	O
are	O
many	O
different	O
problems	O
of	O
optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
,	O
different	O
in	O
the	O
nature	O
of	O
jobs	B-General_Concept
,	O
the	O
nature	O
of	O
machines	O
,	O
the	O
restrictions	O
on	O
the	O
schedule	O
,	O
and	O
the	O
objective	O
function	O
.	O
</s>
<s>
In	O
the	O
simpler	O
optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
problems	O
,	O
each	O
job	O
j	O
consists	O
of	O
a	O
single	O
execution	O
phase	O
,	O
with	O
a	O
given	O
processing	O
time	O
pj	O
.	O
</s>
<s>
1	O
:	O
Single-machine	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
P	O
:	O
Identical-machines	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
Q	O
:	O
Uniform-machines	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
R	O
:	O
Unrelated-machines	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
O	O
:	O
Open-shop	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
F	O
:	O
Flow-shop	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
J	O
:	O
Job-shop	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
,	O
or	O
:	O
the	O
processing	O
time	O
is	O
equal	O
for	O
all	O
jobs	B-General_Concept
.	O
</s>
<s>
,	O
or	O
:	O
the	O
processing	O
time	O
is	O
equal	O
to	O
1	O
time-unit	O
for	O
all	O
jobs	B-General_Concept
.	O
</s>
<s>
Jobs	B-General_Concept
are	O
revealed	O
at	O
their	O
release	O
times	O
.	O
</s>
<s>
In	O
this	O
context	O
the	O
performance	O
of	O
an	O
algorithm	O
is	O
measured	O
by	O
its	O
competitive	B-Algorithm
ratio	I-Algorithm
.	O
</s>
<s>
The	O
idea	O
is	O
that	O
every	O
job	O
should	O
complete	O
before	O
its	O
due	O
date	O
and	O
there	O
is	O
some	O
penalty	O
for	O
jobs	B-General_Concept
that	O
complete	O
late	O
.	O
</s>
<s>
pmtn	O
:	O
Jobs	B-General_Concept
can	O
be	O
preempted	O
and	O
resumed	O
possibly	O
on	O
another	O
machine	O
.	O
</s>
<s>
This	O
is	O
an	O
important	O
parameter	O
in	O
the	O
variant	O
called	O
parallel	B-Algorithm
task	I-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
Precedence	O
relations	O
might	O
be	O
given	O
for	O
the	O
jobs	B-General_Concept
,	O
in	O
form	O
of	O
a	O
partial	O
order	O
,	O
meaning	O
that	O
if	O
i	O
is	O
a	O
predecessor	O
of	O
i	O
in	O
that	O
order	O
,	O
i	O
can	O
start	O
only	O
when	O
i	O
is	O
completed	O
.	O
</s>
<s>
Am-order	O
:	O
Am	O
orders	O
are	O
a	O
superclass	O
of	O
over-interval	O
orders	O
defined	O
in	O
Moukrim	O
and	O
Quilliot	O
:	O
"	O
A	O
relation	O
between	O
multiprocessor	B-Algorithm
scheduling	I-Algorithm
and	O
linear	O
programming.	O
"	O
</s>
<s>
One	O
difference	O
is	O
the	O
notation	O
where	O
the	O
goal	O
is	O
to	O
maximize	O
the	O
number	O
of	O
jobs	B-General_Concept
that	O
complete	O
before	O
their	O
deadline	O
.	O
</s>
<s>
is	O
the	O
maximum	O
completion	O
time	O
;	O
also	O
known	O
as	O
the	O
makespan	B-Algorithm
.	O
</s>
<s>
There	O
is	O
a	O
unit	O
profit	O
for	O
jobs	B-General_Concept
that	O
complete	O
on	O
time	O
,	O
i.e.	O
</s>
<s>
–	O
assigning	O
each	O
of	O
given	O
jobs	B-General_Concept
to	O
one	O
of	O
the	O
two	O
identical	O
machines	O
so	O
to	O
minimize	O
the	O
maximum	O
total	O
processing	O
time	O
over	O
the	O
machines	O
.	O
</s>
<s>
–	O
assigning	O
jobs	B-General_Concept
to	O
parallel	O
identical	O
machines	O
,	O
where	O
each	O
job	O
comes	O
with	O
a	O
number	O
of	O
machines	O
on	O
which	O
it	O
must	O
be	O
scheduled	O
at	O
the	O
same	O
time	O
,	O
minimizing	O
maximum	O
completion	O
time	O
.	O
</s>
<s>
See	O
parallel	B-Algorithm
task	I-Algorithm
scheduling	I-Algorithm
.	O
</s>
