<s>
The	O
nurse	B-Application
scheduling	I-Application
problem	I-Application
(	O
NSP	O
)	O
,	O
also	O
called	O
the	O
nurse	B-Application
rostering	I-Application
problem	I-Application
(	O
NRP	O
)	O
,	O
is	O
the	O
operations	O
research	O
problem	O
of	O
finding	O
an	O
optimal	O
way	O
to	O
assign	O
nurses	O
to	O
shifts	O
,	O
typically	O
with	O
a	O
set	O
of	O
hard	B-Application
constraints	I-Application
which	O
all	O
valid	O
solutions	O
must	O
follow	O
,	O
and	O
a	O
set	O
of	O
soft	B-Application
constraints	I-Application
which	O
define	O
the	O
relative	O
quality	O
of	O
valid	O
solutions	O
.	O
</s>
<s>
Solutions	O
to	O
the	O
nurse	B-Application
scheduling	I-Application
problem	I-Application
can	O
be	O
applied	O
to	O
constrained	O
scheduling	O
problems	O
in	O
other	O
fields	O
.	O
</s>
<s>
The	O
nurse	B-Application
scheduling	I-Application
problem	I-Application
has	O
been	O
studied	O
since	O
before	O
1969	O
,	O
and	O
is	O
known	O
to	O
have	O
NP-hard	O
complexity	O
.	O
</s>
<s>
The	O
nurse	B-Application
scheduling	I-Application
problem	I-Application
involves	O
the	O
assignment	O
of	O
shifts	O
and	O
holidays	O
to	O
nurses	O
.	O
</s>
<s>
hard	B-Application
constraints	I-Application
:	O
if	O
this	O
constraint	O
fails	O
then	O
the	O
entire	O
schedule	O
is	O
invalid	O
.	O
</s>
<s>
soft	B-Application
constraints	I-Application
:	O
it	O
is	O
desirable	O
that	O
these	O
constraints	O
are	O
met	O
but	O
not	O
meeting	O
them	O
does	O
not	O
make	O
the	O
schedule	O
invalid	O
.	O
</s>
<s>
Hard	B-Application
constraints	I-Application
typically	O
include	O
a	O
specification	O
of	O
shifts	O
(	O
e.g.	O
</s>
<s>
Differences	O
in	O
qualifications	O
between	O
nurses	O
also	O
create	O
hard	B-Application
constraints	I-Application
.	O
</s>
<s>
Soft	B-Application
constraints	I-Application
may	O
include	O
minimum	O
and	O
maximum	O
numbers	O
of	O
shifts	O
assigned	O
to	O
a	O
given	O
nurse	O
in	O
a	O
given	O
week	O
,	O
of	O
hours	O
worked	O
per	O
week	O
,	O
of	O
days	O
worked	O
consecutively	O
,	O
of	O
days	O
off	O
consecutively	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
The	O
shift	O
preferences	O
of	O
individual	O
nurses	O
may	O
be	O
treated	O
as	O
a	O
soft	B-Application
constraint	I-Application
,	O
or	O
as	O
a	O
hard	B-Application
constraint	I-Application
.	O
</s>
<s>
Solutions	O
to	O
the	O
problem	O
use	O
a	O
variety	O
of	O
techniques	O
,	O
including	O
both	O
mathematically	O
exact	O
solutions	O
and	O
a	O
variety	O
of	O
heuristic	O
solutions	O
using	O
decomposition	B-Algorithm
,	O
parallel	B-Operating_System
computing	I-Operating_System
,	O
stochastic	B-Algorithm
optimization	I-Algorithm
,	O
genetic	B-Algorithm
algorithms	I-Algorithm
,	O
colony	B-Algorithm
optimization	I-Algorithm
,	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
quantum	B-Algorithm
annealing	I-Algorithm
Tabu	B-Algorithm
search	I-Algorithm
,	O
and	O
coordinate	B-Algorithm
descent	I-Algorithm
.	O
</s>
<s>
(	O
2004	O
)	O
summarised	O
the	O
state	O
of	O
art	O
of	O
academic	O
research	O
to	O
the	O
nurse	B-Application
rostering	I-Application
problem	I-Application
,	O
including	O
brief	O
introductions	O
of	O
various	O
then	O
published	O
solutions	O
.	O
</s>
