<s>
Scheduling	B-Application
is	O
the	O
process	O
of	O
arranging	O
,	O
controlling	O
and	O
optimizing	O
work	O
and	O
workloads	O
in	O
a	O
production	O
process	O
or	O
manufacturing	O
process	O
.	O
</s>
<s>
Scheduling	B-Application
is	O
used	O
to	O
allocate	O
plant	O
and	O
machinery	O
resources	O
,	O
plan	O
human	O
resources	O
,	O
plan	O
production	O
processes	O
and	O
purchase	O
materials	O
.	O
</s>
<s>
In	O
manufacturing	O
,	O
the	O
purpose	O
of	O
scheduling	B-Application
is	O
to	O
keep	O
due	O
dates	O
of	O
customers	O
and	O
then	O
minimize	O
the	O
production	O
time	O
and	O
costs	O
,	O
by	O
telling	O
a	O
production	O
facility	O
when	O
to	O
make	O
,	O
with	O
which	O
staff	O
,	O
and	O
on	O
which	O
equipment	O
.	O
</s>
<s>
Production	B-Application
scheduling	I-Application
aims	O
to	O
maximize	O
the	O
efficiency	O
of	O
the	O
operation	O
,	O
utilize	O
maximum	O
resources	O
available	O
and	O
reduce	O
costs	O
.	O
</s>
<s>
In	O
some	O
situations	O
,	O
scheduling	B-Application
can	O
involve	O
random	O
attributes	O
,	O
such	O
as	O
random	O
processing	O
times	O
,	O
random	O
due	O
dates	O
,	O
random	O
weights	O
,	O
and	O
stochastic	O
machine	O
breakdowns	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
scheduling	B-Application
problems	O
are	O
referred	O
to	O
as	O
"	O
stochastic	B-Algorithm
scheduling	I-Algorithm
"	O
.	O
</s>
<s>
Scheduling	B-Application
is	O
the	O
process	O
of	O
arranging	O
,	O
controlling	O
and	O
optimizing	O
work	O
and	O
workloads	O
in	O
a	O
production	O
process	O
.	O
</s>
<s>
Companies	O
use	O
backward	O
and	O
forward	O
scheduling	B-Application
to	O
allocate	O
plant	O
and	O
machinery	O
resources	O
,	O
plan	O
human	O
resources	O
,	O
plan	O
production	O
processes	O
and	O
purchase	O
materials	O
.	O
</s>
<s>
Forward	O
scheduling	B-Application
is	O
planning	O
the	O
tasks	O
from	O
the	O
date	O
resources	O
become	O
available	O
to	O
determine	O
the	O
shipping	O
date	O
or	O
the	O
due	O
date	O
.	O
</s>
<s>
Backward	O
scheduling	B-Application
is	O
planning	O
the	O
tasks	O
from	O
the	O
due	O
date	O
or	O
required-by	O
date	O
to	O
determine	O
the	O
start	O
date	O
and/or	O
any	O
changes	O
in	O
capacity	O
required	O
.	O
</s>
<s>
The	O
benefits	O
of	O
production	B-Application
scheduling	I-Application
include	O
:	O
</s>
<s>
Production	B-Application
scheduling	I-Application
tools	O
greatly	O
outperform	O
older	O
manual	O
scheduling	B-Application
methods	O
.	O
</s>
<s>
These	O
provide	O
the	O
production	O
scheduler	O
with	O
powerful	O
graphical	O
interfaces	O
which	O
can	O
be	O
used	O
to	O
visually	O
optimize	O
real-time	O
work	O
loads	O
in	O
various	O
stages	O
of	O
production	O
,	O
and	O
pattern	O
recognition	O
allows	O
the	O
software	O
to	O
automatically	B-Application
create	I-Application
scheduling	I-Application
opportunities	I-Application
which	O
might	O
not	O
be	O
apparent	O
without	O
this	O
view	O
into	O
the	O
data	O
.	O
</s>
<s>
For	O
example	O
,	O
an	O
airline	O
might	O
wish	O
to	O
minimize	O
the	O
number	O
of	O
airport	O
gates	O
required	O
for	O
its	O
aircraft	O
,	O
in	O
order	O
to	O
reduce	O
costs	O
,	O
and	O
scheduling	B-Application
software	O
can	O
allow	O
the	O
planners	O
to	O
see	O
how	O
this	O
can	O
be	O
done	O
,	O
by	O
analysing	O
time	O
tables	O
,	O
aircraft	O
usage	O
,	O
or	O
the	O
flow	O
of	O
passengers	O
.	O
</s>
<s>
A	O
key	O
character	O
of	O
scheduling	B-Application
is	O
the	O
productivity	O
,	O
the	O
relation	O
between	O
quantity	O
of	O
inputs	O
and	O
quantity	O
of	O
output	O
.	O
</s>
<s>
Resource	B-Algorithm
allocation	I-Algorithm
:	O
Resource	B-Algorithm
allocation	I-Algorithm
is	O
assigning	O
inputs	O
to	O
produce	O
output	O
.	O
</s>
<s>
Production	B-Application
scheduling	I-Application
can	O
take	O
a	O
significant	O
amount	O
of	O
computing	O
power	O
if	O
there	O
are	O
a	O
large	O
number	O
of	O
tasks	O
.	O
</s>
<s>
Therefore	O
,	O
a	O
range	O
of	O
short-cut	O
algorithms	O
(	O
heuristics	B-Algorithm
)	O
(	O
a.k.a.	O
</s>
<s>
Batch	O
production	B-Application
scheduling	I-Application
is	O
the	O
practice	O
of	O
planning	B-Application
and	I-Application
scheduling	I-Application
of	O
batch	O
manufacturing	O
processes	O
.	O
</s>
<s>
Although	O
scheduling	B-Application
may	O
apply	O
to	O
traditionally	O
continuous	O
processes	O
such	O
as	O
refining	O
,	O
it	O
is	O
especially	O
important	O
for	O
batch	O
processes	O
such	O
as	O
those	O
for	O
pharmaceutical	O
active	O
ingredients	O
,	O
biotechnology	O
processes	O
and	O
many	O
specialty	O
chemical	O
processes	O
.	O
</s>
<s>
Batch	O
production	B-Application
scheduling	I-Application
shares	O
some	O
concepts	O
and	O
techniques	O
with	O
finite	O
capacity	O
scheduling	B-Application
which	O
has	O
been	O
applied	O
to	O
many	O
manufacturing	O
problems	O
.	O
</s>
<s>
The	O
specific	O
issues	O
of	O
scheduling	B-Application
batch	O
manufacturing	O
processes	O
have	O
generated	O
considerable	O
industrial	O
and	O
academic	O
interest	O
.	O
</s>
<s>
Note	O
that	O
the	O
organization	O
here	O
is	O
intended	O
to	O
capture	O
the	O
entire	O
process	O
for	O
scheduling	B-Application
.	O
</s>
<s>
The	O
Gantt	B-Application
chart	I-Application
is	O
a	O
display	O
that	O
shows	O
activities	O
on	O
a	O
horizontal	O
bar	O
graph	O
in	O
which	O
the	O
bars	O
represent	O
the	O
time	O
of	O
the	O
activity	O
.	O
</s>
<s>
Below	O
is	O
an	O
example	O
of	O
a	O
Gantt	B-Application
chart	I-Application
for	O
the	O
process	O
in	O
the	O
example	O
described	O
above	O
.	O
</s>
<s>
Another	O
time	O
chart	O
which	O
is	O
also	O
sometimes	O
called	O
a	O
Gantt	B-Application
chart	I-Application
shows	O
the	O
time	O
during	O
which	O
key	O
resources	O
,	O
e.g.	O
</s>
<s>
The	O
previous	O
figures	O
show	O
this	O
occupancy-style	O
Gantt	B-Application
chart	I-Application
.	O
</s>
<s>
When	O
scheduling	B-Application
situations	O
become	O
more	O
complicated	O
,	O
for	O
example	O
when	O
two	O
or	O
more	O
processes	O
share	O
resources	O
,	O
it	O
may	O
be	O
difficult	O
to	O
find	O
the	O
best	O
schedule	O
.	O
</s>
<s>
A	O
number	O
of	O
common	O
scheduling	B-Application
problems	O
,	O
including	O
variations	O
on	O
the	O
example	O
described	O
above	O
,	O
fall	O
into	O
a	O
class	O
of	O
problems	O
that	O
become	O
very	O
difficult	O
to	O
solve	O
as	O
their	O
size	O
(	O
number	O
of	O
procedures	O
and	O
operations	O
)	O
grows	O
.	O
</s>
<s>
A	O
wide	O
variety	O
of	O
algorithms	O
and	O
approaches	O
have	O
been	O
applied	O
to	O
batch	O
process	O
scheduling	B-Application
.	O
</s>
<s>
Mathematical	O
programming	O
methods	O
involve	O
formulating	O
the	O
scheduling	B-Application
problem	O
as	O
an	O
optimization	O
problem	O
where	O
some	O
objective	O
,	O
e.g.	O
</s>
<s>
Practitioners	O
may	O
use	O
problem-specific	O
simplifications	O
in	O
the	O
formulation	O
to	O
get	O
faster	O
solutions	O
without	O
eliminating	O
critical	O
components	O
of	O
the	O
scheduling	B-Application
model	O
.	O
</s>
<s>
Constraint	B-Application
programming	I-Application
is	O
a	O
similar	O
approach	O
except	O
that	O
the	O
problem	O
is	O
formulated	O
only	O
as	O
a	O
set	O
of	O
constraints	O
and	O
the	O
goal	O
is	O
to	O
arrive	O
at	O
a	O
feasible	O
solution	O
rapidly	O
.	O
</s>
<s>
A	O
new	O
development	O
and	O
framework	O
addresses	O
how	O
to	O
exploit	O
the	O
aggregation	O
of	O
several	O
digital	O
twins	O
,	O
representing	O
different	O
physical	O
assets	O
and	O
their	O
autonomous	O
decision-making	O
,	O
together	O
with	O
a	O
global	O
digital	O
twin	O
,	O
in	O
order	O
to	O
perform	O
production	B-Application
scheduling	I-Application
optimization	O
.	O
</s>
