The document discusses the application of mathematical concepts to operations management, focusing on business processes, process re-engineering, and the modeling of business organizations. It outlines definitions, examples, and methodologies for improving efficiency and hierarchical organization in businesses, particularly through ERP projects. The text emphasizes the importance of structured processes and the dynamic nature of these organizational layers.

1. MATHEMATICAL
CONCEPTS
APPLIED
TO
OPERATIONS
MANAGEMENT
IN
20
SLIDES
©
North
Delta
College
2015
Mathema'cs
applied
to
Opera'ons
Management
1

2. SUMMARY
PART
1:
BUSINESS
PROCESSES
A)
DefiniFons/Examples
PART
2:
PROCESS
RE-­‐ENGINEERING
A)
Process
Re-­‐Engineering
B)
Examples
C)
ERP
projects
(Enterprise
Resources
Planning)
PART
3:
MODELLING
BUSINESS
ORGANISATIONS
A)
A
business
organisaFon
seen
as
a
MathemaFcal
Space
B)
The
T&P
layer
PART
4:
MATHEMATICAL
PART
A)
Layered
spaces
B)
Examples
C)
Changes
&
DisrupFons
Mathema'cs
applied
to
Opera'ons
Management
2

3. PART
1:
BUSINESS
PROCESSES
Axiom
1:
A
business
process
is
the
accomplishment
of
a
repeFFve
work
by
an
employee
inside
a
company
in
order
to
achieve
a
given
funcFonality
Mathema'cs
applied
to
Opera'ons
Management
3
PROCESSES
AND
TASKS
Remark:
This
work
is
generally
formally
codified
by
management
so
that
the
individual
employee's
thinking
doesn't
come
into
the
equaFon.
His
individual
intelligence
is
only
used
to
perform
the
work.
Axiom
2:
Each
process
is
made
up
of
tasks
that
can
be
performed
either:
1) Linearly
2)
by
mulF-­‐tasking
Axiom
3:
ulFmately
a
business
organisaFon,
seen
as
a
profit
generaFng
enFty
is
nothing
more
than
the
set
of
all
its
processes.
A
process-­‐machine.

4. Example:
Order-­‐Intake
process
Process:
order-­‐intake
Task
1:
OI
Clerk
receives
order
from
customer
over
email
or
phone
Task
2:
OI
Clerk
enters
order
in
the
computer
system
Task
3:
OI
clerk
sends
confirmaFon
to
OI
Department
Manager
Task
4:
OI
clerk
acknowledges
receipt
of
order
to
the
client
Mathema'cs
applied
to
Opera'ons
Management
4
PART
1:
BUSINESS
PROCESSES
Order
Receipt
Order
Entry
Internal
Confirma'on
Order
Acknowledgement

5. PART
2:
PROCESS
RE-­‐ENGINEERING
Business
processes
form
chains
inside
the
organisaFon.
Each
process
leads
to
one
or
more
other
processes.
Process
re-­‐engineering
intends
to
re-­‐design
these
internal
chains
of
processes
in
order
to
fulfill
the
business
needs
of
the
organisaFon
and
in
view
of
course
of
improving
them.
Among
the
targeted
objecFves,
we
could
have:
gain
of
Fme,
increased
efficiency,
cost
cuang
etc...
Mathema'cs
applied
to
Opera'ons
Management
5
DefiniFon

6. THE
PROBLEM:
Company
Kamera
has
hundreds
of
reports
reaching
management
every
month.
These
reports
are
produced
by
Finance
department
but
the
data
originally
comes
from
MIS
department.
For
this
reason
when
a
problem
occurs
in
the
report,
each
department
blames
the
other
for
the
mistake
and
no
soluFon
is
found.
THE
SOLUTION:
The
process
engineer
could
create
a
data
owner
inside
either
department.
A
person
in
charge
of
checking
accuracy
of
data
and
cleaning
it
if
necessary
in
order
to
streamline
the
reporFng
process.
MIS
would
sFll
provide
the
data,
but
the
data
owner
would
check
and
amend
it
first
before
Finance
proceeds
with
the
reporFng.
This
is
a
perfect
example
of
process
re-­‐engineering.
Mathema'cs
applied
to
Opera'ons
Management
6
PART
2:
PROCESS
RE-­‐ENGINEERING
Example:
creaFng
a
data
owner
inside
a
department

7. ERP
projects
(Enterprise
Resources
Planning)
The
IT
systems
in
many
organisaFons
prior
to
an
ERP
are
generally
products
of
historic
factors
rather
than
raFonal
ones.
They
ocen
use
different
plaeorms
and
are
mutually
incompaFble.
The
principal
objecFve
of
an
ERP
project
is
precisely
to
put
ALL
the
IT
systems
of
the
organisaFon
into
one
common
roof,
from
the
general
ledger
of
accounFng,
to
order-­‐intake
or
procurement.
All
the
processes
of
the
organisaFon
are
under
different
computer
screens
but
the
same
socware.
Mathema'cs
applied
to
Opera'ons
Management
7
PART
2:
PROCESS
RE-­‐ENGINEERING

8. Why
is
an
ERP
a
process
re-­‐engineering?
An
ERP
project
is
an
example
of
process
re-­‐engineering.
Why?
Because
in
order
to
put
all
the
processes
of
an
organisaFon
under
a
common
IT
plaeorm,
the
project
manager
has
to
re-­‐design
these
processes,
re-­‐arrange
them
and
amend
the
structure
of
the
process-­‐
chain.
The
process-­‐chain
structure
has
therefore
been
re-­‐engineered
acer
an
ERP.
Mathema'cs
applied
to
Opera'ons
Management
8
PART
2:
PROCESS
RE-­‐ENGINEERING

9. Benefits
of
an
ERP
There
are
many
benefits
of
undertaking
an
ERP
project.
1)
Beher
accuracy
of
data.
Less
mistakes.
2)
Beher
reporFng
system
and
therefore
beher
visibility
over
the
business
3)
A
more
customer
friendly
IT
system
for
the
internal
users
4)
a
more
efficient
and
reliable
way
of
working
for
the
office
clerks
cuang
therefore
on
unnecessary
costs.
Mathema'cs
applied
to
Opera'ons
Management
9
PART
2:
PROCESS
RE-­‐ENGINEERING

10. A
business
organisaFon
seen
as
a
MathemaFcal
Space
Once
a
process
is
completed,
it
impacts
on
following
processes.
These
subsequent
processes
are
either
at
the
same
hierarchical
level
inside
the
company
or
levels
below.
The
set
of
all
processes
forms
therefore
organisaFonal
layers
of
hierarchy
inside
the
company.
These
layers
are
disFnct
and
ordered.
A
given
layer
is
made
up
of
processes
within
the
same
horizontal
level.
Furthermore
the
whole
organisaFon
as
a
profit-­‐making
enFty
can
be
seen
as
the
total
sum
of
its
business
processes.
Mathema'cs
applied
to
Opera'ons
Management
10
PART
3:
MODELLING
BUSINESS
ORGANISATIONS

11. OrganisaFonal
layers
-­‐
Picture
It
is
therefore
possible
to
draw
a
picture
of
the
organisaFonal
structure
of
any
company.
Many
big
companies
have
4,
5
or
more
layers.
Layer
1:
strategic
layer
Layer
2:
upper
managerial
layer
Layer
3:
lower
managerial
layer
Layer
4:
work
layer
Mathema'cs
applied
to
Opera'ons
Management
11
PART
3:
MODELLING
BUSINESS
ORGANISATIONS
Layer
1
Layer
2
Layer
3
Layer
4

12. The
T&P
layer
The
actual
process
re-­‐engineering
project
takes
place
on
its
own
transverse
layer:
the
T&P
layer.
Because
it
is
transverse
this
layer
is
THE
engine
of
change
inside
the
organisaFon.
In
any
case,
this
layer
where
the
project
manager
sits
is
situated
between
the
lower
managerial
and
the
work
layer.
Thus
the
real
happening
of
any
organisaFon
is
in
between
the
lower
managerial
and
the
work
layer.
Mathema'cs
applied
to
Opera'ons
Management
12
PART
3:
MODELLING
BUSINESS
ORGANISATIONS
Lower
Management
Layer
T&P
Layer
Worker/Clerk
Layer

13. Layered
spaces
From
the
study
of
business
organisaFons
we
want
to
introduce
a
new
mathemaFcal
object:
a
layered
space.
Mathema'cs
applied
to
Opera'ons
Management
13
PART
4:
MATHEMATICAL
PART

14. Cells
DefiniFon:
the
most
fundamental
unit
in
a
layered
space
is
the
cell.
The
whole
space
is
made
up
of
cells.
Property:
each
cell
has
the
following
ahributes:
1)
Individual
Energy
2)
Momentum
Property:
each
cell
can
communicate
to
other
cells.
This
is
called
impulse.
Every
impulse
has
a
sender
and
a
receiver.
Impulses
go
only
one
way,
from
the
sender
to
the
receiver
and
not
the
reverse.
Mathema'cs
applied
to
Opera'ons
Management
14
PART
4:
MATHEMATICAL
PART

15. Layered
spaces
DefiniFon:
impulses
can
be
either
horizontal
or
downward
verFcal.
Property:
Cells
which
are
in
the
same
line
of
horizontal
impulses
form
a
layer.
Property:
Every
cell
belongs
to
a
parFcular
layer
whose
consFtuent
cells
remain
fixed.
Some
layers
are
below
others.
Mathema'cs
applied
to
Opera'ons
Management
15
PART
4:
MATHEMATICAL
PART

16. Example
–
Business
OrganisaFons
A
business
organisaFon
is
a
layered
space.
The
consFtuent
cells
are
the
business
processes.
Example:
a
business
organisaFon
with
4
layers
Layer
1:
leadership
Layer
2:
upper
management
Layer
3:
lower
management
Layer
4:
workers
&
office
clerks
Mathema'cs
applied
to
Opera'ons
Management
16
PART
4:
MATHEMATICAL
PART

17. Example
–
Society
as
a
whole
A
given
human
society
can
also
be
seen
as
a
layered
space.
The
component
cells
are
the
individual
persons
making
up
the
society.
Some
socieFes
can
be
seen
as
a
4
layer
space.
Layer
1:
priests
/
intellectuals
Layer
2:
warriors/
aristocracy
Layer
3:
business
people
Layer
4:
workers
Mathema'cs
applied
to
Opera'ons
Management
17
PART
4:
MATHEMATICAL
PART

18. EvoluFon
in
Fme
The
layered
space
would
remain
staFc
in
Fme
if
there
were
not
transverse,
invisible
layers
permeaFng
the
whole
space
and
allowing
it
to
move
forward.
In
the
case
of
business
organisaFons,
it
is
the
T&P
layer
Without
it
there
would
be
no
change
or
progress.
Mathema'cs
applied
to
Opera'ons
Management
18
PART
4:
MATHEMATICAL
PART
T&P
Layer

19. Changes
As
we
have
seen
layers
are
in
a
hierarchical
order
from
top
to
bohom.
The
transverse
layers
allow
the
whole
system
to
remain
dynamic
and
not
just
responsive
to
the
environment.
However
real
change
happens
only
when
2
or
more
layers
collide
at
a
given
moment
in
Fme.
In
the
case
of
business
organisaFons
this
happens
during
major
re-­‐engineering
projects
like
ERPs.
Mathema'cs
applied
to
Opera'ons
Management
19
PART
4:
MATHEMATICAL
PART

20. DisrupFon
A
disrupFon
occurs
when
all
the
layers
collide
at
the
same
Fme.
Acer
the
turmoil,
you
get
a
new
layered
space
with
a
new
structure.
In
our
societal
example,
we
could
take
the
Zoroastrian
revoluFon
in
ancient
Persia
or
more
recently
the
French
RevoluFon.
Mathema'cs
applied
to
Opera'ons
Management
20
PART
4:
MATHEMATICAL
PART