Agenda
Production
Operations Management
TPPE37and
Manufacturing
Control
• Sequencing rules
• Purchasing
• Managing waiting time
Lecture 4
Production activity control
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1
© Ou Tang
The Planning Hierarchy
Master planning
Master (production) scheduling
Final assembly
schedule
Master prod.
schedule
Material
planning
Feedback
Vendor
systems
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Gantt chart
Sales and operations planning
Production
Resource
planning
planning
Demand
management
2
Order
Order focused
focused
Front
end
Rough-cut
capacity plan
Detailed capacity
Engine
planning
Shop floor
systems
Back
end
3
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Work Center
Typical Scheduling and Control Functions
• A work center is an area in a business in which productive
resources are organized and work is completed
• Can be a single machine, a group of machines, or an area
where a particular type of work is done
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•
•
•
•
Allocating orders, equipment, and personnel
Determining the sequence of order performance
Evaluating performance of the scheduled work
Shop-floor control
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Work-Center Scheduling Objectives
6
Static or dynamic planning?
• Meet due dates
•• Dynamic
Dynamic planning
planning problems
problems
• Minimize lead time
–– Sequencing
Sequencingof
ofan
anunknown
unknownnumber
numberof
ofjobs.
jobs.
–– New
jobs
arrive
continuously.
New jobs arrive continuously.
• Minimize setup time or cost
•• Static
Static planning
planning problems
problems
–– Sequencing
Sequencingof
ofaaknown
knownnumber
numberof
ofjobs.
jobs.
–– No
new
jobs
arrive
before
the
jobs
are
No new jobs arrive before the jobs arefinished
finished
• Minimize work-in-process inventory
• Maximize machine utilization
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Priority Rules for Job Sequencing
First-Come First-Served
1. First-come, first-served (FCFS)
Jobs (in order
of arrival)
A
B
C
D
There
Thereare
arefour
fourjobs
jobsto
tobe
be
processed
on
one
machine
processed on one machine
2. Shortest operating time (SOT)
3. Earliest due date first (DDate)
What
Whatis
isthe
theFCFS
FCFSschedule?
schedule?
4. Critical ratio (CR)
CR =
Jobs (in order
of arrival)
A
B
C
D
5. Last come, first served (LCFS)
6. Random order, etc
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What
Whatis
isthe
theSOT
SOTschedule?
schedule?
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Processing
Time (days)
1
3
4
7
Processing
Time (days)
4
7
3
1
Due Date
(days hence)
5
10
6
4
Do
Doall
allthe
thejobs
jobsget
getdone
doneon
ontime?
time?
Due Date Flow Time
(days hence)
(days)
4
1
6
4
5
8
10
15
10
Earliest Due Date First
Answer: Shortest Operating Time Schedule
Jobs (in order
of arrival)
D
C
A
B
Due Date Flow Time
(days hence)
(days)
5
4
10
11
6
14
4
15
No,
No,Jobs
JobsB,
B,C,
C,
and
andDDare
aregoing
going
to
tobe
belate
late
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Shortest Operating Time
Jobs (in order
of arrival)
A
B
C
D
Processing
Time (days)
4
7
3
1
Due Date
(days hence)
5
10
6
4
Do
Doall
allthe
thejobs
jobsget
getdone
doneon
ontime?
time?
Answer: FCFS Schedule
(Due date - Current date)
Number of days remaining
The
Thesame
samejobs
jobs
Processing
Time (days)
4
7
3
1
Jobs (in order
of arrival)
A
B
C
D
What
Whatis
isthe
theearliest
earliestdue
duedate
datefirst
first
schedule?
schedule?
Processing
Time (days)
4
7
3
1
Due Date
(days hence)
5
10
6
4
Do
Doall
allthe
thejobs
jobsget
getdone
doneon
ontime?
time?
Answer: Earliest Due Date First
No,
No,Jobs
JobsAAand
and
BBare
aregoing
goingto
to
be
belate
late
11
Jobs (in order
of arrival)
D
A
C
B
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Processing
Time (days)
1
4
3
7
Due Date Flow Time
(days hence)
(days)
4
1
5
5
6
8
10
15
No,
No,Jobs
JobsCCand
and
BBare
aregoing
goingto
to
be
belate
late
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Critical Ratio Method
Jobs (in order
of arrival)
A
B
C
D
What
Whatis
isthe
theCR
CRschedule?
schedule?
Sequencing in two machines - Johnson’s algorithm
Processing
Time (days)
4
7
3
1
Due Date
(days hence)
5
10
6
4
Do
Doall
allthe
thejobs
jobsget
getdone
doneon
ontime?
time?
CRs have be calculated for each job. If we let today be Day 1
and allow a total of 15 days to do the work. The resulting CR’s
and order schedule are:
CR(A)=(5-0)/4=1.25
CR(B)=(10-0)/7=1.4
CR(C)=(6-0)/3=2
CR(D)=(4-0)/1=4
Sequence: A, B, C, D
No,
No,Jobs
JobsB,
B,C,
C,
and
andDDare
aregoing
going
to
tobe
belate
late
Description:
Description:
All
Alljobs
jobsneed
needfirst
firstprocess
processininMachine
Machine11(M1)
(M1)and
andthen
thenininMachine
Machine22(M2)
(M2)
Aim:
Aim:
Minimise
Minimisethe
themakespan
makespanofofthe
thewhole
wholework
work
Decision
Decisionrule:
rule:
1.1.Select
Selectjob
jobwith
withthe
thesmallest
smallestinineither
eitherM1
M1or
orM2
M2
2.2.IfIfthis
thistime
timeisisassociate
associatewith
withM1,
M1,schedule
schedulethis
thisjob
jobfirst
first
3.3.IfIfthis
time
is
associate
with
M2,
schedule
this
job
last
this time is associate with M2, schedule this job last
4.4.Remove
Removethis
thisjob
job
5.5.Repeat
1-4
until
Repeat 1-4 untilall
alljobs
jobshave
havebeen
beenconsidered
considered
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© Ou Tang
Johnson’s algorithm - Example
14
Order splitting (1)
Five cars need to be washed and waxed in a work station
(J)aguar
(C)adillac
(F)ord
(H)onda
(L)exus
0 1
Wash
F
4
J
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F
C
L
15
H
13
9
J
Lead
Lead time
time reduction
reduction of
of an
an order
order
13
8
3 4
0 1
Wax
Wash (hours) Wax (hours)
3
5
5
3
1
2
2
1
4
4
L
16 17
C
H
15
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Order splitting (2)
Over lapping
Lead
Leadtime
timeand
andWIP
WIPreduction
reduction
Lead-time
Lead-time reduction
reduction of
of aa high
high priority
priority order
order
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Make or buy decisions, Outsourcing
18
Purchasing
•• What
What isis actually
actually bought?
bought?
–– Specific
Specificitems
items
–– Capacity
Capacityof
ofthe
thesupplier
supplier(for
(formanufacturing
manufacturingof
ofaa
type/family
type/familyof
ofitems)
items)
•• Long
Long term
term (strategical)
(strategical)
–– Purchasing
Purchasingor
ordeveloping
developingaanew
newengine
enginefor
foraacar
car
•• Medium
Medium term
term (tactical)
(tactical)
•• Motive
Motive for
for purchasing
purchasing
–– Selecting
Selectingsupplier
supplierfor
forstandard
standardcomponents
components
–– The
Thecapability
capabilityto
toproduce
producean
anitem
itemisisoutside
outsidethe
the
scope
of
the
own
enterprise
scope of the own enterprise
–– Patent
Patentor
ortrade
tradesecrets
secretspossessed
possessedby
bythe
thesupplier
supplier
–– Cost
advantages
of
the
supplier
Cost advantages of the supplier
–– The
Thesupplier
supplierisissimply
simplyaabetter
bettermanufacturer
manufacturerof
of
the
specific
products
the specific products
•• Short
Short term
term (operative)
(operative)
–– Sub-contracting
Sub-contractingdue
dueto
totemporary
temporarylack
lackof
ofcapacity
capacity
(alternative
to
over-time)
(alternative to over-time)
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© Ou Tang
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Queue in manufacturing and service systems
Classification of purchasing
1. In a manufacturing system, queue = congestion inventory
waste, expense, not value-added, etc.
2. In a service system, queue = poor service
3. In a stochastic system, queues are unavoidable!
•• Non-product
Non-productrelated
related
––
––
––
Process
Processparts
parts(machines
(machinesetc.)
etc.)
Material
handling
Material handlingequipment
equipment
Communication
Communicationequipment
equipment
But they can be reduced if disturbances and variability
are handled well and/or by adding to the capacity of the system
•• Product
Productrelated
related
––
––
Sub
Subsystems
systems(e.g.
(e.g.engines,
engines,instrument
instrumentpanels
panels))
Components
(e.g.
wires,
tires)
Components (e.g. wires, tires)
•• Consumable
Consumablesupplies
supplies
–– Office
Officesupplies
supplies(t.ex.
(t.ex.papper,
papper,kuvert)
kuvert)
–– Other
Other(e.g.
(e.g.light
lightbulbes,
bulbes,paper
papertowels)
towels)
Who
Whowants
wantsto
tobe
beour
oursupplier?
supplier?
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Reasons for study queueing theory
22
An overview of the lead times
Queueing theory is the branch of operations research concerned
with waiting lines (delays/congestion)
In a manufacturing system, it aims to balance the following
performance measures
WIP inventory
Lead times
Throughput
Capacity utilisation
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Queueing time often
occupies the largest
portion of the lead
time
23
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Other queueing examples
Why do queues form?
Call Arrival
No time
Airport check-in
Automated Teller Machines (ATM)
Fast food restaurants
Traffic control
Telecommunications
Computer operations
Health services
Bank, post office etc
1
2
3
4
5
6
7
8
9
10
0
10
20
30
40
50
60
70
80
90
Call number
Processing
time
10
9
9
9
9
9
9
9
9
9
9
9
8
7
6
5
4
3
2
1
0
20
40
60
80
100
TIME
When the arrival time and processing time are deterministic and synchronized, there is
no queues built up.
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© Ou Tang
Why do queues form?
Call Arrival
No time
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
Processing
time
Why do queues form?
•
Call number
10
9
9
9
9
9
9
9
9
9
9
9
26
8
variability:
– arrival times
– service times
– processor availability
7
6
When variability exits, queues are
built up
5
Call number
10
9
8
7
6
5
4
3
2
1
0
0
20
40
4
60
80
100
80
100
TIME
3
Number of calls in system
2
5
1
4
0
20
40
60
80
100
3
TIME
2
When the arrival time and processing time are not synchronized, queues are built up.
1
0
0
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20
40
60
TIME
28
Structure of queueing models
Little’s law
L s = λ eff W s
C
C
In
Input
source
Out
Inventory = Throughput X Lead time
C
C C C C
C
C
λeff is the effective arrival rate at the system. It equals the nominal arrival
rate λ when all customers can join the system.
C
Arrival
process
Size of user
Service
mechanism
Queue discipline and
queue capacity
Number of servers
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© Ou Tang
A queueing approximation
30
Example
The expected number of customer (inventory) in the queue is
Lq =
ρ
2 ( k +1)
1− ρ
Ci + C p
2
×
• A manufacturing process (for example making plastic parts)
consists of five machines.
• Processing times have a mean of 5.4 days and standard
deviation of 4 days.
• Management has collected date on customer orders, and
verified that the time between orders has a mean of 1.2 days and
variance of 0.72 days.
2
2
ρ - capacity utilisation
k - number of server
Ci- coefficient of variant of interarrival time
Cp- coefficient of variant of service time
Coefficient of variant is defined as the ratio between the standard deviation
and the mean of a random variable.
• Question: What is the average waiting time for an order ?
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Throughput delay curve
Example
k=5
Ci = 0.72/1.2 = 0.6
Co = 4/5.4 = 0.74
Arrival rate = 1/1.2=0.8333
Service rate = 1/5.4=0.185
ρ =
0.8333
= 0.90
0.185 × 5
Lq =
0.9 2(5+1) 0.62 + 0.742
×
= 3.15
1 − 0.9
2
Queue
(length/time)
Variability increases
Waiting time in the queue = Lq/arrival rate
=3.15/0.8333=3.78
Load/capacity
100%
In the presence of variability, high capacity utilisation is accompanied by
long waiting time.
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Consequences of planned lead times
The
Thevicious
viciouslead
leadtime
timecircle
circle
Increase the
planned lead time
More delays
Actual lead times increases
Increased load
More order releases
Increased queue time
due to early orders
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© Ou Tang
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