The Corrupting Influence of Variability
When luck is on your side, you can do without brains.
– Giordano Bruno,burned
at the stake in 1600
The more you know the luckier you get.
– “J.R. Ewing” of Dallas
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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1
Performance of a Serial Line
Measures:
•
•
•
•
•
•
Links to Business Strategy:
Throughput
Inventory (RMI, WIP, FGI)
Cycle Time
Lead Time
Customer Service
Quality
Evaluation:
• Comparison to “perfect”
values (e.g., rb, T0)
• Relative weights consistent
with business strategy?
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
• Would inventory reduction
result in significant cost
savings?
• Would CT (or LT) reduction
result in significant
competitive advantage?
• Would TH increase help
generate significantly more
revenue?
• Would improved customer
service generate business over
the long run?
Remember – standards
change over time!
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2
Capacity Laws
Capacity Law: In steady state, all plants will release work
at an average rate that is strictly less than average
capacity.
Utilization Law: If a station increases utilization without
making any other change, average WIP and cycle time
will increase in a highly nonlinear fashion.
Notes:
• Cannot run at full capacity (including overtime, etc.)
• Failure to recognize this leads to “fire fighting”
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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3
Cycle Time vs. Utilization
24
22
20
Cycle Time (hrs)
18
16
14
12
High
Variability
10
8
6
Low
Variability
4
Capacity
2
0
0
0.1
0.2
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
0.3
0.4
0.5
0.6
0.7
0.8
Release Rate (entities/hr)
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0.9
1
1.1
1.2
4
What Really Happens:
System with Insufficient Capacity
700
600
500
WIP
400
300
200
100
0
0
5
10
15
20
25
30
35
40
45
Day
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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5
120
120
100
100
80
80
WIP
WIP
What Really Happens:
Two Cases with Releases at 100% of Capacity
60
60
40
40
20
20
0
0
0
10
20
30
40
50
60
0
10
Day
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
20
30
40
50
60
Day
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6
120
120
100
100
80
80
WIP
WIP
What Really Happens:
Two Cases with Releases at 82% of Capacity
60
60
40
40
20
20
0
0
0
10
20
30
40
50
60
0
10
Day
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
20
30
40
50
60
Day
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7
Overtime Vicious Cycle
1. Release work at plant capacity.
2. Variability causes WIP to increase.
3. Jobs are late, customers complain,…
4. Authorize one-time use of overtime.
5. WIP falls, cycle times go down, backlog is
reduced.
6. Breathe sigh of relief.
7. Go to Step 1!
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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8
Mechanics of Overtime Vicious Cycle
50
CT without
Overtime
45
40
Cycle Time (hrs)
35
30
25
20
15
Original
Capacity
10
CT with
Overtime
5
Capacity
with Overtime
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Release Rate (entities/hr)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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1.2
1.3
1.4
1.5
9
Influence of Variability
Variability Law: Increasing variability always degrades the
performance of a production system.
Examples:
• process time variability pushes best case toward worst case
• higher demand variability requires more safety stock for same
level of customer service
• higher cycle time variability requires longer lead time quotes to
attain same level of on-time delivery
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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10
Variability Buffering
Buffering Law: Systems with variability must be buffered by
some combination of:
1. inventory
2. capacity
3. time.
Interpretation: If you cannot pay to reduce variability, you will pay in
terms of high WIP, under-utilized capacity, or reduced customer service
(i.e., lost sales, long lead times, and/or late deliveries).
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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11
Variability Buffering Examples
Ballpoint Pens:
• can’t buffer with time (who will backorder a cheap pen?)
• can’t buffer with capacity (too expensive, and slow)
• must buffer with inventory
Ambulance Service:
• can’t buffer with inventory (stock of emergency services?)
• can’t buffer with time (violates strategic objectives)
• must buffer with capacity
Organ Transplants:
• can’t buffer with WIP (perishable)
• can’t buffer with capacity (ethically anyway)
• must buffer with time
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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12
Simulation Studies
TH Constrained System (push)
1
2
3
4
ra, ca B(1)= te(1), ce(1) B(2)= te(2), ce(2) B(3)= te(3), ce(3) B(4)= te(4), ce(4)
WIP Constrained System (pull)
Infinite
raw
materials
1
2
te(1), ce(1)
B(2)
te(2), ce(2)
3
B(3)
te(3), ce(3)
4
B(4)
te(4), ce(4)
ra  arrival rate
ca  CV of interarriv al times
te (i )  effective process time at station i
ce (i )  effective CV at station i
B(i )  buffer size in front of station i
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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13
Variability in Push Systems
Case
1
2
3
4
te(i),
te(3) c(i), i = 1-4 TH
CT
WIP CT
Comments
i = 1, 2, 4 (min) (unitless) (j/min) (min) (jobs) (min)
(min)
1
1.2
0
0.8
4.2
3.4
0.0
best case
1
1.2
1
0.8
44.6 35.7 26.8
WIP buffer
1
1.0
1
0.8
20.0 16.0 10.3 capacity buffer
1
1.2
0.3
0.8
7.8
6.2
3.3
reduced
variability
Notes:
• ra = 0.8, ca = ce(i) in all cases.
• B(i) = , i = 1-4 in all cases.
Observations:
• TH is set by release rate in a push system.
• Increasing capacity (rb) reduces need for WIP buffering.
• Reducing process variability reduces WIP, CT, and CT variability
for a given throughput level.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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14
Variability in Pull Systems
Case
1
2
3
4
5
te(i), te(3) c(i), i = 1-4 B(3)
TH
CT
WIP CT
i = (min) (unitless) (jobs) (j/min) (min) (jobs) (min)
1,2,4
(min)
1
1.2
0
0
0.83
4.6
3.8
0.0
1
1.2
1
0
0.48
6.4
3.1
2.4
1
1.2
1
1
0.53
7.2
3.8
2.6
1
1.2
0.3
0
0.72
5.0
3.6
0.6
1
1.2
0.3
1
0.76
6.0
4.5
0.8
6
1
1.2
0.3
0
0.73
6.3
4.6
0.7
Comments
best case
plain JIT
inv buffer
var reduction
inv buffer +
var reduction
non-bottleneck
buffer
Notes:
• Station 1 pulls in job whenever it becomes empty.
• B(i) = 0, i = 1, 2, 4 in all cases, except case 6, which has B(2) = 1.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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15
Variability in Pull Systems (cont.)
Observations:
•
•
•
•
•
•
•
Capping WIP without reducing variability reduces TH.
WIP cap limits effect of process variability on WIP/CT.
Reducing process variability increases TH, given same buffers.
Adding buffer space at bottleneck increases TH.
Magnitude of impact of adding buffers depends on variability.
Buffering less helpful at non-bottlenecks.
Reducing process variability reduces CT variability.
Conclusion: consequences of variability are different in push
and pull systems, but in either case the buffering law implies
that you will pay for variability somehow.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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16
Example – Discrete Parts Flowline
process
buffer
process
buffer
process
Inventory Buffers: raw materials, WIP between processes, FGI
Capacity Buffers: overtime, equipment capacity, staffing
Time Buffers: frozen zone, time fences, lead time quotes
Variability Reduction: smaller WIP & FGI , shorter cycle times
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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17
Example – Batch Chemical Process
reactor
column
tank
reactor
column
tank
reactor
column
Inventory Buffers: raw materials, WIP in tanks, finished goods
Capacity Buffers: idle time at reactors
Time Buffers: lead times in supply chain
Variability Reduction: WIP is tightly constrained, so target is
primarily throughput improvement, and maybe FGI reduction.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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18
Example – Moving Assembly Line
in-line buffer
fabrication lines
final assembly line
Inventory Buffers: components, in-line buffers
Capacity Buffers: overtime, rework loops, warranty repairs
Time Buffers: lead time quotes
Variability Reduction: initially directed at WIP reduction, but
later to achieve better use of capacity (e.g., more throughput)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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19
Buffer Flexibility
Buffer Flexibility Corollary: Flexibility reduces the amount
of variability buffering required in a production system.
Examples:
• Flexible Capacity: cross-trained workers
• Flexible Inventory: generic stock (e.g., assemble to order)
• Flexible Time: variable lead time quotes
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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20
Variability from Batching
VUT Equation:
• CT depends on process variability and flow variability
Batching:
• affects flow variability
• affects waiting inventory
Conclusion: batching is an important determinant of
performance
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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21
Process Batch Versus Move Batch
Dedicated Assembly Line: What should the batch size be?
Process Batch:
• Related to length of setup.
• The longer the setup the larger the lot size required for the same
capacity.
Move (transfer) Batch: Why should it equal process batch?
• The smaller the move batch, the shorter the cycle time.
• The smaller the move batch, the more material handling.
Lot Splitting: Move batch can be different from process batch.
1. Establish smallest economical move batch.
2. Group batches of like families together at bottleneck to avoid setups.
3. Implement using a “backlog”.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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22
Process Batching Effects
Types of Process Batching:
1. Serial Batching:
• processes with sequence-dependent setups
• “batch size” is number of jobs between setups
• batching used to reduce loss of capacity from setups
2. Parallel Batching:
• true “batch” operations (e.g., heat treat)
• “batch size” is number of jobs run together
• batching used to increase effective rate of process
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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23
Process Batching
Process Batching Law: In stations with batch operations or
significant changeover times:
1. The minimum process batch size that yields a stable
system may be greater than one.
2. As process batch size becomes large, cycle time grows
proportionally with batch size.
3. Cycle time at the station will be minimized for some
process batch size, which may be greater than one.
Basic Batching Tradeoff: WIP versus capacity
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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24
Serial Batching
Parameters:
k  serial batch size (10)
t  time to process a single part (1)
s  time to perform a setup (5)
ce  CV for batch (parts  setup) (0.5)
ra  arrival rate for parts (0.4)
ca  CV of batch arrivals (1.0)
k
ra,ca
ts
setup
t0
Time to process batch: te = kt + s
te = 10(1) + 5 = 15
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
forming
batch
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queue of
batches
25
Process Batching Effects (cont.)
Arrival rate of batches: ra/k
ra = 0.4/10 = 0.04
Utilization: u = (ra/k)(kt + s)
u = 0.04(10·1+5) = 0.6
sra
For stability: u < 1 requires k 
1  tra
k
5(0.4)
 3.33
1  1(0.4)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
minimum batch size required
for stability of system...
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26
Process Batching Effects (cont.)
Average queue time at station:
 ca2  ce2
CTq  
 2
 u 
 1  0.5  0.6 

t


 1  u  e  2  1  0.6 15  16 .875

Average cycle time depends on move batch size:
Note: we assume
arrival CV of
batches is ca
regardless of
batch size – an
approximation...
• Move batch = process batch
CTnon split  CTq  te  CTq  s  kt
 16 .875  15  31 .875
• Move batch = 1
k 1
t
2
10  1
 16 .875  10 
(1.0)  27 .375
2
CTsplit  CTq  s 
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Note: splitting move
batches reduces wait
for batch time.
27
Cycle Time vs. Batch Size – 5 hr setup
80.00
Cycle Time (hrs)
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
0
5
10
Optimum
Batch Sizes
15
20
25
35
40
45
50
Batch Size (jobs/batch)
No Lot Splitting
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
30
Lot Splitting
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28
Cycle Time vs. Batch Size – 2.5 hr setup
80.00
Cycle Time (hrs)
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
0
5
Optimum
Batch Sizes
10
15
20
25
35
40
45
50
Batch Size (jobs/batch)
No Lot Splitting
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
30
Lot Splitting
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29
Setup Time Reduction
Where?
• Stations where capacity is expensive
• Excess capacity may sometimes be cheaper
Steps:
1. Externalize portions of setup
2. Reduce adjustment time (guides, clamps, etc.)
3. Technological advancements (hoists, quick-release, etc.)
Caveat: Don’t count on capacity increase; more flexibility will
require more setups.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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30
Parallel Batching
Parameters:
k  parallel batch size (10)
t  time to process a batch (90)
ce  CV for batch (1.0)
ra  arrival rate for parts (0.05)
ca  CV of batch arrivals (1.0)
B  maximum batch size (100)
Time to form batch: W 
k 1 1
2 ra
ra,ca
t
k
W = ((10 – 1)/2)(1/0.005) = 90
Time to process batch: te = t
forming
batch
queue of
batches
te = 90
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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31
Parallel Batching (cont.)
Arrival of batches: ra/k
ra/k = 0.05/10 = 0.005
Utilization: u = (ra/k)(t)
u = (0.005)(90) = 0.45
For stability: u < 1 requires k  ra t
minimum batch size required
for stability of system...
k > 0.05(90) = 4.5
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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32
Parallel Batching (cont.)
Average wait-for-batch time:
WT 
k  1 1 10  1 1

 90
2 ra
2 0.05
batch size affects
both wait-for-batch
time and queue time
Average queue plus process time at station:
 ca2 / k  c02
CT  
2

 u 
 0.1  1  0.45 

t

t




90  90  130 .5
 1  u 
 2  1  0.45 

Total cycle time:
CT  WT  90 130.5  220.5
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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33
Cycle Time vs. Batch Size in a Parallel Operation
queue time due to
utilization
1400.00
wait for batch time
Total Cycle Time
1200.00
1000.00
800.00
600.00
400.00
200.00
0.00
0
10
20
Optimum
Batch Size
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
30
40
50
60
70
Nb
http://www.factory-physics.com
80
90
100
110
B
34
Variable Batch Sizes
Observation: Waiting for full batch in parallel batch operation may not
make sense. Could just process whatever is there when operation
becomes available.
Example:
•
•
•
•
•
Furnace has space for 120 wrenches
Heat treat requires 1 hour
Demand averages 100 wrenches/hr
Induction coil can heat treat 1 wrench in 30 seconds
What is difference between performance of furnace and coil?
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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35
Variable Batch Sizes (cont.)
Furnace: Ignoring queueing due to variability
•
•
•
•
•
Process starts every hour
100
100 wrenches in furnace
50
50 wrenches waiting on average
150 total wrenches in WIP
CT = WIP/TH = 150/100 = 3/2 hr = 90 min
Induction Coil: Capacity same as furnace (120 wrenches/hr), but
• CT = 0.5 min = 0.0083 hr
• WIP = TH × CT = 100 × 0.0083 = 0.83 wrenches
Conclusion: Dramatic reduction in WIP and CT due to small batches—
independent of variability or other factors.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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36
Move Batching
Move Batching Law: Cycle times over a segment of a routing
are roughly proportional to the transfer batch sizes used over that
segment, provided there is no waiting for the conveyance device.
Insights:
• Basic Batching Tradeoff: WIP vs. move frequency
• Queueing for conveyance device can offset CT reduction from
reduced move batch size
• Move batching intimately related to material handling and layout
decisions
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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37
Move Batching
Problem:
• Two machines in series
• First machine receives individual parts at rate ra with CV of ca(1)
and puts out batches of size k.
• First machine has mean process time of te(1) for one part with CV
of ce(1).
• Second machine receives batches of k and put out individual parts.
• How does cycle time depend on the batch size k?
k
te(1),ce(1)
ra,ca(1)
te(2),ce(2)
single job
batch
Station 1
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Station 2
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38
Move Batching Calculations
Time at First Station:
• Average time before batching is:
ca2 (1)  ce2 (1) u(1)
te (1)  te (1)
2
1  u(1)
regular VUT
equation...
• Average time forming the batch is:
k 1 1 k 1

te (1)
2 ra 2u (1)
first part waits (k-1)(1/ra),
last part doesn’t wait, so
average is (k-1)(1/ra)/2
• Average time spent at the first station is:
ca2 (1)  ce2 (1) u (1)
k 1
CT(1) 
te (1)  te (1) 
te (1)
2
1  u (1)
2u (1)
k 1
 CT(1, no batching ) 
te (1)
2u (1)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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39
Move Batching Calculations (cont.)
Output of First Station:
• Time between output of individual parts into the batch is ta.
because
• Time between output of batches of size k is kta.
cd2(1)=d2/ta2
2
2
• Variance of interoutput times of parts is cd (1)ta , where
by def of CV
cd2 (1)  (1  u (1) 2 )ca2 (1)  u (1) 2 ce2 (1)
• Variance of batches of size k is kcd2(1)ta2. because departures are
independent, so variances add
• SCV of batch arrivals to station 2 is:
kcd2 (1)t a2
c ( 2) 
k 2t a2
2
a
variance divided by
mean squared...
cd2 (1)

k
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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40
Move Batching Calculations (cont.)
independent
process times...
Time at Second Station:
• Time to process a batch of size k is kte(2).
• Variance of time to process a batch of size k is kce2(2)te2(2).
• SCV for a batch of size k is: kce2 (2)t e2 (2) ce2 (2)
2 2
e
k t ( 2)

k
• Mean time spent in partial batch of size k is:
first part doesn’t wait,
k 1
last part waits (k-1)te(2),
t e ( 2)
2
so average is (k-1)te(2)/2
• So, average time spent at the second station is:
cd2 (1) / k  ce2 (2) / k u (2)
k 1
CT (2) 
kte (2) 
t e (2)  t e (2)
2
1  u (2)
2
VUT equation to
k 1
compute queue time
 CT(2, no batching) 
t e (2)
2
of batches...
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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41
Move Batching Calculations (cont.)
Total Cycle Time:
CT(batching )  CT(no batching) 
k 1
k 1
te (1) 
te (2)
2u (1)
2

 k  1  te (1)
 CT(no batching )  
 te (2) 

 2  u (1)

Insight:
inflation factor due
to move batching
• Cycle time increases with k.
• Inflation term does not involve CV’s
• Congestion from batching is more bad control than randomness.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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42
Assembly Operations
Assembly Operations Law: The performance of an assembly
station is degraded by increasing any of the following:
1. Number of components being assembled.
2. Variability of component arrivals.
3. Lack of coordination between component arrivals.
Observations:
• This law can be viewed as special instance of variability law.
• Number of components affected by product/process design.
• Arrival variability affected by process variability and production
control.
• Coordination affected by scheduling and shop floor control.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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43
Attacking Variability
Objectives
• reduce cycle time
• increase throughput
• improve customer service
Levers
•
•
•
•
•
reduce variability directly
buffer using inventory
buffer using capacity
buffer using time
increase buffer flexibility
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Cycle Time
Definition (Station Cycle Time): The average cycle time
at a station is made up of the following components:
cycle time = move time + queue time + setup time +
process time + wait-to-batch time +
wait-in-batch time + wait-to-match time
delay times
typically
make up
90% of CT
Definition (Line Cycle Time): The average cycle time in a
line is equal to the sum of the cycle times at the individual
stations less any time that overlaps two or more stations.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Reducing Queue Delay
CTq = V U t
 ca2  ce2

 2





 u 


1 u 
Reduce Variability
Reduce Utilization
• failures
• setups
• uneven arrivals, etc.
• arrival rate (yield, rework, etc.)
• process rate (speed, time,
availability, etc)
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Reducing Batching Delay
CTbatch = delay at stations + delay between stations
Reduce Process Batching
Reduce Move Batching
• Optimize batch sizes
• Reduce setups
– Stations where capacity is
expensive
– Capacity vs. WIP/CT tradeoff
• Move more frequently
• Layout to support
material handling (e.g.,
cells)
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Reducing Matching Delay
CTbatch = delay due to lack of synchronization
Reduce Variability
Improve Coordination
• on high utilization
fabrication lines
• usual variability
reduction methods
• scheduling
• pull mechanisms
• modular designs
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Reduce Number
of Components
• product redesign
• kitting
48
Increasing Throughput
TH = P(bottleneck is busy)  bottleneck rate
Reduce Blocking/Starving
• buffer with inventory (near
bottleneck)
• reduce system “desire to queue”
CTq = V U t
Reduce Variability
Increase Capacity
• add equipment
• increase operating time (e.g.
spell breaks)
• increase reliability
• reduce yield loss/rework
Reduce Utilization
Note: if WIP is limited, then system degrades
via TH loss rather than WIP/CT inflation
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Customer Service
Elements of Customer Service:
• lead time
• fill rate (% of orders delivered on-time)
• quality
Law (Lead Time): The manufacturing lead time for a routing
that yields a given service level is an increasing function of
both the mean and standard deviation of the cycle time of the
routing.
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Improving Customer Service
LT = CT + z CT
Reduce CT Visible
to Customer
• delayed
differentiation
• assemble to order
• stock components
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Reduce Average CT
Reduce CT Variability
• queue time
• batch time
• match time
generally same as methods
for reducing average CT:
• improve reliability
• improve maintainability
• reduce labor variability
• improve quality
• improve scheduling, etc.
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Cycle Time and Lead Time
0.18
CT = 10
CT = 3
0.16
0.14
Lead Time = 14 days
Densities
0.12
0.1
0.08
CT = 10
CT = 6
Lead Time = 27 days
0.06
0.04
0.02
0
0 2
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Cycle Time in Days
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Diagnostics Using Factory Physics®
Situation:
• Two machines in series; machine 2 is bottleneck
• ca2 = 1
• Machine 1: t 0  19 min
c02  0.25
MTTF  48 hr, MTTR  8 hr
• Machine 2: t 0  22 min
c02  1
MTTF  3.3 hr, MTTR  10 min
– Space at machine 2 for 20 jobs of WIP
• Desired throughput 2.4 jobs/hr, not being met
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Diagnostic Example (cont.)
Proposal: Install second machine at station 2
• Expensive
• Very little space
Analysis Tools:
ca2  ce2 u
CTq 
te
2 1 u
cd2  u 2 ce2  (1  u 2 )ca2
Analysis:
VUT equation
propogation equation
Ask why five times...
Step 1: At 2.4 job/hr
• CTq at first station is 645 minutes, average WIP is 25.8 jobs.
• CTq at second station is 892 minutes, average WIP is 35.7 jobs.
• Space requirements at machine 2 are violated!
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Diagnostic Example (cont.)
Step 2: Why is CTq at machine 2 so big?
• Break CTq into
 ca2  ce2  u 

CTq  
te  (3.16)(12.22)( 23.11 min)
 2  1  u 
• The 23.11 min term is small.
• The 12.22 correction term is moderate (u  0.9244)
• The 3.16 correction is large.
Step 3: Why is the correction term so large?
• Look at components of correction term.
• ce2 = 1.04, ca2 = 5.27.
• Arrivals to machine are highly variable.
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Diagnostic Example (cont.)
Step 4: Why is ca2 to machine 2 so large?
• Recall that ca2 to machine 2 equals cd2 from machine 1, and
cd2  u 2 ce2  (1  u 2 )ca2  (0.887 2 )(6.437)  (1  0.887 2 )(1.0)  5.27
• ce2 at machine 1 is large.
Step 5: Why is ce2 at machine 1 large?
• Effective CV at machine 1 is affected by failures,
ce2  c02  2 A(1  A)
mr
 0.25  6.18  6.43
t0
• The inflation due to failures is large.
• Reducing MTTR at machine 1 would substantially improve
performance.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Procoat Case – Situation
Problem:
•
•
•
•
Current WIP around 1500 panels
Desired capacity of 3000 panels/day (19.5 hr day with breaks/lunches)
Typical output of 1150 panels/day
Outside vendor being used to make up slack
Proposal:
• Expose is bottleneck, but in clean room
• Expansion would be expensive
• Suggested alternative is to add bake oven for touchups
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Procoat Case – Layout
Loader
Clean
Coat 1
Coat 2
Unloader
IN
Touchup
Unloader
Bake
D&I
Inspect Develop
Manufacturing Inspect
Loader
Expose
Clean Room
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Procoat Case – Capacity Calculations
Process Std Dev
or Load Process Conveyor Number
Machine
Time
Time
Trip Time
of
Name
(min)
(min)
(min)
Machines MTTF MTTR
Clean1
0.33
0
15
1
80
4
Coat1
0.33
0
15
1
80
4
Coat2
0.33
0
15
1
80
4
Expose
103
67
5
300
10
Develop
0.33
0
2.67
1
300
3
Inspect
0.5
0.5
2
Bake
0.33
0
100
1
300
3
MI
161
64
8
Touchup
9
0
1
-
Avail
0.95
0.95
0.95
0.97
0.99
1.00
0.99
1.00
1.00
Setup
Rate
Time (p/day)
0
3377
0
3377
0
3377
15
2879
0
3510
0
4680
0
3510
0
3488
0
7800
2879
Time
(min)
36.5
36.5
36.5
121.9
22.7
0.5
121.0
161.0
9.0
545.7
rb = 2,879 p/day
T0 = 546 min = 0.47 days
W0 = rbT0 = 1,343 panels
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Procoat Case – Benchmarking
TH Resulting from PWC with WIP = 1,500:
TH 
w
1,500
rb 
2,879  1,520
w  W0  1
1,500  1,343  1
Higher than
actual TH
Conclusion: actual system is significantly worse than PWC.
Question: what to do?
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Procoat Case – Factory Physics® Analysis
1) Bottleneck Capacity (Expose)
- rate: operator training, setup reduction
- time: break spelling, shift changes
2) Bottleneck Starving
- process variability: operator training
- flow variability: coater line – field ready
replacements
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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reduces “desire to
queue” so that
clean room buffer
is adequate
61
Procoat Case – Outcome
3300
Best Case
3000
TH (panels/day)
2700
After
2400
"Good" Region
Practical Worst Case
2100
1800
"Bad" Region
1500
1200
Before
900
600
300
Worst Case
0
-300
0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
WIP (panels)
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Corrupting Influence Takeaways
Variance Degrades Performance:
• many sources of variability
• planned and unplanned
Variability Must be Buffered:
• inventory
• capacity
• time
Flexibility Reduces Need for Buffering:
• still need buffers, but smaller ones
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63
Corrupting Influence Takeaways (cont.)
Variability and Utilization Interact:
• congestion effects multiply
• utilization effects are highly nonlinear
• importance of bottleneck management
Batching is an Important Source of Variability:
• process and move batching
• serial and parallel batching
• wait-to-batch time in addition to variability effects
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Corrupting Influence Takeaways (cont.)
Assembly Operations Magnify Impact of Variability:
• wait-to-match time
• caused by lack of synchronization
Variability Propagates:
• flow variability is as disruptive as process variability
• non-bottlenecks can be major problems
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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65