The Effects of Process Variability
35E00100 Service Operations and Strategy
#3 Fall 2015
Topics on Variability
Variability basics
 Measure of variability
 Process variability
 Flow variability
 Key points
The corrupting influence of variability
 Factory physics “laws”
 Batching
 Serial system
 Parallel system
 Transfer batching
 Ways to improve operations
 Key points
Useful material: Hopp, W. & Spearman, M. (2000), Factory Physics, Chapters 8, 9 and 15.3
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Basics - The Concept of Variability
Variability
 Any departure from uniformity (regular, predictable behavior)
 Sources and causes
 Compared to randomness?
Use of intuition
Measuring variability
 Coefficient of variation (CV)
te = mean process time of a job
 e = standard deviation of process time
e
te
 Classification based on the values of CV:
CV  ce 
Low variability (LV)
0
Moderate variability (MV)
High variability (HV)
0.75
1.33
 Natural process times have generally low variability (LV)
 Effective process times can be LV, MV, or HV
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ce
Hopp and Spearman 2000, 248-254
Aalto/BIZ Logistics
Measuring Variability
What is the
variability of each
machine?
Day
Machine 1
1
22
2
25
3
23
4
26
5
24
6
28
7
21
8
30
9
24
10
28
11
27
12
25
13
24
14
23
15
22
mean
24,8
st dev
2,6
CV
0,1
35E00100 Service Operations and Strategy #3
Machine 2
5
6
5
35
7
45
6
6
5
4
7
50
6
6
5
13,2
15,9
1,2
4
Illustrative
example
Machine 3
5
6
5
35
7
45
6
6
5
4
7
500
6
6
5
43,2
127,0
2,9
Aalto/BIZ Logistics
Natural Variability
Variability without explicitly analyzed cause(s)
Sources in process
 Operator pace
 Material fluctuations
 Product type (if not explicitly considered)
 Product quality
Observation
 Natural process variability is usually in the low variability
category
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Hopp and Spearman 2000, 255
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Mean Effects of Breakdowns
Definitions
t0  natural (base) process time
c0  CV of natural process time
r0  1
t0
 base capacity rate
m f  mean time to failure (MTTF)
mr  mean time to repair (MTTR)
Availability A is the fraction of time machine is up:
A
mf
m f  mr
Effective process time te and rate re can be calculated as follows:
t0
te 
A
m
m
re   A  Ar0
te
t0
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Hopp and Spearman 2000, 256
Aalto/BIZ Logistics
Example 1
Which machine is better?
Two machines, Tortoise 2000 and Hare X19,
 are subject to the same average workload: 69 jobs per day
 operate 24 hours per day  2.875 jobs per hour
 have unpredictable breakdowns
 Tortoise 2000 has long, infrequent breakdowns
 Hare X19 has short, more frequent breakdowns
How would you compare?
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Example 1
Calculating Machine Availability
Tortoise 2000
 t0

0
Hare X19
= 15 min
 t0
= 3.35 min

0 = 3.35 min
 c02 = 02/t02= 3.352/152 = 0.05
= 02/t02= 3.352/152 =
 c02
= 15 min
0.05
 mf
= 1.9 hrs (114 min)
 mf
= 12.4 hrs (744 min)
 mr
= 0.633 hrs (38 min)
 mr
= 4.133 hrs (248 min)
 cr
= 1.0
 cr
= 1.0
Availability of the machine
Availability
m f of the machine
744
A

 0.75
m f  mr 744  248
A
mf
m f  mr

114
 0.75
114  38
No difference between the machines in terms of availability.
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Hopp and Spearman 2000, 256
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Variability Effects of Downtime
Assumptions
 Times between failures are exponentially distributed
 Time to repair follows some probability distribution
Effective variability
te  t0 / A
0 
2
2
(
m


2
r
r )(1  A)t 0
σe    
A
 A
2

mr
2
2
2
e
ce  2  c0  (1  cr ) A(1  A)
te
t0
2
Variability depends on
repair times in addition
to availability
Conclusions
 Failures inflate mean, variance, and CV of effective process time
 Mean te increases proportionally with 1/A
 For constant availability A, long infrequent breakdowns increase SCV
more than short frequent ones
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Hopp and Spearman 2000, 257
Aalto/BIZ Logistics
Example 1
Estimating Variability
Hare X19
Tortoise 2000
te 
ce2

t0
15

 20 min
A 0.75
c02
 (1  cr2 ) A(1 
m
A) r
t0
 0.05  (1  1)0.75(1  0.75)
 6.25
te 
ce2
248
15
c02
 (1  cr2 ) A(1 
mr
A)
t0
 0.05  (1  1)0.75(1  0.75)
 1.0
High variability
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
t0
15

 20 min
A 0.75
38
15
Moderate variability
10
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Mean and Variability Effects of Setups
Analysis
N s  average number of jobs between setups (batch size)
t s  average setup duration
 s  standard deviation of setup time
ce2 
 e2
te2
te t0 
ts
Ns
2

Ns 1 2
s
2
2
 e  0   2 ts
Ns Ns
Observations
 Setups increase the mean and variance of processing times
 Variability reduction is one benefit of flexible machines
 Interaction is complex
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Hopp and Spearman 2000, 259
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Example 2
Mean Effects of Setups
Two machines
 Fast, inflexible machine: 2 hour setup every 10 jobs
 1 hr
 0.25
 10 jobs/setup
 2 hrs
t
2
te  t0  s  1 
 1.2 hrs
Ns
10
1
2
re   1/(1  )  0.8333 jobs/hr
te
10
 Slower, flexible machine: no setups
t0  1.2 hrs
c0  0.5
re  1/ t0  1/1.2  0.833 jobs/hr
t0
c0
Ns
ts
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In traditional analysis
there is no difference
between the machines.
Hopp and Spearman 2000, 260
Aalto/BIZ Logistics
Example 2
Variability Effects of Setups
Fast, inflexible machine
Slower, flexible machine
2 hour setup every 10 job
no setups
t0  1 hr
c02  0.0625
N s  10 jobs/setup
ts  2 hrs
t0  1.2 hrs
c02  0.25
re 
cs2  0.0625
2

Ns 1 
c
2
2
2
s

σ e   0  ts 

2 
N
Ns 
 s
 0.4475
ce2  0.31
1
1

 0.833 jobs/hr
t0 1.2
ce2  c02  0.25
Flexibility can reduce variability.
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Example 2
Variability Effects of Setups
Third Machine
New machine
 Otherwise same than the fast machine but more frequent setups
N s  5 jobs/setup
t s  1 hr

 hrs
t0  1 hr
te  1  1
c02  0.252  0.0625
cs2  0.252  0.0625
5
Analysis
re  1 / te  1 /(1  1 / 5)  0.833 jobs/hr
2

c
Ns 1 
2
2
2
s
σ e   0  ts 

  0.2350
2
 Ns
N s 

ce2  0.16
Conclusion
 Shorter, more frequent setups induce less variability
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Hopp and Spearman 2000, 260
Aalto/BIZ Logistics
Inflators of Process Variability
Sources e.g.
 Operator unavailability
 Batching
 Material unavailability
 Recycle
Effects of process variability
 Inflate the mean processing time te
 Inflate the CV of te
 Effective process variability can be LV, MV, or HV
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Flow Variability
Low variability arrivals
t
High variability arrivals
t
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Propagation of Variability
re(i)
ra(i)
ca
2(i)
re(i+1)
rd(i) = ra(i+1)
i
cd
2(i)
= ca
2(i+1)
ce2(i)
i+1
ce2(i+1)
Departure SCV in single machine station
cd2  u 2 ce2  (1  u 2 )ca2
where station utilization u is given by u = rate
Departure SCV in multi-machine station
cd2  1  (1  u 2 )(ca2  1) 
u2
m
ra te
where u 
m
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Departure variance
depends on arrival
variance and process
variance
(ce2  1)
Hopp and Spearman 2000, 262
Aalto/BIZ Logistics
Propagation of Variability
Low Utilization Stations
Low flow Var
Low flow Var
High process Var
High flow Var
High flow Var
High process Var
Low flow Var
Low flow Var
Low process Var
High flow Var
High flow Var
Low process Var
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Propagation of Variability
High Utilization Stations
Low flow Var
High flow Var
High process Var
High flow Var
High flow Var
High process Var
Low flow Var
Low flow Var
Low process Var
High flow Var
Low flow Var
Low process Var
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Variability Pooling
Basic idea
 CV of a sum of independent random variables decreases with
the number of random variables
Time to process a batch of parts
t0  time to process a single part
 0  standard deviation of time to process a single part
t0 (batch)  nt0
 02 (batch)  n 02
c02 (batch)
 02 (batch)
n 02
 02
c02
 2
 22  2 
n
t0 (batch) n t0 nt0
 c0 (batch) 
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c0
n
20
Hopp and Spearman 2000, 280
Aalto/BIZ Logistics
Key Points
Variability
 Cannot be eliminated
 Causes congestion
 Propagates
 Interacts with utilization
Components of process variability
 Failures, setups and many others deflate capacity and inflate
variability
 Long infrequent disruptions are worse than short frequent ones
Measure of variability: coefficient of variation (CV)
Pooled variability is less destructive than individual
variability
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Notation
ca2
ce2
cr2
c02
mf
mr
n
Ns
ra
re
rd
r0
ta
te
ts
t0
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
SCV of the inter-arrival time
SCV of the effective process time
SCV of the repair times
SCV of the base process time
mean time to failure
mean time to repair
number of jobs or parts in a batch
number of jobs or parts between setups
arrival rate
service rate
departure rate
base capacity rate
inter-arrival time
process time
setup time
base process time
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Abbreviations Used
CV
HV
LV
MTTF
MTTR
MV
SCV
= coefficient of variation
= high variability
= low variability
= mean time to failure
= mean time to repair
= moderate variability
= squared coefficient of variation
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The Corrupting Influence of
Variability
Factory Physics “Laws”
Law 1: Variability Law

Increasing variability degrades the performance of a production system.
Law 2: Variability Buffering Law

Systems w/ variability must be buffered by some combination of inventory, capacity and time.
Law 3: Product Flows Law

In a stable system, over the long run, the rate out of a system will equal to the rate in, less any yield loss, plus
any parts production within the system.
Law 4: Capacity Law

In steady state, all plants will release work at an average rate that is strictly less than the average capacity.
Law 5: Utilization Law

If a station increases utilization without making any other changes, average WIP and cycle time will increase in
a highly nonlinear fashion.
Law 6: Process Batching Law

In stations with batch operations or significant changeover times minimum process batch size yielding a stable
system may be over 1, cycle time at the station will be minimized for some process batch size (may be greater
than one), and as process batch size becomes large, average cycle time grows proportionally with batch size.
Law 7: Move Batching Law

Cycle times over a segment of a routing are roughly proportional to transfer batch sizes used over that
segment, provided there is no waiting for the conveyance device.
Law 8: Assembly Operations Law

The performance of an assembly station is degraded by increasing any of the following: the number of
components being assembled, variability of component arrivals, or lack of coordination between component
Hopp and Spearman 2000
arrivals.
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”Law 1”
Variability Law
Increasing variability degrades the performance
of a production system.
For example:
 Higher demand variability requires more safety stock for same level of customer
service.
 Higher cycle time variability requires longer lead time quotes to attain the same
level of on-time delivery.
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Hopp and Spearman 2000, 294-295
Aalto/BIZ Logistics
”Law 2”
Variability Buffering Law
Systems with variability must be buffered
by some combination of inventory,
capacity, and time.
Is variability always harmful?
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Hopp and Spearman 2000, 295-296
Aalto/BIZ Logistics
”Law 2”
Variability Buffering Law
Systems with variability must be buffered by some
combination of inventory, capacity, and time.
Inventory
Capacity
Time
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Hopp and Spearman 2000, 295-296
Aalto/BIZ Logistics
”Laws 3-5”
Material Flow Laws
Product flows
In a stable system, over the long run, the rate out of a system
will equal to the rate in, less any yield loss, plus any parts
production within the system.
Capacity
In steady state, all plants will release work at an average rate
that is strictly less than the average capacity.
Utilization
If a station increases utilization without making any other
changes, average WIP and cycle time will increase in a highly
nonlinear fashion.
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Hopp and Spearman 2000, 301-304
Aalto/BIZ Logistics
Cycle Time versus 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
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Release Rate (entities/hr)
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”Law 6”
Process Batching Law
In stations with batch operations or significant
changeover times
 The minimum process batch size that yields a stable system may
be greater than one.
 Cycle time at the station will be minimized for some process
batch size, which may be greater than one.
 As process batch size becomes large, average cycle time grows
proportionally with batch size.
Hopp and Spearman 2000, 306
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Recap: Forms of Batching
Serial batching
 Processes with sequence-dependent setups
 Batch size is the number of jobs between setups
 Reduces loss of capacity from setups
Parallel batching
 True batch operations
 Batch size is the number of jobs run together
 Increases the effective rate of process
Transfer batching
 Batch size is the number of parts that accumulate before being
transferred to the next station (not necessarily equal to the
process batch  lot splitting)
 Less material handling
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Process Batch Versus Move Batch
Case “Batch Size in a Dedicated Assembly Line”
Process batch
 Depends on the 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”.
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Batching and Process Performance
Impact of batching
 Flow variability
 Waiting inventory
 ca2  ce2
CTq  
 2

  u 2( m 1) 1 
 te

  m(1  u ) 


Impact of lot splitting
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Serial Batching
Parameters
k
ra
ca
k  serial batch size = 10
t  time to process a single part = 1
ts  time to perform a setup = 5
Forming
batch
ce2  SCV for batch (parts  setup) = 0.5
ra  arrival rate for parts = 0.4
Setup
ts
t
Queue of
batches
ca  CV of batch arrivals = 1.0
Effective process time
te  t s  kt  5  10  1  15
Arrival of batches
ra 0.4

 0.04
k
10
r
t
 5

u  a (t s  kt )  ra ( s  t )  0.4   1   0.6
k
k
 10 
rt
0.4  5.0
k as

 3.33
1  ra t
1  0.4  1.0
Utilization
For stability (u < 1)
Minimum batch size required
for stability of system
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Hopp and Spearman 2000, 307-310
Aalto/BIZ Logistics
Serial Batching
Average queue time at station
 c a2  ce2
CT q  
 2
 u 
 1  0 . 5  0 . 6 

t

 1  u  e  2  1  0.6 15  16 .875

Arrival CV of batches
is assumed ca
regardless of batch
size.
Average cycle time depends on move batch size
 Move batch = process batch
CTnon split  CTq  te  CTq  (t s  WIBTnonsplit  t )
 CTq  t s  (k  1)t  t  CTq  t s  kt
 16.875  5  10(1)  31.875
 Move batch = 1
CTsplit  CTq  ts  WIBTsplit
 16.875  5 
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k 1
 t =CTq  t s 
t
2
10  1
(1.0)  27.375
2
37
Splitting move
batches reduces
wait-in-batch time
Hopp and Spearman 2000, 307-310
Aalto/BIZ Logistics
Effect of Batch Size on Average Total CT
An analysis of a Series System
38
Cycle Time versus Batch Size
Cycle Time versus Batch Size in a Series System
350
300
Cycle Time
250
200
150
100
50
0
0
5
10
Optimum
batch size
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20
25
30
35
40
45
50
Batch size k
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Optimal Serial Process Batch Sizes
One Product
Assumptions
 Identical product families in terms of process and setup times
 Poisson arrivals
Effective process time
te  s  kt
Utilization
ra te ra
u
 ( s  kt )
k
k
Good approximation of the serial batch size minimizing
cycle time at a station is given by

k 
ra s

u  u0
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
ra s
CT is minimized through finding
the optimal station utilization.
u0  u0
Good approximation:
40
u   u0
Hopp and Spearman 2000, 502-504
Aalto/BIZ Logistics
Optimal Serial Process Batch Sizes
Multiple Products
Assumptions
 Multiple products
 Poisson arrivals
n
Eff. process time te 
  (s  k t ), where 
i
i i
i 1
Utilization
n
u

i 1
i

rai ki
n raj

i 1
ki
rai
( si  ki ti )
ki
Good approximation of the serial batch size minimizing
cycle time at a station is given by
L  si
k 
, where L 
ti

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
n
r st
i 1 ai i i
u *  u0
41
s
Hopp and Spearman 2000, 504-507
Aalto/BIZ Logistics
Parallel Batching
ra
ca
k
t0
Parameters
k  parallel batch size = 10
t  time to process a batch = 90
ce  effective CV for processing a batch = 1.0
ra  arrival rate for parts = 0.05
ca  CV of batch arrivals = 1.0
B = maximum batch size
Wait-to-batch time
Forming
batch
Queue of
batches
k  1 1 10  1 1
WTBT 

 90
2 ra
2 0.05
Time to process a batch te  t  90
Arrival rate of batches
Utilization
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ra 0.05
ra (batch ) 
 0.005
k
10
ra
u  t  0.005  90  0.45
Hopp and Spearman 2000, 310-311
k
Aalto/BIZ Logistics
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Parallel Batching
Minimum batch size required for system stability (u<1)
k  ra t
 k  0.05  90  4.5
Average queue + process time at station = CTq+ t
 ca2 / k  ce2   u 
CT  
t t
 


2

 1 u 
 0.1  1   0.45 

90  90  130.5



 2   1  0.45 
Total cycle time
CT  WTBT  CTq  t
k  1  ca2 / k  ce2

t 

2ku
2

 90  130.5  220.5
35E00100 Service Operations and Strategy #3
 u 
t t
 

 1 u 
43
Batch size affects
both WTBT and CTq.
Aalto/BIZ Logistics
Effect of Batch Size on Average Total CT
Analysis of a Parallel System
44
Cycle Time versus Batch Size
Parallel System
1400
Queue time due to
too high utilization
Total Cycle Time
1200
Wait for batch time
1000
800
600
400
200
0
B
0
10
Optimum
Batch Size
20
35E00100 Service Operations and Strategy #3
30
40
50
60
Nb45
70
80
90
100
110
Aalto/BIZ Logistics
”Law 7”
Move Batching Law
Cycle times over a segment of a routing are roughly
proportional to transfer batch sizes used over that
segment, provided there is no waiting for the conveyance
device.
Insights
 Queuing for conveyance device can offset cycle time reduction
from reduced move batch size.
 Move batching intimately related to material handling and layout
decisions.
35E00100 Service Operations and Strategy #3
46
Hopp and Spearman 2000, 312
Aalto/BIZ Logistics
Effects of Transfer Batching
Two machines in series
 Machine 1
 Receives individual parts at rate ra with CV of ca(1)
 Mean process time of te(1) for one part with CV of ce(1)
 Puts out batches of size k
 Machine 2
 Receives batches of k
 Mean process time of te(2) for one part with CV of ce(2)
 Puts out individual parts
 How does cycle time depend on the batch size k?
ra
ca(1)
te(1)
ce(1)
te(2)
ce(2)
k
batch
single job
Machine 1
Machine 2
Hopp and Spearman 2000, 312-314
35E00100 Service Operations and Strategy #3
47
Aalto/BIZ Logistics
Transfer Batching – Machine 1
 Average time forming the batch:
1st part waits (k-1)(1/ra), last part does not wait.
 Average time after batching:
k 1 1
k 1

te (1)
2 ra 2u (1)
ca2 (1)  ce2 (1) u (1)
te (1)  te (1)
2
1  u (1)
 Average total time spent at the 1st station:
ca2 (1)  ce2 (1) u (1)
k 1
k 1
CT(1) 
te (1)  te (1) 
te (1)  CT 
te (1)
2
1  u (1)
2u (1)
2u (1)
 Time between output of individual parts into the batch: ta
 Time between output of batches of size k: kta
 Variance of inter-output times of parts is cd2(1)ta2, where
cd2 (1)  (1  u (1) 2 )ca2 (1)  u (1) 2 ce2 (1)
 Variance of batches of size k:
35E00100 Service Operations and Strategy #3
kcd2 (1)ta2
48
By definition CV
cd2(1)=d2/ta2
Departures are independent
 variances add
Hopp and Spearman 2000, 312-314
Aalto/BIZ Logistics
Transfer Batching - Machine 2
 SCV of batch arrivals:
kcd2 (1)ta2
 Time to process a batch of size k:
kte (2)
 Variance of time to process a batch of size k:
kce2 (2)te2 (2)
 SCV for a batch of size k:
kce2 ( 2)t e2 ( 2) ce2 ( 2)

2 2
k
k t e ( 2)
k 2 ta2
 Mean time spent in partial batch of size k:
1st part doesn’t wait, last part waits (k-1)te(2)
cd2 (1)

k
k 1
t e ( 2)
2
 Average time spent at the 2nd station:
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
k 1
 CT(2, no batching) 
t e ( 2)
2
Hopp and Spearman 2000, 312-314
35E00100 Service Operations and Strategy #3
49
Aalto/BIZ Logistics
Transfer Batching – Total System
CTbatch  CT(1)  CT(2)
k 1
k 1
te (2)
te (1) 
 CT(no batching) 
2
2u (1)

 k  1   te (1)
 te (2) 
 CT(no batching)  


 2   u (1)

Inflation factor due
to transfer batching
Hopp and Spearman 2000, 312-314
35E00100 Service Operations and Strategy #3
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Aalto/BIZ Logistics
”Law 8”
Assembly Operations Law
The performance of an assembly station is
degraded by increasing any of the following
 The number of components being assembled
 Variability of component arrivals
 Lack of coordination between component arrivals
Hopp and Spearman 2000, 315-316
35E00100 Service Operations and Strategy #3
51
Aalto/BIZ Logistics
Ways to Improve Operations
1. Increase throughput
2. Reduce queue time
3. Reduce batching delay
4. Reduce matching delay
5. Improve customer service
35E00100 Service Operations and Strategy #3
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Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
1. Increase Throughput
Throughput =
P(bottleneck is busy)  bottleneck rate
Reduce blocking/starving
Increase capacity
•Buffer with inventory (near
bottleneck)
•Reduce system “desire to queue”
•Add equipment
•Increase operating time
•Increase reliability
•Reduce yield loss
•Quality improvements
CTq = VUT
Reduce
variability
35E00100 Service Operations and Strategy #3
Reduce
utilization
53
Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
2. Reduce Queue Delay
CTq =VUT
 ca2  ce2

 2





 u 


1 u 
Reduce variability
Reduce utilization
•Process variability
•Increase bottleneck rate
- Decrease time to repair
- Cross-training
- Repair times, setups
•Arrival variability
•Reduce flow into bottleneck
- Decrease process
variability in upstream
- Pull system
- Eliminate batch releases
35E00100 Service Operations and Strategy #3
- Improve yield
- Reduce rework, etc
54
Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
3. Reduce Batching Delay
CTbatch = delay at stations + delay between stations
Reduce process batching
Reduce move batching
•Optimize batch sizes
•Reduce setups
•Move more frequently
•Layout to support material
handling
- Stations where capacity is
expensive
- Capacity versus WIP tradeoff
35E00100 Service Operations and Strategy #3
- E.g. cell manufacturing
55
Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
4. Reduce Matching Delay
CTmatch = delay due to lack of synchronization
Reduce variability
Improve coordination
•Scheduling
•Pull mechanisms
•Modular designs
35E00100 Service Operations and Strategy #3
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Reduce number
of components
•E.g. product
redesign
Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
5. Improve Customer Service
LT = CT + zCT
Safety lead time
Reduce avg CT
•Queue time
•Batch time
•Match time
35E00100 Service Operations and Strategy #3
Reduce quoted LT
•Assembly to order
•Stock components
•Delayed differentiation
57
Reduce CT variability
(Generally same methods as for CT
reduction)
•Improve reliability
•Improve maintainability
•Reduce labor variability
•Improve quality
•Improve scheduling, etc.
Hopp and Spearman 2000, 324-32
Aalto/BIZ Logistics
Variability Influences Cycle Times and
Lead Times
0,18
0,16
CT = 10
CT = 3
0,14
Lead Time = 14 days
Densities
0,12
0,10
0,08
Lead Time = 27 days
CT = 10
CT = 6
0,06
0,04
0,02
0,00
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
35E00100 Service Operations and Strategy #3
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Aalto/BIZ Logistics
Key Points
Factory physics laws!
Variability
 Decreases performance
 Buffering through inventory, capacity, and time
 Interacts with utilization
 Congestion effects multiply
 Nonlinear effects of utilization on cycle time
Batching
 In serial and parallel batching minimum feasible batch size may
be greater than one
 Cycle time increases proportionally with batch size
 Without wait-for-batch time, cycle time decreases in batch size
 Lot splitting can reduce the effects of batching
 Batching delay is essentially separate from a variability delay.
35E00100 Service Operations and Strategy #3
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Aalto/BIZ Logistics
Notation
ce2
cd2
CT
D/d
k
LT
n
Ns
ra
rb
re
rd
ts
t0
u0
WTBT
WIBT
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
SCV of the effective process time (parts and setups)
SCV of the departure times
cycle time
demand
serial batch size
lead time quoted to customer
number of products (i=index for products, i=1,…,n)
number of jobs or parts between setups
arrival rate
bottleneck rate
service rate
departure rate
setup time
time to process a part
utilization without setups
wait to batch time
wait in batch time
35E00100 Service Operations and Strategy #3
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Aalto/BIZ Logistics