Basic Factory Dynamics
Physics should be explained as simply as possible,
but no simpler.
– Albert Einstein
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
1
HAL Case
Large Panel Line: produces unpopulated printed circuit boards
Line runs 24 hr/day (but 19.5 hrs of productive time)
Recent Performance:
•
•
•
•
throughput = 1,400 panels per day (71.8 panels/hr)
WIP = 47,600 panels
CT = 34 days (663 hr at 19.5 hr/day)
customer service = 75% on-time delivery
Is HAL lean?
What data do we need to decide?
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
2
HAL - Large Panel Line Processes
Lamination (Cores): press copper and prepreg into core blanks
Machining: trim cores to size
Internal Circuitize: etch circuitry into copper of cores
Optical Test and Repair (Internal): scan panels optically for defects
Lamination (Composites): press cores into multiple layer boards
External Circuitize: etch circuitry into copper on outside of composites
Optical Test and Repair (External): scan composites optically for defects
Drilling: holes to provide connections between layers
Copper Plate: deposits copper in holes to establish connections
Procoat: apply plastic coating to protect boards
Sizing: cut panels into boards
End of Line Test: final electrical test
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
3
HAL Case - Science?
External Benchmarking
• but other plants may not be comparable
Internal Benchmarking
• capacity data: what is utilization?
• but this ignores WIP effects
Need relationships between WIP, TH, CT, service!
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
4
Definitions
Workstations: a collection of one or more identical machines.
Parts: a component, sub-assembly, or an assembly that moves through
the workstations.
End Items: parts sold directly to customers; relationship to constituent
parts defined in bill of material.
Consumables: bits, chemicals, gasses, etc., used in process but do not
become part of the product that is sold.
Routing: sequence of workstations needed to make a part.
Order: request from customer.
Job: transfer quantity on the line.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
5
Definitions (cont.)
Throughput (TH): for a line, throughput is the average quantity of
good (non-defective) parts produced per unit time.
Work in Process (WIP): inventory between the start and endpoints of
a product routing.
Raw Material Inventory (RMI): material stocked at beginning of
routing.
Crib and Finished Goods Inventory (FGI): crib inventory is
material held in a stockpoint at the end of a routing; FGI is material
held in inventory prior to shipping to the customer.
Cycle Time (CT): time between release of the job at the beginning of
the routing until it reaches an inventory point at the end of the
routing.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
6
Factory Physics®
Definition: A manufacturing system is a goal-oriented network
of processes through which parts flow.
Structure: Plant is made up of routings (lines), which in turn are
made up of processes.
Focus: Factory Physics® is concerned with the network and flows
at the routing (line) level.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
7
Parameters
Descriptors of a Line:
1) Bottleneck Rate (rb): Rate (parts/unit time or jobs/unit time)
of the process center having the highest long-term utilization.
2) Raw Process Time (T0): Sum of the long-term average
process times of each station in the line.
3) Congestion Coefficient (α): A unitless measure of
congestion.
• Zero variability case, α = 0.
• “Practical worst case,” α = 1.
• “Worst possible case,” α = W0.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Note: we won’t use α quantitatively,
but point it out to recognize that lines
with same rb and T0 can behave very
differently.
http://www.factory-physics.com
8
Parameters (cont.)
Relationship:
Critical WIP (W0): WIP level in which a line having no
congestion would achieve maximum throughput (i.e., rb)
with minimum cycle time (i.e., T0).
W0 = rb T0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
9
The Penny Fab
Characteristics:
•
•
•
•
Four identical tools in series.
Each takes 2 hours per piece (penny).
No variability.
CONWIP job releases.
Parameters:
rb
=
0.5 pennies/hour
T0
=
8 hours
W0
=
0.5 × 8 = 4 pennies
α
=
0 (no variability, best case conditions)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
10
The Penny Fab
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
11
The Penny Fab (WIP=1)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
12
The Penny Fab (WIP=1)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
13
The Penny Fab (WIP=1)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
14
The Penny Fab (WIP=1)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
15
The Penny Fab (WIP=1)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
16
The Penny Fab (WIP=1)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
17
The Penny Fab (WIP=1)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
18
The Penny Fab (WIP=1)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
19
The Penny Fab (WIP=1)
Time = 16 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
20
Penny Fab Performance
WIP
1
2
3
4
5
6
TH
0.125
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
CT
8
http://www.factory-physics.com
TH×CT
1
21
The Penny Fab (WIP=2)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
22
The Penny Fab (WIP=2)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
23
The Penny Fab (WIP=2)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
24
The Penny Fab (WIP=2)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
25
The Penny Fab (WIP=2)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
26
The Penny Fab (WIP=2)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
27
The Penny Fab (WIP=2)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
28
The Penny Fab (WIP=2)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
29
The Penny Fab (WIP=2)
Time = 16 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
30
The Penny Fab (WIP=2)
Time = 18 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
31
Penny Fab Performance
WIP
1
2
3
4
5
6
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH
0.125
0.250
CT
8
8
http://www.factory-physics.com
TH×CT
1
2
32
The Penny Fab (WIP=4)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
33
The Penny Fab (WIP=4)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
34
The Penny Fab (WIP=4)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
35
The Penny Fab (WIP=4)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
36
The Penny Fab (WIP=4)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
37
The Penny Fab (WIP=4)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
38
The Penny Fab (WIP=4)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
39
The Penny Fab (WIP=4)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
40
Penny Fab Performance
WIP
1
2
3
4
5
6
TH
0.125
0.250
0.375
0.500
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
CT
8
8
8
8
http://www.factory-physics.com
TH×CT
1
2
3
4
41
The Penny Fab (WIP=5)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
42
The Penny Fab (WIP=5)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
43
The Penny Fab (WIP=5)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
44
The Penny Fab (WIP=5)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
45
The Penny Fab (WIP=5)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
46
The Penny Fab (WIP=5)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
47
The Penny Fab (WIP=5)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
48
Penny Fab Performance
WIP
1
2
3
4
5
6
TH
0.125
0.250
0.375
0.500
0.500
0.500
TH×CT
1
2
3
4
5
6
CT
8
8
8
8
10
12
49
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH vs. WIP: Best Case
0.6
rb
0.5
TH
0.4
0.3
1/T0
0.2
0.1
0
0
1
2
3
4
W0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
5
6
7
8
9 10 11 12
WIP
http://www.factory-physics.com
50
CT vs. WIP: Best Case
26
24
22
20
18
16
14
12
10
T0 86
4
2
0
CT
1/r
1/rb
0 1 2 3 4 5 6 7 8 9 10 11 12
W0 WIP
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
51
Best Case Performance
Best Case Law: The minimum cycle time (CTbest) for a given
WIP level, w, is given by
if w ≤ W0
⎧T ,
CTbest = ⎨ 0
⎩w / rb , otherwise.
The maximum throughput (THbest) for a given WIP level, w is
given by,
⎧w / T0 , if w ≤ W0
TH best = ⎨
otherwise.
⎩ rb ,
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
52
Best Case Performance (cont.)
Example: For Penny Fab, rb = 0.5 and T0 = 8, so W0 = 0.5 × 8 = 4,
if w ≤ 4
⎧8,
CTbest = ⎨
⎩2w, otherwise.
⎧w / 8, if w ≤ 4
TH best = ⎨
⎩0.5, otherwise.
which are exactly the curves we plotted.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
53
A Manufacturing Law
Little's Law: The fundamental relation between WIP, CT, and
TH over the long-term is:
WIP = TH × CT
parts =
parts
× hr
hr
Insights:
• Fundamental relationship
• Simple units transformation
• Definition of cycle time (CT = WIP/TH)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
54
Penny Fab Two
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
55
http://www.factory-physics.com
Penny Fab Two
Station
Number
1
Number of
Machines
1
Process
Time
2 hr
Station
Rate
0.5 j/hr
2
2
5 hr
3
6
10 hr
0.4 j/hr
0.6 j/hr
4
2
3 hr
0.67 j/hr
0.4 p/hr
20 hr
8 pennies
rb = ____________
T0 = ____________
W0 = ____________
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
56
Penny Fab Two Simulation (Time=0)
2
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
57
Penny Fab Two Simulation (Time=2)
7
4
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
58
Penny Fab Two Simulation (Time=4)
7
6
9
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
59
Penny Fab Two Simulation (Time=6)
7
8
9
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
60
Penny Fab Two Simulation (Time=7)
17
12
8
9
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
61
Penny Fab Two Simulation (Time=8)
17
12
10
9
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
62
Penny Fab Two Simulation (Time=9)
17
19
12
10
14
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
63
Penny Fab Two Simulation (Time=10)
17
19
12
12
14
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
64
Penny Fab Two Simulation (Time=12)
17
19
17
22
14
14
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
65
Penny Fab Two Simulation (Time=14)
17
19
17
22
19
24
16
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
66
Penny Fab Two Simulation (Time=16)
17
19
17
22
19
24
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
67
Penny Fab Two Simulation (Time=17)
27
19
22
22
19
24
20
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
68
Penny Fab Two Simulation (Time=19)
27
29
22
22
20
24
24
22
2 hr
5 hr
3 hr
10 hr
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
69
Penny Fab Two Simulation (Time=20)
27
Note: job will arrive at
bottleneck just in time
to prevent starvation.
29
22
22
24
24
22
22
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
70
Penny Fab Two Simulation (Time=22)
27
29
27
32
24
24
25
24
2 hr
5 hr
Note: job will arrive at
bottleneck just in time
to prevent starvation.
3 hr
10 hr
71
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Penny Fab Two Simulation (Time=24)
27
29
27
32
25
29
34
27
2 hr
5 hr
3 hr
10 hr
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
And so on….
Bottleneck will just
stay busy; all others
will starve periodically
72
Worst Case
Observation: The Best Case yields the minimum cycle time and
maximum throughput for each WIP level.
Question: What conditions would cause the maximum cycle time
and minimum throughput?
Experiment:
• set average process times same as Best Case (so rb and T0
unchanged)
• follow a marked job through system
• imagine marked job experiences maximum queueing
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
73
Worst Case Penny Fab
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
74
Worst Case Penny Fab
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
75
Worst Case Penny Fab
Time = 16 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
76
Worst Case Penny Fab
Time = 24 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
77
Worst Case Penny Fab
Time = 32 hours
Note:
CT = 32 hours
= 4× 8 = wT0
TH = 4/32 = 1/8 = 1/T0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
78
TH vs. WIP: Worst Case
0.6
rb
Best Case
0.5
TH
0.4
0.3
0.2
1/T0
Worst Case
0.1
0
0
1
2
3
4
5
6
7
8
9 10 11 12
W0 WIP
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
79
http://www.factory-physics.com
CT vs. WIP: Worst Case
Worst Case
CT
32
28
24
20
16
12
T0 8
4
0
Best Case
0 1 2 3 4 5 6 7 8 9 10 11 12
W0 WIP
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
80
Worst Case Performance
Worst Case Law: The worst case cycle time for a given WIP
level, w, is given by,
CTworst = w T0
The worst case throughput for a given WIP level, w, is given
by,
THworst = 1 / T0
Randomness? None - perfectly predictable, but bad!
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
81
Practical Worst Case
Observation: There is a BIG GAP between the Best Case and
Worst Case performance.
Question: Can we find an intermediate case that:
• divides “good” and “bad” lines, and
• is computable?
Experiment: consider a line with a given rb and T0 and:
• single machine stations
• balanced lines
• variability such that all WIP configurations (states) are equally
likely
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
82
PWC Example – 3 jobs, 4 stations
clumped
up states
State
1
2
3
4
5
6
7
8
9
10
Vector
(3,0,0,0)
(0,3,0,0)
(0,0,3,0)
(0,0,0,3)
(2,1,0,0)
(2,0,1,0)
(2,0,0,1)
(1,2,0,0)
(0,2,1,0)
(0,2,0,1)
State
11
12
13
14
15
16
17
18
19
20
Vector
(1,0,2,0)
(0,1,2,0)
(0,0,2,1)
(1,0,0,2)
(0,1,0,2)
(0,0,1,2)
(1,1,1,0)
(1,1,0,1)
(1,0,1,1)
(0,1,1,1)
Note: average WIP at any station is 15/20 = 0.75,
so jobs are spread evenly between stations.
spread
out states
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
83
Practical Worst Case
Let w = jobs in system, N = no. stations in line, and t =
process time at all stations:
CT(single)
= (1 + (w-1)/N) t
CT(line)
= N [1 + (w-1)/N] t
= Nt + (w-1)t
= T0 + (w-1)/rb
TH
= WIP/CT
= [w/(w+W0-1)]rb
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
From Little’
Little’s Law
http://www.factory-physics.com
84
Practical Worst Case Performance
Practical Worst Case Definition: The practical worst case
(PWC) cycle time for a given WIP level, w, is given by,
CTPWC = T0 +
w −1
rb
The PWC throughput for a given WIP level, w, is given by,
TH PWC =
w
rb ,
W0 + w − 1
where W0 is the critical WIP.
85
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH vs. WIP: Practical Worst Case
0.6
rb
Best Case
0.5
TH
0.4
0.3
0.2
1/T0
PWC
Good (lean)
Worst Case
Bad (fat)
0.1
0
0
1
2
3
4
5
6
7
8
9 10 11 12
W0 WIP
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://www.factory-physics.com
86
CT vs. WIP: Practical Worst Case
Worst Case
32
28
24
20
16
12
T0 8
4
0
PWC
CT
Bad (fat)
Best Case
Good
(lean)
0 1 2 3 4 5 6 7 8 9 10 11 12
W0 WIP
87
http://www.factory-physics.com
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Penny Fab Two Performance
0.5
Note: process
times in PF2
have var equal
to PWC.
Best Case
rb 0.4
Fab 2
Penny
0.3
TH
al
Practic
0.2
But… unlike
PWC, it has
unbalanced
line and multi
machine
stations.
ase
Worst C
0.1
1/T0
Worst Case
0
0
2
4
6
8
10
W0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
12
14
16
18
20
22
24
26
WIP
http://www.factory-physics.com
88
Penny Fab Two Performance (cont.)
80
70
Worst Case
60
50
CT
40
a se
tC
o rs
W
al
2
ctic
Fab
Pra
ny
n
e
P
1/rb
30
T0 20
Best Case
10
0
0
2
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
4
6
8
W0
10
12
14
16
18
20
22
24
26
WIP
89
http://www.factory-physics.com
Back to the HAL Case - Capacity Data
Process
Lamination
Machining
Internal Circuitize
Optical Test/Repair - Int
Lamination – Composites
External Circuitize
Optical Test/Repair - Ext
Drilling
Copper Plate
Procoat
Sizing
EOL Test
rb, T0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Rate (p/hr)
191.5
186.2
150.5
157.8
191.5
150.5
157.8
185.9
136.4
146.2
126.5
169.5
126.5
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Time (hr)
1.2
5.9
6.9
5.6
1.2
6.9
5.6
10.0
1.5
2.2
2.4
1.8
33.1
90
HAL Case - Situation
Critical WIP: W0 = rbT0 = 126.5 × 33.9 = 4,187
Actual Values:
• CT = 34 days = 816 hours (at 24 hr/day)
• WIP = 37,000 panels
• TH = 45.8 panels/hour
Conclusions:
• Throughput is 36% of capacity
• WIP is 15 times critical WIP
• CT is 24.6 times raw process time
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
91
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HAL Case - Analysis
TH Resulting from PWC with WIP = 47,600?
TH =
w
37,400
rb =
126.5 = 105.4
w + W0 − 1
37,400 + 4,187 − 1
Much
higher
than actual
TH!
WIP Required for PWC to Achieve TH = 0.63rb?
TH =
w=
w
rb = 0.36rb
w + W0 − 1
0.36
0.36
(W0 − 1) =
(4,187 − 1) = 2,354
0.64
0.64
Much lower than
actual WIP!
Conclusion: actual system is much worse than PWC!
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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92
HAL Internal Benchmarking Outcome
Throughput (panels/hour)
120.0
“Lean" Region
100.0
Current
TH = 45.8
WIP = 37,000
80.0
60.0
“Fat" Region
40.0
Best
Worst
PWC
20.0
0.0
0
10,000 20,000 30,000 40,000 50,000
WIP
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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93
Labor Constrained Systems
Motivation: performance of some systems are limited by labor or
a combination of labor and equipment.
Full Flexibility with Workers Tied to Jobs:
•
•
•
•
WIP limited by number of workers (n)
capacity of line is n/T0
Best case achieves capacity and has workers in “zones”
ample capacity case also achieves full capacity with “pick and run”
policy
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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94
Labor Constrained Systems (cont.)
Full Flexibility with Workers Not Tied to Jobs:
• TH depends on WIP levels
• THCW(n) ≤ TH(w) ≤ THCW(w)
• need policy to direct workers to jobs (focus on downstream is
effective)
Agile Workforce Systems
•
•
•
•
bucket brigades
kanban with shared tasks
worksharing with overlapping zones
many others
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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95
Factory Dynamics Takeaways
Performance Measures:
•
•
•
•
throughput
WIP
cycle time
service
Range of Cases:
• best case
• practical worst case
• worst case
Diagnostics:
• simple assessment based on rb, T0, actual WIP,actual TH
• evaluate relative to practical worst case
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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96