Basic Factory Dynamics

1
Basic Factory Dynamics
Physics should be explained as simply as
possible, but no simpler.
Albert Einstein
2
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?
3
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

4
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!
5
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.

6
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.

7
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.

8
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 (?) A unitless
  measure of congestion.
• Zero variability case, a 0.
• Practical worst case, a 1.
• Worst possible case, a W0.

Note we wont use ? quantitatively, but point it
out to recognize that lines with same rb and T0
can behave very differently.
9
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

10
The Penny Fab

• Characteristics
• Four identical tools in series.
• Each takes 2 hours per piece (penny).
• No variability.
• CONWIP job releases.
• Parameters
• rb
• T0
• W0
• a

0.5 pennies/hour
8 hours
0.5 ? 8 4 pennies
0 (no variability, best case conditions)
11
The Penny Fab
12
The Penny Fab (WIP1)
Time 0 hours
13
The Penny Fab (WIP1)
Time 2 hours
14
The Penny Fab (WIP1)
Time 4 hours
15
The Penny Fab (WIP1)
Time 6 hours
16
The Penny Fab (WIP1)
Time 8 hours
17
The Penny Fab (WIP1)
Time 10 hours
18
The Penny Fab (WIP1)
Time 12 hours
19
The Penny Fab (WIP1)
Time 14 hours
20
The Penny Fab (WIP1)
Time 16 hours
21
Penny Fab Performance
22
The Penny Fab (WIP2)
Time 0 hours
23
The Penny Fab (WIP2)
Time 2 hours
24
The Penny Fab (WIP2)
Time 4 hours
25
The Penny Fab (WIP2)
Time 6 hours
26
The Penny Fab (WIP2)
Time 8 hours
27
The Penny Fab (WIP2)
Time 10 hours
28
The Penny Fab (WIP2)
Time 12 hours
29
The Penny Fab (WIP2)
Time 14 hours
30
The Penny Fab (WIP2)
Time 16 hours
31
The Penny Fab (WIP2)
Time 18 hours
32
Penny Fab Performance
33
The Penny Fab (WIP4)
Time 0 hours
34
The Penny Fab (WIP4)
Time 2 hours
35
The Penny Fab (WIP4)
Time 4 hours
36
The Penny Fab (WIP4)
Time 6 hours
37
The Penny Fab (WIP4)
Time 8 hours
38
The Penny Fab (WIP4)
Time 10 hours
39
The Penny Fab (WIP4)
Time 12 hours
40
The Penny Fab (WIP4)
Time 14 hours
41
Penny Fab Performance
42
The Penny Fab (WIP5)
Time 0 hours
43
The Penny Fab (WIP5)
Time 2 hours
44
The Penny Fab (WIP5)
Time 4 hours
45
The Penny Fab (WIP5)
Time 6 hours
46
The Penny Fab (WIP5)
Time 8 hours
47
The Penny Fab (WIP5)
Time 10 hours
48
The Penny Fab (WIP5)
Time 12 hours
49
Penny Fab Performance
50
TH vs. WIP Best Case
rb
1/T0
W0
51
CT vs. WIP Best Case
1/rb
T0
W0
52
Best Case Performance

• Best Case Law The minimum cycle time (CTbest)
  for a given WIP level, w, is given by
• The maximum throughput (THbest) for a given WIP
  level, w is given by,

53
Best Case Performance (cont.)

• Example For Penny Fab, rb 0.5 and T0 8, so
  W0 0.5 ? 8 4,
• which are exactly the curves we plotted.

54
A Manufacturing Law

• Little's Law The fundamental relation between
  WIP, CT, and TH over the long-term is
• Insights
• Fundamental relationship
• Simple units transformation
• Definition of cycle time (CT WIP/TH)

55
Penny Fab Two
2 hr
5 hr
3 hr
10 hr
56
Penny Fab Two
0.5
0.4
0.6
0.67
0.4 p/hr
20 hr
8 pennies
rb ____________ T0 ____________ W0
____________
57
Penny Fab Two Simulation (Time0)
2
2 hr
5 hr
3 hr
10 hr
58
Penny Fab Two Simulation (Time2)
7
4
2 hr
5 hr
3 hr
10 hr
59
Penny Fab Two Simulation (Time4)
7
6
9
2 hr
5 hr
3 hr
10 hr
60
Penny Fab Two Simulation (Time6)
7
8
9
2 hr
5 hr
3 hr
10 hr
61
Penny Fab Two Simulation (Time7)
17
12
8
9
2 hr
5 hr
3 hr
10 hr
62
Penny Fab Two Simulation (Time8)
17
12
10
9
2 hr
5 hr
3 hr
10 hr
63
Penny Fab Two Simulation (Time9)
17
19
12
10
14
2 hr
5 hr
3 hr
10 hr
64
Penny Fab Two Simulation (Time10)
17
19
12
12
14
2 hr
5 hr
3 hr
10 hr
65
Penny Fab Two Simulation (Time12)
17
19
17
22
14
14
2 hr
5 hr
3 hr
10 hr
66
Penny Fab Two Simulation (Time14)
17
19
17
22
16
19
24
2 hr
5 hr
3 hr
10 hr
67
Penny Fab Two Simulation (Time16)
17
19
17
22
19
24
2 hr
5 hr
3 hr
10 hr
68
Penny Fab Two Simulation (Time17)
27
19
22
22
20
19
24
2 hr
5 hr
3 hr
10 hr
69
Penny Fab Two Simulation (Time19)
27
29
22
22
20
24
24
22
2 hr
5 hr
3 hr
10 hr
70
Penny Fab Two Simulation (Time20)
27
Note job will arrive at bottleneck just in
time to prevent starvation.
29
22
22
22
24
24
22
2 hr
5 hr
3 hr
10 hr
71
Penny Fab Two Simulation (Time22)
27
29
27
32
25
24
24
24
2 hr
5 hr
3 hr
Note job will arrive at bottleneck just in
time to prevent starvation.
10 hr
72
Penny Fab Two Simulation (Time24)
27
29
27
32
25
29
34
27
2 hr
5 hr
3 hr
And so on. Bottleneck will just stay busy all
others will starve periodically
10 hr
73
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

74
Worst Case Penny Fab
Time 0 hours
75
Worst Case Penny Fab
Time 8 hours
76
Worst Case Penny Fab
Time 16 hours
77
Worst Case Penny Fab
Time 24 hours
78
Worst Case Penny Fab
Time 32 hours
Note CT 32 hours 4? 8 wT0 TH 4/32
1/8 1/T0
79
TH vs. WIP Worst Case
Best Case
rb
Worst Case
1/T0
W0
80
CT vs. WIP Worst Case
Worst Case
Best Case
T0
W0
81
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!
82
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

83
PWC Example 3 jobs, 4 stations
clumped up states
spread out states
Note average WIP at any station is 15/20 0.75,
so jobs are spread evenly between stations.
84
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/(wW0-1)rb

From Littles Law
85
Practical Worst Case Performance

• Practical Worst Case Definition The practical
  worst case (PWC) cycle time for a given WIP
  level, w, is given by,
• The PWC throughput for a given WIP level, w, is
  given by,
• where W0 is the critical WIP.

86
TH vs. WIP Practical Worst Case
Best Case
rb
PWC
Good (lean)
Worst Case
Bad (fat)
1/T0
W0
87
CT vs. WIP Practical Worst Case
Worst Case
PWC
Bad (fat)
Best Case
Good
(lean)
T0
W0
88
Penny Fab Two Performance
Note process times in PF2 have var equal to
PWC. But unlike PWC, it has unbalanced line
and multi machine stations.
Best Case
rb
Penny Fab 2
Practical Worst Case
1/T0
Worst Case
W0
89
Penny Fab Two Performance (cont.)
Worst Case
Practical Worst Case
Penny Fab 2
1/rb
T0
Best Case
W0
90
Back to the HAL Case - Capacity Data
91
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

92
HAL Case - Analysis
Much higher than actual TH!
TH Resulting from PWC with WIP 47,600?

• WIP Required for PWC to Achieve TH 0.63rb?

Much lower than actual WIP!
Conclusion actual system is much worse than PWC!
93
HAL Internal Benchmarking Outcome
Lean" Region
Fat" Region
94
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

95
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

96
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