RJS Penny Fab Model.ppt
-
Upload
ram-janm-singh -
Category
Documents
-
view
392 -
download
6
Transcript of RJS Penny Fab Model.ppt
![Page 1: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/1.jpg)
Basic Factory DynamicsDefinitions:
• 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.
![Page 2: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/2.jpg)
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.
![Page 3: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/3.jpg)
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.
![Page 4: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/4.jpg)
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, = 0.• “Practical worst case,” = 1.• “Worst possible case,” = W0.
Note: we won’t use quantitatively,but point it out to recognize that lineswith same rb and T0 can behave verydifferently.
![Page 5: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/5.jpg)
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
![Page 6: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/6.jpg)
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 =
=
0.5 pennies/hour
8 hours
0.5 8 = 4 pennies
0 (no variability, best case conditions)
![Page 7: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/7.jpg)
The Penny FabThe Penny Fab
![Page 8: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/8.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 0 hours
![Page 9: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/9.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 2 hours
![Page 10: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/10.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 4 hours
![Page 11: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/11.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 6 hours
![Page 12: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/12.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 8 hours
![Page 13: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/13.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 10 hours
![Page 14: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/14.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 12 hours
![Page 15: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/15.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 14 hours
![Page 16: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/16.jpg)
The Penny Fab (WIP=1)The Penny Fab (WIP=1)
Time = 16 hours
![Page 17: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/17.jpg)
Penny Fab Performance
WIP TH CT THCT 1 0.125 8 1 2 3 4 5 6
![Page 18: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/18.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 0 hours
![Page 19: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/19.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 2 hours
![Page 20: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/20.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 4 hours
![Page 21: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/21.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 6 hours
![Page 22: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/22.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 8 hours
![Page 23: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/23.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 10 hours
![Page 24: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/24.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 12 hours
![Page 25: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/25.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 14 hours
![Page 26: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/26.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 16 hours
![Page 27: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/27.jpg)
The Penny Fab (WIP=2)The Penny Fab (WIP=2)
Time = 18 hours
![Page 28: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/28.jpg)
Penny Fab Performance
WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 4 5 6
![Page 29: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/29.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 0 hours
![Page 30: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/30.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 2 hours
![Page 31: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/31.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 4 hours
![Page 32: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/32.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 6 hours
![Page 33: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/33.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 8 hours
![Page 34: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/34.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 10 hours
![Page 35: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/35.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 12 hours
![Page 36: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/36.jpg)
The Penny Fab (WIP=4)The Penny Fab (WIP=4)
Time = 14 hours
![Page 37: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/37.jpg)
Penny Fab Performance
WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 6
![Page 38: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/38.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 0 hours
![Page 39: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/39.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 2 hours
![Page 40: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/40.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 4 hours
![Page 41: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/41.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 6 hours
![Page 42: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/42.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 8 hours
![Page 43: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/43.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 10 hours
![Page 44: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/44.jpg)
The Penny Fab (WIP=5)The Penny Fab (WIP=5)
Time = 12 hours
![Page 45: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/45.jpg)
Penny Fab Performance
WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 0.500 10 5 6 0.500 12 6
![Page 46: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/46.jpg)
TH vs. WIP: Best Case
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
TH
rrbb
WW00
1/T1/T00
![Page 47: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/47.jpg)
CT vs. WIP: Best Case
02468
101214161820222426
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
CT
TT00
WW00
1/r1/rbb
![Page 48: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/48.jpg)
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,
otherwise.
if
,/
,CT 00
best
Ww
rw
T
b
otherwise.
if
,
,/TH 00
best
Ww
r
Tw
b
![Page 49: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/49.jpg)
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.
otherwise.
4 if
,2
,8CTbest
w
w
otherwise.
4 if
,5.0
,8/THbest
ww
![Page 50: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/50.jpg)
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)
CTTHWIP
hrhr
partsparts
![Page 51: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/51.jpg)
Penny Fab Two
10 hr
2 hr
5 hr 3 hr
![Page 52: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/52.jpg)
Penny Fab Two
StationNumber
Number ofMachines
ProcessTime
StationRate
1 1 2 hr j/hr
2 2 5 hr j/hr
3 6 10 hr j/hr
4 2 3 hr j/hr
rb = ____________ T0 = ____________ W0 = ____________
0.5
0.4
0.6
0.67
0.4 p/hr 20 hr 8 pennies
![Page 53: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/53.jpg)
Penny Fab Two Simulation (Time=0)
10 hr
2 hr
5 hr 3 hr
2
![Page 54: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/54.jpg)
Penny Fab Two Simulation (Time=2)
10 hr
2 hr
5 hr 3 hr
4
7
![Page 55: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/55.jpg)
Penny Fab Two Simulation (Time=4)
10 hr
2 hr
5 hr 3 hr
6
7
9
![Page 56: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/56.jpg)
Penny Fab Two Simulation (Time=6)
10 hr
2 hr
5 hr 3 hr
8
7
9
![Page 57: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/57.jpg)
Penny Fab Two Simulation (Time=7)
10 hr
2 hr
5 hr 3 hr
8
12
9
17
![Page 58: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/58.jpg)
Penny Fab Two Simulation (Time=8)
10 hr
2 hr
5 hr 3 hr
10
12
9
17
![Page 59: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/59.jpg)
Penny Fab Two Simulation (Time=9)
10 hr
2 hr
5 hr 3 hr
10
12
14
17
19
![Page 60: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/60.jpg)
Penny Fab Two Simulation (Time=10)
10 hr
2 hr
5 hr 3 hr
12
12
14
17
19
![Page 61: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/61.jpg)
Penny Fab Two Simulation (Time=12)
10 hr
2 hr
5 hr 3 hr
14
17
14
17
19
22
![Page 62: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/62.jpg)
Penny Fab Two Simulation (Time=14)
10 hr
2 hr
5 hr 3 hr
16
17
19
17
19
22
24
![Page 63: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/63.jpg)
Penny Fab Two Simulation (Time=16)
10 hr
2 hr
5 hr 3 hr
17
19
17
19
22
24
![Page 64: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/64.jpg)
Penny Fab Two Simulation (Time=17)
10 hr
2 hr
5 hr 3 hr
22
19
27
19
22
24
20
![Page 65: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/65.jpg)
Penny Fab Two Simulation (Time=19)
10 hr
2 hr
5 hr 3 hr
22
24
27
29
22
24
20
22
![Page 66: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/66.jpg)
Penny Fab Two Simulation (Time=20)
10 hr
2 hr
5 hr 3 hr
22
24
27
29
22
24 22
22
Note: job will arrive atbottleneck just in timeto prevent starvation.
![Page 67: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/67.jpg)
Penny Fab Two Simulation (Time=22)
10 hr
2 hr
5 hr 3 hr
27
24
27
29
32
24
2524
Note: job will arrive atbottleneck just in timeto prevent starvation.
![Page 68: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/68.jpg)
Penny Fab Two Simulation (Time=24)
10 hr
2 hr
5 hr 3 hr
27
29
27
29
32
34
25
27
And so on….Bottleneck will just stay busy; all others will starve periodically
![Page 69: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/69.jpg)
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
![Page 70: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/70.jpg)
Worst Case Penny FabWorst Case Penny Fab
Time = 0 hours
![Page 71: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/71.jpg)
Worst Case Penny FabWorst Case Penny Fab
Time = 8 hours
![Page 72: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/72.jpg)
Worst Case Penny FabWorst Case Penny Fab
Time = 16 hours
![Page 73: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/73.jpg)
Worst Case Penny FabWorst Case Penny Fab
Time = 24 hours
![Page 74: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/74.jpg)
Worst Case Penny FabWorst Case Penny Fab
Time = 32 hours Note:
CT = 32 hours= 4 8 = wT0
TH = 4/32 = 1/8 = 1/T0
![Page 75: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/75.jpg)
TH vs. WIP: Worst Case
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
TH
rrbb
WW00
1/T1/T00
Best CaseBest Case
Worst CaseWorst Case
![Page 76: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/76.jpg)
CT vs. WIP: Worst Case
048
121620242832
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
CT
TT00
WW00
Best CaseBest Case
Worst CaseWorst Case
![Page 77: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/77.jpg)
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!
![Page 78: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/78.jpg)
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
![Page 79: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/79.jpg)
PWC Example – 3 jobs, 4 3 jobs, 4 stationsstations
State Vector State Vector1 (3,0,0,0) 11 (1,0,2,0) 2 (0,3,0,0) 12 (0,1,2,0) 3 (0,0,3,0) 13 (0,0,2,1) 4 (0,0,0,3) 14 (1,0,0,2) 5 (2,1,0,0) 15 (0,1,0,2) 6 (2,0,1,0) 16 (0,0,1,2) 7 (2,0,0,1) 17 (1,1,1,0) 8 (1,2,0,0) 18 (1,1,0,1) 9 (0,2,1,0) 19 (1,0,1,1) 10 (0,2,0,1) 20 (0,1,1,1)
clumped up states
spread out states
![Page 80: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/80.jpg)
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
From Little’s LawFrom Little’s Law
![Page 81: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/81.jpg)
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.
br
wT
1CT 0PWC
,1
TH0
PWC brwW
w
![Page 82: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/82.jpg)
TH vs. WIP: Practical Worst Case
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
TH
rrbb
WW00
1/T1/T00
Best CaseBest Case
Worst CaseWorst Case
PWCPWCGood (lean)Good (lean)
Bad (fat)Bad (fat)
![Page 83: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/83.jpg)
CT vs. WIP: Practical Worst Case
048
121620242832
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
CT
TT00
WW00
Best CaseBest Case
Worst CaseWorst Case PWCPWC
Bad (fat)Bad (fat)
GoodGood(lean)(lean)
![Page 84: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/84.jpg)
0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12 14 16 18 20 22 24 26
WIP
TH
Penny Fab Two Performance
Worst Case
Penny Fab 2
Best Case
Practical Worst Case
1/T0
rb
W0
Note: processtimes in PF2have var equalto PWC.
But… unlike PWC, it hasunbalancedline and multimachine stations.
![Page 85: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/85.jpg)
Penny Fab Two Performance (cont.)
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20 22 24 26
WIP
CT
Worst Case
Penny Fab 2
Best Case
Practical Worst C
ase
T0
1/rb
W0
![Page 86: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/86.jpg)
Back to the HAL Case - Capacity Data
Process Rate (p/hr) Time (hr) Lamination 191.5 4.7 Machining 186.2 0.5 Internal Circuitize 114.0 3.6 Optical Test/Repair - Int 150.5 1.0 Lamination – Composites 158.7 2.0 External Circuitize 159.9 4.3 Optical Test/Repair - Ext 150.5 1.0 Drilling 185.9 10.2 Copper Plate 136.4 1.0 Procoat 117.3 4.1 Sizing 126.5 1.1 EOL Test 169.5 0.5 rb, T0 114.0 33.9
![Page 87: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/87.jpg)
HAL Case - Situation
• Critical WIP: rbT0 = 114 33.9 = 3,869
• Actual Values:• CT = 34 days = 663 hours (at 19.5 hr/day)• WIP = 47,600 panels• TH = 71.8 panels/hour
• Conclusions:• Throughput is 63% of capacity• WIP is 12.3 times critical WIP• CT is 24.1 times raw process time
![Page 88: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/88.jpg)
HAL Case - Analysis
• WIP Required for PWC to Achieve TH = 0.63rb?
•
586,6)1869,3(37.0
36.0)1(
37.0
63.0
63.01
0
0
Ww
rrWw
wTH bb
Much lower thanactual WIP!
Conclusion: actual system is much worse than PWC!
4.1051141869,3600,47
600,47
10
brWw
wTH Much higher
than actual TH!
TH Resulting from PWC with WIP = 47,600?
![Page 89: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/89.jpg)
HAL Internal Benchmarking Outcome
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 10,000 20,000 30,000 40,000 50,000
WIP
Th
rou
gh
pu
t (p
an
els/
hou
r)
Best
Worst
PWC
CurrentTH = 71.8WIP = 47,600“Lean" Region
“Fat" Region
![Page 90: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/90.jpg)
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
![Page 91: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/91.jpg)
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
![Page 92: RJS Penny Fab Model.ppt](https://reader033.fdocuments.net/reader033/viewer/2022061322/55cf9051550346703ba4d9b9/html5/thumbnails/92.jpg)
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