### Penny Fab Example Simulation

1. WIP controlling - Example line Unbalanced line Jesse Uitto
2. Unbalanced line simulation • Source: Factory Physics by Wallace Hopp & Mark Spearman - Chapter 7, Intuition building exercise 1 • Unlike in the book, in this example there is only 5, not 6, machines in the third phase. • More about the theory can be found at http://jesseuitto.fi/?p=464 (example line 2)
3. 2 h 5 h 10 h 3 h Phase 1 - 1 machine - 2 hour raw process time - Capacity 0,5 products/hour
4. 2 h 5 h 10 h 3 h Phase 2 - 2 machines - 5 hour raw process time - Capacity 0,4 products/hour
5. 2 h 5 h 10 h 3 h Phase 3 - 5 machines - 10 hour raw process time - Capacity 0,5 products/hour
6. 2 h 5 h 10 h 3 h Phase 4 - 2 machines - 3 hour raw process time - Capacity 0,67 products/hour
7. Experiment #1 • First we try this line with WIP limit of 7 jobs • Red balls are jobs • Each slide simulates the beginning of that particular hour. – Example at the beginning of the hour 1 first job is released and it is finished when hour 2 changes into hour 3 (slide = hour 3) – The number below each work station tells what process hour is going with that part.
8. 2 h 5 h 10 h 3 h Hour 1 1
9. 2 h 5 h 10 h 3 h Hour 2 2
10. 2 h 5 h 10 h 3 h Hour 3 1 1
11. 2 h 5 h 10 h 3 h Hour 4 2 2
12. 2 h 5 h 10 h 3 h Hour 5 1 3 1
13. 2 h 5 h 10 h 3 h Hour 6 2 4 2
14. 2 h 5 h 10 h 3 h Hour 7 1 5 3
15. 2 h 5 h 10 h 3 h Hour 8 2 1 4 1
16. 2 h 5 h 10 h 3 h Hour 9 1 2 5 2
17. 2 h 5 h 10 h 3 h Hour 10 2 3 1 3 1
18. 2 h 5 h 10 h 3 h Hour 11 1 4 2 4 2
19. 2 h 5 h 10 h 3 h Hour 12 2 5 3 5 3
20. 2 h 5 h 10 h 3 h Hour 13 1 1 4 6 4 1
21. 2 h 5 h 10 h 3 h Hour 14 2 2 5 7 5 2
22. 2 h 5 h 10 h 3 h Hour 15 3 1 8 6 3 1
23. 2 h 5 h 10 h 3 h Hour 16 4 2 9 7 4 2
24. 2 h 5 h 10 h 3 h Hour 17 5 3 10 8 5 3
25. 2 h 5 h 10 h 3 h Hour 18 1 4 9 6 4 1 1
26. 2 h 5 h 10 h 3 h Hour 19 2 5 10 7 5 2 2
27. 2 h 5 h 10 h 3 h Hour 20 3 8 6 3 3 1 1
28. 2 h 5 h 10 h 3 h Hour 21 4 9 7 4 2 2 1
29. 2 h 5 h 10 h 3 h Hour 22 5 10 8 5 3 3 2
30. 2 h 5 h 10 h 3 h Hour 23 1 9 6 4 1 1 1
31. 2 h 5 h 10 h 3 h Hour 24 2 10 7 5 2 2 2
32. 2 h 5 h 10 h 3 h Hour 25 3 1 8 6 1 3 3
33. 2 h 5 h 10 h 3 h Hour 26 4 2 9 7 2 1 4
34. 2 h 5 h 10 h 3 h Hour 27 5 3 10 8 3 2 5
35. 2 h 5 h 10 h 3 h Hour 28 1 1 1 9 4 1 6
36. 2 h 5 h 10 h 3 h Hour 29 2 2 2 10 5 2 7
37. 2 h 5 h 10 h 3 h Hour 30 3 1 3 1 1 3 8
38. 2 h 5 h 10 h 3 h Hour 31 4 2 1 2 2 4 9
39. 2 h 5 h 10 h 3 h Hour 32 5 3 2 3 3 5 10
40. 2 h 5 h 10 h 3 h Hour 33 1 4 1 1 4 6 1
41. 2 h 5 h 10 h 3 h Hour 34 2 5 2 2 5 7 2
42. 2 h 5 h 10 h 3 h Hour 35 3 1 3 1 6 8 3
43. 2 h 5 h 10 h 3 h Hour 36 4 2 4 2 7 91
44. 2 h 5 h 10 h 3 h Hour 37 5 3 5 3 8 102
45. 2 h 5 h 10 h 3 h Hour 38 1 4 6 4 9 1 1
46. Notices of simulation with WIP = 7 • This hour 38 is exactly the same as hour 18 so it starts to go round between hours 18 -> 37 • Notice that after the beginning there is no queue in front of the phase 2. – Actually during the hours 20-24 both stations at phase 2 aren’t even fully utilized. – Bottleneck station should be fully utilized, right ? • So let’s try this with an WIP level of 8 jobs
47. 2 h 5 h 10 h 3 h Hour 1 1
48. 2 h 5 h 10 h 3 h Hour 2 2
49. 2 h 5 h 10 h 3 h Hour 3 1 1
50. 2 h 5 h 10 h 3 h Hour 4 2 2
51. 2 h 5 h 10 h 3 h Hour 5 1 3 1
52. 2 h 5 h 10 h 3 h Hour 6 2 4 2
53. 2 h 5 h 10 h 3 h Hour 7 1 5 3
54. 2 h 5 h 10 h 3 h Hour 8 2 1 4 1
55. 2 h 5 h 10 h 3 h Hour 9 1 2 5 2
56. 2 h 5 h 10 h 3 h Hour 10 2 3 1 3 1
57. 2 h 5 h 10 h 3 h Hour 11 1 4 2 4 2
58. 2 h 5 h 10 h 3 h Hour 12 2 5 3 5 3
59. 2 h 5 h 10 h 3 h Hour 13 1 1 4 6 4 1
60. 2 h 5 h 10 h 3 h Hour 14 2 2 5 7 5 2
61. 2 h 5 h 10 h 3 h Hour 15 3 1 8 6 3 1 1
62. 2 h 5 h 10 h 3 h Hour 16 4 2 9 7 4 2 2
63. 2 h 5 h 10 h 3 h Hour 17 5 3 10 8 5 3
64. 2 h 5 h 10 h 3 h Hour 18 1 4 9 6 4 1 1
65. 2 h 5 h 10 h 3 h Hour 19 2 5 10 7 5 2 2
66. 2 h 5 h 10 h 3 h Hour 20 3 8 6 3 3 1 11
67. 2 h 5 h 10 h 3 h Hour 21 4 9 7 4 2 2 1 2
68. 2 h 5 h 10 h 3 h Hour 22 5 10 8 5 3 3 2 3
69. 2 h 5 h 10 h 3 h Hour 23 4 9 6 4 1 1 1 1
70. 2 h 5 h 10 h 3 h Hour 24 5 10 7 5 2 2 2 2
71. 2 h 5 h 10 h 3 h Hour 25 1 1 8 6 3 3 3 1
72. Notices of simulation with WIP = 8 • This hour 25 is exactly the same as hour 20 so it starts to go round between hours 20 – 24 • So after the start there is no queue in front of the second phase. But it’s still fully utilized. – Bottleneck stations are fully utilized, so this is the best solution? • Let’s try this once again with WIP limit of 9 jobs
73. 2 h 5 h 10 h 3 h Hour 1 1
74. 2 h 5 h 10 h 3 h Hour 2 2
75. 2 h 5 h 10 h 3 h Hour 3 1 1
76. 2 h 5 h 10 h 3 h Hour 4 2 2
77. 2 h 5 h 10 h 3 h Hour 5 1 3 1
78. 2 h 5 h 10 h 3 h Hour 6 2 4 2
79. 2 h 5 h 10 h 3 h Hour 7 1 5 3
80. 2 h 5 h 10 h 3 h Hour 8 2 1 4 1
81. 2 h 5 h 10 h 3 h Hour 9 1 2 5 2
82. 2 h 5 h 10 h 3 h Hour 10 2 3 1 3 1
83. 2 h 5 h 10 h 3 h Hour 11 1 4 2 4 2
84. 2 h 5 h 10 h 3 h Hour 12 2 5 3 5 3
85. 2 h 5 h 10 h 3 h Hour 13 1 1 4 6 4 1
86. 2 h 5 h 10 h 3 h Hour 14 2 2 5 7 5 2
87. 2 h 5 h 10 h 3 h Hour 15 3 1 8 6 3 1 1
88. 2 h 5 h 10 h 3 h Hour 16 4 2 9 7 4 2 2
89. 2 h 5 h 10 h 3 h Hour 17 5 3 10 8 5 3 1
90. 2 h 5 h 10 h 3 h Hour 18 1 4 9 6 4 1 1 2
91. 2 h 5 h 10 h 3 h Hour 19 2 5 10 7 5 2 2
92. 2 h 5 h 10 h 3 h Hour 20 3 8 6 3 3 1 11
93. 2 h 5 h 10 h 3 h Hour 21 4 9 7 4 2 2 1 2
94. 2 h 5 h 10 h 3 h Hour 22 5 10 8 5 3 3 2 3
95. 2 h 5 h 10 h 3 h Hour 23 4 9 6 4 1 1 1 1
96. 2 h 5 h 10 h 3 h Hour 24 5 10 7 5 2 2 2 2
97. 2 h 5 h 10 h 3 h Hour 25 1 1 8 6 3 3 3 1
98. Notices of simulation with WIP = 9 • Notice that here too hour 25 is same than hour 20. So it goes same round than with WIP of 8 jobs • Now after the start there is always 1 job in queue waiting to be processed at the second phase
99. Variability at the phase 2 • If process time at the second phase would be shorter they could take a new job from the queue. On the other hand it would mean that stations have variability and they would also have longer process times which would increase the queue.
100. Differences • With WIP limit of 7 second work phase sometimes starves and is not fully utilized. So the cycle time for the line is same as theoretical raw process time T0 = 20 h • With second example and WIP limit of 8 jobs the second phase is always fully utilized. And still there is no queue in front of it. So the cycle time still remains at 20 hours. • With the WIP of 9 jobs there is always queue in front of the second phase. After the start when all the WIP is in use, jobs will wait 2 hours to get processed at the phase 2. – So the cycle time is 22 hours
101. Summarize • As calculated in post (http://jesseuitto.fi/?p=464) Critical WIP is W0 = rb* T0 = 0,4 * 20 = 8 jobs – In simulations we noticed that line works quite perfectly with this WIP limit. • Machines at second phase are fully utilized • No queues in the line • Cycle time = raw process time T0 • So if we have perfect line with no variability, no loss, optimum situation would be to limit the WIP for 8 jobs – Achieve maximum TH with minimum WIP and CT