Basic Factory Dynamics
Chapter 7
Lecture 10
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
www.factoryphysics.com
1
Topics
Part I
Part II
Part III
•
•
•
•
•
•
•
•
•
•
Introduction (Chapter 0)
Inventory Control (Chapter 2)
Materials Requirements Planning (Chapter 3)
Just-in-Time and Lean manufacturing (Chapter 4)
Basic factory dynamics (Chapter 7)
Variability basics (Chapter 8)
Push and Pull Systems (Chapter 10)
Shop Floor Control (Chapter 14)
Production Scheduling (Chapter 15)
Aggregate Planning (Chapter 16)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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2
Introduction
•
Focus: Examine basic behavior of production lines
(process flows)
• Production line, instead of an entire factory or a single workstation
• A line is simple enough to analyze but complex enough to provide
a link between the operational and financial performance
•
Goal: Understand the factors that influence performance
of production processes (Part II – Chapters 7-10)
• Later in Part III (Chapters 14-16) we will address the problem of
how to improve or optimize performance
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Introduction (Cont’d)
Definition: A manufacturing plant is a network of processes
through which parts flow.
Structure: Plant is made up of routings (lines), which in turn are
made up of processes.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Definitions
Workstations: a collection of one or more identical machines.
Ex: A turning station made up of several lathes.
Part: a raw material, component or sub-assembly that moves through
workstations.
End Item: parts sold directly to customers; its relationship to constituent (lowerlevel) items is defined in bill of material.
Consumable: materials used in process but do not become part of the product
that is sold
Ex: bits, chemicals, gasses
Routing (Line): sequence of workstations that the part passes through during its
production
Order: request from customer for a part; contains quantity and due date of the
request.
Job: a part that traverses the production line along with associated info (e.g.,
BOM, drawings).
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Definitions: Inventory
Raw Material Inventory (RMI): material stocked at beginning of
routing.
Crib Inventory: intermediate inventory prior to further processing
Finished Goods Inventory (FGI): inventory for storing end items
prior to shipping to customer.
Work in Process (WIP): inventory between the start and endpoints
of a product routing.
E.g., parts
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Definitions: Performance Measures
Throughput (TH): Average production rate of a process (machine,
workstation, line, plant) per unit time
E.g., parts per hour
Capacity: Upper limit of the TH of a process.
Cycle Time (CT): time from release of the job at beginning of routing
until it reaches an inventory point at end of routing (time part spends
as WIP).
E.g., hours
CT is defined for single routings only.
Utilization: the fraction of time a workstation is not idle for lack of
parts
Utilization = (Arrival Rate )/ (Effective Production Rate)
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Parameters
Descriptors of a Line:
1) Bottleneck Rate (rb): Rate (parts per hour) of the workstation
with the highest utilization.
2) Raw Process Time (T0): Sum of the average process times of
each station in the line.
3) Critical WIP (W0): WIP level for which a line can achieve
maximum throughput (rb) with minimum cycle time (T0).
W0 = rb T0
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Basic Factory Dynamics
Chapter 7
Lecture 11
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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7.3.1. Best Case Performance
Simulation of Penny Fab One
Characteristics:
•
•
•
•
Four machines in series.
Each machine takes 2 hours to process a penny
No variability in processing times
WIP kept constant over time – CONWIP (Chapter 10)
Parameters:
rb
=
0.5 pennies/hour
T0
=
8 hours
W0
=
0.5 × 8 = 4 pennies
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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11
The Penny Fab (WIP=1)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=1)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=1)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=1)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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15
The Penny Fab (WIP=1)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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16
The Penny Fab (WIP=1)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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17
The Penny Fab (WIP=1)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=1)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=1)
Time = 16 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Penny Fab Performance
WIP
1
2
3
4
5
6
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH
0.125
CT
8
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TH×CT
1
21
The Penny Fab (WIP=2)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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26
The Penny Fab (WIP=2)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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27
The Penny Fab (WIP=2)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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29
The Penny Fab (WIP=2)
Time = 16 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=2)
Time = 18 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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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
www.factoryphysics.com
TH×CT
1
2
32
The Penny Fab (WIP=4)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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36
The Penny Fab (WIP=4)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=4)
Time = 14 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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40
Penny Fab Performance
WIP
1
2
3
4
5
6
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH
0.125
0.250
0.375
0.500
CT
8
8
8
8
www.factoryphysics.com
TH×CT
1
2
3
4
41
The Penny Fab (WIP=5)
Time = 0 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=5)
Time = 2 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=5)
Time = 4 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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44
The Penny Fab (WIP=5)
Time = 6 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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45
The Penny Fab (WIP=5)
Time = 8 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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46
The Penny Fab (WIP=5)
Time = 10 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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The Penny Fab (WIP=5)
Time = 12 hours
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Penny Fab Performance
Critical
WIP
WIP
1
2
3
4
5
6
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
TH
0.125
0.250
0.375
0.500
0.500
0.500
CT
8
8
8
8
10
12
www.factoryphysics.com
TH×CT
1
2
3
4
5
6
49
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
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CT vs. WIP: Best Case
26
24
22
20
18
16
14
12
10
T0 86
4
2
0
CT
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
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A Manufacturing Law
Little's Law: (John D.C. Little) The fundamental relation
between WIP, CT, and TH 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
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Best Case Performance
Best Case Law: The minimum cycle time (CTbest) for a given
WIP level, w, is given by
CTbest
if w ≤ W0
⎧T0 ,
=⎨
⎩w / rb , otherwise.
The maximum throughput (THbest) for a given WIP level, w is
given by,
TH best
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
⎧w / T0 , if w ≤ W0
=⎨
otherwise.
⎩ rb ,
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Best Case Performance (cont.)
Example: For Penny Fab One, rb = 0.5 and T0 = 8, so W0 = 0.5 ×
8 = 4,
CTbest
if w ≤ 4
⎧8,
=⎨
⎩2 w, otherwise.
TH best
⎧w / 8, if w ≤ 4
=⎨
⎩0.5, otherwise.
which are exactly the curves we plotted.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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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
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Worst Case Penny Fab
Time = 0 hours
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Worst Case Penny Fab
Time = 8 hours
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Worst Case Penny Fab
Time = 16 hours
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Worst Case Penny Fab
Time = 24 hours
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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
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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
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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
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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
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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