[/1 llfllfllllmfllhlWWIWWW

1293m

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

'An Experimental Analysis of
Bottlenecks Within a Theoretical

Job Shop: A Simulation Study
presented by

Young Jin Ahn

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Management

 

 

 

M profesfl ‘ '
Date '~ use [f/jf)

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

 

 

* MSU 5 RETURNING MATERIALS:
Place in book drop to
LJBRARJES remove this checkout from

 

.—_-_. your record. FINES will

, be charged if book is
returned after the date
stamped below.

 

 

FEB fl :84 “$4301
0 A. 8

SEP '2‘5Qnfio

 

 

 

AN EXPERIMENTAL ANALYSIS OF BOTTLENECKS
WITHIN A THEORETICAL JOB SHOP:
A SIMULATION STUDY

By

Young Jin Ahn

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Management

1987

Copyright by
YOUNG JIN AHN
1987

ABSTRACT

AN EXPERIMENTAL ANALYSIS OF BOTTLENECKS
WITHIN A THEORETICAL JOB SHOP:
A SIMULATION STUDY

by

Young Jin Ahn

The purpose of this study was. to identify and assess
the problems present when trying to manage a bottleneck job
shop in which one of the work centers experiences
consistently higher machine loads. The bottleneck job shop,
while fairly common in practice,- has received little

attention from researchers.

Due to the lack of detailed knowledge surrounding
bottlenecks, combined with their .crucial impact on shop
performance, the first step in the research was to develop a
theoretical framework of a bottleneck job shop. This
framework provided the basis of the study.

The control procedures examined were dispatching rules
and order review/release mechanisms. The two bottleneck
characteristics studied were location of the bottleneck and
prevalence or extent of the bottleneck.

The research vehicle for the study was a computer

Young Jin Ahn

simulation of a quasi-random job shop which was modeled
using SLAMII. Analysis was conducted using primarily
analysis of variance.

Several conclusions can be drawn from the findings of
the study. The selection of dispatching rules had a greater
impact on system performance than that of order
review/release mechanisms. Specifically, the SPT rule
consistently performed well under almost all conditions
tested in this study.

The use of order review/release mechanisms, when
compared to the immediate release mechanism, resulted in an
improvement in the level of lead time and work-in—process.
However, its use did result in degradation in both the
levels of mean tardiness and the percentage of jobs tardy.

Shop performance was significantly influenced by both
of the bottleneck characteristics: location and prevalence.
In addition, there existed many higher significant
interactions among experimental factors. Furthermore, the
presence of the bottleneck affected the performance of not
only bottleneck jobs but also non-bottleneck jobs.

In summary, the results of the study suggest that both
managers and researchers must first describe the bottlenecks
in terms of their characteristics and, then, apply the most

adequate control procedures.

 

To My Family

 

ACKNOWLEDGMENTS

This dissertation could not be completed without the
contribution of many people. I wish to express my sincere
appreciation and thanks for the people who made this study
possible.

I would like to thank the members of my dissertation
committee for their support and valuable ideas.

Dr. Steven A. Melnyk, the Chairman of the Dissertation
Committee and Associate Professor of Department of
Management, stimulated the initial idea for this research.
His probing suggestions, continuing interest, and personal
concerns provided a needed impetus for this research. He
provided invaluable encouragement and constructive criticism
at every stage of the project. He meticulously edited this
paper with warm and enthusiastic support. He helped me
believe in my ability. His contribution to my professional
development is acknowledged with sincere gratitude.

Dr. Phillip L. Carter, a member of the Dissertation
Committee and Associate Dean of College of Business,
provided valuable comments and suggestions. He met each of
the countless interruptions with a willingness to help. His

in-depth knowledge and wisdom made a significant

contribution to this research study. I am grateful.

Dr. Gary L. Ragatz, a member of the Dissertation
Committee and Assistant Professor. of the Department of
Management, spent countless hours of reading and discussing
the initial drafts of this research. His valuable comments,
corrections, and above all his in-depth knowledge of the
methodology and analysis portion of the research was an
asset to the investigation. His contribution is greatly
appreciated.

My gratitude extends to Dr. Ram Narasimhan, the
Academic Advisor and the Chairman of the Department of
Management. He provided significant financial support. His
continuous interest, guidance, and encouragement were
invaluable. His support and help during my stay at Michigan
State is greatly appreciated.

Also, I wish to express my sincere appreciation to my
parents, Dr. Sang Yong Ahn and Mrs. Hae Kyung Kim. They
supplied the opportunity for higher education. They provided
incredible support, confidence, and inspiration from tens of
thousands miles away.

Most of all, I wish to express my sincere appreciation
to my wife, Kyu Sook. Without her devotion, inspiration, and
above all her sacrifice, this dissertation could never be
completed. Also I appreciate the involuntary sacrifices of
my two sons, Kyung Seon and Kyung Min.

Of course, I, alone, am fully responsible for any

errors and omissions of this paper.

TABLE OF CONTENTS

Page
CHAPTER 1 - BOTTLENECK JOB SHOP ..................... 1
1.1 Introduction ............................ 1
1.2 The Research Premise .................... 5
1.3 The Research Objectives ................. 5
1.4 The Organization of the Study ........... 7
CHAPTER 2 - BOTTLENECKS: CONCEPTUAL CONSIDERATIONS 9
2.1 Introduction ............................ 9
2.2 Literature Review........................ 10
2.3 Definition of a Bottleneck Work Center .. 17
2.3.1 Definition of a Bottleneck Work Center
in this Study ........................... 17
2.4 The Framework of a Bottleneck Job Shop .. 20
2.4.1 Cause of a Bottleneck ................... 21
2.4.2 Status of a Bottleneck .................. 23
2.4.3 Location of a Bottleneck in the Routing . 23
2.5 Uniqueness of a Bottleneck Job Shop ..... 24
2.6 Impact of Bottleneck Operations on
Shop Floor .............................. 25
2.7 Tactics to Cope with Bottlenecks ........ 26
2.7.1 Tactics to Manage Capacity .............. 26
2.7.2 Tactics to Manage Workload .............. 27
2.7.2.1 Dispatching Rules ....................... 27
2.7.2.2 Order Review/Release Mechanism ......... 28
2.7.2.2.1 Past Study on Order Review/Release ...... 29
2.7.2.2.2 Potential Benefits of Order
Review/Release .......................... 32
2.7.2.2.3 Mechanics of Order Review/Release ....... 33
2.8 Summary ................................. 34

CHAPTER 3 "' RESEARCH METHODOLOGY 0 o o o o o e o o o o o e o o o o o o o 35

3.1 Introduction ............................ 35
3.2 A Quasi Random Job Shop ................. 35
3.3 The Operating Logic of the Model ........ 36
3.4 The Shop Size ........................... 36
3.5 Job Arrival Distribution ................ 37
3.6 Routing of Jobs ..-...................... 37
3.7 Processing Times of Jobs ................ 38

viii

3.8

3.9

3.10

3.11
CHAPTER 4 -
4.1

4.2

4.2.1
4.2.2
4.2.2.1
4.2.2.2
4.2.2.3
4.2.2.4
4.2.2.5
4.2.3
4.2.4
4.2.5

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10
CHAPTER 5 -
5.1

5.2

5.3

5.3.1
5.3.2
5.3.2.1
5.3.2.1.1
5.3.2.1.2
5.3.2.1.3
5.3.2.1.4
5.3.2.2
5.3.2.2.1
5.3.2.2.2
5.3.2.2.3
5.3.2.2.4
5.3.2.2.5
5.3.2.3
5.3.2.3.1
5.3.2.3.2
5.3.2.3.3
5.3.2.3.4

Due Date Setting of Jobs

The Assumptions of the Model

The Simulation Model

summary OOOOOOOOOOOOOIOOOOIIOOOOOOOOOOOOO

EXPERIMENTAL DESIGN

Introduction
Experimental Factors

DispatChing Rules OOOOOOOOOOOOOOOOIOOOIO.

Order Review/Release Mechanisms
Control of Workload
The Immediate Release Mechanism

The Aggregate Release Mechanism .........
The Bottleneck Release Mechanism ..
Determination of Load Limit Levels
The Location of a Bottleneck

The Prevalence of a Bottleneck

Summary of Experimental Design ..........
Hypothe81s Testing OOOOOOOOOOOOIOCOOOI...

Performance Criteria

Initial Condition Setting ...............

Test for Independence

Steady-State Equilibrium ................
Variance Reduction Technique
The sample Size OCOOOOOOOOOOOOOOOOOOOIOOO

Summary

ANALYSIS OF THE SIMULATION RESULTS

Introduction

.00...

Assumptions in an Analysis of Variance ..

Experimental Results
General Overview
Detailed Analysis
Work-in-Process ..

Dispatching Rule * Location * Prevalence.
Order Review/Release * Prevalence .

Discussion

Summary for Work-in-Process .............

Mean Flow Time in the Shop

OOOOOOOOOOO...

Order Review/Release * Dispatching Rule .

Order Review/Release * Location

Prevalence
Discussion

Summary for Mean Flow Time in the Shop ..
Variance of Flow Time in the ShOp .
Order Review/Release * Dispatching Rule .

Order Review/Release * Location

Prevalence
Discussion

ix

Page

39
39
40
41

42

42
42
44
49
50
52
52
52
53
59
59
59
60
66
68
68
69
70
71
73

74

74

74
104
104
107
108
108
111
113
115
116
116
118
119
120
123
123
124
126
127
128

UIUIU1UIUIUIUIUIUIUIUI UIUIUIUIUIUIUiUImUIUIUIUIUI U1
0 O O O O O O O O O O O O O
Lnbbk-bhbbwww wwwwwwwwwwwwww w
0 O
O O O O I
UlkLoNr-a

O‘O‘O‘ O‘ChUIUIUIUIU‘UIbJ-‘J-‘#§4> OJ

NNN NNNNNNNNNNNNNN N
O 0-.
O O O

O‘U‘ibUJNl-A

CHAPTER 6

o o o e
U‘puNNNNNNNi-l

O‘O‘O‘O‘O‘O‘O‘O‘O‘G

APPENDIX

APPENDIX

APPENDIX

UI

H Ul-L‘LnNt-o

#wN

A:

B:

C:

Summary for Variance of Flow Time
in the Shop 00.000.00.00...
Mean Tardiness

Order Review/Release * Dispatching Rule

Order Review/Release * Prevalence ..
Location * Prevalence
Discussion ...
Summary for Mean Tardiness
Variance of Tardiness ....

Order Review/Release * Dispatching Rule

Dispatching Rule * Prevalence .....
Location ........
Discussion

Summary for Variance of Tardiness .......

Percent of Jobs Tardy ...

Order Review/Release * Dispatching Rule

* Location

Order Review/Release * Prevalence .....

Discussion ................. .. .....
Summary for Percent of Jobs Tardy ..
Bottleneck Jobs vs.
Work—in-Process

Mean Flow Time in the Shop ... ..... ..

Variance of Flow Time in the Shop
Mean Tardiness
Variance of Tardiness ....
Percent of Jobs Tardy . .............
Summary ...........

SUMMARY, MANAGERIAL IMPLICATIONS,
FUTURE RESEARCH ....................
Introduction ........ .. . ..........
Summary of the Major Findings
Research Question One ... ..... ......
Research Question Two
Research Question Three
Research Question Four ....
Research Question Five
Research Question Six ...
Managerial Implications ......
Future Research
Summary ......

FLOWCHART OF THE
RELEASE MECHANISM

AGGREGATE

FLOWCHART OF THE BOTTLENECK
RELEASE MECHANISM

ANALYSIS OF VARIANCE
(TRANSFORMED MODELS) ...............

X

Non— Bottleneck J38é°'

AND

Page

129
130
130
132
133
134
138
138
139
140
142
142
143
144

144
147
149
152
153
153
155
157
159
162
163
164

165

165
165
166
167
169
170
171
173
174
175
177

179

180

181

Page
APPENDIX D: SUMMARY TABLES FOR TRANSFORMED DATA ..... 187
APPENDIX E: POWER OF THE F—TEST ..................... 192
APPENDIX F: DUNCAN PROCEDURE FOR WORK-IN-PROCESS .... 194
G.

APPENDIX ' DUNCAN PROCEDURE FOR

MEAN FLOW TIME IN THE SHOP 0.00.00.00.00. 197

APPENDIX H: DUNCAN PROCEDURE FOR
VARIANCE OF FLOW TIME IN THE SHOP ....... 199

APPENDIX I: DUNCAN PROCEDURE FOR MEAN TARDINESS ..... 201

APPENDIX J: DUNCAN PROCEDURE FOR
VARIANCE OF TARDINESS ................... 204

APPENDIX K: DUNCAN PROCEDURE FOR
PERCENT OF JOBS TARDY 000.000.000.0000000 206

APPENDIX L: ANALYSIS OF VARIANCE
(BOTTLENECK JOBS) 0.00.00.00.000000000000 210

APPENDIX M: ANALYSIS OF VARIANCE
(NON‘BOTTLENECK JOBS) 0000.0000000000000. 216

LIST OF REFERENCES 000000000000000000.0000000000000000 222

xi

LIST OF TABLES

TABLE Page

3-1 MEAN PROCESSING TIME OF THE
BOTTLENECK AND NON-BOTTLENECK WORK CENTER ...... 39

4-1 MEAN FLOW TIME IN THE SHOP
(PRELIMINARY STUDY) 00.00000000.000.000.00000000 46

4-2 VARIANCE OF FLOW TIME IN THE SHOP
(PRELIMINARY STUDY) 0...0.000.000..000000000000. 47

4-3 MEAN TARDINESS (PRELIMINARY STUDY) ............. 47
4-4 VARIANCE OF TARDINESS (PRELIMINARY STUDY) ...... 48
4-5 PERCENT OF JOBS TARDY (PRELIMINARY STUDY) ...... 48
4—6 EXAMPLE FOR CALCULATING TWLS AND TWLB .......... 51

4-7 LOAD LIMIT LEVEL DETERMINATION FOR
AR/FCFS/lOOZ/FRONT 000.000.00.000.000.000.000.00 55

4-8 AVERAGE JOB WAITING TIME IN THE BACKLOG FILE ... 56

4-9 LOAD LIMIT LEVEL DETERMINATION FOR
BR/FCFS/looz/FRONT 00.00.000.000000000 000000 0000 57

4-10 LOAD LIMIT LEVEL DETERMINATION FOR
BR/FCFS/looz/EXIT 00.000000000000000000000000000 58

4-11 LOAD LIMIT LEVELS IN THE MAIN EXPERIMENT ....... 58
4-12 SAMPLE SIZE DETERMINATION 00.0000000000000000000 73

5-1 SUMMARY TABLES FOR WORK-IN-PROCESS
'(ORIGINAL MODEL: 10 OBSERVATIONS) .............. 76

5-2 SUMMARY TABLES FOR MEAN FLOW TIME IN THE SHOP
(ORIGINAL MODEL: 10 OBSERVATIONS) 0 0 0 . 0 0 0 0 0 0 0 0 0 0 77

5-3 SUMMARY TABLES FOR VARIANCE OF FLOW TIME IN THE
SHOP (ORIGINAL MODEL: 10 OBSERVATIONS) ......... 78

xii

TABLE Page

5-4 SUMMARY TABLES FOR MEAN TARDINESS
(ORIGINAL MODEL: 10 OBSERVATIONS) .............. 79

5-5 SUMMARY TABLES FOR VARIANCE OF TARDINESS
(ORIGINAL MODEL: 10 OBSERVATIONS) .............. 80

5-6 SUMMARY TABLES FOR PERCENT OF JOBS TARDY
(ORIGINAL MODEL: 10 OBSERVATIONS) .............. 81

5—7 ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: INVERSE MODEL) 0 o o o o o o o c o o o o o o 93

5-8 ANALYSIS OF VARIANCE
(MEAN FLOW TIME IN THE SHOP: INVERSE MODEL) .... 94

5-9 ANALYSIS OF VARIANCE (VARIANCE OF FLOW TIME
IN THE SHOP: LOGARITHMIC MODEL) ................ 95

5-10 ANALYSIS OF VARIANCE
(MEAN TARDINESS: LOGARITHMIC MODEL) ............ 96

5-11 ANALYSIS OF VARIANCE _
(VARIANCE OF TARDINESS: LOGARITHMIC MODEL) ..... 97

5-12 THE EFFICIENCY OF THE BLOCKING FACTOR .......... 104
5-13 ANOVA RESULTS ....0............OOOOOOOOOOOOOOOOO 106

5-14 THREE-WAY SUMMARY TABLE FOR WORK—IN-PROCESS
(DISPATCHING RULE * LOCATION * PREVALENCE) ..... 109

5-15 TWO—WAY SUMMARY TABLE FOR WORK-IN-PROCESS
(ORDER REVIEW/RELEASE * LOCATION) .............. 112

5-16 AVERAGE WORKLOAD AT THE BOTTLENECK WORK CENTER
(ORDER REVIEW/RELEASE * LOCATION) .............. 114

5-17 AVERAGE JOB WAITING TIME IN THE BACKLOG FILE
(DISPATCHING RULE * LOCATION * PREVALENCE) ..... 115

5~18 TWO-WAY SUMMARY TABLE FOR MEAN FLOW TIME IN THE
SHOP (ORDER REVIEW/RELEASE * DISPATCHING RULE) . 117

5-19 TWO-WAY SUMMARY TABLE FOR MEAN FLOW TIME IN THE
SHOP (ORDER REVIEW/RELEASE * LOCATION) ......... 119

5-20 TABLE FOR MEAN FLOW TIME IN THE SHOP
(PREVALENCE) 00.0.0000.........OOOOOOOOOOOOOOO.I 120

5-21 AVERAGE JOB WAITING TIME IN THE SHOP
(ORDER REVIEW/RELEASE * LOCATION) .............. 121

xiii

TABLE

5-22

5-23

5-24

5-25

5-26

5-27

5-28

5-29

5-30

5-31

5-32

5-33

5-34

5-37

Page

AVERAGE JOB WAITING TIME AT THE BOTTLENECK WORK
CENTER, IN THE SHOP, AND IN THE BACKLOG FILE

(PREVALENCE) 122

TWO-WAY SUMMARY TABLE FOR VARIANCE OF
FLOW TIME IN THE SHOP

(ORDER REVIEW/RELEASE * DISPATCHING RULE) 124

TWO WAY SUMMARY TABLE FOR VARIANCE OF
FLOW TIME IN THE SHOP

(ORDER REVIEW/RELEASE * LOCATION) .............. 126

TABLE FOR VARIANCE OF FLOW TIME IN THE SHOP

(PREVALENCE) 128

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS

(ORDER REVIEW/RELEASE * DISPATCHING RULE) 130

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS

(ORDER REVIEW/RELEASE * PREVALENCE) 133

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS

(LOCATION * PREVALENCE) 134

MEAN FLOW TIME IN THE SYSTEM

(ORDER REVIEW/RELEASE * DISPATCHING RULE) 135

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE

(ORDER REVIEW/RELEASE * DISPATCHING RULE) 135

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE

(ORDER REVIEW/RELEASE * PREVALENCE) 137

AVERAGE JOB WAITING TIME AT THE BOTTLENECK

AND NON-BOTTLENECK WORK CENTER

(LOCATION * PREVALENCE) .......... ..... ......... 137
TWO-WAY SUMMARY TABLE FOR VARIANCE OF TARDINESS

(ORDER REVIEW/RELEASE * DISPATCHING RULE) ... 140

TWO-WAY SUMMARY TABLE FOR VARIANCE OF TARDINESS

(DISPATCHING RULE * PREVALENCE) 141

TABLE FOR VARIANCE OF TARDINESS

(PREVALENCE) 142

THREE-WAY SUMMARY TABLE FOR PERCENT OF JOBS
TARDY (ORDER REVIEW/RELEASE * DISPATCHING

RULE * LOCATION) 146

TWO-WAY SUMMARY TABLE FOR PERCENT OF JOBS TARDY

(ORDER REVIEW/RELEASE * PREVALENCE) 148

xiv

TABLE Page
5-38 AVERAGE JOB WAITING TIME IN THE BACKLOG FILE

(ORDER REVIEW/RELEASE * DISPATCHING RULE

*LOCATION) 0.0.......OOOOOOOOOCOCOOOOCI00...... 150
5-39 MEAN FLOW TIME IN THE SYSTEM

(ORDER REVIEW/RELEASE * DISPATCHING RULE

*LOCATION) 000......0...........OOOOOIOOOOIOOOO 151

5-40 AVERAGE JOB WAITING TIME AT THE BOTTLENECK WORK
CENTER (ORDER REVIEW/RELEASE * PREVALENCE) ..... 152

C-1 ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: ORIGINAL MODEL) 0 o o o o o o o o o o o o o 181

C-2 ANALYSIS OF VARIANCE
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL) ... 182

C-3 ANALYSIS OF VARIANCE (VARIANCE OF
FLOW TIME IN THE SHOP: ORIGINAL MODEL) ......... 183

c-4 ANALYSIS OF VARIANCE
(MEAN TARDINESS: ORIGINAL MODEL) ............... 184

C-5 ANALYSIS OF VARIANCE
(VARIANCE OF TARDINESS: ORIGINAL MODEL) . ...... . 185

C-6 ANALYSIS OF VARIANCE
(PERCENT OF JOBS TARDY: ORIGINAL MODEL) . ....... 186

D-l SUMMARY TABLES FOR WORK—IN-PROCESS
(INVERSE MODEL: 10 OBSERVATIONS) ............... 187

D-2 SUMMARY TABLES FOR MEAN FLOW TIME IN THE SHOP
(INVERSE MODEL: 10 OBSERVATIONS) ............... 188

D-3 SUMMARY TABLES FOR VARIANCE OF FLOW TIME IN THE
SHOP (LOGARITHMIC MODEL: 10 OBSERVATIONS) ...... 189

D-4 SUMMARY TABLES FOR MEAN TARDINESS
(LOGARITHMIC MODEL: 10 OBSERVATIONS) ........... 190

D-5 SUMMARY TABLES FOR VARIANCE OF TARDINESS
(LOGARITHMIC MODEL: 10 OBSERVATIONS) ........... 191

E-l POWER OF THE F-TEST 0000.0 000000000000 0000000000 192

L-l ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: BOTTLENECK JOBS) .......... .... 210

L-2 ANALYSIS OF VARIANCE
(MEAN FLOW TIME IN THE SHOP: BOTTLENECK JOBS) .. 211

XV

TABLE Page

L-3 ANALYSIS OF VARIANCE (VARIANCE OF
FLOW TIME IN THE SHOP: BOTTLENECK JOBS) ........ 212

L-4 ANALYSIS OF VARIANCE
(MEAN TARDINESS: BOTTLENECK JOBS) .............. 213

L-5 ANALYSIS OF VARIANCE
(VARIANCE OF TARDINESS: BOTTLENECK JOBS) . ...... 214

L-6 ANALYSIS OF VARIANCE
(PERCENT OF JOBS TARDY: BOTTLENECK JOBS) .. ..... 215

M-l ANALYSIS OF VARIANCE
' (WORK-IN-PROCESS: NON-BOTTLENECK JOBS) ......... 216

M-2 ANALYSIS OF VARIANCE (MEAN FLOW TIME
IN THE SHOP: NON-BOTTLENECK JOBS) .............. 217

M-3 ANALYSIS OF VARIANCE (VARIANCE OF
FLOW TIME IN THE SHOP: NON-BOTTLENECK JOBS) .... 218

M-4 ANALYSIS OF VARIANCE
(MEAN TARDINESS: NON-BOTTLENECK JOBS) o o o o 000000 219

M-5 ANALYSIS OF VARIANCE
(VARIANCE OF TARDINESS: NON-BOTTLENECK JOBS) ... 220

M-6 ANALYSIS OF VARIANCE
(PERCENT OF JOBS TARDY: NON-BOTTLENECK JOBS) ... 221

xvi

FIGURE

2-1
5-1

5-2

5-4
5-5
5—6

5-7

5—9

5-10
5-11

5-12

LIST OF FIGURES

THE FRAMEWORK OF A BOTTLENECK JOB SHOP . ...... ..

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(WORK-IN-PROCESS: ORIGINAL MODEL) ..............

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL) ...

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(VARIANCE OF FLOW TIME IN THE SHOP:
ORIGINAL MODEL) ..........OOOOOOOOOOOOOOO .......

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN TARDINESS: ORIGINAL MODEL) ...............

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(VARIANCE OF TARDINESS: ORIGINAL MODEL) ... .....

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(PERCENT OF JOBS TARDY: ORIGINAL MODEL) ........

CELL STANDARD DEVIATION VS. SQUARE OF CELL MEAN
(WORK-'IN-PROCESS: ORIGINAL MODEL) 0 o o o o o o o o I o o O 0

CELL STANDARD DEVIATION VS. SQUARE OF CELL MEAN
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL) ...

CELL STANDARD DEVIATION VS. CELL MEAN
(VARIANCE OF FLOW TIME IN THE SHOP:
ORIGINAL MODEL) 00............CCOOOOOOOOOOOO....

CELL STANDARD DEVIATION VS. CELL MEAN
(MEAN TARDINESS: ORIGINAL MODEL) ...... .........

CELL STANDARD DEVIATION VS. CELL MEAN
(VARIANCE OF TARDINESS: ORIGINAL MODEL) ........

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(WORK-IN-PROCESS: INVERSE MODEL) ........ .......

xvii

Page

22

83

84

85

86

87

88

89

89

91

91

92

98

FIGURE

5-13

5-14

5-15

5-16

5-17

5-18

5-19

5-20

5-21

5-22

5-23

5-24

5-25

5-26

5—27

5-28

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN FLOW TIME IN THE SHOP: INVERSE MODEL)

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(VARIANCE OF FLOW TIME IN THE SHOP:
LOGARITHMIC MODEL) .............................
NORMALITY AND HOMOGENEITY OF VARIANCE TEST

(MEAN TARDINESS: LOGARITHMIC MODEL) .... ........
NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(VARIANCE OF TARDINESS: LOGARITHMIC MODEL)

LOCATION * DISPATCHING RULE INTERACTION
(WORK‘IN-PROCESS: 100% PREVALENCE) o o o o o o o o o o o o 0
LOCATION * DISPATCHING RULE INTERACTION
(WORK-IN-PROCESS: 50% PREVALENCE) ..............
LOCATION * ORDER REVIEW/RELEASE INTERACTION
(WORK—IN-PROCESS)

ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (MEAN FLOW TIME IN THE SHOP) .......

LOCATION * ORDER REVIEW/RELEASE INTERACTION
(MEAN FLOW TIME IN THE SHOP) ...................
ORDER REVIEW/RELEASE * DISPATCHING RULE

INTERACTION (VARIANCE OF FLOW TIME IN THE SHOP).

LOCATION * ORDER REVIEW/RELEASE INTERACTION
(VARIANCE OF FLOW TIME IN THE SHOP) ............

ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (MEAN TARDINESS) . ...... ...... ......

PREVALENCE * ORDER REVIEW/RELEASE INTERACTION
(MEAN TARDINESS) ....

......OOOOOOOOOOOOOO .......

PREVALENCE * LOCATION INTERACTION
(MEAN TARDINESS) 00............OOOOOOOOOOOOOOOOI
ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (VARIANCE OF TARDINESS) ............
PREVALENCE * DISPATCHING RULE INTERACTION
(VARIANCE OF TARDINESS)

ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (PERCENT'OF JOBS TARDY:
FRONT LOCATION) ........

xviii

Page

99

100

101

102

110

110

112

117

118

125

127

131

132

133

139

141

144

FIGURE

5-30

5-31

5-33
5-34
5-35
5—36
5-37
5-38
5-39
5-40
5-41
5-42
.5-43

5—44

ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (PERCENT OF JOBS TARDY:
EXIT LOCATION)

ORDER REVIEW/RELEASE * DISPATCHING RULE
INTERACTION (PERCENT OF JOBS TARDY:
MIXED LOCATION) ...

00.000.00.00...0.00000.......

PREVALENCE * ORDER REVIEW/RELEASE INTERACTION
(PERCENT OF JOBS TARDY) ........................
ORDER REVIEW/RELEASE MAIN EFFECT
(WORK-IN-PROCESS: BN VS. NBN) .. ..... . ........ ..

DISPATCHING RULE MAIN EFFECT
(WORK—IN-PROCESS: BN VS. NBN)

BOTTLENECK LOCATION MAIN EFFECT
(WORK-IN-PROCESS: BN VS 0 NBN) o o o 000000000000000

ORDER REVIEW/RELEASE MAIN EFFECT
(MEAN FLOW TIME IN THE SHOP: BN VS.

DISPATCHING RULE MAIN EFFECT
(MEAN FLOW TIME IN THE SHOP: BN VS. NBN)

BOTTLENECK LOCATION MAIN EFFECT
(MEAN FLOW TIME IN THE SHOP: BN VS.

ORDER REVIEW/RELEASE MAIN EFFECT

(VARIANCE OF FLOW TIME IN THE SHOP: BN VS. NBN).
DISPATCHING RULE MAIN EFFECT

(VARIANCE OF FLOW TIME IN THE SHOP: BN VS. NBN).
ORDER REVIEW/RELEASE MAIN EFFECT

(MEAN TARDINESS: BN VS. NBN) ...................

BOTTLENECK LOCATION MAIN EFFECT
(MEAN TARDINESS: BN VS. NBN) .... ...... . ........

ORDER REVIEW/RELEASE MAIN EFFECT
(VARIANCE OF TARDINESS: BN VS. NBN)

ORDER REVIEW/RELEASE MAIN EFFECT
(PERCENT OF JOBS TARDY: BN VS. NBN) ..... .......

FLOWCHART OF THE AGGREGATE RELEASE MECHANISM ...
FLOWCHART OF THE BOTTLENECK RELEASE MECHANISM ..

xix

Page

145

145

148

154

155

156

156

158

158

160

160

161

161

162

163
179
180

CHAPTER 1

BOTTLENECK JOB SHOP

1.1 Introduction

Effective shop floor control1 plays a critical role in
any successful manufacturing system. As pointed out by
Melnyk, Carter, Dilts and Lyth (1985), effective shop floor
control is the necessary complement to good planning. Shop
floor control is primarily concerned with the smooth flow
of materials, orders and information to satisfy customer
needs (as represented by the production schedules) in a
timely and cost effective manner. To meet these objectives,
the shop floor control system draws on a wide range of
different activities.

Traditionally, the focus has been directed at the
detailed scheduling phase of the shop floor control system.
For example, Melnyk, Carter, Dilts, and Lyth (1985) noted
that of over 1200 articles on shop floor control, 213 dealt
primarily with issues involving scheduling, sequencing, and

dispatching. The primary emphasis among these articles was

 

1. Melnyk and Carter (1985) define shop floor control as the
very detailed short-term planning, execution and monitoring
activities needed to control the flow of an order from the
moment the order is released by the planning system for
execution until the order is filled and its disposition
completed. '

2
placed on dispatching rules. Recently, however, researchers
and practicing managers have begun shifting their attention
away from the dispatching function to other activities (such
as order review/release). This shift in attention is also
taking place in other areas such as capacity management.

Traditionally, questions involving shop floor control
activities were studied within the context of a very
specific manufacturing setting: the job shop manufacturing
setting.2 Under this setting, researchers made several
general but key assumptions about the nature of the setting.
.One such crucial assumption was that the shop was
essentially "balanced." This implied that while there were
short-term work imbalances, in the long run, no one machine
or work center persistently constrained the operation of the
other work centers. In other words, a "balanced" shop was
one in which the long term workload was randomly but evenly
distributed across the various work centers. Such a shop
setting, while important, is not necessarily representative
of all possible job shop settings.

There exists another category of job shop. This is one
which is not "balanced." Consideration should be given to
such a shop for several reasons. It is a better
representation of the reality encountered on the shop floor.
(Prather 1983) Bottlenecks, a critical characteristic of the
unbalanced job shop, also have a significant impact on the

operation of entire shop floor control system. In this shop,

 

2. A job shop is a shop in which routings of orders are
distributed randomly. -

3

there exists one or more constraining machines or work
centers which significantly affect the flow of work through
the system. These are bottleneck machines or work centers.
The presence of bottleneck work centers in a job shop
manufacturing system can and does create a unique set of
problems, which otherwise would not happen in balanced job
shop settings.

Wight (1970) noted that any small capacity bottleneck
is followed by an aggravation of the backlog situation in
the shop. This is followed by an increased level of
expediting activities. It is not expected, however, that the
increased level of expediting is a desirable resolution to
this bottleneck shop.

Goldratt and Cox (1984, pp. 138) also recognized the
importance of bottleneck resources. They noted that it was
the type of bottleneck resources which determined the
effective capacity of the system to be managed.

Despite their potential and crucial importance,
bottleneck job shops have been largely ignored in the study
of shop floor control. Very little is known about how to
manage a shop floor control system in the presence of
bottleneck operations. The study on bottlenecks is further
complicated by the lack of general framework for
understanding or for providing insight into bottlenecks.

There are three important reasons why research is
needed on the bottleneck job shop. First, bottleneck job

shops are fairly common in practice. Prather (1983) observed

4
that most factories have bottlenecks. The capacity of these
bottlenecks ultimately determines the total level of
shipments or output.

However, as pointed out previously, our knowledge of
bottlenecks, their critical characteristics, and the impact
of bottleneck operations on the performance of the shop
floor is relatively limited. Research is needed to identify
the unique characteristics of bottleneck operations and to
help clarify how their presence affects the shop floor.

Second, there is a growing awareness of the role played
by the presence of bottleneck work centers. Managers and
researchers are beginning to recognize that the presence of
one or more bottleneck work centers affects the resulting
Operation of the shop floor. As pointed out by Goldratt and
Cox (1984), bottlenecks must be recognized within the
scheduling system.

Third, research is needed to evaluate the effectiveness
of practices developed specifically for "balanced" shops
when they are applied to bottleneck shops. Practices and
procedures which do not recognize the presence of
bottlenecks may create more problems than they solve when
used to manage bottleneck operations.

The lack of detailed knowledge surrounding bottlenecks
combined with their potential importance forms a major
foundation of the justification for the research study. In
the following sections, the research premise and specific

research objectives underlying this study will be presented.

5
1.2 The Research Premise
This study is specifically concerned with evaluating
the following premise:

The development of an effective shop floor control
system can not be done without first understanding the
manufacturing environment in which it must operate and
the resulting requirements and constraints imposed by
this environment. The process of developing an
effective shop floor control system then focuses on
identifying and selecting those control procedures
which best satisfy the particular requirements of the
given manufacturing environment. A key characteristic
which shapes the specific nature of the manufacturing
environment is the presence or absence of bottleneck
operations.

1.3 The Research Objectives
This study will address the following research
questions. These questions will form the major objectives
of the study.

1. What major characteristics of a bottleneck job
shop must be considered when studying their impact
on the operation of the shop floor?

2. Which control procedures (dispatching rules or
order review/release mechanisms) have a greater

effect on a bottleneck work center (and under what
conditions)?

3. Can usage of information about workload for a
bottleneck work center significantly improve shop
performance?

4. In a bottleneck job shop, where there is a mixture

of bottleneck and non-bottleneck jobs, how does
the presence of a bottleneck work center influence
these two types of jobs? Bottleneck jobs are those
requiring the operation of a bottleneck work
center.

5. How do such bottleneck characteristics as
prevalence (i.e., does the bottleneck work center
affect the routings of all jobs or just a portion)
and the location of the bottleneck (does the
bottleneck always occur at the start of the
routing, the end or is it randomly distributed?)

6
affect shop floor operations and the performance

of dispatching rules and order review/release
mechanisms?

6. Can we identify any general guideline which can be
used when dealing with a bottleneck job shop?

To answer the first question, a framework for the
bottleneck job shop will be developed. In this study, the
framework will look at four different dimensions: causes of
the bottleneck, status of the bottleneck, location of the
bottleneck, and prevalence. Definition for these various
dimensions will be provided later in this thesis.

To answer the second question, this study will look at
two fundamental control procedures: local dispatching rules
and order review/release mechanisms.

To answer the third question, this study will present
various alternative order review/release mechanisms which
will utilize a wide range of information for releasing
orders.

To answer the fourth question, this study will divide
incoming orders into two categories (bottleneck orders and
non-bottleneck orders). Information about both types of
orders will be separately collected and analyzed.

To answer the fifth question, this study will evaluate
and compare various performance measurements gathered for
shops having a bottleneck operating at three different
locations (front, exit, and mixed) and operating at two
different levels of prevalence (1002 and 502).

To answer the final question, this study will analyze

and compare three well-known dispatching rules (the

first-come-first-served rule, the shortest processing time
rule, and the slack per remaining operation rule).

These questions reflect the writer's concern to
understand the problems created by a bottleneck operation
and to develop effective control procedures to cope with

those problems in the job shop manufacturing setting.

1.4 The Organization of the Study

This dissertation has been divided into six chapters.
In this first chapter, a rationale for the study on the
bottleneck job shop and a description of the objectives has
been presented.

In the second chapter, the conceptual considerations of
bottleneck operations are examined. The chapter begins with
a literature review pertaining to bottleneck operations, and
provides the theoretical basis for the development of the
bottleneck job shop framework. The definition of a
bottleneck work center is presented. Problems created by
bottlenecks and tactics used to manage them are also
presented.

Chapter three contains the research methodology used in
the dissertation. The simulated shop is described in detail.
Included is the description of "quasi-random" job shop, the
operating logic of the model, the shop size, the
characteristics of orders, the assumptions of the model, and
the simulation model.

In chapter four, the experimental design of the study

is presented. The experimental factors and levels of each

8
factor are presented. Statistical problems pertaining to
the simulation model, which is stochastic and dynamic in
nature, are examined. The hypotheses and the performance
criteria of this study are also presented.

The examination of the simulation results is presented
in chapter five. The primary research procedure is that of
the analysis of variance (ANOVA). This procedure is used to
determine if any of the control procedures or bottleneck
characteristics have a significant impact on the observed
performance measurements. In analyzing the results, we focus
our attention on six major performance measures. The major
performance measures consist of work-in-process, mean flow
time in the shop, variance of flow time in the shop, mean
tardiness, variance of tardiness, and the percent of jobs
tardy. The results of this analysis are used to test the
hypotheses presented in Chapter four.

Chapter six presents the major findings and managerial
implications of the study and suggests future research areas

relevant to the bottleneck job shop.

CHAPTER 2

BOTTLENECKS: CONCEPTUAL CONSIDERATIONS

2.1 Introduction

As noted in the preceding chapter, there are several
important reasons for studying in detail the bottleneck job
shop. To date, however, little research has been devoted to
.examining bottleneck models in a job shop setting. Little
has been made to develop models which adequately represent
more realistic job shops and to investigate problems
encountered in such settings. As a result, there is little
known about the nature of bottlenecks and their problems.
This chapter explicitly examines manufacturing systems with
bottleneck operations. The primary purpose of this chapter
is to develop a framework of a bottleneck job shop. This
framework helps provide insight and a more detailed
understanding of the bottleneck job shop. It also provides a
theoretical basis for this study and the resulting structure
of the experiment.

The chapter starts with a literature review regarding
bottleneck operations in a wide range of manufacturing
configurations. The review provides a background for the

development of the framework for the bottleneck job shop. As

10
will be shown, this framework is based on four dimensions.

In order to define the bottleneck work center, the
concept of the load-capacity coefficient is presented.

The uniqueness of the bottleneck job shop, when
compared to a pure random job shop and project scheduling,
is described. Problems created by the presence of a
bottleneck work center are discussed. To cope with these
problems, several tactics are presented. Specifically,
emphasis is placed on dispatching rules and order

review/release mechanisms.

2.2 Literature Review

Despite the . potential importance of bottlenecks,
research to date on bottlenecks is very limited compared to
the extensive body of the traditional job shop. There are
currently very few works specifically dealing with
manufacturing system in which one or more bottleneck
operations are located. Within these works, there is little
agreement over the type of manufacturing setting to be
examined. Each work describes a different type of bottleneck
operation or system. This lack of agreement indicates that
bottlenecks are diverse and may be drawn from a broad
spectrum of configurations. In each work, the importance of
bottlenecks in the system is recognized and some procedures
are attempted to control problems created by bottleneck
operations.

Solberg (1981) raised an issue of the bottleneck model

for capacity planning. Solberg defined the bottleneck work

11

center to be that work center for which the workload per
server is greatest. Solberg argued that the bottleneck
model, for purposes of capacity estimation, suffered from
the false assumption that it systematically overestimated
true capacity. Even the most heavily loaded servers at times
were idled. Therefore, it was sensible to use a more
realistic model, called a stochastic model, for estimating
capacity planning. Although Solberg did not directly deal
with the operation of bottleneck shops, he noted the
importance of the bottleneck station by describing that in a
flow shop, or one in which all processes pass through the
bottleneck station, it was rather obvious that the
productive capacity of the system was equal to that of the
bottleneck station.

Huang, Rees, and Taylor (1983) recognized the critical
aspects of bottlenecks in their simulation analysis of the
Japanese Kanban system. Like Solberg, the primary research
focus was not on the operation of a bottleneck shop. In the
second phase of their simulation experiments, they examined
the transition period (when the Just-in-Time system was
implemented. It was then that the problems of dealing with
bottlenecks were raised. The problems resulted from the
system's unbalanced condition in which processing times were
not the same at each work station. They created a bottleneck
operation by altering processing times at each stage. The
experimental results implied that additional kanbans, i.e.,

buffer, would not solve a bottleneck situation. A bottleneck

12
must be dealt with by reducing the bottleneck itself (i.e.,
setup time reduction at the bottleneck work center,
bottleneck capacity expansion, or intensive worker training
and cross training).

Prather (1983) emphasized the importance of bottlenecks
by stating the capacity of bottleneck work centers
ultimately determined the total level of shipments or
output. In his presentation of good production control
practices, he provided two approaches to identify
bottlenecks.

One approach was to calculate an average percentage of
utilization of work centers in one year. Work centers with
over 90 percent utilization were designated as bottlenecks.
The other approach was to review completed work orders and
find the work centers where orders sat in the longest queue.
Since the capacity of bottleneck work centers limited total
system output, it was critical to fully utilize bottleneck
work centers. To do so, queues, workload, and priorities of
orders at bottleneck work centers were reviewed daily.

Another important factor identified by Prather involved
what portion of all fabricated parts was supposed to go
through bottleneck work centers. This was important for two
reasons. First, it was possible to predict the loading of
bottleneck work centers in advance. Second, it was possible
to evaluate the impact of order release on the bottleneck
work centers before release. Prather also suggested an A-B-C

classification analysis of resource utilization of all work

13
centers.

Fogarty and Hoffmann (1983, pp. 18) also suggested such
an A-B-C control scheme to the control and management of
bottlenecks.

Recently, there has been a growing interest in a
scheduling simulation procedure called OPT (Optimized
Production Technology). The OPT first was developed by
Goldratt and Pazgal in Israel. It has been marketed in the
United States since 1979. The goal of the OPT was to make
money through simultaneously increasing throughput, reducing
inventory, and cutting operating expenses. To accomplish
this goal, ten OPT rules were developed. (see Fox 1982b)
Among these rules, the key ingredient was the focus of the
OPT on the bottleneck resources as the basis for production
scheduling and capacity planning.

Goldratt and Cox (1984, pp. 138) defined a bottleneck
as any resource with capacity equal to or less than the
demand placed upon it. When bottlenecks exist, managers used
information about them to control the flow through the
system and into the market. Since the capacity of bottleneck
resources determined the capacity of the system, it was
critical to utilize bottleneck resources to their full
potential.

OPT separated resources into two groups for scheduling
purposes: critical and non-critical resources. The first
group was finite forward scheduled using a secret central

OPT module developed by Goldratt. The second was backward

14
scheduled. This procedure was repeated until all resources
were not utilized over 100 percent.

Although some significant successes of the OPT in terms
of reduction of work in process inventory and improvement of
on-time delivery were reported in a limited number of
companies (Meleton 1986), it was too early to appreciate the
OPT's true value. This situation was due to the following
two reasons: 1) the central OPT module is a 'black box'
because its logic is proprietary.: 2) it has a rather short
history.

The proponents of the OPT view it as a combination of
the best from MRP II (Manufacturing Resource Planning) and
Just-in-Time (Fox 1982a; Lundrigan 1986). It eliminates
waste more efficiently than JIT and produces more a feasible
and efficient schedule than MRP. If the OPT runs as claimed,

it will increase system output, reduce work-in-process

inventory, improve cycle time, and reduce space
requirements. Furthermore, it has the capability of
simulating production scheduling, master schedules,

workload, and product mix quickly and easily. It provides a
new way of looking at manufacturing system.

The OPT system, however, appears to have some
drawbacks. It requires huge data maintenance for a tight
network organization (Meleton 1986). It does not consider
costs (Jacobs 1983). It creates much more work-in-proceSs
inventory levels than normal and requires non-bottleneck

machines go through many more setups (Aggarwal 1985). It is

15
anything but transparent (Vollmann 1986). It appears the OPT
system works best in a high volume, large batch size
operation with few individual production operations.

Ow (1985) attempted to use the knowledge of restricted
resources to minimize the total weighted tardiness of jobs
to be scheduled in the proportionate flow shop. He
acknowledged that the order in which jobs eventually come
out of the shop depends on which jobs are completed at the
bottleneck. He proposed a focused approach which works
primarily on the bottleneck work center for the purpose of
scheduling. The simulation results indicate the focused
approach to scheduling provide the best results when
compared with other experimental approaches such as Weighted
Shortest Processing Time rule, Earliest Due Date Rule, First
Come First Serve rule, COVERT, and Lead Time Iteration. Like
Goldratt and Cox (1984), Ow explicitly utilized information
on the bottleneck to control scheduling in the special flow
shop.

Billington (1985) tested the relative magnitude of cost
reduction through capacity expansion of the bottleneck in an
assembly system with one bottleneck. The primary performance
criterion was the cost. Cost was the combined setup costs
and inventory holding costs. Although the paper did not
measure customer performance criteria, it had two important
implications. First, the location of bottleneck was found
to be a significant factor for evaluating bottleneck

resources. Second, better scheduling of bottlenecks was more

16
important than mere capacity expansion to reduce production
delay.

Billington, McClain and Thomas (1986) investigated a
bottleneck shop setting for the purpose of evaluating a
heuristic method for multilevel lot-sizing with the
extension of Billington's 1985 model. They examined the
capacitated lot-sizing problem by introducing a single
bottleneck facility. In their study, they ignored capacity
limitations at all work centers other than the bottleneck.
Test result showed feasible solutions were possible for
problems too difficult to solve with exact methods.

As shown in the preceding review, there (is a very
little agreement over the type of shop setting to be
examined. Certain conclusions, however, can be drawn from
this limited but diverse body of literature. The most
important of these conclusions include the following:

* Bottlenecks are very crucial and pervasive factor
which determine the resulting performance of a
manufacturing system.

* There is little agreement over the exact definition
of bottlenecks.

* Bottlenecks, if any, must be first identified.

* Bottlenecks must be used as the primary basis for
production scheduling and capacity planning.

* The location and the condition of bottlenecks are
important factors for scheduling.

* The performance of the OPT is yet to be conclusively
proven.

17
2.3 Definition of a Bottleneck Work Center

In the studies on bottlenecks, there was little
agreement over the definitions of a bottleneck work
center.3One view of bottlenecks involves the comparison of
input rate with output rate at a work center (Goldratt and
Cox 1984, Wallace 1984). A bottleneck work center is then
the one where input rate is equal to or greater than output
rate. Another method is to examine a work center which has
capacity utilization above 90% or the longest queue (Prather
1983). There are, however, some problems with these
definitions which must be pointed out.

'The first definition is theoretically impossible to
apply. It is not feasible to generate a work center in which
the input rate exceeds the output rate. The reason is that
such a work center would be unstable due to an explosive
waiting line. The strict specification of a certain capacity
utilization of the second one is relatively artificial. It
also offers too broad definition for theoretical
application. Both are good terms from a practical

standpoint, but are of limited use for theoretical research.

2.3.1 Definition of a Bottleneck Work Center in this Study

The definition of a bottleneck work center used in this

study differs somewhat from those two above. Before defining

 

3. A work center is defined as a specific production
facility, consisting of one or more people and/or machines,
which can be considered as one unit for purposes of capacity
requirements planning and detailed scheduling. (APICS
dictionary 1984)

18
a bottleneck work center, let us consider what really
creates it. In general, a bottleneck is created by two
factors: inadequate capacity and/or high workload. Here,
capacity may include machines, manpower, and tooling. An
insufficient amount of capacity to be able to process
existing and planned workload is the major cause of
bottlenecks. Note that the relative value, not the absolute
value, of capacity of resources and workload is of
importance. Whether or not the capacity of a work center is
sufficient depends upon the amount of workload imposed in a
certain time period. The ratio of these two factors
determines the condition of a bottleneck. To define the
bottleneck, therefore, the concept of the load-capacity
coefficient is introduced.
A load-capacity coefficient (Aij) can be defined as

follows:

Aij . Lij/Cij

where:

Lij - the workload planned to be completed for
work center i in the planning period j.

Cij - the capacity (in standard hours -
demonstrated or effective) of machine

hours for work center i in the planning
period j.

Lij is the sum of setup and processing times of jobs
planned to be completed for work center i in the planning
period j.

Cij is the number of standard machine hours for work

center i in planning period j. For example, the weekly

19
capacity of a work center i consisting of only one machine
is 40 hours.

For each work center in the shop, a load-capacity
coefficient is calculated. A load-capacity coefficient takes
the value between 0 and 1, inclusive.

Formally defined, a bottleneck is the work center with
the highest load-capacity coefficient over the long run. In
other words, we define a bottleneck operation as one at
which the average workload is persistently high, when
compared to other work centers.

This definition does have some advantages over others
previously discussed. It considers both capacity and
workload in a relative manner when identifying a bottleneck.
It also identifies the most critical work center. The most
critical work center is the one which has the highest load-
capacity coefficient. This is the major work center which
most significantly affect the flow of work through the
system. Finally, it provides a definition for theoretical
study.

This is, however, a very restrictive conceptual
definition. It is of limited significance for practical
purposes. For example, a job shop has four work centers with
the Aij of each work center A, B, C, and D for the period j
is .57, .35, .37,and .33, respectively. By definition, work
center A is designated as the bottleneck, because it has the
highest Aij. Practically, none will be considered as a

bottleneck work center. As a result, additional quantifying

20
conditions are described below in order to make the
definition significant practically as well as
theoretically.

* The bottleneck work center at which Aij is
significantly deviated from 1.0 is not regarded as a
bottleneck. Here, we have no bottleneck.

* Any non-bottleneck work center at which Aij is
-smaller than Aij of the bottleneck but close to
1.0 is also considered as a bottleneck. Here, we have
multiple bottlenecks.

2.4 The Framework of a Bottleneck Job Shop

As seen in 2.2, no general universally accepted scheme
has yet been presented in the literature for categorizing a
bottleneck. The intent of categorization is to help identify
understanding of the problem inherent in the study of
bottlenecks and important theoretical developments for those
specific areas. A bottleneck can be described using three
major classification dimensions in the context of a job shop
which is the main setting for this study:

1. Cause of a bottleneck

a. A systematic bottleneck
b. A random bottleneck

2. Status of a bottleneck

a. Stationary
b. Floating

3. Location of a bottleneck in the routing
a. Front

b. Exit
c. Mixed

21
2.4.1 Cause of a Bottleneck

In Figure 2-1, a bottleneck is first divided into two
groups in terms of the cause of a bottleneck. The first
group is systematic; the second is the random bottleneck.
This is a key distinction for control purposes. A systematic
bottleneck results from two factors. The workload for a
specific work center is too high (due to problems with
product mix or scheduling), or, a bottleneck may result from
the lack of adequate capacity. Either of these two factors
(alone or together) creates a systematic bottleneck. The
systematic bottleneck persistently exists and limits the
total output of the system over the long run.

As the name implies, a random bottleneck occurs in a
random fashion in the shop. It exists temporarily in the
system, then disappears. A random bottleneck results from
the following factors:

* Machine breakdown

* Employee absenteeism

* Reworks due to defects

* Unexpected temporary large demand

* Tooling breakdown

* Expediting

* Product mix
A random bottleneck is ever changing across machines in the
system. The problems created by a random bottleneck may be
solved by relatively naive procedures (for example,

overtime).

film mzauHm
momm mow uomzmqbbom < mo umozmz<mm mm;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a a H. a fig a
o c o c
x s o x a o
H H H u
z n.— .m 2 m m
2 l _ , , ,
2 wcauuo; _ huucowumum—

 

 

 

 

_ L 7.2:: _.

II!

 

 

 

 

 

 

 

 

23
In this study, we focus exclusively on problems created
by the presence of a systematic bottleneck. It is the
systematic bottleneck which constrains and restricts the

performance of shop floor.

2.4.2 Status of a Bottleneck

A systematic bottleneck can be further divided into two
categories in terms of the bottleneck status: stationary and
floating. The status of the bottleneck identifies the extent
to which a bottleneck is fixed at one specific work center.
If a bottleneck does not move across work centers, it is
stationary. The bottleneck work center is fixed. On the
other hand, a floating bottleneck moves across work centers.
The bottleneck work center is floating due to changes in

demand pattern, capacity expansion, or scheduling problems.

2.4.3 Location of a Bottleneck in the Routing

A stationary or floating bottleneck is further divided
into two categories in terms of the bottleneck's location:
front, exit, and mixed. The location of the bottleneck
refers to the relative location of the bottleneck in the
routings of orders. The location is frequently seen in the
front of or at the end of order routings in practice. As an
example of the exit location of the bottleneck, a final
inspection operation, packaging, or coating would be the
cases. Examples of a front location for the bottleneck may
include milling machine or lathe. Also considered is a mixed

location in which the bottleneck can appear anywhere in the

24
routings of orders.

Specifically, systematic and stationary bottleneck
along with three bottleneck locations in Figure 2-1 is the
primary focus of this study. In addition, another dimension
which should be considered when studying a bottleneck job
shop is that of prevalence. Prevalence refers to the extent
to which orders are subject to pass through the bottleneck.
Specifically, prevalence is the percent of all orders which
must go through the bottleneck operation. For example, 100%
prevalence means that all incoming orders to the system must
go through the bottleneck operation. On the other hand, 0%
prevalence represents a shop in which a bottleneck operation

does not exist. Prevalence is a continuous term.

2.5 Uniqueness of a Bottleneck Job Shop

The main manufacturing setting to be dealt with in this
study is a job shop having a bottleneck work center. It is
called a bottleneck job shop. In this section, the unique
characteristics of the bottleneck job shop are discussed. In
addition, the bottleneck job shop is compared with a pure
job shop and project scheduling.

The key difference between the bottleneck job shop and
the pure job shop is that in the bottleneck job shop there
exists one or more dominant resources which determines the
level of overall system performance measurement. The
bottleneck work center's capacity is the system's capacity.
The utilization of the bottleneck work center is relatively

high compared to other non-bottleneck work centers. In the

25
pure job shop, the average capacity utilization across all
work centers is approximately the same in the long run.

The bottleneck job shop scheduling appears similar to
the project scheduling in that both have constraining
resources which affect system performance. However, they
differ from each other in that the bottleneck job shop
scheduling has the continuous nature of work input and flow
to the system (Davis 1973). Therefore, it is more difficult

to manage the bottleneck job shop than the project.

2.6 Impact of Bottleneck Operations on Shop Floor

The bottleneck work center is a major dominant work
center in influencing the shop performance. It aggravates
the shop floor by creating a set of unique problems. This
section looks at the impact of bottleneck work center on
shop floor and system performance. It is critical for
several significant reasons.

* It hinders the smooth flow of orders through the
shop.

* It lengthens manufacturing lead times.

* It persistently constrains the operation of other
work centers.

* It increases the number of expediting.

* It increases work-in-process inventory levels.

* It increases variance of load balancing.

* It determines the overall output of the system.
When a bottleneck work center exists, the effectiveness of
shop floor control is directly affected by the manager's

ability to control the bottleneck.

26
2.7 Tactics to Cope with Bottlenecks

After identifying a bottleneck work center, the next
question faced by researchers and practicing managers is how
to tackle the problems created by this bottleneck operation.
In order to cope with these problems, it is reasonable to
look at what really causes the bottleneck work center to
exist in the first place. As discussed previously in 2.3 and
2.4, there are two systematic factors for the real causes of
the bottleneck: inadequate capacity of resources and high
workload. To reduce the impact of a bottleneck operation on
shop floor, therefore, researchers and managers must either
expand the capacity of bottleneck resources or reduce the
workload for the bottleneck work center or both. In this

section, these two tactics are discussed in more detail.

2.7.1 Tactics to Manage Capacity

The decision of how to manage inadequate capacity
basically concerns the expansion of capacity of bottleneck
resources. This decision generally takes time and demands a
high price to implement. Potential tactics to expand the
capacity of critical resources are as follows:

* Purchase of a bottleneck machine

* Subcontracting

* Setup reduction of a bottleneck work center'

* Cross worker training

* Additional tooling

* Increase of employment

These tactics are long-term solutions and may not be

27

feasible or may be excessively expensive in the short time.

2.7.2 Tactics to Manage Workload

Tactics for solving problems created by insufficient
capacity of a bottleneck work center may take relatively
long or medium time to implement. On the other hand, tactics
used to manage workload for a bottleneck work center may be
quickly implemented. As pointed out by Melnyk and Carter
(1987), shop floor control deals with very detailed short-
term planning, execution and monitoring activities needed to
control order flows. Shop floor control is primarily
concerned with the operation of the order flows, not the
expansion of capacities. One of the goals of shop floor
control is how to utilize given resources in a most
efficient and cost-effective manner. Therefore, this study
explicitly looks at tactics used to manage workload.

One approach to reduce workload for the bottleneck work
center is the use of alternative routings. The change of
routings containing the bottleneck Operation definitely
helps reduce the current workload as well as the planned
workload. In this study, we assume the use of alternative

routings is infeasible. Specifically, this study examines

two control procedures: dispatching rules and order

review/release mechanisms.

2.7.2.1 Dispatching Rules
Dispatching, defined as the activity for selecting the

next job in queue for processing on [a machine (Melnyk,

28
Carter, Dilts and Lyth 1985), is an essential activity in a
production scheduling system. The research on dispatching
rules are well documented. Dispatching rules are easy to
implement. They affect the performance of the system. They
also affect the rate at which each individual job progresses
through the system. Therefore, the selection of dispatching
rules affects workload for the bottleneck work center. Some
"global"A dispatching rules are suggested to reduce queue
lengths and inventory levels at the overloaded work center.
Conway, Maxwell, and Miller (1967, pp. 223) proposed the
WINQ (Work in Next Queue) rule and the XWINQ (Expected Work
in Next Queue) rule and Schonberger (1979) suggested the

clearest-road-ahead-priorities.

2.7.2.2 Order Review/Release Mechanisms

Order review/release was recently attracted the
attention of both researchers and managers. Order
review/release is the first phase of shop floor control
system. It controls the rate of input flow to the shop
floor. It is a screening process by which potential problem
orders are identified and kept off the shop floor until the
underlying difficulties are solved. It links the planning
system with the shop floor control system (Melnyk and Carter
1987).

Order review/release controls the total workload in the

shop. Order review/release mechanisms thus have the

 

4. According to Conway and Maxwell (1962), "global" rules
are ones which require information about jobs or machine
states at other machines.

29
capability of controlling workload for the bottleneck work
center implicitly or explicitly depending on the type of
order review/release mechanisms to be implemented. Since the
body of knowledge on order review/release is relatively new
and less extensive than that of dispatching rules, we review

past study on order review/release in the following.

2.7.2.2.1 Past Study on Order Review/Release

Harty (1969) presented the first extensive study of
order review/release by focusing on the relationship between
order review/release and short-term capacity control. Harty
pointed out the fact that the control of input rate into the
shop floor affects current capacity requirements. Although
Harty did not provide a detailed order review/release
mechanism, he identified the importance of order
review/release to effective production operating system.

Nicholson and Pullen (1971) also emphasized the
importance of order review/release by suggesting a
centralized control system. Reduction of control points on
the shop floor greatly simplified production scheduling
system. They illustrated a very simple example in which all
jobs were available at the same time and produced an optimal
solution for this simple problem. However, they did not
present a clear mechanics of order review/release mechanism.

Irastorza and Deane (1974, 1976) developed a controlled
releasing algorithm which attempted to balance workload
among machine centers in the computer simulation study of

ten machine job shop. Using the pool system concept (Deane

30

and Moodie 1972) and applying a mixed integer linear
programming, the algorithm used the information about due
dates and work center load level to determine the selection
of an order to be released. The results indicated that the
use of order review/release reduced work-in-process
inventory levels and the variability of queue length.

Sandman and Hayes (1980), based on a study of over 600
job shops, realized that the total lead time of a released
job usually takes 10 to 30 times longer than the actual
processing time. They identified the reason as a long queue
which in turn reduced productivity. To cope with this
problem, they recommended the use of order review/release.

Bechte (1982) proposed load-oriented order release
mechanism. to control manufacturing lead time and work-in-
process inventory level in the simulation study of the
actual data. Bechte first linked order review/release to
planning system through planned orders. The load-oriented
order release has two steps. Step one was to establish
urgent orders by means of backward scheduling 'and time
limit. Step two released workable orders according to
capacity availability. The simulation study showed that the
use of load oriented order release algorithm reduced lead-
time and inventory up to 60% without noticeable effect on
capacity utilization.

Bertrand (1983) investigated the performance of the
order release mechanism in terms of the mean and the

variance of job lateness in a five—machine job shop

31

simulation model. The order release mechanism attempted to
control the amount of workload in the shop by establishing
the minimum load level. The simulation result indicated that
the controlled release mechanism did not have direct impact
on the variance of the lateness. Instead, the use of the
order release mechanism did amplify the effect of the
sequencing rule and the due-date assignment rule.

Baker (1984) examined the effects of input control in
the simulation of one-machine shop in terms of job
tardiness. Similar to the approach taken by Bertrand (1983),
the releasing mechanism tried to keep the minimum amount of
workload in the shop. The main finding was that the use of a
job releasing mechanism was far less important to the system
performance than was the use of an effective priority
scheme. In his explanation of this finding, Baker argued
that input control removes some options from the set of
choices available to a scheduling system. Although he
concluded with a warning that input control can be counter—
productive, he suggested that more research on input control
was needed to investigate some complex actual system.

Ragatz (1985) conducted a job shop simulation to
examine the impact of various job releaSing mechanism on
system performance and the interaction of dispatching rules
with the releasing functions. Ragatz developed several
releasing mechanisms which required varying range of
information. The result showed that the the use of order

release substantially improved shop performance although the

32
effect was not as impressive as the use of dispatching
rules. The study also showed that the increasing use of
information improved the effectiveness of the order release
mechanism.

As can be seen in the literature review thus far, order
review/release mechanisms attempt to control lead time,
work-in-process inventory level, load leveling, the
aggregate workload in the shop and cost. Although there is a
very little agreement over the detailed mechanics of order
review/release, most researchers agree over the use of order

review/release for better production scheduling.

2.7.2.2.2 Potential Benefits of Order Review/Release

Effective order review/release plays a major role in a
production operating system. Order review/release operates
as a filter through which all orders must pass. Order
review/release has' final authorization to release jobs to
the shop floor. Effective use of order review/release
provides following potential benefits. They result from the
fact that:

* It reduces work-in-process inventory levels.

* It reduces the mean and variance of queue length.

* It facilitates workload leveling.

* It provides the savings of space and capital.

* It simplifies the shop floor control activities.

* It provides the feasibility and visibility.
As mentioned previously in 2.6, the presence of bottleneck

work centers creates severe problems in the shop. These

33
problems could be reduced by the use of order
review/release. The input flow of incoming orders which need
the operation of a bottleneck work center must be controlled
before release because the bottleneck work center is already

heavily overloaded.

2.7.2.2.3 Mechanics of Order Review/Release

Any order review/release mechanism must determine what
to release and when to release it. The first issue, what to
release, selects jobs to be released to the floor while the
second issue, when to release, determines the timing of
release.

Jobs are selected through the use of a wide range of
information, from very simple, like first-come-first-served
(Bertrand 1983 and Baker 1984), to very complex like finite
loading (Ragatz 1985). Although a complicated mechanism like
finite loading does not necessarily always produce best
performance, a mechanism which considers both
characteristics of the job ‘and shop congestion usually
outperforms one which does not. (Ragatz 1985)

The timing of release is categorized into two types:
periodic and non-periodic. By periodic release we mean jobs
are released into the shop floor every specified period.
(See Irastorza and Deane 1974, Bechte 1982, Ragatz 1985) Any
release other than periodic can be regarded as non-periodic.
Non-periodic is relatively more sensitive to the status of
the shop while the time before release is shorter than the

former. The preference of one over another type, however,

34

has yet to be examined.

2.8 Summary

In this chapter, the literature review regarding
bottleneck operations was described. This review provided a
background for the development of the framework for the
bottleneck job shop. The definition of a bottleneck work
center was also presented using the load-capacity
coefficient. Two control procedures to cope with the
problems created by the bottleneck work center were were
presented.

In Chapter three, a research methodology in this study
will be presented. Included there are a quasi-random job
shop model, job characteristics, shop characteristics, the

assumptions of the model, and a simulation model.

CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

The major technique used in this study is that of
computer simulation. The problem examined is in nature
dynamic and stochastic. Computer simulation is the most
appropriate technique to deal with this nature of the model.
The main manufacturing setting of this study is a "quasi-
random" job shOp. In the following section, the "quasi-
random" job shop is described and compared with the
traditional job shop. In section three, a detailed
description and the operation of this "quasi-random" job
shop is presented. Also discussed in this chapter are job
and shop characteristics. These include areas such as the
shop size, job arrival distribution, routing of jobs,
processing times of jobs, and due date setting of jobs.
Finally, the underlying assumptions of the model are also

described.

3.2 A Quasi Random Job Shop
The shop being modeled in this study is a "quasi-
random" job shop. The "quasi-random" job shop differs from

the traditional job shop primarily in terms of the routing

35

36
generated. In the pure job shop, order routing is purely
random. Under the "quasi-random" job shop, however, order
routing is not completely random. Consistent with the focus
of this study, a work center is identified and fixed in
advance as the bottleneck. The inclusion of this bottleneck
and its location in the routing is a controlled variable.
The order routing is then determined by the nature of
location of a bottleneck and prevalence in the experimental

model.

3.3 The Operating Logic of the Model

The operating logic of this model follows that used by
Ragatz (1985). There are three stages to control the flow of
orders in the shop. The first stage is the order entry stage
at which orders arrive from customers. Once a job enters the
order entry stage, job characteristics such as the routing,
the processing times at each machine, and the due date are
determined. The second stage is the order review/release
stage. During this stage, jobs are reviewed every period,
eligible jobs are then released onto the shop floor. During
the third stage, the flow of released jobs on the shop floor

is then controlled by local dispatching rules.

3.4 The Shop Size
The "quasi-random" job shop consists of six work
centers. Each work center is treated as a unique machine
which is able to process only one job at a time. Machines

are the only constraining factor to the production system.

37
The size of a shop does not significantly affect the result
of simulation (Baker and Dzielinski 1960). Buffa (1968, pp.
338) also noted that since shop size has never appeared as a
major variable, it seems that we may be able to experiment
with relatively small shops and generalize the resulting

conclusions.

3.5 Job Arrival Distribution

Job interarrival times are generated using an
exponential distribution with mean of 5.263 simulated hours.
This mean of 5.263 generated the overall shop capacity
utilization at 82%. The use of an exponential distribution
does not affect the shop performance since the distribution
with respect to shape and range of the arrival rate for
incoming jobs is not a significant variable in evaluating

shop scheduling. (Elvers 1974).

3.6 Routing of Jobs

In this study, routings are not randomly generated in
the strictest sense of the word. Instead, routing is a
controlled variable used to create a bottleneck work center.
The routing is generated by the combination of location and
prevalence of a bottleneck. Here, three types of locations
and prevalences are examined. Three types of locations are
entry, exit, and mixed. Two levels of prevalence are 100%
and 50%. .Throughout the simulation run, work center one is
designated as a bottleneck in the experiment.

Routings of non-bottleneck work centers are drawn

38
without replacement from a uniform distribution. For these
jobs, routing follows a uniform distribution without
replacement using five non-bottleneck work centers.
For each job, the number of operations in the routing
is uniformly distributed with range running from two to five

operations.

3.7 Processing Times of Jobs

Processing times at each work center are drawn from an
exponential distribution. The mean processing time at each
work center, however, is not the same throughout the
simulation run. The mean processing time of the bottleneck
and non-bottleneck work centers varies in conjunction with
the prevalence of a bottleneck. Such controlled processing
time enables the output of the simulation to be evaluated at
a stable capacity utilization. Table 3-1 illustrates the
mean processing time of the bottleneck and non-bottleneck
work centers being used in the experiment. Under this study,
the overall capacity utilization is set at 82% while a
bottleneck work center is at 95% and non-bottleneck work

centers are at 79%.

39
TABLE 3—1

MEAN PROCESSING TIME OF BOTTLENECK
AND NON-BOTTLENECK WORK CENTER

Mean Processing Mean Processing
Time of Time of
Bottleneck Non-Bottleneck
Work Center Work Center
100% Prevalence 5.000 Hours 8.358 Hours
50% Prevalence 10.000 Hours 6.965 Hours

3.8 Due Date Setting:of Jobs

The due date is set in multiple of the total operation
time of the corresponding job (i.e., TWK rule).

Due Date a k * Total Work Content

where k is a controlled factor
Due date setting relating to processing time performs very
well when compared to other procedures such as random or
total number of operation (Baker and Bertrand 1981).
Blackstone, Phillips, and Hogg (1982) also suggested that
the TWK. method is the most rational method of assigning due
dates. Under this simulation run, k is set at eight

indicating relatively loose due date. (Elvers 1973)

3.9 The Assumptions of the Model
The general assumptions of the simulation model follow
those of conventional hypothetical job shops typified by
many simulation studies. The following list includes the
assumptions of the model in this study. Some of them are

adapted from Baker (1974, pp. 215).

40

1. Jobs consist of strictly ordered operation
sequences.

2. A given operation can be performed by only one
type of work center in the shop.

3. There is only one machine per work center in the
shop.

4. Processing times as well as due dates are known
in advance.

5. Setup times are sequence independent.

6. Once an operation is begun on a machine, it must
not be interrupted.

7. An operation may not begin until its predecessors
are complete.

8. Each machine can process only one operation at a
time.

9. Each machine is continuously available for
production.

10. Actual and estimated processing times are
identical.
3.10 The Simulation Model

The inherent complexity pertinent to the model being
studied prohibits the use of an analytical procedure. A
computer simulation is, therefore, the most appropriate
vehicle for this study.

The operation of the shop is modeled in the SLAMII
(Pritsker 1984) simulation language. SLAMII is an advanced
FORTRAN based language which provides the flexibility to
combine network, discrete event, and continuous modeling
capabilities into a single integrated framework. For the
simulated shop of this study, however, the operation is

modeled only in discrete-event subroutines.

41
3.11 Summary

In this chapter, a quasi—random job shop model, as
compared to the traditional job shop model, used in this
study was described. Shop characteristics as well as job
characteristics were also identified. In addition, the
assumptions underlying the model were described. In Chapter
four, the experimental factors and associated levels of the
experimental design will be presented. Included there are
discussions of the performance criteria and statistical

characteristics of the stochastic model.

CHAPTER 4

EXPERIMENTAL DESIGN

4.1 Introduction

This chapter describes the structure of the research
design used in this study. This design forms the foundation
for obtaining the data on which this study will base its
answers to the major questions posed in Chapter One.

In addition, this chapter identifies the experimental
factors and establishes the levels for each factor. The
chapter also presents the statistical hypotheses tested in
this study. The performance criteria to be collected are
also identified and their significance to the study
discussed.

The simulation model in this study involves variability
inherent to all computer simulation models. As a result, it
is also necessary to examine the statistical aspects of the
simulation model needed to maintain a certain level of

statistical accuracy.

4.2 Experimental Factors

 

The major purpose of this study is to examine the
impact of two control procedures used to manage the
bottleneck job shop which is itself characterized by two key

42

43
environmental variables: location and prevalence. The study
is interested in examining not only how these factors
influence system performance directly but also the nature of
the interactions that exist between the control and
environmental factors.

To test these interests of this study, the experimental
design, by necessity, must be a full fixed factorial design.
A full fixed factorial design is also needed because this
study has been described as being an exploratory study. We
do not know in advance the nature of the effects of the
experimental factors on system performance.

A full fixed factorial design is one in which all
levels of a factor are combined with all levels of each of
the other factors (Kleijnen 1975, pp. 289). The use of a
full factorial design allows the study to not only derive
estimates of the main effects but to also identify key
interaction effects between the main effects (Kleijnen 1975,
pp. 289-290). Both of these effects are of concern to this
study.

Furthermore, the term 'fixed' denotes that all possible
levels of the factors selected have been included in the
study.

This full fixed factorial design used in this study
consists of four major qualitative factors - each having
different levels. These factors and the associated levels

are discussed in the next section.

44
4.2.1 Dispatchinngules

One control procedure for coping with the problems
created by the bottleneck operation is the use of
dispatching rules. There are, however, a large number of
alternative dispatching rules. The problem facing the
researcher is that of picking dispatching rules applicable
to the problem setting. Given the need to control the size
of the experimental design, it was decided to limit the
number of levels for this factor to three. To select the
levels, a preliminary study was carried out.

The dispatching rules used in the preliminary study,
however, were not selected at random. Several dispatching
rules which are commonly well-known in the literature were
selected.

In the preliminary study conducted by Ahn, Melnyk, and
Ragatz (1987), jobs were immediately released to the shop
floor as they arrived to the bottleneck job shop. The
purpose of the preliminary study was first to evaluate
relative effectiveness of several selected dispatching rules
and to select those which should be used in the main
experiment. In addition, another purpose of the preliminary
study was to investigate the impacts of the environmental
factors of the bottleneck job shop on shop performance.

Four dispatching‘ rules were used in the preliminary
study:

* The Shortest Processing Time Rule (The SPT rule):

Job priority equals processing-time of the imminent
operation (Conway, Maxwell, and Miller 1967). The SPT

45

rule only considers the operation time (setup plus
processing time). It does not consider the due date.
The SPT rule is best in terms of the average flow time.
(Baker and Dzielinski 1960). One weakness of the SPT is
the large variance of the lateness distribution. Conway
(1965, pp. 129) felt the SPT rule should be considered
the 'standard' in scheduling research.

* The Earliest Due Date Rule (The EDD rule):

Job priority equals its order due-date (Conway, Miller,
and Maxwell 1967). The EDD rule does not consider the
operation time. It only considers the due-date. The EDD
rule is relatively good in reducing the variance of job
lateness (Conway 1965). However, it works poorly when
due dates are tight or infeasible.

* The Slack Per Remaining Operations Rule (The S/OPN
rule):

Job priority equals the ratio of job slack-time to the
number of remaining operations (Conway, Maxwell and
Miller 1967). The S/OPN considers the amount of
remaining operations time and the number of remaining
operation. The S/OPN works best among due-date oriented
rules in minimizing the variance of job lateness and
the number of tardy jobs. The S/OPN works best when the
due-dates established are either feasible or loose
(Conway 1965).

* The Work in Next Queue Rule (The WINQ Rule):

Job priority equals the sum of the imminent operation

processing-times of the other jobs in the queue that

this job will next enter. A job waiting for its last
operation has a priority of zero (Conway, Maxwell and

Miller 1967). In this study, the tie is broken using

the earliest due-date. The WINQ rule primarily

considers the shop status to reduce the downstream
congestion.

The four dispatching rules were evaluated using five
performance measures: (1) mean flow time in the shop; (2)
variance of flow time in the shop; (3) mean tardiness; (4)
variance of tardiness; and (5) percent of jobs tardy. An
analysis of variance (ANOVA) was used to evaluate the

significance of dispatching rules.

The Duncan multiple comparison procedure was next used

to determine whether there was any statistically significant

difference present

Tables 4-1

the EDD

mean flow

of jobs tardy.

statistically significant

and the

rule, the S/OPN rule, and the WINQ rule in reducing

The Duncan

other dispatching

through 4-5

procedure also

performance measures.

The

performed

in the

significant difference

shop and

results

best in reducing the variance of flow time

also

46

between cell

show that the SPT rule outperformed

indicated

the variance

means at

confirmed
difference between

rules with

of tardiness.

that

the

that

the

.05

the SPT

S/OPN

time in the shop, mean tardiness, and the percent

there

respect to the three

There was also

between the S/OPN rule and the other

dispatching rules for these two performance measures.

TABLE 4-1

MEAN FLOW TIME IN THE SHOP
(PRELIMINARY STUDY)

(Measured in Hours)

DispatchinggRule

 

Prev. Loca. SPT EDD SOPN WINQ Avg.
100% Front 86.31 165.85 163.36 146.17 140.43
Exit 88.73 164.06 161.30 153.55 141.91
Mixed 94.27 184.96 176.62 180.30 159.04
Avg. 89.77 171.62 167.09 160.61 147.13
50% Front 86.50 154.47 155.68 152.64 137.32
Exit 83.29 137.75 131.92 126.47 119.86
Mixed 89.93 163.04 163.90 157.37 143.56
“Avg. 86.57 151.75 150.50 145.49 133.58
Grand Avg. 88.17 161.69 ‘ 158.80 152.75 140.36

 

level.

rule

rule

47

TABLE 4-2

VARIANCE OF FLOW TIME IN THE SHOP

(PRELIMINARY STUDY)

(Measured in Hours)

Dispatching Rule

 

 

 

 

Prev. Loca. SPT EDD SOPN WINQ Avg.
100% Front 26725 21985 18789 20512 22003
Exit 33522 17372 17069 14663 20657
Mixed 47033 23555 20266 36471 31831
Avg. 25873 18809 16840 23882 24830
50% Front 35504 19679 17823 31141 26037
Exit 20619 16827 15403 14380 16807
Mixed 53039 25054 23419 37058 34643
Avg. 36387 20520 18882 27526 25829
Grand Avg. 31130 19665 17861 25704 25330
TABLE 4-3
MEAN TARDINESS
(PRELIMINARY STUDY)

(Measured in Hours) Dispatching Rule
Prev. Loca. SPT EDD SOPN WINQ Avg.
100% Front 9.02 22.80 21.90 26.84 20.14
Exit 10.65 22.56 18.93 21.01 18.29
Mixed 14.25 30.35 26.10 51.05 30.44
Avg. 11.31 25.24 22.31 32.97 22.96
50% Front 9.93 24.49 24.98 39.16 24.64
Exit 6.89 14.17 12.41 16.62 12.52
Mixed 12.35 32.51 30.74 44.28 29.97
Avg. 9.72 23.72 22.71 33.55 22.38
Grand Avg. 10.52 24.48 22.51 33.16 22.67

 

VARIANCE 0F TARDINESS
(PRELIMINARY STUDY)

48

TABLE 4-4

 

 

 

 

 

(Measured in Hours) DispatchingRule
Prev. Loca. SPT EDD SOPN WINQ Avg.
100% Front 16186 1904 2093 5540 6431
Exit 21641 1254 1125 1535 6389
Mixed 32213 2857 2625 16287 13496
Avg. 23347 2005 1948 7787 8772
50% Front 21323 3127 3743 14829 10756
Exit 9790 2115 2034 2564 4126
Mixed 36086 6516 7476 19072 17288
Avg. 22400 3919 4418 12155 10723
Grand Avg. 22874 2962 3183 9971 9748

TABLE 4-5
PERCENT OF JOBS TARDY
(PRELIMINARY STUDY)

(Measured in Percentage) Dispatching Rule
Prev. Loca. SPT EDD SOPN WINQp, Avg.
100% Front 4.22 27.82 25.90 24.64 20.65
Exit 4.05 29.16 26.93 29.01 22.29
Mixed 5.22 32.34 28.10 31.09 24.19
Avg. 4.50 29.77 26.98 28.25 22.38
50% Front 4.43 20.24 20.98 23.16 17.20
Exit 3.19 14.17 12.01 17.92 11.82
Mixed 4.35 22.21 22.04 24.28 18.22
Avg. 3.99 18.87 18.33 21.79 15.75
Grand Avg. 4.25 24.32 22.66 25.02 19.07

 

49
Based on the results of the preliminary study, both the
EDD rule and the WINQ rule were discarded in the main
experiment. In addition to the SPT and the S/OPN rule, the
first-come-first-served rule (FCFS) was introduced in the
main experiment. The FCFS rule was used as the base case
against which other dispatching rules could be evaluated.

The factor of dispatching rules in the main experiment
is tested at three levels: (1) the FCFS; (2) the SPT; and
(3) the S/OPN rule.

4.2.2 Order Review/Release Mechanisms

As mentioned previously in 3.4, any order
review/release mechanism must answer two fundamental
questions: (1) what to release?; and, (2) when to release?

In this study, there are two ways to review and release
jobs. The first way is to release jobs immediately as jobs
arrive to the system. The backlog file is not needed for
this scheme. The second approach, on the other hand, reviews
jobs every week. As jobs arrive to the system, they are
maintained in the backlog file until the start of next week.
At the start of next week, jobs in the backlog file are
reviewed and released if eligible.

Order review/release mechanisms are used at the start
of each week to determine which jobs are eligible for
release. These mechanisms use a wide range of information
such as due date, slack, and shop congestion in determining
the specific order jobs are to be released to the shop

floor. In this study, jobs in the backlog file are released

50

on the basis of minimum SLACK rule (where SLACK is the due
date minus time now).

The release of jobs is controlled by a workload limit.
A workload limit is set in an effort to control the maximum
load either in the shop or at the bottleneck work center.
This workload limit is a controlled variable. The
determination of this workload limit will be discussed later

in this chapter.

4.2.2.1 Control of Workload

 

The total workload in the shop at time j is divided
into two components:
TWLSj = TWLBj + TWLNBj
Where
TWLSj = Total workload in the shop at time j

TWLBj = Total workload for the bottleneck
work center at time j

TWLNBj a Total workload for the non-bottleneck
work centers at time j

TWLBj includes both current and future bottleneck workload
of jobs already released into the shop and passing through
the bottleneck work center. The workload in the shop other
than TWLBj becomes TWLNBj. For example, suppose there are
five jobs in a shop consisting of six work centers. Each
work center consists of a unique machine. Work center one is
designated as a bottleneck. The job characteristics and

location of each job is shown in Table 4.6 below:

51
TABLE 4-6
EXAMPLE FOR CALCULATING TWLS AND TWLB

 

 

Job # Type Routingpand Processing Time

001 B 1 20 3(15) 5(10)

002 NB 23 5) 6 10 4( 5) 3(12)

003 B 3g 5) 4(10) 6( 7) 1(25)

004 NB 5310) 6g 3) 2( 4) 4(10)

005 B 23 7) 3g 4) 1(23) 6(10) 5( 3)

 

Type represents whether a job is bottleneck (B) or non-
bottleneck (NB) job. Routing and processing time is shown in
the next column. For example, Job 001 first requires the
operation of 20 hours at Work Center 1, then the operation
of 15 hours at Work Center 3 and, finally, 10 hours of
operation at Work Center 5. The underline indicates the
completion of operation at that Work Center. Therefore, Job
001 is currently at Work Center 3.

According to this example, TWLS = 134 hours and TWLB =
48 hours. The current workload at the bottleneck work center
is 23 hours while the future workload for the bottleneck
work center is 25 hours. The difference between TWLS and
TWLB is TWLNB (86 hours).

In this research study, three order review/release
mechanisms were developed:
1. Immediate release (NOR)
2. Aggregate release (AR)

3. Bottleneck release (BR)

52
4.2.2.2 The Immediate Release Mechanism
The immediate release (NOR) mechanism releases. jobs
immediately as jobs arrive to the system. No backlog file is
needed. The NOR represents a system in which no order
review/release mechanism is present. As such, it is the base
case - the standard against which the other order

review/release mechanisms can be evaluated.

4.2.2.3 The Agggggate Release Mechanism

The aggregate release (AR) mechanism releases jobs in
the backlog file based on TWLS. That is, the AR mechanism is
designed to control only TWLS. The AR mechanism completely
ignores the presence of any bottleneck work center in the
shop. The AR mechanism is similar to that used by Bertrand
(1983) and Baker (1984).

At the start of each week, the AR mechanism releases a
job with the highest rank to the shop floor if current TWLS
is below the predetermined workload level set by the
experimenter. Jobs are prioritized on the basis of the SLACK
rule. The ranked jobs become eligible in order for release
until the updated TWLS meets the predetermined limit. The

flowchart for the AR mechanism is provided in Appendix A.

4.2.2.4 The Bottleneck Release Mechanism

 

As discussed previously in Chapter 2 (see Goldratt and
Cox 1983, and 0w 1985), one of the conclusions drawn was
that the knowledge about the bottleneck should be used for

bottleneck production scheduling. As such, the bottleneck

53
release (BR) mechanism attempts to control the bottleneck
work center by recognizing the impact of the bottleneck work
center on shop performance.

The BR mechanism releases jobs based on TWLB alone. It

does not consider TWLS. At the start of each week, the BR
mechanism releases prioritized jobs by rank until the

updated TWLB satisfies the planned workload level for the

bottleneck work center. Jobs are again prioritized on the
basis of the SLACK rule. The flowchart for the BR mechanism

is illustrated in Appendix B.

4.2.2.5 Determination of Load Limit Level

A predetermined load limit must be set for the
operation of both the AR and the BR mechanism. Specifically,
the AR mechanism requires a load limit level for TWLS while
the BR mechanism needs that for TWLB.

A load limit level is defined as the amount of load in
the shop as a percentage of theoretical capacity. The
setting of load limit level is expected to significantly
affect the performance of order review/release mechanisms.
Therefore, it is important to establish a reasonable range
of values for the load limit level.

To identify such a range, the operating logic of these
two mechanisms is further examined in light of bottleneck
location. The location of the bottleneck does not affect the
determination of load limit level for the AR mechanism. As
previously noted, the AR mechanism is completely ignorant of

the presence of the bottleneck;

54

The BR mechanism, on the other hand, does require some
elaborate considerations. The bottleneck location has
considerable influence on the determination of load limit
level for the BR mechanism. This is best illustrated by
considering an example.

Suppose the bottleneck is located in the front with
100% prevalence. 100% prevalence is used because it is the
most restricted situation. Under this situation, there is no
time delay between job release time to the shop floor and
job arrival time to the bottleneck work. center. As
contrasted to this, there exists a time delay between job
release and job arrival to the bottleneck when the
bottleneck is at the end.

If the same load limit level for release is imposed on
both locations, then more jobs tend to be released when the
bottleneck is located in the front. Because TWLB for the
front location, as compared to the exit, rapidly decreases.
This results in the release of more jobs into the shop
floor.

For the mixed location of the bottleneck, the position
of the bottleneck in the routing is purely random. It is
determined based on the uniform distribution. In the mixed
location, the load limit level for the front and the exit
location can provide the lower and upper limits. Therefore,
an average of lower and upper limit level provides that load
limit level for the mixed location.

To establish these limits, several pilot runs were

55
conducted only for the following three cases. They were:
.(1) The AR with the front location and 100% prevalence;

(2) The BR with the front location and 100% prevalence;

(3) The BR with the exit location and 100% prevalence.

In each case, seven different load limit levels, ranging
from 100% to 700%, were tested. Five measurements were used
as the performance criteria: (1) mean flow-time in the shop:
(2) variance of flow time in the shop: (3) mean tardiness,
(4) variance of tardiness; and, (5) percent of jobs tardy.
The FCFS rule was used for all cases. -

. Table 4-7 summarizes the results for the case (1). Both
100% and 200% load limit level turned out to be
theoretically infeasible because of instability of the shop.
For these two limits, the waiting line of the backlog file
was growing continuously. Therefore, these two load limit

levels were not used in the main experiment.

TABLE 4-7

LOAD LIMIT LEVEL DETERMINATION
FOR AR/FCFS/lOOZ/FRONT

(Hours) (Hours) (Hours) (Hours) (Percent)
Load Mean Flow Variance of Mean Variance Percent
Limit Time Flow Time Tardi- of of Jobs
Level in the Shop in the Shop ness Tardiness Tardy
300% 118.94 34020 186.52 420967 61.10
400% 147.30 76300 75.56 62778 36.00
500% 165.30 134083 82.43 117271 31.30
600% 181.20 287671 93.14 266309 28.50

700% 189.70 324925 99.52 304326 27.50

56

It was evident from Table 4-8 that at the 600% and

above load limit level, the mechanism tended to dump most

jobs in the backlog file at the start of each week. Jobs

spent little or no time in the backlog file. Therefore, this

led to the use of two load limit levels in the main

experiment: 300% (tight) and 500% (loose).

TABLE 4-8

AVERAGE JOB WAITING TIME
IN THE BACKLOG FILE

 

Experimental AR/Front BR/Front BR/Exit
Design 600% Load 500% Load 700% Load
Cell Number Limit Level Limit Level Limit Level
1 21 hours 21 hours 21 hours
2 20 hours 21 hours 21 hours
3 32 hours 30 hours 25 hours
4 89 hours 49 hours 52 hours
5 20 hours 20 hours 20 hours
6 21 hours 23 hours . 21 hours
7 20 hours 20 hours 20 hours
8 21 hours 20 hours 20 hours
9 20 hours 20 hours 22 hours
10 20 hours 21 hours 21 hours
11 48 hours 35 hours 35 hours

 

The results for the second case is shown in Table 4-9.

is feasible, not used in the main

Although 100% it was

experiment because of the extremely high percentage of jobs

tardy. Table 4-8 also indicates that the load limit level of
500% and above were loose enough to release most jobs at the

very next review time. Therefore, two levels were selected

for use in the main experiment: 200% (tight) and 400%

(loose).

57
TABLE 4-9

LOAD LIMIT LEVEL DETERMINATION
FOR BR/FCFS/100%/FRONT

(Hours) (Hours) (Hours) (Hours) (Percent)
Load Mean Flow Variance of Mean Variance Percent
Limit Time Flow Time Tardi- of of Jobs
Level in the Shop in the Shop ness Tardiness Tardy
100% 99.64 23398 716.23 37349 93.50
200% 150.78 176571 71.96 1632692 31.80
300% 167.62 274740 82.97 256726 29.50
400% 183.25 340930 95.32 319923 27.60
500% 192.30 362178 102.70 340511 27.10
600% 196.52 360699 105.82 337629 27.30
700% 201.27 369092 110.00 345656 27.50

 

The performance measurements for the case (3) is shown

in Table 4-10. As expected, 100% and 200% was theoretically

infeasible due to the increasing number of jobs accumulating

in the backlog file. Although 300% was feasible, it was not

used in the main experiment due to the high number of jobs

tardy and extremely long waiting time experienced by jobs in

the backlog file. The load limit level of 700% and above

were also considered too loose to be used in the main

experiment. (See Table 4-8) There was no significant

difference in performance between 700% load limit level and

above. Therefore, the following two levels were identified

as suitable for the main experiment: 400% (tight) and 600%

(loose).

58
TABLE 4-10

LOAD LIMIT LEVEL DETERMINATION
FOR BR/FCFS/lOO%/EXIT

(Hours) (Hours) (Hours) (Hours) (Percent)
Load Mean Flow Variance of Mean Variance Percent
Limit Time Flow Time Tardi- of of Jobs
Level in the Shop in the Shop ness Tardiness Tardy
300% 104.56 27320 425.62 33895 89.10
400% 135.28 58404 79.83 46336 42.20
500% 152.52 109355 77.37 88607 32.50
600% 162.45 138604 80.97 114833 28.70
700% 171.13 166363 85.92 138737 26.90

 

For the mixed location, an average of the front and the
exit location was used as the load limit level.
In the main experiment, the same load limit level was
used across all levels of the prevalence.
Table 4-11

presents tight and loose load limit levels

for release which are used in the main experiment under the

AR and BR mechanism.

TABLE 4-11

LOAD LIMIT LEVELS IN THE MAIN EXPERIMENT

Tight Loose
AR "'36636? ”36636?
BR Front 200.00% 400.00%
Mixed 300.00% 500.00%
Exit 400.00% 600.00%

59
The combination of the order review/release mechanism
and the two load limit levels resulted in a factor having 5
levels:
1. NOR
2. AR with tight load limit level (ART)
. AR with loose load limit level (ARL)

3
4. BR with tight load limit level (BRT)
5 BR with loose load limit level (BRL)

4.2.3 The Location of a Bottleneck
The location of a bottleneck work center is expected to
affect the system performance. This factor occurred in three

levels: front, exit, and mixed.

4.2.4 The Prevalence of a Bottleneck

The extent to which jobs go through the operation of
bottleneck work center is expected to influence the system
performance. The two levels were set in the main experiment:

100% and 50%.

4.2.5 Summary of experimental design

In this study, a full fixed factorial design is used to
evaluate the effects of not only main factors but also the
interactions among factors on shop performance. Therefore,
the dimensions of the factorial experiment of this study are
indicated by 3 (dispatching rule) * 5 (order review/release
mechanism) * 3 (location) * 2 (prevalence) full factorial
experiment. When combined, the resulting number of

simulation runs, without replication, required by this study

60
is 90.

The entire sample size is further increased by the
number of replications required. There are eleven
replications or repetitions of each of the combinations
discussed previously. (The determination of replications
will be discussed in 4.9.) As a result, the experimental

design for this study requires 990 simulation runs.

4.3 Hypothesis Testing
In evaluating the impact of alternative control
procedures on the management of the bottleneck job shop, the
study focuses its attentions on testing the following
hypotheses:

Main effects: Under this study the bottleneck is

 

characterized by the location and prevalence. To cope with
the problems created by the bottleneck, two control
procedures (dispatching rules and order review/release
mechanisms) have been proposed. We will test whether the
characteristics of the bottleneck and proposed control
alternatives have any significant impact on system
performance (as measured in six major performance criteria).
Each performance is measured in aggregate terms. To test the
main effects, the following hypotheses are used:

Hla: The dispatching rule by itself will not have a
significant impact on system performance.

Hlb: The order review/release mechanism by itself will not
have a significant impact on system performance.

ch: The location of the bottleneck by itself will not have
a significant impact on system performance.

61

Hld: The prevalence of the bottleneck by itself will not
have a significant impact on system performance.

Method of analysis: analysis of variance

 

Initial expectation: Each main factor will have a
significant impact on system performance.

First-order interaction effects: When we apply two
control procedures to the management of bottlenecks, the
impact of these two procedures on system performance may be
affected by the characteristics of the bottleneck. We will
test whether these is any potential interaction between the
characteristics of the bottleneck and two control
alternatives. To test these interaction effects, the
following hypotheses are used:

H23: The location of the bottleneck will not have a
significant impact on the performance of the
dispatching rules.

H2b: The location of the bottleneck will not have a
significant impact on the performance of the order
review/release mechanisms.

H2c: The prevalence of the bottleneck will not have a
significant impact on the performance of the
dispatching rules.

H2d: The prevalence of the bottleneck will not have a
significant impact on the performance of the order
review/release mechanisms.

Method of analysis: analysis of variance

Initial expectation: unknown

 

First-order interaction effect: Regardless of the type

 

of order review/release mechanisms in use, one of the
dispatching rules must be used. We will test if the type of
dispatching rules used on the shop floor has any significant

impact on the Operation of the various order review/release

62

mechanisms. To test this interaction effect, the following
hypothesis is used:

H3: The dispatching rules will not have any significant
impact on the performance of order review/release
mechanisms.

Method of analysis: analysis of variance

 

Initial expectation: unknown

First-order interaction effect: The bottleneck is

 

characterized by one of the six combinations of the location
and prevalence. The performance measured at one particular
type of bottleneck location may be affected by the type of
the prevalence in use. We will test this possible
interaction effect. To test this interaction effect, the
following hypothesis is used:

H4: The type of prevalence in use will not have any
significant impact on the performance of the location.

Method of analysis: analysis of variance

 

Initial expectation: unknown
Second-order interaction effects: The performance of
the control procedures (as described in terms of order
review/release mechanism and dispatching rule) may be
influenced by the specific combination of the location and
prevalence of the bottleneck. We will test if there is any
combinatorial impact of these three factors on system
performance. To test these interaction effects, the
following hypotheses are used:
H53: The performance of the dispatching rules will not be
affected by the specific type of the location and

prevalence of the bottleneck.

HSb: The performance of the order review/release mechanisms

63

will not be affected by the specific type of the
location and prevalence of the bottleneck.

Method of analysis: analysis of variance
Initial expectation: unknown

Main effects for non—bottleneck jobs: Up to this point,
the performance measures we have dealt with are aggregate.

This implies that we combine the performance measures of

bottleneck jobs and non-bottleneck jobs. For the following

hypotheses, we separate jobs into bottleneck and non-
bottleneck jobs. There are two reasons for this separation.

First, we try to examine how the presence of a bottleneck

work center does influence these two types of jobs. Second,

the separation of jobs into two types will facilitate the
understanding of what type of job is most influenced by the
presence of a bottleneck operation and control procedures.

Therefore, we collect data separately for bottleneck
and non-bottleneck jobs, where it is possible (i.e., when we
have 50% prevalence). First, we consider non-bottleneck jobs
in association with the characteristics of a bottleneck
operation and the control procedures.

To test these main effects, the following hypotheses
are used:

H6a: The location of a bottleneck operation will not have a
significant impact on the system performance of non-
bottleneck orders.

H6b: The prevalence of a bottleneck operation will not have
a significant impact on the system performance of non-
bottleneck orders.

H6c: The dispatching rules will not have any significant

impact on the the system performance of non-bottleneck
jobs. '

64
H6d: The order review/release mechanisms will not have any
significant impact on the system performance of non-
bottleneck jobs.

Method of analysis: analysis of variance

 

Initial expectation: unknown
Main effects for bottleneck gjobs: Now, we shift our

attention on bottleneck jobs in conjunction with the

characteristics of a bottleneck operation. To test these

main effects, the following hypotheses are used:

H7a: The location of a bottleneck operation will not have
any significant impact on the system performance of
bottleneck jobs

H7b: The prevalence of a bottleneck operation will not have
any significant impact on the system performance of
bottleneck jobs

H7c: The dispatching rules will not have any significant
impact on the system performance of bottleneck jobs.

H7d: The order review/release mechanisms will not have any
significant impact on the system performance of
bottleneck jobs.

Method of analysis: analysis of variance

Initial expectation: Each main factor will have a
significant impact on system performance of bottleneck

jobs.

The full fixed factorial experiment: As mentioned

 

earlier, the full fixed factorial experiment as a design was
selected for this study. In a full fixed factorial
experiment, all levels of a given factor are combined with
all levels of every other factor in the experiment. The
observations obtained in the full fixed factorial experiment
can be used to test the significance of the main effects and

interactions. This is done by the Analysis of Variance

(ANOVA).

65

ANOVA - an overview: The analysis of variance is used

 

to determine if there are significant differences between
the cells, and if so, whether these differences can be
attributed to either the main effects (the impact of each
factor alone) or to the interactions effects. However, the
analysis of variance is a limited test. It does not tell the

researcher which levels of a specific factor are

significant. Furthermore, it does not estimate the response
of the of the primary performance criterion to a given
factor or its levels (Kleijnen 1975, pp. 295-307). The
analysis of variance, as a result, gives some insight into
the nature of the relationships present between the factors
and system performance, but it does not provide complete
insight.

Multiple copparison procedure: Linear contrasts (or

 

pairwise multiple comparisons) on group means are performed.
The purpose of these comparisons is to determine which
levels of a specific factor are significantly different from
the other levels of that factor. The linear contrast test
achieves this goal by ranking the cell means from high to
low and indicating how these cell means are grouped
statistically. While differentiating the various levels,
this comparison does not indicate how much more effective
one level or factor is than any other.

The comparison of means can be done on either an 'a

I

priori' (planned comparison) basis or on an a posteriori'

basis (data exploration). Given the exploratory orientation

66
of this project, the 'a posteriori' approach is used. This
method of contrasting cell means systematically compares all
possible pairs of group means. The result of these
comparisons are then used in identifying the homogeneous
subsets (i.e., the set of all group means where the
difference between the means of any two groups is not

significant at some specified level).

Of the various procedures available for comparing group
means, Duncan's multiple range test is used in this research
(Winer 1971, pp. 196-201).

Finally, as part of this procedure, a test of
homogeneity of variance is run on all groups, using

Cochran's C (Winer 1971, pp. 205-210).

4.4 Performance Criteria

 

A shop floor control system attempts to achieve a
smooth flow of orders and to minimize work—in-process
inventory while meeting planned customer delivery promises
in most cost effective manner. In general, using this
perspective, the performance of a shop floor control system
can be measured along three dimensions: lead-time,
inventory, and customer service. For each dimension,
performance can be measured using either cost or non-cost
yardsticks. Non-cost measures of performance were chosen
because of problems inherent to cost structure assumptions
used in various studies. In those studies, the performance
was significantly affected by the specific structure of the

cost function.

To

performance,

capture

selected:

67

adequately all three type of non-cost

the following performance measures were

Lead-time measures

*

a:

Mean flow time in the shop
Variance of flow time in the shop

Inventory measure

:3

Mean work-in-process inventory in the system

Customer service measures

a:

2|:
a:

In addition

Mean tardiness
Variance of tardiness

Percent

of jobs tardy

to these six major performance measures,

other performance measures were also recorded. These minor

measures provide further more detailed insight into how each

factor affected

the shop floor. These measures included the

Mean flow time in the system

Variance of flow time in the system

following:

*

*

* Average

* Average

* Average
center

* Average

* Average

:1:

Average

waiting time in the backlog file
waiting time at the bottleneck work center

waiting time at the non-bottleneck work

total workload in the shop
workload at the bottleneck work center

workload at the non-bottleneck work center

Where possible (i.e., when prevalence is 50 percent),

information was

collected on both the bottleneck jobs and

the non—bottleneck jobs.

68
4.5 Initial Condition Setting
The research study deals with a system operating in the
steady-state. The steady-state, however, is frequently
affected by the initial conditions of the simulation. In

this section, initial simulation settings are examined.

In most stochastic models there is an initial bias not

typical of steady-state conditions. This is because it takes

some time for the model to overcome the atypical or
artificial situations created by the starting condition of
the simulation. (Shannon 1975, pp. 182) Conway (1963)
suggested three approaches for the initial condition
setting:
(1) Test each system starting "empty and idle."
(2) Test each system using a common set of starting
conditions that is essentially a compromise between
the two different sets of reasonable starting

conditions.

(3) Test each system with its own "reasonable" starting
conditions.

In general, it was more efficient to use (2) or (3) than
(1). In this study, however, approach (1) was used since it
was difficult to obtain good initial condition data for this

bottleneck operation model.

4.6 Test for Independence

 

For the statistical analysis to be valid, the samples
in each run must be independent of each other (i.e.,
uncorrelated). Correlated and dependent samples violate the
assumptions of many statistical tests. Analysis based on

such data provides results which are unreliable for drawing

69
statistical inferences.
Shannon (1973) listed two methods of dealing with
autocorrelated data.
(1) Dividing the simulation run into equal subgroups
and treat each subgroups as a single independent

observation.

(2) Estimate the autocorrelation function and include
its effects in the estimation of the parameters.

For this study, (1) was selected. In order to decide
the number of observations per batch which is uncorrelated
and independent, the technique suggested by Fishman (1978)
was employed. Fishman's method groups the observations on a
run into batches and determines the size of a batch which is
independent of each other. These batches then are used as
the basic data for analysis.

Several computer simulation runs were conducted
initially with 128 batches, each consisting of 100 completed
jobs (i.e., each simulation run has 12800 completed jobs).
Using Fishman's method, the number of batches was reduced by
half each time until each batch is independent of each
other. The necessary number of observations per batch was
found to be 1600 completed jobs. Therefore, a batch of 1600

completed jobs which were uncorrelated and independent of

each other were used in the main experiment.

4.7 Steady-State Equilibrium
This research was interested in studying the behavior
of a non-terminating system operating in its steady-state.

Since the system starts initially "empty and idle", there

70
was a transient state before the system reached the steady-
state. Steady-state defines a situation in which performance
measurements are independent of the initial condition
setting. In the previous section, the number of jobs
comprising a batch which were independent of each other was
determined. Each batch was independent of each other. As a
result, the first batch was regarded as the transient period

and discarded before doing the statistical analysis. Once
steady-state has been attained, the terminal conditions of
one subrun forms excellent candidates for the optimal

conditions of the next. (Kaczka 1970)

4.8 Variance Reduction Technique

 

It is desirable to reduce the variance of the data for
statistical analysis. There are two approaches. The first is
to increase the sample sizes. The other is to use variance
reduction techniques.

Since the research being studied was concerned with
evaluating and comparing several competing alternatives, it
was reasonable to do the simulation using the same operating
environments.

A technique called blocking was used to provide a
reduction of variance in the experimental errors. Under
blocking, common random number streams were used for all
alternatives. If common random numbers were used, the
performance measurements for different alternatives were
positively correlated. This reduced the variance of the

difference between the alternatives.

71
In this study, the common random number streams were
used for all the simulation models as the variance reduction

technique.

4.9 The Sample Size

Since the simulation model being studied dealt with
random samples, the result had some degree of imprecision
associated with the measurements. It was therefore necessary
either to estimate the confidence interval attributable to
the conclusions with a given sample size or determine the
sample size with a desired precision.

There are two approaches, replicated runs and continued
runs, to do this for nonterminating systems. (Kleijnen,
1974, pp.86) Although replication of runs using different
sequence of pseudo-random numbers was more desirable for
statistical analysis than continued runs, it was very
expensive and had to discard the transient observations at
the beginning of each run. With this respect, it was decided
to conduct a continued run with batch sampling.

To determine the appropriate sample size at the .05
level, several computer runs were conducted. For purposes of
estimating the variability of results, the batch mean was
considered as the single observation. This satisfied the
assumption of normality because of the central limit
theorem. A studentized t distribution was applied to
determine the adequate sample size using the following

formula. (Shannon, 1975, pp. 189)

72
N a T*T*S*S/D*D
Where:
N - The sample size
T - Tabulated t value for the desired confidence
level and the degree of freedom of the initial

sample

D a The half—width of the desired confidence
interval

S = The estimate of the variance obtained in pilot
run

Table 4-12 illustrates the appropriate sample size
where D equals +- 15% of the mean. The appropriate sample
size had wide values ranging from 1 to 53 depending on the
type of load limit level, order review/release mechanism,
and the performance measurement being used. However, the
procedure of how the sample sizes were determined in Table
4-12 ignored the efficiency of the blocking factor used to
reduce the error variability. The efficiency of the blocking
factor reduced the sample size without affecting statistical
significance.

In an effort to reduce the sample size of the main
experiment, the efficiency of the blocking factor as
identified by Ragatz (1985) was consulted. The simulation
model used by Ragatz was very similar to the model of this
study in- terms of operating logic, relative shop size, and
use of order review/release mechanisms. The efficiency
factor in Ragatz's model was approximately 3.5. Since the
reduction of experimental error variance through the

blocking factor can lead to a reduction in sample size

73
without losing a power of the test, the sample size could be
reduced in the main experiment.

In the main experiment, each run had 11 independent
subruns, each of which had 1600 completed jobs. The first
subrun was discarded since this represented the transient
state. As the result, each run had 10 independent subruns

with 16000 completed jobs.

TABLE 4—12

SAMPLE SIZE DETERMINATION

Mean Flow Variance Mean Variance Percent
Time of Flow Time Tardi- of of Jobs
in the Shop in the Shop ness Tardiness Tardy
Run 1 ""1633 """" 2536‘" 2536' ""3536" "136'
Run 2 1.19 5.56 33.38 6.76 32.24
Run 3 12.01 37.67 32.83 45.08 0.57
Run 1 The NOR/FCFS/100%/Mixed

Run 2
Run 3

The ART/FCFS/100%/Mixed
The ARL/FCFS/100%/Mixed

4.10 Summary

 

In this chapter, the factors and levels of each factor
of the experimental design were described. Also discussed
were the statistical hypotheses and performance criteria in
this study. The statistical aspects of the simulation model
was also discussed. In the next chapter, the results of this
study will be analyzed. In addition, the appropriateness of

the ANOVA model will be examined.

CHAPTER 5

ANALYSIS OF THE SIMULATION RESULTS

5.1 Introduction

This chapter describes the analysis of the experimental
results. The simulation results are evaluated by an analysis
of variance procedure to determine the statistical
significance. The assumptions underlying the analysis of
variance are tested in section 2. Original model, if
necessary, is transformed. Section 3 presents detailed
analysis of significant main and interaction effects of the
experimental design in light of aggregate performance
measurements. In section 4, then, the performance of
bottleneck jobs is compared with that of non-bottleneck

jobs.

5.2 Assumptions in an Analysis of Variance

Univariate 5-factor analysis of variances was used to
determine if any of the experimental factors had a
significant effect on the major performance criteria at the
.05 level. The data analysis was performed using the
Statistical Package for Social Sciences (SPSS), release 9.0
MANOVA package on the CDC Cyber 750 at Michigan State
University. A

74

75
The results of the ANOVA, as measured by the six major
performance measurements, are presented in Appendix C. It
was assumed that all interactions involving the blocking
factor, Jobset, were to be zero and included in the
experimental error. Summary tables of the results of the
main experiment are presented in Tables 5-1 through 5-6.

. Before going on to an analysis of the statistical
inferences, one factor must be examined. This is the
appropriateness of the assumptions in the ANOVA to assure
conformity to F-test assumptions. Each six ANOVA model is
examined separately. The basic assumptions in the ANOVA are
as follows:

(1) Each experimental observation should be independent.
(2) Distributions of experimental errors should be normal.

(3) Experimental errors should be homogeneous in their
variance.

The independence of each experimental observation was
satisfied by using independent subruns previously mentioned
in 4.6. ‘

Deviations from the assumptions about normality and
homogeneity of variance of experimental errors were detected
by the analysis of standardized residuals. The assumption of
normality of experimental errors were tested using bar chart
of the standardized residuals and through a Chi-square
goodness of fit test. The assumption of homogeneity of
variance ‘of experimental errors were examined using
standardized residual plots by each cell and the use of

Cochran's test for homogeneity at the .01 level.

76

TABLE 5-1
SUMMARY TABLES FOR WORK-IN-PROCESS
(ORIGINAL MODEL: 10 OBSERVATIONS)
(Measured in Hours)

100% Prevalence Order Review/Release Mechanism

 

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 302.61 271.36 302.92 317.92 316.15 302.19
SPT 149.22 145.22 148.64 154.17 150.32 149.51
SOPN 271.80 256.20 266.10 267.49 266.37 265.59
Exit FCFS 817.91 745.71 790.08 518.04 656.84 705.72
SPT 217.49 210.96 216.64 182.14 201.60 205.77
SOPN 609.76 536.35 609.52 328.63 446.63 506.18
Mixed FCFS 787.64 557.83 731.02 552.37 632.52 652.28
SPT 185.10 173.93 182.51 172.98 179.92 178.89
SOPN 449.74 363.76 412.38 332.80 383.15 388.37
Avg. 421.25 362.37 406.65 314.06 359.28 372.72
50% Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
FFOnt FCFS 322.90 306.16 307.02 341.46 330.60 321.63
SPT 138.44 134.52 136.58 154.40 149.27 142.64
SOPN 250.60 255.33 242.77 297.54 274.03 264.05
Exit FCFS 555.76 455.37 510.63 376.31 451.02 469.82
SPT 181.93 177.60 183.30 160.70 172.70 175.25
SOPN 413.89 380.51 413.00 296.30 316.97 364.13
Mixed FCFS 647.94 453.21 580.49 403.55 518.50 520.74
SPT 166.85 157.55 164.38 163.55 167.52 163.97
SOPN 396.14 334.14 367.28 352.78 337.78 357.62
Avg. 341.61 294.93 322.83 282.95 302.04 308.87

77

TABLE 5-2

SUMMARY TABLES FOR MEAN FLOW TIME IN THE SHOP

(Measured in Hours)

100% Prevalence

(ORIGINAL MODEL:

10 OBSERVATIONS)

Order Review/Release Mechanism

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 196.48 118.93 165.34 150.77 183.24 162.95
SPT 86.31 88.74 92.84 86.99 90.13 89.00
SOPN 163.36 134.37 154.78 134.28 157.77 148.91
Exit FCFS 197.88 163.72 189.55 132.58 162.45 169.24
SPT 88.73 88.46 90.57 83.72 88.26 87.95
SOPN 161.31 156.04 166.11 131.46 145.51 152.09
Mixed FCFS 220.69 151.20 215.00 150.97 186.65 184.90
SPT 94.28 89.59 95.43 86.88 90.96 91.43
SOPN 176.62 150.75 169.67 139.60 157.35 158.80
Avg. 153.96 126.87 148.81 121.92 140.26 138.36
50% Prevalence Order ReviewlRelease Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 183.10 123.39 158.31 128.44 151.26 148.90
SPT 86.51 83.47' 88.05 85.85 87.53 86.28
SOPN 155.68 135.05 148.54 132.05 137.52 141.77
Exit FCFS 165.88 142.97 166.12 125.61 144.51 149.02
SPT 83.28 83.53 85.65 83.47 84.72 84.13
SOPN 131.91 135.81 135.55 140.19 131.63 135.02
Mixed FCFS 203.05 141.68 187.95 131.17 153.02 163.37
SPT 89.95 86.01 90.49 87.68 89.68 88.76
SOPN 163.90 145.05 158.03 150.45 148.26 153.14
Avg. 140.36 119.66 135.41 118.32 125.35 127.82

78

TABLE 5-3
SUMMARY TABLES FOR VARIANCE 0F FLOW TIME IN THE SHOP
(ORIGINAL MODEL: 10 OBSERVATIONS) -
(Measured in Hours)

100% Prevalence Order Review/Release Mechanism

 

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 449451 34026 134202 176573 340937 227038
SPT 26724 15205 25962 9243 18803 19188
SOPN 18792 7355 13663 9838 15045 12939
Exit FCFS 293140 164374 248459 58404 138604 180596
SPT 33520 29923 32610 10201 23870 26025
SOPN 17068 12101 17305 5586 10976 12607
Mixed FCFS 401611 107197 366025 118410 285405 255730
SPT 47028 31122 46586 13879 27117 33147
SOPN 20266 9210 16364 8625 13432 13580
Avg. 145290 45613 100131 45640 597133 86761
50% Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 367105 58027 273876 56969 205659 192327
SPT 35505 17733 34459 8881 14757 22267
sopn 17829 8522 13132 8551 9765 11560
Exit FCFS 170395 110692 166067 43295 86103 115310
SPT 20621 20259 22117 8625 13920 17108
SOPN 15402 12236 16100 7229 8867 11967
Mixed FCFS 531833 142354 372075 .57450 153541 251450
SPT 53034 27555 50694 10560 17633 31895
SOPN 23417 12641 20259 10233 10829 15476
Avg. 137238 45558* 107643 523533 ‘57898 74374

79

TABLE 5-4
SUMMARY TABLES FOR MEAN TARDINESS
(ORIGINAL MODEL: 10 OBSERVATIONS)
(Measured in Hours)

100% Prevalence Order Review/Release Mechanism

 

 

 

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 105.60 186.51 82.43 71.94 95.31 108.36
SPT 9.01 10.52 11.29 15.18 11.14 11.43
SOPN 21.90 53.33 30.14 31.01 30.15 33.31
Exit FCFS 102.16 76.94 98.50 79.81 80.97 87.68
SPT 10.63 11.88 12.26 14.54 12.64 12.39
SOPN 18.92 31.32 29.04 120.02 30.66 45.99
Mixed FCFS 121.27 93.91 122.74 87.83 104.56 106.06
SPT 14.24 14.43 15.65 25.56 17.33 17.44
SOPN 26.09 62.59 35.33 63.99 38.89 45.38
Avg. 47.76 60.16 48.60 56.65 46.85 52.00
50% Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 93.47 125.87 82.33 106.79 101.00 101.89
SPT 9.94 19.62 11.34 68.71 42.92 30.51
SOPN 24.98 87.05 40.40 94.58 65.22 62.45
Exit FCFS 72.90 60.31 77.40 158.29 66.86 87.15
SPT 6.91 8.30 8.53 22.39 13.00 11.83
SOPN 12.41 32.36 17.50 172.82 37.64 54.55
Mixed FCFS 109.07 102.96 102.86 194.54 110.74 124.03
SPT. 12.34 21.33 13.46 63.33 41.84 30.46
SOPN 30.73 77.85 36.42 204.91 93.29 88.64
Avg. 41.42 59.52 43.36 120.71 63.61 65.72

80

TABLE 5-5

SUMMARY TABLES FOR VARIANCE OF TARDINESS

(Measured in Hours)

100% Prevalence

(ORIGINAL MODEL:

10 OBSERVATIONS)

Order Review/Release Mechanism

 

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 420975 35211 117273 163282 319916 211331
SPT 16185 8067 15964 4619 11316 11230
SOPN 2093 4052 2789 2841 2784 2912
Exit FCFS 251379 137321 214054 46342 114833 152786
SPT 21640 19819 21348 4604 14863 16455
SOPN 1124 1599 1550 9515 1681 3094
Mixed FCFS 356029 91017 329161 103291 259075 227715
SPT 32216 21784 32868 8359 18132 22672
SOPN 2624 6165 3649 6653 4251 4668
Avg. 122697 36115 82073 38834 82984 72541
50% Prevalence Order Review/Release Mechanism
Loca.. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 337742 52944 254948 54425 194204 178853
SPT 21323 10921 21633 9979 11494 15070
SOPN 3741 7952 5071 9084 6442 6458
Exit FCFS 142222 90944 142018 42595 69267 97409
SPT 9792 10822 11304 5168 6903 8797
SOPN 2034 4064 2652 12570 4039 5072
Mixed FCFS 494484 129556 344791 -63332 144518 235336
SPT 36093 18808 35078 12793 15211 23597
SOPN 7478 11166 8013 19918 12351 11785
Avg. 117213 “37464 91725 25541 51604 64709

81

TABLE 5-6

SUMMARY TABLES FOR PERCENT OF JOBS TARDY

(ORIGINAL MODEL:

(Measured in Percentage)

100% Prevalence

 

10 OBSERVATIONS)

Order Review/Release Mechanism

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 19.60 61.10 31.30 31.80 27.60 19.60
SPT 4.00 13.90 12.10 21.80 14.00 13.16
SOPN 25.20 44.90 35.40 36.20 35.40 35.42
Exit FCFS 18.60 24.60 25.10 42.40 28.70 27.88
SPT 4.10 10.10 10.20 18.20 13.20 11.16
SOPN 27.30 40.40 37.40 59.80 37.90 40.56
Mixed FCFS 20.60 40.50 27.00 38.40 31.80 31.66
SPT 4.60 14.10 11.10 26.50 18.50 14.96
SOPN 27.90 48.40 36.50 50.10 36.90 39.96
Avg. 16.88 33.11 25.12 36.13 27T11 27.67
50% Prevalence Order Review/Release Mechanism
Loca. Dipp. NOR ART ARL BRT BRL Avg.
Front FCFS 17.30 48.90 28.00 45.00 39.50 35.74
SPT 3.90 18.80 9.40 39.50 29.80 20.28
SOPN 20.60 45.70 32.00 50.20 39.80 37.66
Exit FCFS 18.30 24.20 24.80 57.70 29.80 30.96
SPT 3.70 8.90 8.80 21.60 15.00 11.60
SOPN 12.00 28.70 19.80 72.90 34.70 33.62
Mixed FCFS 18.50 41.10 26.30 .57.40 41.60 36.98
SPT 4.30 15.20 9.50 39.90 28.10 19.40
SOPN 21.50 43.80 28.70 68.40 47.70 42.02
Avg. 13.34 30.59 20.81 50.29 34.00 29.81

82

Figures 5-1 through 5-6 illustrate the bar charts of
the standardized residuals and the Chi-square goodness of
fit tests, and standardized residual plots by experimental
design cell number and Cochran's tests for each of the six
major performance measurements.

The ANOVA model with respect to the percent of jobs
tardy was the only one which, although slightly violating
the assumption of nomality, satisfied the assumption of
homogeneity of variance of experimental residuals (see
Figures 5-1 through 5-6). The failure to meet the
assumptions of normality and homogeneity of variance for
other ANOVA models indicated that the original data should
be transformed in order for each ANOVA to produce meaningful
results.

Since heterogeneity of error variance usually arose
from a relationship of variance to mean (Kempthorne 1966,
pp. 155), the choice of appropriate transformation for each
ANOVA model was determined by examining the relationship
between cell variance, or cell standard deviation, and cell
mean, or square of cell mean.

To the ANOVA models for work-in-process and mean flow
time, an inverse or reciprocal transformation was applied to
reduce the variability of experimental errors. Figures 5-7
and 5-8 show plots of cell standard deviation versus square
of cell mean of the ANOVA models for work-in-process and
mean flow time in the shop, respectively. When the standard

deviation is proportional to the square of the mean, the

Frw

CHI-SQUARED - 314.692

Rand.) nixed Roan-1 male

.303

83

Stan dordiz ed Residuals

Cwm—in-m Origins! lubed]

 

290i
2&1
240-1
zap-1
2m-J
1&-
1&4
“ID-
113-1
tm-J

mu

”-1

”-1

m.

 

     
   
     
 

\;\\:‘~1 X '

   
   
   

at
ffifixx

\

EL". 3;

M x "\ \
" \ fl
"- L ‘4‘; x Xxx.‘

\.

\

D. ' '4‘ \ \ \.
“s ‘5 ‘31“-
3.

\.\ x....._
. A . \ A

 

 

 

 

 

SKEWNESS - 3.932

11

 

J.
' fiiij

0.15
Um Limit a! Oat-gay

1.75

DOF. - 14

SIGNIF. -

3.28

KURTOSIS - 38.705

.000

Standardized ResiduoIs by Cell

(Wanda-Frauen Origi no: Maud]

 

 

 

+
10 -1
g.
9 .1
13-4 r
7 .,
a A
S d +
+
4 - *
‘ +
.3 d
9 c- .
4.
- - + 'P *'
1-1 * I 3" 3 ‘ 4 I I 7' I I
p . . g ..1, . ,{‘_+++ J
D 3: t," ‘E‘l , I 31‘ 3&1“ “' ¥:=“~;:.g.;.;t 13c}- 'Lédiz..r
7 V ‘+ -- ‘ ' i 7' ~ ' ;; 7335‘" .I‘V‘l- ‘ g -‘ o I
‘0 I z . k m ‘_ 1 “4’“
-1 d ¢.§#++’ my: ’9’ CI ++ 4+ «1* * :m' H;
-2 a f 3 I 7' I a " I I 4'" + I
O o I E O
p
-3 I j I t 1 fi
0 20 40 60 .30

 

$1:ch Design Cd. Numb.

COCHRAN'S C I 0.172
CRITICAL VALUE (a . .01) - 0.047

NORMALITY AND HOMOGENEITY 0F VARIANCE TEST
(WORK—IN-PROCESS: ORIGINAL MODEL)

FIGURE 5-1

84

Standardized P‘eisid'J‘Ji‘a

[Men How Til-nu: Original Meson

 

 

    
 

 

 

 

 

 

 

 

 

 

24c- _.
WI.
220 d if."
fit-".1
200 4 7",.»1
"1}".
1 a II ?:}1
1 J 4’1
w I" {.../1
i I m f j {I/
.A if? .
“1‘” 15::
11’. too 4 "4" r?"
' I?“
m .1 ’ r p’ .1
r' ,1 :1
.. /
r
o d if." //'
.21 4,:
an I 3' ’ ' .
d 4' //1 , ’ ' EC"
0 r .4 /{',I1 . I . - I lr‘j-f‘ m w
0.28 1.78 3.23

SKEWNESS I 1.896 KURTOSIS I 11.434

CHI-SQUARED - 168.461 D.F. I 14 SIGNIF. I .000

 

 

 

 

 

standardized Residuals by; Cell
, (Moan H4:-1v Tin-n: Original mm
H 0-
7 _ #
6-4
¢
0 5"
‘5’
3 3 .1 . 4'
'f *' <-
3 .. I t +
7,! .3 «b. ‘ 1 + o-
0 «-
'3 ‘3-1 0- * .l 9' 7* g I 'I '
3 . *3 t ‘¢*.+ .3: "
.1 ¢
3 “Tb“? .:+a.:i. “I‘I‘bt-“fifi ‘¢+*.+TF'IP‘A
a 01 ‘ :: YVMJ'C: «$3
a: "‘
¢+ 4:
- I w? * ‘figffi
1 1:15“: H; V-f 9; 3.1% ”‘1‘?“th
-2 I ‘fi ":1 t
I o
-3 I I T I v I
O 20 40 BO 30
Minute! Design Cdl‘ Numb.
COCHRAN'S C I 0.091

CRITICAL VALUE (3 I .01) I 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL)

FIGURE 5-2

85

Standardized Residuals

(Ver. a! Plan 11111.: Origins! new)
6m _

 

 

 

 

 

   

 

 

M
/ "
goo - /"
5"?
2
m d 7:
g Q
L 3a: -4 %
u. Q1
:00 - /}-
{fly
/
. 5».
"34 ‘r
, . 2?: .
0 t 1 I :57! m f: ’ tr... ' M
-2.78 - 1 .23 0.28 1 .78 3.25
Uppc Limit of Can-gay
SKEWNESS I 7.789 KURTOSIS I 94.446

CHI-SQUARED I 1342.414 D.F. I 14 SIGNIF. I .000

Standardized Residuals by Cell
(Va. 5! Plan Til-no: Originot Meal) .

 

Standardized Rosidualo
D
L
I
f

 

 

 

 

Ecca-I-imntcl 0039' n Cdl‘ Numb.

COCHRAN'S C I 0.255
CRITICAL VALUE (3 I .01) I 0.047

NORMALITY AND HOMOGENEITY 0F VARIANCE TEST
(VARIANCE 0F FLOW TIME IN THE SHOP: ORIGINAL MODEL)

FIGURE 5-3

86

Standardized Residuals

(Moan Tomlin-s: Criginal Moduli]

 

 

 

 

 

 

 

323
an 5;
un- fig
20 ‘l f}:
2‘0 '1 ,/".l
m . A
and éfl
.... y _
5 1m " I;
L: 140 ‘l g/A
1 a: -I 4"
.... S-il ._
a q "A". /’/1 :
..o . A: 'f.
m .. :1 '1'“; It,“
a _ ,, 2" I.-

   

9
H

Um Um“ 6! Gauge):

SKEWNESS I 1.936 KURTOSIS I 11.875
CHI-SQUARED . 347.438 D.F. I 14 SIGNIF. I .000

Standardized Residuals by Cell

[when Tomlin-I: (ti-36nd Modal}

 

7- *

a.
6-4 ‘*

 

 

 

3.

3

I:

“

3

5

a A.

a $
-.3 I Q ‘
-‘t l I fi 1 I 1 v 1 i

0 2° ‘0 6° 30

 

 

launch-name! notion Cd! NW

COCHRAN'S C I 0.105
CRITICAL VALUE (3 I .01) I 0.047

NORMALITY AND HOMOGENEITY 0F VARIANCE TEST
(MEAN TARDINESS: ORIGINAL MODEL)

FIGURE 5-4

F roquortoy

CHI-

flanda rained Residuals-I

87

Standardized Residuals

":0 (Var. .3! Tat-rain“ Clrig'nal Mead!

 

aco-

503-!

100-

 

 

 

 

 

3.23

 

SKEWNESS I 7.924 KURTOSIS I 96.637
SQUARED I 1377.67 D.F. I 14 SIGNIF. I .000

Sta n d a rd i: e cl R ere id u a ls '0 f?" C? el l

, t"."-:r. :f Tamil-:58: Cari-jam Mead!

 

 

 

 

2::de Danica Cd! NW

COCHRAN'S C I 0.263
CRITICAL VALUE (3 I .01) I 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(VARIANCE OF TARDINESS: ORIGINAL MODEL)

FIGURE 5-5

From-emf

88

Standardized Residuals
{mm :1 J65: Tansy: Original nasal]

 

 
   
  
     
   
 

 

 

 

 

 

 

 

 

210
200 It ~71
:30 ‘ I"! .
13: -
‘ m " 1".11
. an - 1'
1 m d 1".
mo 4 x"
1.33 . .14
f

1 an 1 -‘
1 1° .1 ":4
1 m I fill

90 I 1’1

cpl 6

7D 1 :xl

” 1 {’1

=0 1 /"

o . '2 11 ‘ 2

a d cl A I

a: .l g f

.o . I,“ E4551 I71

0 I". I' ’7 (I 7 ...". 6". Fl.
0.2: 1.73 3.23 '
Um Limit d Cal-gay
SKEWNESS I 0.135 KURTOSIS I 0.023

CHI-SQUARED I 38.920 D.F. I 14 SIGNIF. = .000

Quick) rdlzod Roam-.010

Standardized Residuals by Cell

{99mm a! Jan Tami: Original Mae.“

 

 

 

 

 

COCHRAN'S C I 0.042
CRITICAL VALUE (3 I .01) I 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(PERCENT OF JOBS TARDY: ORIGINAL MODEL)

FIGURE 5—6

89

Standard Deviation 4'3. Square of Mean

chrk- its-Oregon Origi not Mad")

 

 

 

 

6120
I
4.
SW1
4.
f
+
34‘ d
4.
1% + I
+
3 .3004
.3 1'
‘4
¢
3' 2004 + ,+ ++
0- «H-
1'
I. +.'
¢#
1CD ¢i¢
a.
fi'
0 . v
0 103 2:00 330 400

CELL STANDARD DEVIATION VS. SQUARE OF CELL MEAN
(WORK-IN-PROCESS: ORIGINAL MODEL)

FIGURE 5-7

Sta n d a rd De wiati on was . S a ua re of M e a n

:13 lMIcn flow Tin-II: Drigimt Mean

 

*
*

dad
404

£1 4‘

Mean
J
4O

.91 It

01 C

9mm-
1-
+
f
0
1
1

‘1

. - o- I

2: 4+ 1’1;
+

00:

13-

10 -l 4, ¢
4
I I l’ 1 I '. I ‘ I
0 20 IO 60 80
Coll 91M Motion

 

 

 

CELL STANDARD DEVIATION VS. SQUARE OF CELL MEAN
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL)

FIGURE 5-8

9O
reciprocal transformation of the original data was
recommended. (Anderson and McLean 1974, pp. 25)

A logarithmic transformation was used for the ANOVA
models for the variance of flow time in the shop, mean
tardiness, and the variance of tardiness. When the cell mean
is approximately proportional to its standard deviation, the
logarithmic transformation is effective. (Walker and Lev
1953, pp. 424) Figure 5-9 through 5-11 illustrate the plots

of cell standard deviation versus cell mean of the ANOVA

models for variance of flow time in the shop, mean
tardiness, and the variance of tardiness measures,
respectively. The logarithmic transformation is also

particularly effective in normalizing distributions which
have high positive skewness. (Winer 1971, pp. 400) The
skewness of these criteria were relatively high as compared
to other dependent variables (see Figure 5-3 and 5-5).

The ANOVA results on the transformed data for the five
major performance measurements are given in Table 5-7
through 5-11.

Figure 5-12 through 5-16 show the results of the bar
chart of the standardized residuals, the Chi-square goodness
of fit test, the plot of standardized residuals by
experimental design cell number and Cochran's test on the
transformed data for the five performance measures. Although
the Chi-square test for variance of flow time in the shop
again indicated non-normality of the residuals, it was

evident that both the skewness and kurtosis had been

91

St a n d a r d D e i a ti a n we: - M e a n
(Va. 01 Her» Time; Original Modal)

 

 

 

 

am
4
960 I
4
Am I o.
H + 1' +

3% “

.300 I ,,
1:3 * +
U 9

V
203 I "
+ 4+ I
#4.“
.u
100 d *'
Q
I!
.3 1 V 7 T I I I Y Y T
0 I12 0‘ 0.6 0.3 1
[Tl-100.0033!

Call Sim Deviation

CELL STANDARD DEVIATION VS. CELL MEAN
(VARIANCE OF FLOW TIME IN THE SHOP: ORIGINAL MODEL)

FIGURE 5-9

Sm n d a rd De via ti a n 3 . M 9'1“"

A‘n (than Tomlin“ Crigiml Moo-l in

r
zoo-l *
190 "
133

PHD-i 4-
183-l . I

IwI
I‘D-l 1-
1.”-
123‘ ' 4-
110I + ...

1m-l *’

so-l " *"

Col Mean

0
00- e
ADI *
.‘DII
”‘4-
1° 1 1 T t I T

 

 

 

CELL STANDARD DEVIATION VS. CELL MEAN
(MEAN TARDINESS: ORIGINAL MODEL)

FIGURE 5-10

92

Standard Deviation vs. Mean

(Var. d Twain‘s: Orig'nal Mead)
am I

 

4.

1CD-

f
i +
0 I r t fl

I T
O 320 400 633
Call Stardom Marian

 

 

 

CELL STANDARD DEVIATION VS. CELL MEAN
(VARIANCE OF TARDINESS: ORIGINAL MODEL)

FIGURE 5-11

TABLE 5-7

ANALYSIS OF VARIANCE

INVERSE MODEL)

(WORK-IN-PROCESS:

W A R If; N c t I I I I I I I I I I I I I I I I I I

0 F

o O I I o a o o 0 o I I o I O I I 0 I I ‘." A L V S I SO

VISIS 0F SIGIIFICINCE FOR INHIP USING SEQUENTIAL SUNS 0f SQUARES

923

3'60 0' f

F

MEAN SQUARE

BC; 2016110

or

SQUARES

SUM 0'

SOURCE OF VIOIAIICN

““9”“WCMO
N

C #05 “0.0
I. “O “0009‘
I «a. 0.01».

n

O

O

'

o

I)

ocumuowunowuncwuwnuho
OWOOOOMCOIVWOO
mono 0.0.0 HOMO“
ongmoemwnouhm
cwao cu! “I'WIFWMDFGhi

MO.“NFCW”O
mac-099.999...“
muoooaoeoooom
IOIBOOIIIIIOIIIII
muouuuwufl

O

“MOOOONNO DO. 0
It on

hamommmuow

Inmadwuaauuaacumnumuafl

Elmnuwlwflcnnwaumuncala

9000900909.-. I I I I

GMNIBGINuOMRMuflhuMNMmJ

IIIDIIIIoucwunoqwuamlb
6

203930
‘03’3‘
20600

9

a

2

6

6

ALL"
3' PRCVILEN

Ima.u->Iu->
t-(cacsv-a
Q a: t
zzzuuutzzu:
uouccmuuoou
Imumaunmnunap
C-nl l.." c
IstannIrumutru
wummmmmum
Ham. —*"3 ‘
-I IZZOJKZIZ 09.11.:
0'. DUI.) QUG
:I- h-nahhnMI—mu-IIu-b
=h. cu~;::fi;u:u-;:ui:_
rnn AC
mamaumxzcmwwacmm
..ua—«unxmcmm-oamur~a
c 590...“. 3:99.24ch ca-

‘07016657

33313

--

dd
I."

HP
00
1!-
v-

535 3.5695323881

Q-SUUIPID

’UJUSV'O Q-SOUAREC

TABLE 5-8

ANALYSIS OF VARIANCE

INVERSE MODEL)

(MEAN FLOW TIME IN THE SHOP:

V A R l A u c E I I I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I A N A L V S I S
as SIGMIF1CIVCE row tanrt usxue SEQUENIIAL suns or SIUAncs

TI'SI'I

€94

SIEI OF ‘

p

MCI“ SQUARE

VI”IATION SUI 0F SQUARES OF

I":

swuncr

ODOOOOCHDCOC «cannu-
mmuhuhobwm
NNI-IflheOOc-ID
nun—umCO-No
GuenCN—CU*O

I I I I I I I I I I

wflhctnhwhfifl‘OENNO
90'30 FnCdt'WNI-ID'D-flfllf
“Ophflnsflflfll‘nhflcfi
noonec'nv-I-«nhumnm
DefinO-r;omcc-IIINCONN
IIIIIIIIIIIIIIII
MOOI'IGN'IN" I...
HMNF
I- n

N

FN'SNNFIIIOO 0‘35 ‘9 ”NF
omocecacooooeae
GOONOOODOOODOOOOO

N DIDI‘NNI-‘OOC.
a ocnhnlnnohh
F snow—«NI-nu
N moo-Imam
I I I I I I I I I I I
O N—IdI-IOI-IIIQNN

I-IO ONNIICDO ONNOC 000
2 III II

OWFOMIIOUN'I‘PQ
WBMOQBOOCQCO
onmoeooceooeaooe
COWOBOOODI I GOD I I
99909969: DUN 60° UN

IIIOIIIIIIQQIIIIQC

CC

In“: w” .-

l'-5] OHM.

.l ""3" I

65.22813

30

I'S'DUM’“

\ )J'! 3' Ell R-SOHIREH

TABLE 5-9

ANALYSIS OF VARIANCE
(VARIANCE OF FLOW TIME IN THE SHOP: LOGARITHMIC MODEL)

I I I I I I I I I I I I I I I I I I I A N A L V 8 I S-

V A R I A N C E I I I I I I I I I I I I I I I I I I

0 F

IFSIS OF SIUAIFICANCE FOR LOVFT USING SEQUENIIAL SUNS QF SQUARES

0F F

F

MEAN SQUARE

CF

SQUARES

SUM OF

SOURCE OF VAPIAIICN

PE PL
ao$§9¥

95

OOOOOOWOOOCC‘GOO
OOODFdQOOOOO

N‘OFOOOHQOONOflOF
«nonnoo¢~a«whnoc
.OONOHNCOCHODnOn

C
......OOOOOOO...
...Ouflnuudfld fl
comma

0.0.0.0000000'0000
hdflfitdd
UN“

"O'NNGQQCCNNOUOC‘
C! H G
O

annOOONOOGFOOhon
NFNCO~NO°FOOflflflnO
“WHOMFIDU‘IIPDffl
“OnOCFFCOGOOflOONN
auncoucnhnnoouomw
IIIIIIIIIIIIIIIII
OQQOQCOZNNquQNu
005G—

Nu O

REVAlEN

ALEN
8' P

92¢ O
ZZZJABZJ
OUU O
”ddrbbuh
FC‘OSDPO
<3, 4
:zzuuuzzzu;
UOUOGKUUOGU
h—aauu PI-O'OJO-
Q—d 11h C
u¢:b~>mu¢>u
vauuacawmumm
22:2d112200325
UGU Duo

PN-l” hub—bani- )- bgb
Ch¢:;;d¢h:z:¢;
u<> 3;“ B
cmuucxzmmuxzzmz
ghézaux-~C¢zq~9

SSI709‘7

*i:zsiaz

9
E9

n0
DIR
O-

38

131i

333?

:9

P'SHUAREF =
ADJ Sliu R-SOUARID

.0...
SIGI

MEAN SQUARE

VARIANCEIIIIIIIIIII
OF

TABLE 5-10
ANALYSIS OF VARIANCE

(MEAN TARDINESS: LOGARITHMIC MODEL)
sun or snuaazs

I I I I I I I I I I I I A N A L V S I S

O O

O
SlztilClNCE FOR LOMYA USING SERUENIIAL SUNS 0F SQUARES

0F Vflnllllflfl

HF
mac"

fvSI?

I
D

9E5

0996'? Uw-IFWCNU-QNC 9

Ir. Ionrcmc one
C Ices-unto»:
¢ cwmnwrwcuhmc
riiuoOMN=~01Hno
O O O O 0 O O O O O O

In

IDMI'IIII" CU‘flOO O ‘ 0.-
CFNNOflflnO 00 '9‘50' 6‘
“HOP O CIIIIIIHFO ORG—IF
unbonnmcov-oae‘oc

-— FWOHDNMIIHNCEFO

QQOOOOOOOOOOOOOO
chflr «puma run
“°1:‘ II

IMDOOMWWMMDflOlmwmnuh

poumwoocme—oowuwmoe

~acrmmnoawnna—«u~vaumu

d0-G‘DOFNUM5FIFOIINC OF.

guacamooC—ohonooo

OOOOOIDOOOOOIHQOQO.
VCMMD o—wh- N—I
VON:-

IIIG QNNI‘GCOONNOCQOC
g d —

HOOOnflf-Qtfl‘QFhOMF
unhoaonncnuonooeo
mooooowm—omnonoch
NlhanwhwmnmrMNm—neaun
NFOO-INQOCIBU‘OOWO-I
OOOOOIDOOOOQIIOOOOO
1HV¢GNU1LQFNr|nwnI¢Vu
UHVOFmfl h ¢v a
01!!—

REIALEN

VALEN
RV P

ION
LEN
LEM
DRE
ID"

II“ b

‘1
€911CH
LHCAIIGH
uv n

N R
.5“)
)un

"”EVALE"
"IS”1I.

‘IIS"3'

20.862I6

GO

A LIU'H F0 R-SQUAREU

Q-SQUQREO

TABLE S-ll

LOGARITHMIC MODEL)

ANALYSIS OF VARIANCE

(VARIANCE OF TARDINESS

I I I I I I I I I I I I I I I I A u A L I 3'] S

0 F

V A R I R N C E I I I I I I I I I I I I I I I I I I

SIGNIFICANCE FOR LOVIA USING SEQUENIIAL SUNS 0F SQUARES

I'SIS 0F

97

SIBI 0F F

F

NEAN SQUARE

OF

SUN 0F SQUARES

SNUHCE OF VARIAIICN

CMOBMWQMMOO
n FOOOOCOWC
. COOOHNODM
d FanOn’“
O on‘OCFOOC
O O O O C I C O O O O

‘

I09A9

«WMOamflflwOn
BOOFMQWONOCM

.O1IOOIIOQIDOOOIDOOI
0&0 a mu

..1IOOOIDOOOIIOOIDOQQ
“”00 kW
noon
0'00

In

EQQNNMGCCflflgflflO:
O

MFWWODMO
mannm—oonom
«OwflCwIIFIIU'K‘U.
"mnmnhuounnmn
MM°D$O°N~O°ONO
......OOCOOOOOOOO
N01.“ DMD-06:0 N“
on. IIICU‘ III

M N N

III“ In

VALEN
N UV PREVALEN

ZZZU

CAIIO
RINILI
fiv BE
CAIIO

0

OK
(28.4;de
DUI“ 0
Uta—n-bfiu-b
I-CIHEDQn-a

‘3,
IZZUUUZI'NJX
Claw-31¢ UUOOU
puufiaaurwnnap
cunt <Iau- c
n‘:u->bu4r"¢
Inaumuzmwnnumnn

nu“ _~'.I an
d ZZICI-IAZIZOOJZO
v 0653 UUO U
:r- I-C-dra-I-I-I-c-I-t-b—I-
3w CPQ&:: ctr-2.1.3.4.“.
~wfl “‘3' 81¢
wazmuuxzsmmuzxcmm
II LII!— JZQCB-‘C‘OKBB'AB‘
mSC“ I—JQUCJUE‘C-IJUUC Gnu

SSIAISQS

‘Z:8838!

.38

IvaU:l£D nzsauanrn

°-SUUAREC

F raqumy

CHI-

E'iand-J rdlzI-i Fwd-raid

98

Standardized r-. esidua :2:

(Wok-6n -9v~a=I-: Mum's. Mead!

2:04
«ao-
I”.
140‘
1:0-
Him-I
a.
'01
”-1

=31

 

 

 

 

 

 

 

 

 

mathmataanay
SKEWNESS I -O.214 KURTOSIS - 1.043

 

 

 

 

SQUARED - 32.759 D.F. - 14 SIGNIF. - .001
Stand ar‘dized Residuals b Cell
4 swan-in Juan-z "wot-II Mead: '
fln
SJ + I-
. * + I - «I
: q ‘ 5+ *1+.'~¢* ‘ *+ 4'
I ‘1". - + y r ** :3“; I I
1 -4 i +£‘fi Hit.- .‘. .I I :9“... }?:*'h
5533*“1jww wfifig “I: ' #:4- l
0 d "I" -'= 1.
*9 «z . V’ 45’
-1 ..‘3 I f‘er Iii§£§3.w Q t 3;?:g::{#§141>
”,ftfflr ‘II% I; +YI‘E1: I**x :"‘ “:4" 'I' T In
-2 _+ I: I+ + 1' INF + + ‘H. +bfl¥ ’4' , I-
++ + + +4. I + I-
-.3 '1 * l. *4. +
., I
...; .. +
—& 1 1 r I
0 20 A0 60 80

Erwin-mud Dasha Cd! Mm

COCHRAN'S C - 0.041
CRITICAL VALUE (3 - .01) a 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(WORK-IN—PROCESS: INVERSE MODEL)

FIGURE 5-12

F requomy

5.3nJOWfized Fesumwal

99

2
.w

LMQan Haw T'mu: lm Moo.“

 

 

.213.‘

    
 

... \-
\ a ‘\

35133.35
1' x

‘x

 

 

 

 

 

SKEWNESS I -O.322

 

 

KURTOSIS I 0.537

 

 

 

 

CHI-SQUARED I 23.903 D.F. I 14 SIGNIF. I .025
‘Tanuahh Dd Reaumwab M- 69H
4 ”floor. gem" um: In»-.. Moan
.3-1 I
- + + * *
9“ f- “ ’f 4 Q- '
d + 9 0- °' + I
3 “C :+ ... + #:4- ¢ . I+ 1 - T L
.3 ' ‘m$+flz '2: .EJ?‘¢3;:3§: x:+ *+ .233? z “'
. , * * 1- fi
CE 0 .gfit-g‘fi +‘¢,¢%i ".... 7'; -«r' ,§+‘+
'3 ,I- i Tarp * j; I I
a 1 1‘33"“. 312%?“ J‘**§'1.Etpfi:** *+ I ‘i- “:
fi ‘ , ,4! Int. "ffiflmqt *1- «w’n v ‘1
4,’ I I v 4" ""* ”a“ It.” “3+ ; 3“: +0- 1.”
5 “3 '1’ ‘h-v I + I- 3 ++ $. fl. *1; ”I 1;
a! " I-
"9- 1*
- .1
a Q * ¢
..
-‘q
.p
-5 I Y 1
0 20 ' '
‘0 . so so

amd Dasha Cd Numb.

COCHRAN'S C I 0.034
CRITICAL VALUE (8 I .01) I 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN FLOW TIME IN THE SHOP: INVERSE MODEL)

FIGURE 5-13

From

2C0

100

Stan d 0rd}: ed R 9.31:1 ua l3

"7'."ng :9 Han 11mg: Winn-n6: Mae-n

 

moJ
130-4
1703.1
1&4
133-1
1404
1.33-
1204
110d
10::-
”-1
:34
m.
«H
”I
”It
”-4
201
104

 

o-

 

 

  
   
   

 

 

 

 

 

 

 

 

y) -r_..'
. . I... ...".W
'6. I '. it; "
. ”a; f. .-
.4 ”A
If" ff."
2* If I
J o
A /
x” ’x"
f,1 I {A
f1 /",.4
."I‘ f. Ji‘
,' ,n / I»
[A /."‘
,~ A J A
.~-'l ’ ('f
’34 / {1‘1
1" A 11
9 fl;
1 '/ V 1’
M / ,4
A ",z‘
‘r' I}: '2‘ -"'
I f I
r V x / / E /|
i ’A / f I, ‘ f I. C‘ "
. , #réii Fflpfihfi=
0.28 1 .75 .128

Unmadca-ow
SKEWNESS . 0.605

CHI-SQUARED I 53.217

Standardzod Rod-judo

(VARIANCE OF FLOW TIME IN THE SHOP :

D.F.

KURTOSIS I 1.571

I 14 SIGNIF. I

Standardized Residuals by Cell
(Va. 6! How 11mg: Logarithmic Meal)

 

 

 

 

 

 

animate! Bunion Cd! Numb-

COCHRAN'S C I 0.046

CRITICAL VALUE (3 I

.01) I 0.047

.000

NORMALITY AND HOMOGENEITY OF VARIANCE TEST

FIGURE 5-14

LOGARITHMIC MODEL)

101

Standardized Residuairs

(Moan Twin-s: Wind: Modal)

 

 

 

 

 

 

 

 

...,4/1
2m '1 f/
4
... . 4
1 83 -I A
no - 1")
. ./
3. 1m 4 ,/
3* c5

I

.. we a x; .
u. {q
03 '1':
I i
do 4 :1

iii-j 0
-i ”'34

w ‘ ":1711 .
ifq
' 4'1

 

0.25
Um Limit a! 63.9%

SKEWNESS I -0.257 KURTOSIS I 0.584
CHI-SQUARED I 30.849 D.F. I 14 SIGNIF. I .005

Standardized Residuais by Cell

! Moan Tomlin”: Logarithmic Medan

Ran-:10 rdlzod Roaiduolo
o.
if

-3.

 

 

-4

 

finch—Nd Dasha Cd! W

COCHRAN'S C I 0.050
CRITICAL VALUE (8 I .01) I 0.047

NORMALITY AND HOMOGENEITY OF VARIANCE TEST
(MEAN TARDINESS: LOGARITHMIC MODEL)

FIGURE 5-15

F raj-Juno;

102

Standardized Residuals

(For. a! Tmfimsa: Lagmflhmic Mead]

 

200
190%
1&-
17D-
10‘
1S-
uo-n
139-1
120‘
110-l
1&4

”I!

334

704

  
  

\

"LL

 
 
  

. x "
\
3.3111

'\ \
A

634
=°l
.04

 
  

m.
10-
D ‘

-.‘.\\\

 

 

 

 

 

 

 

- ' . . ‘. “. -
“i 5". ‘\I ‘05 ‘3‘; x} \kk \

 

 

I f"

a, ,4 '0}! | II"

I I" V t L 7L 1 I
0.25 1 .73 3.25
Dept Limit :1 Gauge-y

SKEWNESS I -0.017 KURTOSIS I 0.313

CHI-SQUARED I 23.547 D.F. I 14 SIGNIF. I .050

Standardized Residuals by Cell
(Var. a! Tel-dim Lagari'thmie Mead) .

 

 

 

 

.3
++ *-
+ I-
'fit I
2 .1 + *‘, 4P . Or ... I."
I I . + $ 4- + + *
**'.:*1 ’ I‘ I +‘*“
* + * * Q “ .w . 3 * +
II 1 3f ¢J++ ” {1P ”4 ‘5 + '1' I- T 3+" I- #4.
«t . 3* .14 + + + +. .
Q r'wt' ”5 ‘<h¢* N 1b*+*“’+l”
. ..I- a I * ‘ 1'9. Iv +w * * Id.
“ +‘.++ * nu. 4' '0 ‘1'. § : + t: 3
CE O .. 7" . ”... . x + + _"II- ”I - 141' I” ‘
4 f . , .p _, " ~
,. “F :+ ‘ *Q
1'0: m‘. a + +43%“ + %§&f.+ . * 3 ,r1?* 1;}:
”E -' 9+1“? *+ ‘J‘f + 8 * * {‘- . + w
'3 ‘ I '1- :#+" ‘h “" ‘1: V‘, % ‘1 ~_ * ‘ F +
'0 1' o- * “if 3 " ? 3+: 1’ ‘1' I I If“ t
S I ¢ ‘ + *. E * ¢ t ' ¢ + #Q :1
EH -2 ‘l + + # *+1- 3 + ++ : J
I- t + , * I ...
...
-4
‘- 1 'F I 1 I 1 i
J 20 30 00 BO

figamm Dom CdIl Mm

COCHRAN'S C I 0.047
CRITICAL VALUE (8 I .01) I 0.047

NORMALITY AND HOMOGENEITY 0F VARIANCE TEST
(VARIANCE OF TARDINESS: LOGARITHMIC MODEL)

FIGURE 5-16

103
significantly reduced.

The results of Cochran's tests indicated that only the
ANOVA model for mean tardiness violated the assumption of
homoscedasticity. However, a visual examination of the plots
of standardized residuals versus experimental design cell
number suggested that the variabilities of errors were
greatly reduced when compared to the original ones. The
failure of assumptions may affect both the significance
levels and the sensitivity of F tests. However, the slight
violation of normality was negligible because the F test is
relatively insensitive to departures from normality
(Scheffe, 1959, pp. 350). This also applied to the situation
of the slight violation of the homogeneity of variance
assumption especially when the number of observations in
each cell was same.

All statistical comparisons or confidence interval
estimates were made on the transformed data for all system
performance except the percent of jobs tardy. Appendix D
shows summary tables of the transformed data for the five
dependent variables.

The power of the F test of each ANOVA model for main
effects is presented in Appendix E. It indicates the small
probability of committing a Type II error for most main
effects.

To reduce the error variability of the model the
blocking variance reduction technique was used as discussed

in 4.8. The efficiency of blocking factor for each of the

104
six ANOVA models was calculated to provide an estimate of
the increase in accuracy which results from the grouping
into replicates (Neter and Wasserman, 1974, pp. 738-740).
The estimates are calculated as follows:
E I [(n - 1)*MSB + n*(r - 1)* MSE] / [(n*r - 1)*MSE]
where: n I the number of observations per cell
r I the number of treatments
MSE I the error mean square
MSB I the mean square due to the blocking factor
Table 5-12 shows the efficiency of blocking factor for

the six ANOVA models.

TABLE 5-12
THE EFFICIENCY OF THE BLOCKING FACTOR

 

ANOVA Model Efficiency
Work-in-Process 1.15
Mean Flow Time in the Shop 1.14
Variance of Flow Time in the Shop 1.05
Mean Tardiness 1.09
Variance of Tardiness 1.08

Percent of Jobs Tardy 1.07

 

5.3 Experimental Results

5.3.1 General Overview
This section presents the results of the analysis of

variance for this experiment. Specifically, this section

105

describes significant main and interaction effects at the
.05 level for each performance measurement. The results
discussed in this section are summarized in Table 5-13.

Work-in-Process: All main effects were found to be
significant at the .05 level. Also significant at the .05
level were four two-way interactions. These were: the
interaction of order review/release mechanism and location;
dispatching rule and location; dispatching rule and
prevalence; and location and prevalence. A significant
three-way interaction effect was also observed at the .05
level. This effect involved dispatching rule, location, and
prevalence. No four-way interactions were significant.

Mean Flow Time in the Shop: The main effect of order

 

review/release mechanism was significant, as were the other
main effects at the .05 level. Two two-way interactions were
also found to be significant. They were the interaction of
order review/release mechanism and dispatching rule; and
order review/release mechanism and location. None of the
three-way and four-way interactions were significant at the
.05 level.

Variance of Flow Time in the Shop: ANOVA results for
this performance are also provided in Table 5-13. All main
effects were found to be significant at the .05 level. Two
two-way interactions involving (1) .order review/release
mechanism and dispatching rule and (2) order reviewlrelease
mechanism and location were also significant. None of the

three-way and four-way interactions were significant at the

106

TABLE 5-13
ANOVA RESULTS

Performance Criteria

 

 

 

 

 

 

 

Effects WIP MFT VFT MTA VTA PTA
Main
ORR I I I I I
DIS I I I I I I
LOC I I I I I I
PRE I I I I
Z-Way
ORR I DIS I I I I I
ORR * LOC * * * *
ORR * PRE * *
DIS * LOC *
DIS * PRE * *
LOC * PRE * *
3-Way
ORR * DIS * LOC *
ORR * DIS * PRE
ORR * LOC * PRE
DIS * LOC * PRE *
h-Way
ORR * DIS * LOC * PRE
Where: WIP I Work-in-Process
MFT I Mean Flow Time in the Shop
VFT I Variance of Flow Time in the Shop
MTA I Mean Tardiness
VTA I Variance of Tardiness
PTA I Percent of Jobs Tardy

* indicates

significant effect at the .05 level.

 

107
.05 level.

Mean Tardiness: All main effects except prevalence were

 

found to be significant at the .05 level. Three two-way
interactions were also significant. They were: (1) the
interaction of order review/release mechanism and
dispatching rule; (2) order review/release mechanism and
prevalence; and, (3) location and prevalence. No three-way
or four-way interactions were significant at the .05 level.
Variance of Tardiness: Main effects of dispatching rule
and bottleneck location only were found to be significant.
Two two-way interactions (order review/release mechanism and
dispatching rule, and dispatching rule and prevalence) were
also found to be significant. None of the three-way and
four-way interactions were significant at the .05 level.
Percent of Jobs Tardy: All main effects were found to
be significant at the .05 level. There were three two-way
significant interactions: (1) order review/release mechanism
and dispatching rule; (2) order review/release mechanism and
location; and (3) order review/release mechanism and
prevalence. There also existed a significant three-way
interaction effect. This effect involved order
review/release mechanism, dispatching rule, and bottleneck

location.

5.3.2 Detailed Analysis
The ANOVA results for each of the six major performance
measurements are analyzed in detail in this section.

Duncan's multiple comparison method is used to test for

108
significant differences between multiple pairs of
experimental conditions and to provide further statistical
insight into these differences.

One additional point must be made before proceeding to
this detailed analysis. Since a significant interaction
indicates that the relative effects of one factor change as
we proceed from level to level of the other factor, it might
be misleading to try to interpret significant main effects
in the presence of a significant interaction effects. Under
such conditions, it is generally more appropriate to examine
the effects of one particular factor for each individual
level of another factor and, similarly, to study another
factor for each individual level of the particular factor.
The detailed analysis in this study, therefore, does not
interpret significant main or interaction effects in the

presence of a higher significant interaction effect.

5.3.2.1 Work-in-Process

A subsequent post-hoc multiple comparison test for
significant interaction effects relevant to the detailed
discussion is provided in Appendix F. Duncan's procedure was
used to test pairwise comparisons between means at the .05

protection level.

5.3.2.1.1 DispatchingRule * Location * Prevalence
A significant three-way interaction effect was observed
among dispatching rule, bottleneck location, and bottleneck

prevalence. Table 5—14 presents the 3-way data. The nature

109

of this interaction is shown in Figures 5-17 and 5-18.

Figure 5-17 displays the interaction between dispatching

rule and bottleneck location for the 100% prevalence while

Figure 5-18 portrays the same interaction for the 50%

prevalence.

TABLE 5-14

THREE-WAY SUMMARY TABLE FOR WORK-IN-PROCESS
(DISPATCHING RULE * LOCATION * PREVALENCE)

 

 

(Measured in Hours) Dispatching Rule
Prevalence Location FCFS SPT SOPN Avg3
100% Front 302.19 149.51 265.59 239.10
Exit 705.72 205.77 506.18 472.55
Mixed 652.27 178.89 388.37 406.51
Avg. 553.39 178.06 386.71 372.72
50% Front 321.63 142.64 264.05 242.77
Exit 469.82 175.25 364.13 336.40
Mixed 520.74 163.97 357.62 347.44
Avg. 437.40 160.62 328.60 308.87
Grand Avg. 495.39 169.34 357.66 340.80

 

As illustrated in Figure 5-17 and 5-18, the SPT rule

consistently performed the best in minimizing work-in-

process, regardless of the level of location and prevalence.

The SOPN rule performed the second best and the FCFS rule

performed the worst for all levels of bottleneck location

and prevalence. The results of Duncan‘s multiple comparison

method (see Appendix F) supported these results.

Duncan's multiple comparison procedure in Appendix F

also indicated that the front bottleneck location produced

”Mob-Pm

WM1-h-Plt-Om

110

Location * Dispatching Rule

(Wk-knfiwuaas: ! cox 'M“)

 

 

 

 

lit

0 m 4 ”T -:~ ”PM

LOCATION * DISPATCHING RULE INTERACTION

(WORK-IN-PROCESS:

1001 PREVALENCE)
FIGURE 5-17

Lecatic-n * Dis uat-zhing Rule

kapln-Fhacns: 1:03 PM“:

 

9m-
‘CO-I

3:0:

zoo-i

as”

 

 

 

mo

la“

0 m I '1' 0 m

LOCATION“I DISPATCHING RULE INTERACTION

(WORK-IN-PROCESS: SOZ PREVALENCE)
FIGURE 5-18

111
significantly lower work-in-process than the exit and mixed
location under all of the situations examined.

The mixed location performed better than the exit
location for most situations considered. (see Table 5-14)
However, there was no significant difference in work-in-
process between locations when 50% prevalence was imposed on
the shop. (see Appendix F) However, a significant difference
between these two locations was observed for the 100%
prevalence when the SPT or the SOPN rule was used.

It was apparent from Table 5-14 that for any type of
dispatching rule and location the 100% prevalence had a
higher work-in-process than the 50% prevalence. The only
exception involved the front location and the FCFS rule.
These results implied that the 100% prevalence produced

relatively a higher work—in-process than the 50% prevalence.

5.3.2.1.2 Order Review/Release * Location

A significant interaction was observed between order
review/release (ORR) mechanism and bottleneck location.
Table 5-15 presents the two-way summary data and Figure 5-19
illustrates this interaction pictorially. When the
bottleneck was located in the front. or was mixed, the
selection of order review/release mechanism did not affect
significantly the resulting levels of work-in-process. (see
Appendix F) I ~

The benefit of using an order review/release mechanism
was greatest when the bottleneck was at the exit. Under this

location, however, the only order review/release mechanism

112

Lac ati an ‘* 0 RF:
(Watch-MI:

 

 

Wc-rk-h-Pmc-eaa

 

 

 

 

fl non + an 6 LB. 5 w H n

LOCATION ‘ ORDER REVIEW/RELEASE INTERACTION
(WORK-IN-PROCESS)

FIGURE 5-19

that did perform significantly better than the NOR mechanism

was the BRT.

TABLE 5-15

TWO—WAY SUMMARY TABLE FOR WORK-IN-PROCESS
(ORDER REVIEW/RELEASE * LOCATION)

(Measured in Hours) Order ReviewLRelease Mechanism

 

Location NOR ART ARL BRT BRL Avg;_
Front 239.26 228.13 234.00 255.50 247.79 240.94
Exit 466.12 417.75 453.86 310.35 374.29 404.48
Mixed 438.90 340.07 406.34 329.67 369.90 376.98
Avg. 381.43 328.65 364.74 298.51 330.66 340.80

 

113
The front location yielded significantly lower work-in-
process inventory level than the exit and the mixed location
regardless of the type of order review/release mechanisms
examined. However, there was no significant difference in
performance between the exit and the mixed location for any

of the order review/release mechanisms tested.

5.3.2.1.3 Discussion

It has been long known that the SPT rule performs well
in minimizing work-in-process inventory level in the
traditional job shop. (see Conway, Maxwell, and Miller 1967)
The presence of the bottleneck operation did not affect the
relative performance of the SPT rule as compared to the FCFS
and the SOPN rule. These findings suggest that the SPT rule
which excels in the non-bottleneck job shop is again
appropriate for the bottleneck job shop with respect to the
level of work-in-process.

The BRT mechanism's superiority, when the bottleneck
was located at the exit, may be attributed to its effective-
control over the workload at the bottleneck work center.
(see Table 5-16) These results provide two suggestions.

First, the BRT mechanism, when compared to the other

order review/release mechanisms, can most effectively manage
workload at the bottleneck work center. This in turn
provides a significant reduction in work-in-process
inventory in the shop. SecOnd, as fewer jobs are released to

the shop, less_work-in-process is generated.

114
TABLE 5-16
AVERAGE WORKLOAD AT THE BOTTLENECK WORK CENTER
(ORDER REVIEW/RELEASE * LOCATION)

Order Review/Release Mechanism

 

Location NOR ART ARL BRT BRL Avg.
Front 141.60 92.02 128.38 56.38 94.50 102.57
Exit 112.43 104.24 112.88 57.46 82.85 93.97
Mixed 157.86 111.59 150.54 58.74 95.93 114.93
Avg. 137.30 102.62 130.60 57.52 91.09 103.83

 

The results of the superior performance of the front
location over the exit and the mixed location under all
situations tested can be explained by the following two

reasons. First, higher work-in-process inventory occur as

more operations are completed. That is, the level of

inventory gets accumulated as orders gets close to

completion. Second, the bottleneck work center is the place

at which jobs spend their most time for waiting.

Higher work-in-process was produced when the shop

operated at a 100% prevalence, in contrast to the 50%. As

shown in Table 5-17, regardless of the type of dispatching

rule and location, relatively fewer jobs were released into

the shop for the 50% prevalence than for the 100%

prevalence. This resulted in lower work-in-process inventory

at the 50% prevalence level. The results suggest that

bottlenecks created by routings tend to provide relatively

higher work-in-process inventory than bottlenecks by long

115
processing times. When a large number of jobs requires an
operation of a certain work center having a fixed capacity
in a given time period, bottlenecks are created by routings.
On the other hand, bottlenecks are generated by long
processing times in the situation in which relatively fewer
jobs exist but each of which needs relatively long operation

of the work center.

TABLE 5-17

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE
(DISPATCHING RULE * LOCATION * PREVALENCE)

 

 

(Measured in Hours) Dispatching Rule
Prevalence Location FCFS SPT SOPN Avg;
100% Front 74.56 28.44 42.66 48.55
Exit 39.44 25.36 53.70 39.50
Mixed 47.25 33.47 52.40 44.37
Avg. 53.75 29.09 49.59 44.14
50% Front 83.37 58.57 76.09 72.68
Exit 61.05 29.87 69.98 53.63
Mixed 92.96 56.49 95.33 81.59
Avg. 79.13 48.31 80.47 69.30
Grand Avg. 66.44 38.70 65.03 56.72

 

fl

5.3.2.1.4 Summary for Work-in-Process

The following conclusions can be drawn from the results
of the detailed analysis with respect to work-in-process:
1. The selection of order review/release mechanism makes

virtually no difference in performance when the
bottleneck is at the front or mixed location.

2. In reducing the work-in-process inventory level, the BRT
mechanism is the only order review/release mechanism
which performs significantly better than the NOR

_116

mechanism when the bottleneck is located at the exit.

3. When compared to other dispatching rules, the SPT rule
produces the lowest level of work-in-process under all of
the situations tested.

4. For all situations, significantly lower work-in-process
inventory levels occur when the bottleneck is located at
the front, when compared to the exit and mixed location.

5. Shop floor performance of the 100% prevalence is inferior
to that of the 50% prevalence for the exit or mixed
bottleneck location. Prevalence makes no difference when
the bottleneck is at the front of the routings.

5.3.2.2 Mean Flow Time in the Shop

Duncan's multiple comparison test of significant

interaction effects is provided in Appendix G to test

pairwise comparisons between means at the .05 level.

5.3.2.2.1 Order Review/Release * Dispatching Rule

There existed a significant interaction between order
review/release mechanism and dispatching rule. Table 5-18
and Figure 5-20 illustrate this interaction. The only
significant interaction occurred primarily when tight
release mechanisms were used. Figure 5-20 indicated that the
benefits from using order review/release mechanisms were
greatest when the FCFS rule was used. When used with either
the SPT or the SOPN rule, the selection of order
review/release mechanism did not make any significant
difference in mean flow time in the shop. (see Appendix G)

Both the BRT and the ART mechanism, when used with the
FCFS rule, had significantly lower mean flow times than the
other -three order review/release mechanisms. The BRL

mechanism also performed significantly better than both the

117

ARL and NOR mechanism.

TABLE 5-18

TWO—WAY SUMMARY TABLE FOR MEAN FLOW TIME IN THE SHOP
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

 

 

(Measured in Hours) . Order Review/Release Mechanism

Disp. Rule NOR ART ARL BRT BRL Avg;
FCFS 194.51 140.32 180.38 136.59 163.52 163.06
SPT 88.18 86.63 90.51 85.77 88.55 87.93
SOPN 158.80 142.85 155.45 138.01 146.34 148.29
Avg. 147.16 123.26 142.11 120.12 132.80 133.09

 

ORR * Dispatching Rule

(“can flow Tia. in th- Shae)

”new Tun.

 

 

 

 

D m 4 ’1’ 6 m

ORDER REVIEW/RELEASE ‘ DISPATCHING RULE INTERACTION
(MEAN FLOW TIME IN THE SHOP)

.FIGURE 5—20

118
As shown in Figure 5-20, the SPT rule ’produced the
lowest mean flow time for all situations, performing
significantly better than the SOPN and the FCFS rule with
respect to mean flow time in the shop. (see Appendix G) It
is interesting to note that the FCFS rule performed as well
as the SOPN rule when the tight load limit level was imposed

on the shop.

5.3.2.2.2 Order Review/Release * Location

A significant interaction was observed between order
review/release mechanism and bottleneck location. Table 5-19
and Figure 5-21 illustrate this interaction. The only
significant interaction occurred when the ART mechanism was

used for the front bottleneck location. (see Appendix C) It

Location * ORR

‘0 (Moon MT!!!- in th- Sb)

 

1&-
183-
1‘ ‘
1&4 ,
13 i
1.1: _

129-l

Mom Flow 11m.

1N1

119-J

 

 

1 10 ,
M Bait lit-fl

 

nm+m out All? In.

LOCATION * ORDER REVIEW/RELEASE INTERACTION
(MEAN FLOW TIME IN THE SHOP)

FIGURE 5-21

was apparent

employing

the

that

when

ART

mechanism

119

compared

to

provided

the

NOR mechanism,

a significant

improvement when the bottleneck was located in the front.

There was

in the

mechanisms

Furthermore,

tested,

shop

for

under

type of

among

all

no significant

the

types

the

order

remaining

of

order
bottleneck

review/release

bottleneck location

significant difference in performance.

TABLE 5-19

difference in mean flow time

review/release

did not

locations.

mechanisms

make any

TWO-WAY SUMMARY TABLE FOR MEAN FLOW TIME IN THE SHOP
(ORDER REVIEW/RELEASE * LOCATION)

(Measured in Hours)

Order Review/Release Mechanism

 

Location NOR ART ARL BRT BRL Ayg;_
Front 145.24 113.99 134.64 119.73 134.58 129.64
Exit 138.17 128.42 138.93 116.17 126.18 129.57
Mixed 158.07 123.26 142.11 120.12 132.80 140.07
Avg. 147.16 123.26 142.11 120.12 132.80 133.09

 

5.3.2.2.3 Prevalence
Mean flow time in the shop was significantly influenced

by prevalence. Table 5-20 presents the performance of each

level of prevalence. On average, orders found in the shop

operating at the 50% prevalence experienced mean flow times
which were lower by 8% when compared to those observed when

the shop was at 100% prevalence. Since no higher interaction

120
effects involving prevalence existed, this result can

generally be applied to all situations.

 

 

TABLE 5-20
TABLE FOR MEAN FLOW TIME IN THE SHOP
(PREVALENCE)
Prevalence
(Measured in Hours) 100% 50%
138.36 127.82

 

5.3.2.2.4. Discussion

 

In the traditional job shop, processing-time related
dispatching rules such as the SPT were relatively effective
in lowering mean flow times (Conway, Maxwell, and Miller
1967, pp. 186). The SPT rule, by giving top priority to a
job with shortest imminent processing time, accelerates the
progress of jobs on the whole. Under the bottleneck job
shop, the SPT rule was again shown to be desirable in
obtaining low flow times in the shop.

The performance of the FCFS rule was significantly
affected by tight release mechanisms. The results suggest
that when jobs are tightly controlled for release, due-date-
oriented rules do not provide a significant reduction in
lead times when compared to such simple dispatching rules as
FCFS. This observation partially supports previous work that
suggested that simple dispatching rules would be used

effectively in the situation in which jobs were tightly

121

released (see Nicholson and Pullen 1972). The SPT rule,

however, demonstrated better performance over the FCFS in

terms of mean flow time.

The result that there is no significant difference in

performance among order review/release mechanisms examined

when the SPT rule is used strongly suggest the following.

The selection of dispatching rule is more important than the

selection of order review/release mechanism in minimizing

lead time.

As shown in Table 5-21, when the bottleneck was located

in the front, the ART mechanism reduced average job waiting
time in the shop by 31.23 hours when compared to the NOR
mechanism. For the ART mechanism, this led to a significant

reduction in mean flow time. The use of order review/release

mechanisms, when compared to the NOR mechanism, tended to
shorten average job waiting time in the shop in some
TABLE 5-21

AVERAGE JOB WAITING TIME IN THE SHOP
(ORDER REVIEW/RELEASE * LOCATION )

(Measured in Hours) Order Review/Release Mechanism

 

Location NOR ART ARL BRT BRL Avg,

Front 119.31 88.08 108.72 93.82 108.65 103.71
Exit 112.25 102.52 113.02 90.26 100.29 103.67
Mixed 132.17 101.48 126.84 98.55 111.74 114.15
Avg. 121.24 97.36 116.19 94.21 106.89 107.18

 

situations in the bottleneck

job shop.

122
The 100% prevalence produced a significantly higher
mean flow time in the shop than the 50% prevalence. Although
a bottleneck job's average waiting time at the bottleneck
work center for the 50% prevalence was longer than for the
100% prevalence, a job for the 100% prevalence, in total,
spent more time in waiting in the shop than for the 50%

prevalence by 9.7 hours. (see Table 5—22)

TABLE 5-22

AVERAGE JOB WAITING TIME AT THE BOTTLENECK WORK
CENTER, IN THE SHOP, AND IN THE BACKLOG FILE

 

 

(PREVALENCE)
(Measured in Hours) Prevalence
_Waiting Time 100% 50%
Bottleneck WC 50.85 80.44
Shop 112.44 101.92
Backlog File 44.14 69.30

 

Another reason for the inferior performance of the 100%
prevalence was that the average job waiting time in the
backlog file for the 100% prevalence was on average 25.1
hours shorter than for the 50% prevalence. (see also Table
5-22) This is due primarily to relatively long processing
time of bottleneck jobs for the 50% prevalence. This
subsequently led to release fewer jobs into the shop floor
when compared to the 100% prevalence. This implies that with
respect to lead time, bottlenecks created by routings tend

to create more problems than bottlenecks by long processing

123
times. Bottlenecks are created by routings when many jobs
require a common operation in relatively short time period.
For example, a single inspection stage may be a bottleneck

created by routings.

5.3.2.2.5 Summary for Mean Flow Time in the Shpp
The previous discussion of significant main and

interaction effects involving the mean flow time in the shop

suggests the following:

1. The use of the ART mechanism provides a significant
improvement in reducing mean flow time in the shop over
immediate release mechanism when the bottleneck is
located in the front.

2. The SPT rule, as compared to other dispatching rules,
exhibits superior performance in minimizing lead time.

3. When fewer jobs are released into the shop, simple
dispatching rules such as the FCFS rule can provide
performance equivalent to due-date-oriented rules such as
the SOPN rule when major performance objective is the
minimization of lead time in the shop.

4. The effectiveness of dispatching rules appears to be
greater than that of order review/release mechanism in
managing lead time.

5. Longer lead times are expected when bottlenecks are
caused by routings rather than long operation times. This
is due primarily to the tendency of release mechanisms to

release more jobs to the shop as compared to the 50%
prevalence.

5.3.2.3 Variance of Flow Time in the Shop

Duncan's multiple comparison test of significant
interaction effects is provided in Appendix H to identify

significant differences between means at the .05 level.

124

5.3.2.3.1 Order Review/Release * Dispatching Rule

There .existed a significant interaction between order
review/release mechanism and dispatching rule. Table 5-23
summarizes this two-way data and Figure 5-22 represents it
in a graphic form. When the FCFS rule was used, the BRT, the
ART, and the BRL mechanism yielded a significantly lower
variance of flow time than the NOR mechanism. The only

release mechanism that did not significantly do better than

the NOR mechanism was the ARL mechanism.

TABLE 5-23

TWO—WAY SUMMARY TABLE FOR VARIANCE OF FLOW TIME IN THE SHOP
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

Order Review/Release Mechanism

 

Disp. Rule NOR ART ARL BRT BRL Avg;_
FCFS 368922 102778 260117 85183 201708 203742
SPT 36072 23633 35405 10232 19350 24939
SOPN 18796 10344 16137 8344 11486 13021
Avg. 141264 45585 103887 34587 77515 80568

 

When the SPT rule was used, the BRT mechanism performed
significantly better than the other release mechanisms.
There was no significant difference in variance of flow time
among the remaining release mechanisms with respect to
variance of flow time. (see Appendix H)

Under the SOPN rule, the BRT produced a significantly

lower variance of flow time than the other release

125
mechanisms. Both the ART and the BRL mechanism yielded a

significantly lower variance than the NOR mechanism.

ORR ‘* Dispatching Rule

wthIHPMmflmomflnSMw

 

*flflu:;£?°
:6 g
///f
/
\\\\\
\
,>
\\/
L

 

 

 

 

 

:n- \
1”: V
”1
1-__ A A
0 fl f. 1
MN NW ML I" 'L
D “”3 I ,W O I’N

ORDER REVIEW/RELEASE * DISPATCHING RULE INTERACTION
(VARIANCE OF FLOW TIME IN THE SHOP)

FIGURE 5-22

Figure 5-22 indicated that the FCFS rule was the worst
performer under any order review/release mechanism tested.
The results of Duncan's tests supported this finding. The
disadvantage of using the FCFS rule, however, was smallest
when jobs are tightly released.

The performance of the SPT rule, when the BRT mechanism
was used, provided equivalent performance to the SOPN rule.
The performance of the SOPN rule was superior to that of
using the SPT rule in most cases and about the same in some

cases 0

126

5.3.2.3.2 Order Review/Release * Location

A significant interaction was observed between the
order review/release mechanism and bottleneck location.
Table 5-24 and Figure 5-23 provide this interaction effect.
Referring to Figure 5-23, the tight release mechanisms
produced a significantly lower variance than both the loose
mechanisms and the NOR mechanism when the bottleneck was
located in the front. The results of Duncan's tests

supported these results. (see Appendix H)

TABLE 5-24

TWO-WAY SUMMARY TABLE FOR VARIANCE OF FLOW TIME IN THE SHOP
(ORDER REVIEW/RELEASE * LOCATION)

Order Review/Release Mechanism

 

Location NOR ART ARL BRT BRL Avg.
Front 152568 23478 82549 45009 100828 80887
Exit 91691 58264 83776 22223 47057 60603
Mixed 179531 55013 145334 36526 84659 100213
Avg. 141264 45585 103887 34587 77515 80568

 

When the bottleneck was located at the exit, the BRT
mechanism was the only release mechanism that performed
significantly better than the NOR mechanism. For the mixed
location, the tight release mechanisms yielded a
significantly lower variance than the NOR mechanism.

Within any type of order review/release mechanism

tested, there was no significant difference in variance of

127

Lee ati -.:.-n * 0 RR

‘m (Mariana a? Plan Time in the Shaw

2 70 ,.-'
1 a: --"
1 a , .v”. .1

140 - "\ .f/ /
1 .1: -l . ,,
. l/, l,/
1 no 4
1 so 4 \\ /
‘a: \\'//,/:///

”-1

aa- ’
70-1
0'- 5—

”I
d

”I
a-
”4

Hum Bait Hind

 

Var 0' Flow Ijmo
(1mm;
)

 

 

 

ON“ 4‘"? OAK A” In

LOCATION * ORDER REVIEW/RELEASE INTERACTION
(VARIANCE OF FLOW TIME IN THE SHOP)

FIGURE 5-23

flow time among bottleneck locations, with the exception of
the ART mechanism. (see Appendix H) When the ART mechanism
was used, the front location had a significantly lower

variance than the exit and mixed location.

5.3.2.3.3 Prevalence

Variance of flow time in the shop was also influenced
by bottleneck prevalence. There was no higher interaction
involving prevalence with respect to variance of flow time
in the shop. Table 5-25 presents this main effect. The 50%
prevalence provided a 14% reduction in performance over the

100% prevalence.

128
TABLE 5-25
TABLE FOR VARIANCE OF FLOW TIME IN THE SHOP
(PREVALENCE)
Prevalence
100% 50%
86761 74374

 

5.3.2.3.4 Discussion

It was apparent from the results that the use of the
BRT mechanism led to a considerable reduction in the
variance of flow times in the shop regardless of the type of
dispatching rules used at the work centers. The ART and the
BRL mechanism also provided an improvement in performance
over the NOR mechanism when either the FCFS or the SOPN rule
was used. These results suggest that the use of an order
review/release mechanism performs better than the immediate
release mechanism in minimizing the variance of flow times
in the shop. The results also suggest that tight control of
job release tends to provide further improvement in lowering
lead time variance.

The SOPN rule performs relatively well in minimizing
variance of tardiness in the traditional job shops. (see
Conway, Maxwell, Miller, 1967, pp. 226) The relative
performance of the SOPN rule, as compared to the SPT and the
FCFS rule, did not change in the bottleneck job shop. These
results suggest that due-date oriented dispatching rules

that excel in the traditional job shop again provide

129
considerable improvement in minimizing variance of flow time
in the bottleneck job shop.

Within any of the order review/release mechanisms
tested, in general, there was no significant difference in
variance of flow time among bottleneck locations. The sole
exception was the ART mechanism. (see Appendix H) These
results suggest that the type of bottleneck location does
not appear to significantly affect the performance of each
release mechanism with respect to variance of flow time,
with the exception of the ART mechanism.

The superior performance of the 50% prevalence to that
of the 100% prevalence can be explained by the nature of the
order review/release mechanisms. These mechanisms tend to
release fewer jobs when the 50% prevalence is imposed to the
shop. (See the discussion of bottleneck prevalence for mean

flow time in the shop.)

5.3.2.3.5 Summary for Variance of Flow Time in the Shop

The following conclusions may be drawn from the
analysis of experimental results in terms of variance of
flow time in the shop.

1. Employing order review/release mechanism other than the
NOR mechanism tends to reduce the variance of flow time
in the shop. The BRT mechanism, as compared to other
release mechanisms, consistently performs significantly
better than the NOR mechanism regardless of the type of
dispatching rules and locations examined.

2. The SOPN rule performs the best under virtually all
conditions tested in this experiment with respect to
variance of flow time in the shop.

3. Within a given order review/release mechanism, there is
no significant difference in variance of flow time among

130

locations, with the exception of the ART mechanism and
the front location.

4. Larger variance of flow time in the shop are expected
when bottlenecks are created by routings rather than long
processing times.

5.3.2.4 Mean Tardiness

Mean tardiness under this study represents aggregate
mean tardiness rather than conditional mean tardiness. For
aggregate mean tardiness, jobs completed early are assigned
tardiness of zero and included in the average. Results of
the ANOVA were presented in Table 5-13. Duncan's multiple

comparison test of significant interaction effects is

provided in Appendix I.

5.3.2.4.1 Order Review/Release * Dispatchipg Rule
There existed a significant interaction effect between
the order review/release mechanism and the dispatching rule.

Table 5-26 summarizes the data and Figure 5-24 portrays it.

TABLE 5-26

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

 

 

(Measured in Hours) Order Review/Release Mechanism

Disp. Rule NOR ART ARL BRT BRL Agg;_
FCFS 100.75 107.75 94.38 116.53 93.24 102.53
SPT 10.51 14.35 12.09 34.95 23.15 19.01
SOPN 22.51 57.42 31.47 114.55 49.31 55.05

Avg. 44.59 59.84 45.98 88.68 55.23 58.86

 

131

Overall, the SPT rule performed best and the FCFS rule
was the worst under all of the order review/release
mechanisms considered.

It is interesting to note the rapidly deteriorating
performance of the SOPN rule when it was used with tight
order review/release mechanisms. Specifically, the
performance of the SOPN rule significantly deteriorated when
used with the BRT mechanism.

When jobs were not released tightly, there was no
significant difference in mean tardiness between the SPT
rule and the SOPN rule. (see Appendix I) When the FCFS rule
was used, all order review/release mechanisms performed
similarly regardless of the type of order review/release

mechanisms examined.

ORR * Dispatching Rule

{Moon rm“.

 

 

 

 

 

1 32’
xf~
1 :0 ’
P‘x _/ '/ ."I \:\‘.‘-.
I m \‘1 . ....J I)! \.'.. . ..‘\,V.
. \. ID
90 1 .-’ 'x.
8 m 4 ‘
"x
i 70 I r' "
E / \x
Q .
a A- / \
m ‘ I, ‘\ J" b
I I/ \\\\ I
40 1
///// \\J/
m ..
m _1 r /\
1o .1 r— ‘; ‘1 T
m an AK .7 IL
0 m 4 ’7 6 ”PM

ORDER REVIEW/RELEASE R DISPATCHING RULE INTERACTION
(MEAN TARDINESS)

FIGURE 5-24

132
For both the SPT and the SOPN rule, however, the
performance of mean tardiness was influenced by the specific

order review/release mechanism in place.

5.3.2.4.2 Order Review/Release * Prevalence

The interaction between order review/release mechanism
and bottleneck prevalence was significant. Table 5-27 and
Figure 5-25 illustrate this interaction. The BRT mechanism
was the major source of this significant interaction.
Figure 5-25 indicated that the use of the BRT mechanism
improved shop performance when the prevalence was 100%. This
behavior was contrary to the general trend of other release

mechanisms in which no difference in mean tardiness was

obtained for the 50% prevalence. (see Appendix I)

Prev alen ce * ORR
‘ 33 (“can Twinesil

 

1nd t0
1104 . //
103-4
n-

”I

Mam Tel-dines

70..

 

if?

 

 

 

 

 

”j 1
can: ‘0‘

noon 45“? OAR. 5.7 In.

PREVALENCE ' ORDER REVIEW/RELEASE INTERACTION
(MEAN TARDINESS) ’

FIGURE 5-25

133
TABLE 5-27

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS
(ORDER REVIEW/RELEASE * PREVALENCE)

 

 

(Measured in Hours) Order Review/Release Mechanism
Prevalence NOR ART ARL BRT BRL Avg.
100% 47.76 60.16 48.60 56.65 46.85 52.00
50% 41.42 59.52 43.36 120.71 63.61 65.72
Avg. 44.59 59.84 45.98 88.68 55.23 58.86

 

5.3.2.4.3 Location * Prevalence

 

A significant interaction was also observed between
bottleneck location and extent of bottleneck prevalence.

Table 5-28 presents two-way summary data and Figure 5-26

Prevalence * Location

(Moan Tardiness)

 

than tardines-

 

 

 

 

 

0 PM I and -6 Nix-d

PREVALENCE * LOCATION INTERACTION
(MEAN TARDINESS)

FIGURE 5-26

134
illustrates it in graphic form. For 100% prevalence, there
was no significant difference in mean tardiness among
locations tested. (see Appendix I) For the 50% prevalence,
however, the exit location produced a significantly lower

mean tardiness than the front and mixed location.

TABLE 5-28

TWO-WAY SUMMARY TABLE FOR MEAN TARDINESS
(LOCATION * PREVALENCE)

 

 

 

 

(Measured in Hours) Location
Prevalence Front Exit Mixed Avg.
100% 51.03 48.69 56.29 52.00
50% 64.95 51.17 81.04 65.72
Avg. 57.99 49.93 68.67 58.86
5.3.2.4.4 Discussion
The relatively poor performance of the BRT mechanism
was in part attributable to the relatively long mean flow

times of orders in

the system.

Table

It

is

interesting to note the relationship between average waiting
time in the backlog file and average flow time in the system
for each order review/release mechanism. (see Table 5-29 and
5-30) Keeping an order off the floor did not lower its total
time in the system. These results indicate that the use of
an order review/release mechanism deteriorated mean
tardiness due to its relatively long flow time in the

system, although it appeared to improve flow times in the

135
shop. These results also support the findings reported by
Baker (1984) that the use of release mechanisms tended to
increase mean tardiness due to its restriction of the set of

jobs available for scheduling.

TABLE 5-29

MEAN FLOW TIME IN THE SYSTEM
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

(Measured in Hours) Order Review/Release Mechanism

 

 

Dispatching NOR ART ARL BRT BRL
FCFS 194.51 249.89 210.15 269.65 223.33
SPT 88.18 122.65 111.15 169.40 141.72
SOPN 158.80 220.63 184.81 292.05 210.28

TABLE 5-30

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

 

 

(Measured in Hours) Order Review/Release Mechanism
Dispatching_ NOR ART ARL BRT BRL
FCFS 0.00 109.57 29.76 133.06 59.82
SPT 0.00 36.01 20.65 83.65 53.18
SOPN 0.00 77.79 29.36 154.04 63.95

 

Specifically, the performance of the shop was worst
when the BRT mechanism was used with the SOPN rule. The BRT

mechanism, in contrast to the other order review/release

136

mechanisms, tended to release relatively fewer jobs into the
shop. (see Table 5-30) This may be attributable to the
operating mechanics of the SOPN rule. That is, the SOPN rule
does not perform well when the objective is to minimize
work-in-process inventory or lead times of orders.
Therefore, the SOPN rule created more workload in the shop
which subsequently delays job releasing. These results
suggest that in the bottleneck job shop, the SPT rule
appears to be more effective than the SOPN rule in managing
mean tardiness.

For loose release mechanisms, no significant difference
was observed between the SPT and the SOPN rule with respect
to mean tardiness. Table 5-30 also indicated that there was
relatively a little difference in average job waiting time
in the backlog file between the SPT and the SOPN rule for
loose order review/release mechanisms, when compared to
tight release mechanisms.

The BRT mechanism was the main cause for the
significant interaction between order review/release
mechanisms and bottleneck prevalence. The BRT mechanism
released jobs according to the bottleneck work center
processing time. Under the 50% prevalence, therefore, the
BRT mechanism tended to release a considerably smaller
number of jobs, as compared to other release mechanisms.
(see Table 5-31) This subsequently increased the total flow
time in the system which in turn increased mean tardiness.

This result suggests that the BRT mechanism does not appear

137
to be desirable in lowering mean tardiness when prevalence

in the shop is 50%.

TABLE 5-31

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE
(ORDER REVIEW/RELEASE * PREVALENCE)

(Measured in Hours) Order Review/Release Mechanism

 

Prevalence NOR ART ARL BRT BRL
1002 0.00 73.40 25.75 82.31 39.25
50% 0.00 75.51 27.43 164.86 78.71

 

Although there was no significant difference between
prevalence for all locations (see Appendix I), there was a
considerable improvement in mean tardiness when the shop
operated at 100% prevalence. This behavior may be caused by
the relatively long job waiting time at the bottleneck work
center rather than at the non-bottleneck work centers under
the 50% prevalence due to the long processing time of

bottleneck jobs. (see Table 5-32) These results suggest that

TABLE 5—32

AVERAGE JOB WAITING TIME AT THE BOTTLENECK
AND NON-BOTTLENECK WORK CENTER
(LOCATION * PREVALENCE)

(Measured in Hours) Bottleneck Location

 

Prev Front Exit Mixed

Bottleneck WC 1002 46.86 53.10 52.59
50% 78.86 68.62 93.85

Non-Bottleneck WC 1002 24.28 23.87 25.66
50% 20.66 20.74 21.21

 

138
mean tardiness tends to increase when the cause of

bottlenecks are the long operation time of bottleneck jobs.

5.3.2.4.5 Summary for Mean Tardiness
Several conclusions with respect to mean tardiness may
be summarized as follows:

1. The use of order release mechanisms tends to deteriorate
mean tardiness.

2. The SPT and the SOPN rule perform similarly when the
loose order review/release mechanisms or the NOR
mechanism are used. However, the SPT rule performs
significantly better than both the SOPN and the FCFS rule
with respect to mean tardiness when used with the tight
release mechanisms.

3. The performance of the FCFS rule is not affected by the
selection of order review/release mechanism with respect
to mean tardiness.

4. ShOp performance, when the BRT and the ART mechanisms are
used with the SOPN rule, rapidly deteriorates.

5. The performance of the BR mechanism, when compared to
other release mechanisms, rapidly deteriorates as the
prevalence shifts from 100% to 50%.

6. There is no significant difference among locations when
100% prevalence is imposed on the shop. As prevalence
changes from 100% to 50%, however, the exit location
produces a significantly lower mean tardiness than both
the mixed and front location.

7. As prevalence shifts from 100% to 50%, mean tardiness
tends to increase for all bottleneck locations examined.

5.3.2.5. Variance of Tardiness

Table 5-11 presents the ANOVA results with respect to
the variance of tardiness. The results of Duncan's multiple
comparison test of significant interaction effects is
provided in Appendix J to identify the significant

difference between means at the .05 level.

139
5.3.2.5.1 Order Review/Release * Dispatching Rule
There existed a significant interaction effect between
order review/release mechanism and dispatching rule. Table
5-33 and Figure 5—27 summarize this data. The performance of
order review/release mechanisms was considerably affected by
the specific type of dispatching rules. (see Appendix J)
When the SPT rule was used, there was no significant
difference in the variance of tardiness among order
review/release mechanisms tested.
When the FCFS rule was used, however, the performance
of the shop under tight release mechanisms was significantly
better than those of the ARL, the BRL, and the .NOR

mechanisms.

ORR * Dispatching Rule

3‘0 (Various of Tadi 1"-)

:3 \ //\\‘ ,.
:2: \ /
..- ,/ \/

View( 0' Yard

1mm
m
.01
0.
a —v—
OE’ I

m W

 

 

 

txA‘ b
#— ‘_ :'
ML

.7 .L

 

 

 

 

U m 4 PT 6 m

ORDER REVIEW/RELEASE * DISPATCHING RULE INTERACTION
(VARIANCE OF TARDINESS)

FIGURE 5-27

140
TABLE 5-33

TWO-WAY SUMMARY TABLE FOR VARIANCE OF TARDINESS
(ORDER REVIEW/RELEASE * DISPATCHING RULE)

Order Review/Release Mechanism

 

 

Disp. Rule NOR ART ARL BRT BRL Avg;
FCFS 333805 89499 233707 78878 183635 183905
SPT 22875 15037 23032 7587 12986 16303
SOPN 3182 5833 3954 10097 5258 5665
Avg. 119954 36790 86898 32187 67923 68625

 

Under the SOPN rule, the NOR mechanism outperformed
other release mechanisms. The BRT mechanism performed the
worst.

The SOPN rule, as expected from prior results with this
rule, performed impressively for all order review/release
mechanisms tested. The FCFS rule performed the worst in all
situations. The performance of the SPT rule, when used with

the BR mechanism, approached to that of the SOPN rule.

5.3.2.5.2 Dispatchinngule * Prevalence

A significant interaction effect was also observed between
dispatching rule and bottleneck prevalence. Table 5-34 and
Figure 5-28 illustrate this interaction effect. In general,
the FCFS rule was the worst performer and the SOPN the best
for any type of prevalence. The results of Duncan's multiple
comparison method supported these rankings of significant
difference among dispatching rules examined for all levels

of prevalence. (see Appendix J)

141
TABLE 5-34

. TWO-WAY SUMMARY TABLE FOR VARIANCE OF TARDINESS

(DISPATCHING RULE R PREVALENCE)

DispatchingRule

 

Prevalence FCFS SPT SOPN Ayg;_
100% 197278 16786 3559 72541
50% 170533 15822 7772 64709
Avg. 183905 16304 5665 68625

 

Regardless of the type of dispatching rules considered,

there was no significant difference in the level of variance

of tardiness between the 100% and the 50% prevalence levels.

(see Appendix J)

V0? of “wire

1”-
1m:
1704
1.3-l
1&1
1m:
1D-I
1”“
110a
1&1
”1
”I:
”a
“I
”I
‘4
a.
”-1

Prevalence * Dispatching Rule

(Variance a4 Tani In-)

 

10-1

 

 

 

 

am In on

PREVALENCE R DISPATCHING RULE INTERACTION

(VARIANCE OF TARDINESS)
FIGURE 5-28

142
5.3.2.5.3 Location
Table 5-35 shows a comparison of shop performance for
each bottleneck location. On average, the largest variance
of tardiness occurred when the bottleneck was located at the
mixed and the smallest variance of tardiness occurred when

it was at the exit.

TABLE 5-35
TABLE FOR VARIANCE OF TARDINESS
(LOCATION)
Bottleneck Location
Front Exit? Mixed AvgJ

70976 47269 87629 68625

 

5.3.2.5.4 Discussion

The performance of order review/release mechanisms
considered in this study was significantly affected by the
specific type of dispatching rules in place. It is
interesting to examine the performance of the system under
the BRT mechanism in use. When used with the SOPN rule, the
BRT mechanism performed the worst. However, its best
performance occurred when this mechanism was used with the
FCFS rule. These results suggest that the selection of
dispatching rules appears to significantly affect the
relative performance, as indicated by rankings, of the order
review/release mechanisms in place.

For all situations examined, the SOPN rule, when

143

compared to either the SPT or the FCFS rule, performed
better or at least equivalently. These results suggest that
the SOPN rule, which excels in the traditional job shop on
reducing the varianCe of tardiness, is again the most
appropriate dispatching rule in the bottleneck job shop. The
SPT rule, when compared to the SOPN rule does not perform
well alone. Its impact, however, may be significantly
enhanced if used with the BRT mechanism. The results also
suggest that the selection of dispatching rules is more
critical than the selection of order review/release
mechanisms in lowering variance of tardiness.

The level of prevalence did not make any difference in
the level of the variance of tardiness for any given
dispatching rule considered. These results imply that each
of the dispatching rule tested is insensitive to the level

of prevalence with respect to variance of tardiness.

5.3.2.5.5 Summarypfor Variance of Tardiness

General conclusions for this section are summarized as
follows:

1. The SOPN rule, as compared to the SPT rule, exhibits
consistently better or at least equal performance in
terms of the variance of tardiness.

2. Variance of tardiness appears to be reduced when the
location of the bottleneck in the routing is fixed.

3. The performance of the SPT rule is improved significantly
when used with the BRT mechanism.

4. Each dispatching rule in this experiment is insensitive
to the change in prevalence with respect to variance of
tardiness.

144
5.3.2.6 Percent of Jobs Tardy
Results of the ANOVA are presented in Table 5-13. A
post hoc Duncan's multiple comparison procedure for the
significant interaction effects under discussion was

conducted and provided in Appendix K.

5.3.2.6.1 Order Review/Release R Dippatchingpgule R Location

A significant three-way interaction effect was observed
among order review/release mechanism, dispatching rule, and
bottleneck location. Table 5-36 summarizes this result. The
nature of this interaction is illustrated in Figures 5-29
through 5-31. Figures 5-29through 5-31 show the interaction
of order review/release mechanism and dispatching rule for
each type of bottleneck location (i.e., the front, the exit,
and the mixed, respectively).

ORR * Dispatching Rule

(Pm d Jan Tack: From)

‘°‘ ,/\\/\/\

 

Pore-ht of Jot-o Tardy

so F /’/\-
/

«V

 

 

 

o 1 1 fl

MIR arr AR. '7 '1.

D m 4 ’7 O m

ORDER REVIEW/RELEASE R DISPATCHING RULE INTERACTION
(PERCENT OF JOBS TARDY: FRONT LOCATION)

FIGURE 5-29

145

ORR * Dismatc hing Rule
(w 61 Jab Tatar. lain

 

 

 

PM! of Job. Tardy

 

 

 

 

D m 4 '1’ O m

ORDER REVIEW/RELEASE R DISPATCHING RULE INTERACTION
(PERCENT OF JOBS TARDY: EXIT LOCATION)

FIGURE 5-30

ORR * Dispatching Rule

(W a! ”foray: bliss-:1)

 

 

 

 

a: xk-
\\
“=- /'//-\\\\
t /
6 . / \ / / ’
'5 ° //\:T\ .. " \.
$3 I / ‘. \' (./ AK
2 :3 . //’ \‘x //' /’/ \
3 4/ ’ 7 / \
g I? ( /"/
10 d /\ {I
l
o 1 I
MI! W A ll? .L
a . m 4 ,7 3 9’"

ORDER REVIEW/RELEASE R DISPATCHING RULE INTERACTION
(PERCENT OF JOBS TARDY: MIXED LOCATION)

FIGURE 5-31

146

TABLE 5-36

THREE-WAY SUMMARY TABLE FOR PERCENT OF JOBS TARDY

(ORDER REVIEW/RELEASE * DISPATCHING RULE * LOCATION)

(Measured in Percentage)

Order Review/Release Mechanism

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 18.45 55.00 29.65 38.40 33.55 35.01
SPT 3.95 16.35 10.75 30.65 21.90 16.72
SOPN 22.90 45.30 33.70 43.20 37.60 36.54
Avg. 15.10 38.88 24.70 37.42 31.02 29.42
Exit FCFS 18.45 24.40 24.95 50.05 29.25 29.42
SPT 3.90 9.50 9.50 18.90 14.10 11.38
SOPN 19.65 34.55 28.60 66.35 36.30 37.09
Avg. 14.00 22.82 21.02 45.10 26.55 25.96
Mixed FCFS 19.55 40.80 26.65 47.90 36.70 34.32
SPT 4.45 14.65 10.30 33.20 23.30 17.18
SOPN 24.70 46.10 32.60 59.25 42.30 40.99
Avg. 16.23 33.85 23.18 46.78 34.10 30.83
Grand Avg. 15.11 31.85 22.97 43.21 30.56 28.74

 

of dispatching

As shown

in Figures 5-29 through 5-31,

rules

was

significantly

affected

by

the performance

the

Specific type of order review/release mechanism in place and

the location

of the

SPT

rule

dispatching rules.

presence of

the BRT

was

of the bottleneck.

mechanism.

superior

Its performance

was

The

In general,

that

of the
sensitive

BRT mechanism

adverse impact on the operation of the SPT rule.

There was

tardy among

located in

Appendix K)

to

had

the performance

other
the

an

no significant difference in percent of jobs

the front

Furthermore,

and the

Duncan's

BRT mechanism was used.

multiple

comparison

LEStS

three dispatching rules when the bottleneck was

(see

in

147
Appendix K indicated that when the BRT or the BRL mechanism
was used, there was no significant difference in percent of
jobs tardy between the SPT and the FCFS rule both for the
front and for the mixed location. When the bottleneck moved
to the exit, however, the SPT rule produced the lowest
number of jobs overdue. It performed significantly better
than either the FCFS and the SOPN rule for all order
review/release mechanisms tested.
The performance of order review/release mechanisms was
also significantly influenced by the specific type of
dispatching rule and location. The NOR mechanism yielded the

lowest percent of jobs tardy in all situations examined.

5.3.2.6.2 Order Review/Release * Prevalence

A significant interaction was observed between order
review/release mechanism and bottleneck prevalence. Table 5-
37 presents two-way summary of the data while Figure 5-32
illustrates it graphically. The BR mechanism appeared to be
the main cause of this significant interaction. It is
apparent from Figure 5-32 that the BR mechanism, unlike NOR
and the AR mechanisms, performs better under 100% prevalence
than under 50%. As indicated in Appendix K, there was no
significant difference in percent of jobs tardy between the
100% and the 50% prevalence for the NOR, the ART and the ARL
mechanism. For the BRT and BRL mechanism, however, the 100%
produced significantly lower percent of jobs tardy under the

50% prevalence.

148

Prevalen ce * ORR
(Front d abs Tandy)

 

a
”u
‘I

”It

I

.. fl

 

 

PM of Job. Tandy

 

1O

 

 

1O ,
1m 60!

D NOR 4» W 6 m A BRT I BR.

PREVALENCE R ORDER REVIEW/RELEASE INTERACTION
(PERCENT OF JOBS TARDY)

FIGURE 5-32

TABLE 5-37

TWO-WAY SUMMARY TABLE FOR PERCENT OF JOBS TARDY

(ORDER REVIEW/RELEASE * PREVALENCE)

(Measured in percentage) Order Review/Release Mechanism

Prevalence NOR ART ARL BRT BRL Ayg;

100%
50%

Avg.

16.88 33.11 25.12 36.13 27.11 27.67
13.34 30.59 20.81 50.29 34.00 29.81

15.11 31.85 22.97 43.21 30.56 28.74

 

Regardless of the level of prevalence, the NOR

mechanism performed significantly better than the other

order review/release mechanisms. (see Appendix K) For the

149
1002 prevalence, the BRT and the ART performed similarly.
For the 50% prevalence, however, the ART mechanism provided
a significant improvement in performance over the BRT
mechanism. These findings again suggest that the BRT
mechanism is not desirable when the shop floor performance

is to minimize the number of jobs tardy.

5.3.2.6.3 Discussion

When jobs in the backlog file were released according
to the workload for the bottleneck work center, the number
of jobs tardy was increased. This result occurred regardless
of the type of dispatching rules and bottleneck locations in
place. These findings suggest that when an interest is in
reducing the number of jobs tardy, then the BR mechanism
deteriorates the effectiveness of the dispatching rules.

Although the use of order review/release mechanism
reduced mean flow time in the shop, it actually prolonged
the overall average flow time in the system. This result was
due primarily to the relatively long waiting time
experienced in the backlog file. This subsequently led to an
increase in both the aggregate mean tardiness and the number
of jobs overdue. These findings suggest that for jobs to
have a good chance of meeting their due dates, they should
be released immediately.

It has long been recognized that in traditional job
shops operating at moderate levels of shop capacity
utilization, due-date-oriented dispatching rules are

effective in lowering the percentage of jobs tardy (Conway,

150

Maxwell, and Miller, 1967, pp. 233). For the bottleneck job
shop, however, the SOPN rule produced an even higher percent
of jobs tardy than the FCFS. These findings suggest that for
the bottleneck job shop, due-date based rules do not appear
to be desirable in minimizing proportion of jobs tardy even
at moderate shop capacity utilization.

when the bottleneck was at

Referring to Figure 5-30,

the end, the ART mechanism performed as well the ARL. The
performance of the BRT mechanism, on the other hand,
deteriorated rapidly when the bottleneck shifted from the

front to the exit. As shown in Table 5—38, when the

bottleneck moved from the front to the exit, the BRT

mechanism, when compared to the BRL mechanism, provided

TABLE 5-38

AVERAGE JOB WAITING TIME IN THE BACKLOG FILE
(ORDER REVIEW/RELEASE R DISPATCHING RULE * LOCATION)

(Measured in Hours) Order Review/Release Mechanism

 

Loca. Disp. NOR ART ARL BRT BRL
Front FCFS 0.00 197.11 44.10 93.51 60.11
SPT 0.00 42.30 20.73 94.59 59.91
SOPN 0.00 102.55 39.09 95.29 59.96
Exit FCFS 0.00 34.90 20.03 150.26 46.06
SPT 0.00 23.59 19.96 59.01 35.53
SOPN 0.00 40.22 20.10 196.29 52.29
Mixed FCFS 0.00 96.69 25.16 155.42 73.27
SPT 0.00 42.16 21.25 97.35 64.11
SOPN 0.00 90.60 28.88 170.56 79.30

 

relatively longer

average job

waiting time

in the backlog

151
file. This resulted in lower workload in the shop but longer

flow time in the system (as indicated in Table 5-39). This

in turn adversely affected the performance of percent of

jobs tardy.

TABLE 5-39
MEAN FLOW TIME IN THE SYSTEM
(ORDER REVIEW/RELEASE R DISPATCHING RULE R LOCATION)

(Measured in Hours) Order Review/Release Mechanism

 

 

Loca. Disp. NOR ART ARL BRT BRL
Front FCFS 189.79 318.28 205.94 233.51 227.35
SPT 86.41 128.40 111.16 181.00 148.72
SOPN 159.52 237.26 190.75 228.45 207.61
Exit FCFS 181.88 188.25 197.87 279.36 199.55
SPT 86.01 109.58 108.09 142.60 122.02
SOPN 146.61 186.14 170.94 332.13 191.16
Mixed FCFS 211.87 243.14 226.64 296.49 243.09
SPT 92.12 129.96 '114.22 184.61 154.42
SOPN 170.26 238.50 192.74 315.57 232.09
As shown in Table 5-40, the average job queue time at

the bottleneck work center at the 50% prevalence is longer

than at the 100% prevalence. This caused a higher percent of

jobs tardy. The causes creating bottlenecks again made a

significant difference in performance between the BR

mechanism and the other mechanisms. These findings suggest

that the BR mechanism is not worthwhile with respect to

percent of jobs tardy when the 50% prevalence shop is

operating under.

152
TABLE 5-40

AVERAGE JOB WAITING TIME AT THE BOTTLENECK WORK CENTER
(ORDER REVIEW/RELEASE R PREVALENCE)

(Measured in Hours) Order Review/Release Mechanism

NOR ART ARL BRT BRL

Prevalence 100% 64.82 45.49 60.63 32.90 50.39

50% 117.09 74.02 105.77 38.40 66.93

 

5.3.2.6.3 Summapy for Percent of Jobs Tardy

Several conclusions can be reached after analyzing the

performance of percent of jobs tardy.

1.

As compared to the immediate release mechanism, employing
the AR and BR mechanism tends to increase the number of
jobs tardy. It also appears that relative differences
between order review/release mechanisms tend to be
heightened as fewer and fewer jobs are released into the
shop floor.

Specifically, the performance of the BRT with respect to
percent of jobs tardy is not encouraging in any of the
situations examined.

The performance of the SPT rule consistently outperforms
the SOPN rule and the FCFS rule for the bottleneck job
shop. However, the performance of the SPT rule, when used
with the BRT mechanism, rapidly deteriorates. As a
result, there is no significant difference in performance
among dispatching rules examined for the front location.

Surprisingly, the FCFS rule, as compared the SOPN rule,
performs better or at least equally well in minimizing
percent of jobs tardy.

The performance of both the BRT and the BRL mechanism
deteriorates as prevalence shifts from 100% to 50%.

153
5.4 Bottleneck Jobs vs. Non-Bottleneck Jobs

We have so far examined the experimental results in
light of aggregate performances of jobs. Jobs can, however,
be split into two types: bottleneck jobs and non-bottleneck
jobs. In this section, the emphasis is focused on the impact
of the presence of the bottleneck on the performance of both
bottleneck jobs and non-bottleneck jobs.

Statistics on both types of jobs were separately
collected. ANOVA results for both types of jobs were also
compared. In these analysis, the main factor of prevalence
was ignored. The results for the 100% prevalence were not
used to make comparisons under the same environment, Since
at this level, all jobs are bottleneck jobs.

Appendix L and Appendix M present the ANOVA results for
bottleneck jobs and non-bottleneck jobs, respectively, on

six major performance criteria.

5.4.1 Work-in-Process

As shown in Table L-l and M-1, all main effects were
significant at the .05 level for both types of jobs.
However, more extensive and diverse higher interaction
effects were present among the factors for bottleneck jobs.
The behavior of both types of jobs under each main factor is
compared and examined below.

Figure 5-33 shows average work-in-process for
bottleneck and non-bottleneck jobs for each type of order
review/release mechanisms. It is interesting to note the

performance of the AR mechanism and the BR mechanism and to

154

compare these two mechanisms to the NOR mechanism.

The

bottleneck jobs
non-bottleneck jobs.

exhibited relatively

BR

mechanism effective

was in

The AR mechanism, on

consistent performance

both bottleneck jobs and non-bottleneck jobs.

The SPT

types of

Figure 5-34)

effect of

the

rule demonstrated

jobs relative to the other dispatching rules.

There was a significant difference between the

FCFS rule on the performance

jobs as compared to non-bottleneck jobs.

For both

a significant

Wot}: —in - P moose

 

 

 

 

bottleneck and non-bottleneck jobs,
difference in performance among
Order Rte=..e'iew,.x"R elease Men: han ism
(Wak- in —pro=o-'l
2347\1
210 I "J’s-q.
2m 1 if”...
190 .. ”tr".
n
is: I .
110 .1 -’
1 #3 I “'3"
1 $3 I
140 I
1:53 - ..-.».__~
d. f K.-
120 I ‘f- "' ET
‘~~‘.~..-. ¥'-_~_.-
‘ ‘0 - ....‘.-*--v-d-_d- .
“n I . , a
NOR ANY ML OFT BM.
3 Bank-mu «:9: I -‘.:n—i3artlcraa:v- Jabs

ORDER REVIEW/RELEASE MAIN EFFECT
(WORK—IN-PROCESS: BN VS. NBN)

FIGURE 5-33

dealing

at the slight expense of the performance of
the other hand,

in controlling

strong performance for both

of bottleneck

there was

bottleneck

155

Dis patching Rule

(Wak- in —PH:=.8 ‘2

 

zoo -l
1m I "‘3‘. “.3” 4...

I” I! "'-._ .I'd

Work-h -P room

d
110 I “a.

1 m -‘ .\’--. 3"", ‘4' . .4. ’4'.

 

 

 

SOPN

3
3
at <'

D Bunion-=1: Jab: + f-Ior.-aamcr~ck Jab:

DISPATCHING RULE MAIN EFFECT
(WORK-IN—PROCESS: BN VS. NBN)

FIGURE 5-34

locations. For both types of jobs, the lowest level of work-
in-process was produced when the bottleneck was located in
the front. (see Figure 5-36) These results indicate that the
front bottleneck produce the lowest level of work-in-process

regardless of the type of jobs in the bottleneck job shop.

5.4.2 Mean Flow Time in the Shop

Mean flow time of bottleneck jobs was considerably
reduced by means of the BR mechanism whereas that of non—
bottleneck jobs was slightly increased. (see Figure 5-36)
This result is consistent with the performance of work-in-
process, indicating that the- BR mechanism provided

relatively good performance in lowering lead time and

Wc-fl:—i1—Pmoooo

Fk-w Time

156

Bc-ttl e n e c k Location
(Wick-in ~9m.)

 

240
2.131 '
zma /
2104 '
zoo-i /
1904 /"
'm'l /'/

17OI I/

1QI
1”...

140 "/‘l
..y
1m-l +_

1 m 1
From 8:61 Min-d

 

 

 

8 ”flu-hock Job: I Nan- ”ton-ck Jabs

BOTTLENECK LOCATION MAIN EFFECT
(WORK-IN—PROCESS: BN VS. NBN)

FIGURE 5-35

Or d e r R e ~ i e w R e. l e as e M e c l"! a n l 3 n'.
(Moor. Flew.- Tim in the Shaw

1 so F ~l
1m "l '1‘,” .11
1 70 I ‘ . "'
1 w I
150 .1 U" Al
1 do - , ,x"
1 3:1 - ...o”
1 20 I
' '0 - ,r/’\
100 - ,I".”

90:

 

 

m I I 1
non am am. arr an.

 

D Milan-:1; Jab: + Non- Bunion-ck Jabs

ORDER REVIEW/RELEASE MAIN EFFECT

(MEAN FLOW TIME IN THE SHOP: BN VS. NBN)

FIGURE 5-36

157
work-in-process for bottleneck jobs. This improvement,
however, was accompanied by the deterioration of the
performance of non-bottleneck jobs.

It was apparent from Figure 5—37 that the SPT rule
demonstrated relatively good performance in managing both
bottleneck and non-bottleneck jobs. The FCFS rule, on the
other hand, was ineffective in managing either type of job.

Bottleneck jobs had the highest mean flow time when the
bottleneck was located at the mixed whereas non—bottleneck
jobs had the highest when faced by the exit bottleneck
location. (see Figure 5—38) These results indicated that the
performance of each type of jobs in the bottleneck job shop
was significantly affected by the type of the bottleneck
locations.

As contrasted to the performance of work-in-process,
the behavior of non-bottleneck jobs, rather than bottleneck
jobs, was considerably influenced by the presence of the
bottleneck work center. (see Table L-2 and M-2) The more
higher significant interactions present for the performance
of mean flow time in the shop, when compared to that for
work-in-process indicated this behavior for the non-

bottleneck jobs.

5.4.3 Variance of Flow Time in the Shop

The main effect due to bottleneck location was not
significant when bottleneck jobs were examined only. (see
Table K-3) However, it was found to be significant under

non-bottleneck jobs, indicating that the performance of only

Moan F10.» Tune

Tuna

“49'3" F'OW‘

158

Dispatching Rule
_ - .Moen Haw Tin-Din "‘3‘:
.11.: i
n04“
1904 ' .

1‘70
mo
1:0
140
1.3:

1,0 .\'. "I". ,a"...

103‘ l of!"

I.
I"

3
\\

70 1
mm arr

D Milan-ck Jabs + Nun- Batter-=1: Jabs

DISPATCHING RULE MAIN EFFECT

 

SOPN

(MEAN FLOW TIME IN THE SHOP: BN VS. NBN)

FIGURE 5-37

Eattl e n e c. k: Location

(Moan How Time in tho Shae)

 

 

 

 

 

130
”pl ff/f/,n
loo—l ,..-/
.0 :\ ,,,,,,,
1.10 .1
1.33 I
129 .
1 1a -
mni___——--'_'_flfl-;f_
mm... 2;. min-a
a summer. is... + 1... .- Ball-(longs); 1s...
BOTTLENECK LOCATION MAIN EFFECT
(MEAN FLOW TIME IN THE SHOP: BN VS. NBN)

FIGURE 5-38

159
non-bottleneck jobs was influenced by the type of bottleneck
location. (see Table M-3)

Figure 5-39 showed that the BRT mechanism reduced the
variance of flow time for bottleneck jobs to a level close
to that of non-bottleneck jobs. The BRT mechanism
significantly improved the performance of bottleneck jobs
with respect to both the mean flow time and the variance of
flow time as well.

The bottleneck work center appeared to impose severe
problems on the performance of the FCFS rule in controlling
bottleneck jobs. (see Figure 5-40) This result indicates
that random selection of jobs for process next tends to
considerably increase variance of flow time under the

bottleneck job shop.

5.4.4 Mean Tardiness

The use of the BRT mechanism caused mean tardiness to
deteriorate for both bottleneck jobs and non-bottleneck
jobs. (see Figure 5-41) Specifically, rapidly deteriorating
performance of the non-bottleneck jobs largely contributed
to the overall poor performance of the BRT mechanism. The
ART mechanism, by contrast, provided almost equivalent
performance as the NOR mechanism for bottleneck jobs.
However, the mean tardiness of non-bottleneck jobs, when
compared to the NOR mechanism, significantly increased.

The performance of both bottleneck jobs and non—
bottleneck jobs was equally influenced by the type of the

bottleneck location. (see Figure 5—42) The exit location

160

Order R'eview,.r’Releose Mechanism

2“ (Mariana a! Flow The in the Shqafil

m ‘7""\

230-1

 

2G: CI
130 -t "...... ,2" \u
1 Q J \g' ," x
140 - ‘
1 m 4 .
1 OD -

Var of Flow 1 mo
(mmi

 

so . "~65 \
so - \
‘0 u
so 4 A

 

'3 F ‘ I ‘.
NO" MW ML BRT

 

D Bunion-cl Jab: + Nan- ”my. Jess

ORDER REVIEW/RELEASE MAIN EFFECT
(VARIANCE OF FLOW TIME IN THE SHOP: BN VS. NBN)

FIGURE 5-39

Dis pot-thing Rule

l'a-‘variana a! new Tim. in the Shaw

.320 .1
.300 d
no -+ ,.
zen J ‘-
240 -4
2m -4
:00 -I
1 a: q
1 a
mo 1
120 d
1m d
m «I
so -1
do .
20 1K i
I) I
MP5 SPT SOPN

5m.

(111-3:an

Var of Flow 1'

 

 

 

D ati-neck Jabs + Nan— Button-tn Jabs

DISPATCHING RULE MAIN EFFECT
(VARIANCE OF FLOW TIME IN THE SHOP: BN VS. NBN)

FIGURE 5-40

than Tardiness

Moan Tard'nooa

161

‘33-”"31' '3 r Fife i e w F: e l e. o a: e M a h 2:: n I s. m

(Moor. Tar-aimns:

 

 

 

 

 

 

 

 

1 ED
‘20 4 2 -. ,
‘ 10 q .'.' '3 "a... ‘ . .,
93 q ., If... '._-.\'. ...
m A? I I \ll"\. II
70 q f "K
a -‘ \\_
\.
93 " '1
40 - ,-"'~~... I
so - “x.
i \ i.I
3° ‘ x" f \‘w”
10 ./
o ‘1 fi 1
NOR ART ML BRT an.
O Mink Jabs + Nah- Hflonuck Jcbs
ORDER REVIEW/RELEASE MAIN EFFECT
(MEAN TARDINESS: BN VS. NBN)
FIGURE 5-41
Bottle neck Lo c: otion
[Moan Twims]
1 10
1"?”
1 CO 1 f",
/'/
33 -1 //."
/
70 .. \V
a: J
53 -1
no ..
D 1
M 82"! “and
a Mimi-ck Jeh- + Run-W Jabs

BOTTLENECK LOCATION MAIN EFFECT
(MEAN TARDINESS: BN VS. NBN)

FIGURE 5-42

162
produced the lowest mean tardiness and the mixed location

produced the highest under both types of jobs.

5.4.5 Variance of Tardiness

Like the performance of variance of flow time in the
shop, the variance of tardiness for bottleneck jobs was not
influenced by the type of bottleneck location. (see Table L-
5) These results imply that the type of bottleneck location
makes virtually no impact on the performance of bottleneck
jobs for variance-related performance measures. The type of
bottleneck location, however, did significantly affect the
performance of non-bottleneck jobs. (see Table M-5)

Although mean tardiness deteriorated considerably under
the BRT mechanism, associated variance was greatly reduced.

(see Figure 5-43) This result indicated that the BRT

0rd e r Pavia w R e I e as e M e c ho n 73 m
2‘0 (Variance cf Twins]

220;
no: -« 3"...“
1m -1
1m .
1‘0 d

1m!

(Tho-Joanie)

1004

‘»‘o r. of To rdineao

aoJ
bit-1

‘04

 

it. .1 cf“.

1 a

 

'- , 1 -
NOW is!" ARL BWT BIL
D hit-noel. Jan: 4 N: n- Cataract. Jae

ORDER REVIEW/RELEASE MAIN EFFECT
(VARIANCE OF TARDINESS: BN VS. NBN)

FIGURE 5-43

163
mechanism was relatively effective in lowering variance—

related performance measures.

5.4.6 Percent of Jobs Tardy

There were no significant interaction effects for
bottleneck jobs as compared to non—bottleneck jobs. (see
Table K-6 and L-6)

A similar result was observed between mean tardiness
and the percent of jobs tardy under bottleneck jobs. (see
Figure 5-44) From both Figure 5-41 and 5-44, the BRT
mechanism did really deteriorate the performance of both
non-bottleneck jobs and bottleneck jobs. These results also
suggest that focusing scheduling on bottleneck work center
status greatly deteriorates the performance of both non-

bottleneck jobs and bottleneck jobs in terms of mean

Order Rev“?Wa/Releose Mechanism
Iii-ram at m. tam)

 

 

Percent of Jet-a Yard;-

 

 

1 '- .
NOR ART ML BRT BR.
0 Wk Jab- + Man- MM 45:

ORDER REVIEW/RELEASE MAIN EFFECT
(PERCENT OF JOBS TARDY: BN VS. NBN)

FIGURE 5-44

164
tardiness and percent of jobs tardy.

The SOPN rule had a lower percentage of jobs tardy than
the FCFS rule for non-bottleneck jobs whereas it had higher
percentage tardy for bottleneck jobs. The overall poor
performance of the SOPN rule, when compared to the FCFS

rule, involved primarily bottleneck jobs.

5.5 Summary

In this chapter, the appropriateness of the ANOVA model
assumptions was examined mainly through a Chi-square and
Cochran's test. Based on the original data for percentage
of jobs tardy and transformed data for the other dependent
variables, the experimental results of the study were
analyzed using ANOVA. Then, the experimental results were
examined according to bottleneck and non-bottleneck jobs.

In the next chapter, the major findings of the results
will be summarized and managerial implications of the
results discussed. Suggestions of additional future research
areas relevant to this and other related studies will also

be addressed.

CHAPTER 6

SUMMARY. MANAGERIAL IMPLICATIONS,
AND FUTURE RESEARCH

6.1 Introduction

This research study was concerned with the management
of a bottleneck job shop characterized by location and
prevalence of the bottleneck. In this study, two fundamental
control procedures (order review/release mechanisms and
dispatching rules) were examined as methods of controlling
high workload for the bottleneck work center. This chapter
begins by summarizing major findings of the experiment in
section 2. The results of this study are summarized by
answering the research questions posed in Chapter one.
Section 3 identifies and addresses several important
managerial implications discovered in the study. Finally, in
section 4, further research areas relevant to this study are

outlined.

6.2 Summary of the Major Findings
The following are the major research questions
addressed by this study:
1. What are the major characteristics of a bottleneck

which should be considered when studying its impact
on the operation of the shop floor?

165

166

2. Which control procedures (dispatching rules or order
review/release mechanisms) have the greater impact
on bottleneck work centers (and under what
conditions)?

3. Can usage of information only about workload for
bottleneck work centers improve significantly shop
performance?

4. In a bottleneck job shop, where there is a mixture

of bottleneck and non-bottleneck jobs, how does the
presence of a bottleneck work center influence these

two types of jobs?

5. How do such bottleneck characteristics as prevalence
and the location of the bottleneck affect shop floor
operations and the performance of dispatching rules
and order review/release mechanisms?'

6. Can we identify any general guidelines which can be
used when dealing with a bottleneck job shop?

The focus of the summary of the major findings of this
research study will be placed on these six major research

questions.

6.2.1 Research Question One

The first research question intended to identify major
factors involved when managers and researchers are studying
the problems created by a bottleneck work center. This
question was raised because of the lack of detailed
knowledge surrounding the bottlenecks combined with their
potential importance. A framework for a bottleneck job shop
was first constructed. This framework was based partly on a
review of the literature concerning bottlenecks and partly
on the elaborate investigation of a bottleneck job shop, as
summarized in Chapter two.

These efforts resulted in four major factors which must

be considered when studying bottlenecks.

167

The first factor was the cause of a bottleneck:
systematic or random. This was a very important distinction
for scheduling control purposes. The focus of this study was
on the systematic bottleneck because it is the systematic
bottleneck which persistently exists and limits the total
output of the system over the long run.

The second factor was the status of a bottleneck:
stationary or floating. When the same work center
consistently acts as the bottleneck, it is a stationary
bottleneck. This study examined the impacts of one
stationary bottleneck on shop performance.

The third factor was the location of a bottleneck work
center in the job routing: front, exit and mixed. The
results of this study indicated that the bottleneck location
significantly affect the performance of the shop.

The final factor was the prevalence of a bottleneck:
100% and 50%. The experimental results of this study also
indicated that the shop performance was significantly
influenced by the level of prevalence.

The present research study was guided primarily by this
framework. Specifically, the major focus of this study was
on managing a job shop in which one systematic but
stationary bottleneck work center was present with three

bottleneck locations and two bottleneck prevalences.

6.2.2 Research Question Two
The second research question dealt with the evaluation

of the relative effectiveness of the two control procedures

168
in managing the bottleneck job shop. All system performance
measures were found to be significantly affected by both
types of control procedures. The experimental results of
this study strongly suggest that the selection of
dispatching rules has a greater impact than that of order
review/release mechanisms under all situations considered.

Specifically, the performance of the SPT rule with

respect to work-in-process, mean flow time in the shop, mean
tardiness, and percent of jobs tardy is not very sensitive
to changes of the order review/release mechanism. Neither is
the performance of the SOPN rule with respect to the
variance of flow time and tardiness.

The selection of order review/release mechanism
therefore does not seem to provide significant difference in
system performance when used with a particular dispatching
rule. Rather, it appears to amplify the effect of that
particular dispatching rule.

As compared to dispatching rule, the poor performance
of order review/release mechanism in this research warrants
more investigation. The type of job arrival distribution
into the shop may partly contribute to this. In other words,
the lack of a planning system, which releases jobs to the
order review/release stage in a random fashion, tends to
nullify the purpose of order review/release mechanism. This
suggests that the use of order review/release mechanisms by
itself can not make up for poorly planned (i.e., erratic)

workload.

169
6.2.3 Research Question Three

The experiments performed in this research study
examined a wide range of information used in the releasing
mechanisms. This research question is particularly concerned
with the relative performance of the BR mechanisms which
utilize information only about workload for a bottleneck
work center.

The BRT mechanism provided a significant improvement
over the NOR mechanism when the bottleneck was located at
the exit with respect to the level of work-in-process. For
the mean flow time in the shop, the BRT mechanism performed
significantly better than the NOR mechanism when used with
the FCFS rule. The BRT mechanism, when compared to the ART
and the NOR mechanism, performed better or at least
similarly under all situations examined in terms of the
variance of flow time in the shop.

For the performance measures of mean tardiness and the
percent of jobs tardy, the BRT mechanism, as contrasted to
the NOR and the AR mechanisms, did cause both measures to
deteriorate significantly. .

Relative to other release mechanisms, the BR mechanism
tended to release fewer jobs at any one point into the shop.
Furthermore, the BR mechanisms most effectively controlled
the workload at the bottleneck work center. Although the use
of the BRT mechanism led to a practical improvement in both
the level of work-in-process and the lead time in the shop,

the mean flow time in the system under the BR mechanism was

170
the longest among order review/release mechanisms
considered. This result adversely affected the performance
in both mean tardiness and the number of jobs tardy.

These results strongly suggest that a tradeoff must be
weighed when the BR mechanism is applied to the management
of the bottleneck job shop. That is, the BRT mechanism
provides a slight improvement in the level of work-in-
process and mean and variance of lead time in the shop at
the expense of considerable degradation in both mean

tardiness and the number of jobs tardy.

6.2.4 Research Question Four

In this research study, jobs were divided into two
groups: bottleneck jobs and non-bottleneck jobs. This
research question therefore addresses the impact of the
bottleneck operation on the performance of both types of
jobs.

The results showed that work-in-process, mean flow
time, and the variance of flow time and tardiness for
bottleneck jobs can be controlled quite well by means of the
BR mechanism. The BR mechanism, on the other hand, led to a

significant degradation in mean tardiness and the percent of

jobs tardy for both bottleneck and, particularly, non-
bottleneck jobs. ‘

The SPT rule exhibited relatively good performance for
both bottleneck jobs and non-bottleneck jobs for all
situations considered. The FCFS rule, however, exhibited

rapidly deteriorating performance for bottleneck jobs.

171
The results suggest that the aggregate performance was
largely determined by the performance of bottleneck jobs
rather than non-bottleneck jobs due primarily to the

difference in magnitude.

6.2.5 Research Question Five

We are concerned with the impact of descriptive
characteristics of the bottleneck job shop on shop
performance and the interaction between these
characteristics and the two control procedures.

The result showed that shop performance was
significantly influenced by location. In terms of the level
of work-in-process, 'the highest level was observed for the
exit location. The mixed location, however, performed the
poorest for other performance measures. In general,
performance can be expected to improve when the bottleneck
location in the routing is fixed. That is, a bottleneck
which appears consistently at the beginning of ending of job
routings is easier to manage.

The result also indicates that better performance was
obtained when the bottleneck was located at the end, rather
than in the front. Under the front bottleneck, the input
flow to the work centers following the bottleneck work
center was restricted by the output rate of the bottleneck
work center. This tended to delay the flow of jobs through
the system slightly as compared to the shop in which the
bottleneck was at the exit.

The experimental results indicate that neither mean

172

tardiness nor the variance of tardiness was influenced by
prevalence. Other performance measures, however, were
slightly affected by prevalence. These results suggest that
the impact of prevalence on shop performance is not as
strong as location.

The results also indicate that the 100% prevalence
created more problems than the 50% prevalence in terms of
the level of work-in-process, mean flow time in the shop,
the variance of flow time in the shop, and the variance of
tardiness. Higher mean tardiness and the number of jobs
tardy occurred when the shop operated at 50% prevalence.
This can be attributable to the different causes of
bottleneck: long operation time at the bottleneck work
center (50% prevalence) and routing (100% prevalence).

There existed significant interaction effects between
two control procedures and two bottleneck characteristics
under some performance measures.

The performance of order review/release mechanisms was
significantly influenced by these two characteristics of a
bottleneck. For example, order review/release mechanisms
made virtually no difference in minimizing work-in—process
when the bottleneck was located in the front. Location also
influenced the performance of dispatching rule in terms of
mean flow time in the shop. When a front bottleneck was
present, there was no significant difference between the
SOPN and the FCFS rule. The selection rule used for the

backlog file may contribute to these results. When the

173
bottleneck located at the front, there was virtually little
difference between the FCFS and the SOPN rule if the SLACK
rule was used to select jobs in the backlog file.

It is also interesting to note that the performance of
the BR mechanism greatly deteriorated when 50% prevalence
was imposed on the shop. This was due to long processing
times of bottleneck jobs at the bottleneck work center. This
made the BR mechanism release relatively smaller numbers of
jobs for the 50% prevalence than for the 100% prevalence.
This suggests that the use of the BR mechanism under the 50%
prevalence is not worthwhile when the minimization of mean
tardiness and percent of jobs tardy are the major

objectives.

6.2.6 Research Question Six

The SPT rule outperformed both the SOPN and the FCFS
rule with respect to the level of work-in-process, mean flow
time in the shop, mean tardiness, and the percent of jobs
tardy. Surprisingly, the SPT rule also performed the best in
minimizing mean tardiness and the number of jobs tardy in
the bottleneck job shop in which the shop capacity
utilization is operating at moderate.

The results suggest that the SPT rule is desirable in
the bottleneck job shop even at moderate overall shop load
when minimizing mean tardiness and the percent of jobs tardy
as well.

As expected, the SOPN rule exhibits best performance in

reducing the variance-related measures. It is interesting to

174
note, however, that the FCFS rule performs as well as the
SOPN rule when jobs are tightly released into the shop. This

confirms the observations and findings reported by Nicholson

and Pullen (1972).

6.3 Managerial Implications

While a great deal of research attention has been
devoted to the balanced job shop, very little work has
examined a job shop which is unbalanced. The focus of this
research study was to manage this unbalanced shop by means
of two control procedures. The results of this research
study provide some managerial relevance.

First, shop performance is greatly influenced by both
location and prevalence of the bottleneck. Managers must
first identify these two environmental factors before
implementing any control procedures. Furthermore, managers
must also realize that the management of bottleneck job shop

becomes further complicated due to the presence of

interactions between control procedures and two
characteristics of the bottleneck.
Second, the use of the SPT rule is highly recommended

with respect to any performance measures in managing the

bottleneck job shop. The SPT rule excels not only in
minimizing lead time and work-in-process but also in
reducing mean tardiness and the percent of jobs tardy.
Third, the use of the BR mechanism, which utilizes
information about the bottleneck work center, must be

carefully examined by weighing its advantages against its

175
disadvantages. Specifically, the BRT mechanism provides an
improvement under some situations in reducing lead time,
work-in-process, and the variance of lead time and
tardiness. The BRT mechanism, however, results in
substantial degradation in mean tardiness and the number of
jobs tardy.

Fourth, both researchers and practicing managers must
be aware of the fact that the presence of the bottleneck can
significantly affect not only bottleneck jobs but also non-
bottleneck jobs. These results imply that the progress of
not only bottleneck jobs but also non-bottleneck jobs should
be monitored and controlled when managing bottlenecks.

Fifth, when a linkage between order review/release
stage and planning stage is not in place, the use of an
order review/release mechanism does not have as much impact

on the shop as a dispatching rule does.

6.4 Future Research

The experimental results of this research study provide
a basis for future research into the operation of bottleneck
job shops. Several suggestions for future research on
bottleneck job shop are provided below.

First, considering the relatively poor performance of
order review/release mechanisms with respect to mean
tardiness and the percent of jobs tardy in the bottleneck
job shop, alternative order review/release mechanisms may be
needed. Alternatives may employ different mechanics in terms

of what to release and when to release. In this study, jobs

176
in the backlog file were prioritized according to the
dynamic SLACK rule every week. A mechanism more sensitive to
the status of shop and bottleneck work center may improve
the performance in delivery—related measurements.

One of alternatives is to develop a time-phased order
review/release mechanism. This mechanism realizes the finite
capacity of a bottleneck work center in a given time period.
Therefore, this mechanism releases jobs in the backlog file
in accordance with the available capacity of the bottleneck
work center by segmenting the capacity of the bottleneck
work center by time. This may provide a significant
improvement over the order review/release mechanisms
examined in this study.

Second, more research is needed to broaden this study
to incorporate it with the planning system. That is,
bottlenecks must be managed within the closed-loop system.
Within the closed system, release of jobs from the planning
system to the order review/release stage is controlled in
response to the status of a bottleneck work center and a
shop as well. Nothing has been done about managing the flow
of orders from the planning system to the order
review/release pool. This may provide significant impact on
the performance of order review/release mechanism.

Third, additional research is needed to manage the
bottleneck job shop under varying levels of capacity
utilization. For example, this study examined a job shop

operating under 82 percent capacity utilization. What

177
happens to the general conclusions of this study as capacity
utilizations increase or decrease is not known.

Finally, only a single fixed bottleneck was examined
under this study. It is natural to expand this model to
better represent reality in which multiple floating
bottlenecks are present. The introduction of more complex
models makes the bottleneck job shop research more rich and

viable.

6.5 Summary
The major findings of the experimental results of this
study were discussed. Based on these major findings, several
important managerial implications of this study were also
presented. More research areas relevant a bottleneck job

shop were suggested for future work.

APPENDICES

178

Appendix A and Appendix B presents the flowchart for
the aggregate release mechanism and the bottleneck release
mechanism, respectively. Variables used in Appendix A and
Appendix B are described below.

Variable Description

IMAXI Number of jobs in the backlog file
XLAGG Predetermined workload limit in the shop

minus current workload in the shop

PLAGG Predetermined workload limit in the shop
minus planned workload in the shop

XLABN Predetermined workload limit for the
bottleneck work center minus existing
workload for the bottleneck work center

PLABN Predetermined workload limit for the
bottleneck work center minus planned
workload for the bottleneck work center

179

 

CSUBROUTINE KR)

Schedule the Next Release Time

 

 

 

 

Is No

IMAXI , % Return )
'>0 7

Yes

 

 

[Calculate XLAGG]

 

 

XLAGG X Return )

«>2

[Initialize PLAGG]

 

Remove the Job with the Top

 

 

 

_ Priority from the Backlog File

Increase PLAGG by the Total
Processing Time of the Order

Release the Job to the Floor

PLAGG {fl Return)
LAG

 

 

 

 

 

 

 

 

 

*3

 

Reduce IMAXI by I]

MAXI ){Return)

FLOWCHART OF THE AGGREGATE RELEASE MECHANISM

No

52

0

FIGURE A-l

 

180
(SUBROUTINE BR)

 

 

 

Schedule the Next Release Time]

 

Is No
)0
Yes

 

 

[Calculate XLABN

 

5 Yes
XLABN

‘0 - 7%. Return )

No

 

[Initialize PLAEE]

- L

.______e[Remove the Job with the Highest
Priority from the Backlog File

‘ elease the o
to the Floor I

 

 

 

 

 

 

[Release the Job to the Floori

Is Yes

LAB

 

No

 

 

 

[Reduce IMAXI by {k

 

 

am
No J//IE\\\ Yes
IMAXI .m
\0/

FLOWCHART OF THE BOTTLENECK RELEASE MECHANISM
FIGURE B-l

TABLE C-l

ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: ORIGINAL MODEL)

0 F

V A R I A N C E o a a o o o o o o o o o a o o a o o

o a o o o o a o o o o o o o o a o 0 o o A N A L V S'I-S

FOR HIP USINI SEQUENIIAL SUNS 0F SQUARES

SIGNIFICANCE

OF

IESIS

or F

MEAN SOUAIC

SUN 0F SQUARES

SOURCF 0F VARIAIION

1531

96669:: C‘OFQU‘BO'AC
C- 9 nece—
N OnflOO
nwneo
OO¢°¢
OO‘IOO

.000“
0‘5

3.755935-0

romcoho—creoennb
uWNDO'NNFMNtcaNHDOdk-
«d—umnatnm—uwupmhwwo
o—nmwmonihHuONCO
ahwmm—umhnwcuanntmh-
00.1D00001IOOOOIIOO
oil: 8 GI" Chudflcol '-
Q-IU'IOF can
0 on

hoflmuhwtnhflkummnnwfi
naeooawmonuonuooa
nunccnco¢¢onmoo~o
NedNNQNNO—Ciflcconc
ennuconweooooocun
0.000000000000000
CNOUOnC‘ONFCO’OnnG
anwn—nmnonewhnchh
NHOOONGOOOOOOOCN”
“duhOF—HOOONOOWM
"COW, MOCOGOON O
fldOHO I?“
O“

“O'NNdOCOONNUOCCC
8 d

hohooaouooauuocoo‘

QM’MONQOOWOQ
DNNHQHCI Q '05 «av-condo
«unmooowonamomn
”MOQQU‘OOMNONNO"

......OOOCOCOOOOC
FQOOOHOOOBOc-Odhnaa
UU‘OCON'H‘OVDWOQFNQGN

hflFOODOh onhn n
O. :0 N

«a

ZZZJEI’J
CU O

U
~dd>>>~>
:;;==ab¢
C
:22u3uzzzur
Cb‘anUCCU
buddnnbh—Jb
(pt ddb d
BC)>>>O.Q¢>O.
WUVCEGVMUSV
~CN nun-Inf I-
d ZZZCdAISZQCJIC
( UCU UUC U
2» b~4>>>hh—>>>b>
Cw Cbcexchhzzz<z
~¢ c<> 31¢ c
e
L
K

u_01\

26.0001R

AJJHSIED R:SQUAR£n =

R-SIUAREU

- - - - - - - - - - - - - - - - - - - - - - - -- - - --- - - - - - - - - - ‘ - - - - - -
. .- .

TABLE C—2

ANALYSIS OF VARIANCE
(MEAN FLOW TIME IN THE SHOP: ORIGINAL MODEL)

I A R l A I C t o o o o o o o o o o o o o o o o o a o

F

o o a o a a o o o o o o o o o o o o o o A N A L V S I IV

I'SIS 0F SIGNIFICANCE FOR NEANFLSP USING SEOUENIIAL SUNS UF SIUAIES

3". or F

F

0F

;

SUN 0' SOUAIES

CF VANIAIION

SOUR CI.

NEAN SQUARE.

1532

...:rnnoom O

”GOMMOU
:: WHO-MID.
C O “DD-“CID”
w “0091!”.
.. 0000000000

 

0.00.00.00.0000.
.-Dm
Gag-nun

mommoouuoucc
c . on o-
.

VALEN
0 UV PREVALEN

IION
ALEN
AL N
P E
II N

(,,b‘
UNI-ICU

01¢ O
zz:.s.;az.a
DU“ 0
—d-JP>)->
padaaao—a

,, C

C
zazuuuzzzuz
UOBOCKUUOQU

0 C3Pfibuafiha

”Dunedin-muov.

c-uc' ~u-o -
-l :zzoaaziuzocazc.
< UOu- 003 U
:0- bonds-tnu-o-o-n-r-t-o-u-
3|... Ch«.&.’.;aq—.:.::<:.

~00 {5‘ 3
”LZmUWCCWWUGSZWK
tuck—Occult: ~~Da¢¢=a
0. 3( can:

21.16356

'zezzzazzzz

«.38

-naust£n n3sounnto

" -SbUAR EC

.-.-nooacnnnccnoc‘--.------.OODOOOODICCOOO

SIG. OF E

F

ORIGINAL MODEL)
“can sauna:

V A O l A N C E o o o o o o o o o o o a o o o a o o
”F

O f
SUNS 0F SOUIPES

TABLE C-3

A L Y S I S

ANALYSIS OF VARIANCE

(VARIANCE OF FLOW TIME IN THE SHOP

SUP 0F SOUASES

. o A N

0
[OR VIQFLSF USING SEQUINIIAL

'
C
6

'luhlfICANC
Uf vs’:5110'

rr

I'SIS
UR':

"'

1533

CF“.OOU’OW 9ND"
. FMWOOflv-WNCW
O numnmmnhoau

o 0069000000090
3 n
6 O
F H
n G
o 9
C C

hvdwiouufihcwuh¢oumuu
ocoonmo-ao—ounuoe
essence-nonhuman:
nohoownemc-nmmn
DOCQOCGCMNOMOM
000.000.000.000.
FOG” V..-
O

W86666696
66666 666666666666
99999990999009990
UUUUUUUI-uUUI-IUUUUBI
ounnmmao vase—mo on
count» woo-numewooo
OOOSWOMFCO‘HO
optocwnocmflwwauanmn
lmautdwmrova'wmumvrwun
0.01.09.01D00091D900
”WWOMu-nou

”CCINWC‘ ”O'NNONCoQo
0 ' '~ 0.0
O

V C'. “Cu-0". Waltz-it. COO-"5'0? '9

vvwv v v r—v—v fifi ~— vv—vr‘ ‘

 

Ho. lOUOOUOQOC‘Dflw'UU
99900990909999099
muluuwumuumu hou'bduhug.
wowauanxwma.“vm.wc
«sane-mac 0‘07)”. 0.0019.
U) .on.--Kdo 0.0 ... \CCO-c-ohaf
'cvWCOfluNfi'O-NUJIFN'I'IOW‘U
{.‘wflfllflQU-mndflo at!”
0000.90.09.900090
Pl.0¢|w-Wl—'lafil.ui(truths.

PPLVALIH

LLI.

auto 2
‘02.:4-“ 3‘
C'koAO U
"Juli-F’D-l-
—QQ;.L.' P'—
u): M

:32UH.J=12U:
BM)- '3.‘.J'UUD' 3L!
bhdd“__-‘J—
“h‘ -.¢— 0
.g C 3”P.L.A Q ..L
s’lUbI‘ :3 Ivououtb

'0 J I In... ', .9
.1 77.23.13 2:33:42:
- 602' 94:. L)
De— buApa-ppban-po-a-
3... ’~‘--; - 0'!“ --; 6"—

0-01‘. “> -.. ‘3 ..

$0.. WOO-11.0.3 £106.23: ”ck
en's 3 hu-La .LS.""'~ JO $17-0
1354.“. has 5.45....65 ‘2 I ; ..-

3098907

9'93 £33388”

n'

nu
9 0
Lu.

(III!
”.000
WP;
CI“
. 0
“Q

A-
al.‘

u"
33
'0...
--

Bifurzvr"

r!
‘0-
1h

-$PU5°
ILJU.I

‘

s

SIG. or

F

.‘ ... -..-
r-

Q.

g l n;] g‘. C [to 0.. o o.- o o o o a on. o a o o o
...---. .";.-_._-‘-'-‘... -

‘

“for

IESIS OF SIGNIFICANCE FOR MEANIAR USING SEOUEMIIAL SUFS‘OF SQUARES

0'
m-

TABLE C-4

ANALYSIS OF VARIANCE
(MEAN TARDINESS: ORIGINAL MODEL)

SUM OF SQUARES?

o o o a o o o o c a o o o o a o o 0 o 0:! U A L" Sill.

SOURCE OF VANIAIION

184

.maouom—cnnm B
m“ ODOOOOIIO

.069

O. I a FNOOOFCIOH

"no «canons
«pun. «30001....

E02135

luunamuwoo-nM~F&NMhC
«06666606660600.
omnmmmhnm
”UDQHONOthOQd—N
noun-CIKMB cumapqu)
000l!0.00l|.00l|.00
coo-communa-
Iu—h '-

.1-

o

IIOV‘VQS

I ' .

”mm—om
mmmwm
«ammoonuoofluo

MOM

or i~n¢nu 3001.:
3332333233

90'
mn

0001!.01I0001p0001D0. o.
omnmnowmnfiaowmm~nwmnn IND
dunnmnncnwurowwnowwmnn- cn~
nqumncuumnocvuummuumolnw
IMOOG'NvBFMmhm061nNFnȢM~

“MCWHNNON' N 0"

OCCUR an
N. n - "I‘D
2
U
.l
C
6
U
K
23
U
.16
‘3
6
zzzuu:
DUNK
- fi-l-Ja—
FCC
(666‘
unnuma
01¢ O
‘22d&&2d
In 6
"cl-I66”!-
racemes-z.
(6 C
ZZZUUUIZZUZ
UOUOCGUUOOU
(0.1 6 1|- C
n C 6 l- 6 bag 1 61
vuummmmumm
~03 c-u-cu a-o
.1 :zzzhaxzzztumazo
d UOMI UUO U 0"-

:ss .

RED
ISO R-SOUAREP ‘

:u-uundumnM-h—ou-h—m-.Jd
ahilflln‘SCWLC‘”-Cauh‘=1IH'

I-W) 3‘6 OIJ.‘ B D
WMWUUKKCWWUCKCWC 0°

UUA
S

HG¢~O¢¢¢U—~O¢¢c—a :—
K 19:66 66666-160966 oc-

9-3
AUJU

TABLE C-S

ANALYSIS OF VARIANCE
(VARIANCE OF TARDINESS: ORIGINAL MODEL)

0 F

VA II_AN1CE on no .0 on o. o. o. a. no

on o. a. o. a. on o. c. on 9. AN AL '3 I3
IESIS 0F SISAIFICANCE FOR VARIAN USING SEIUENYIAL SUNS 0F SQUARES

SIS. 0' F

MEAN SQUARE

CF

SUM OF SQUARES ‘

SOURCE OF VARIAIION

185

MCDONMMOOGU‘
. ..“Fd’fid’OFO
. NUS.“MO”.FUMC
. n"! I mucouonnno
. “WOGUIFWOU‘U‘

0 00.0000000000

I02979

W'Wmnmun
.00. omnmoonoo
w.” O Q
WMHQOOWOMFOI‘

QQMMGMMH
0000000000000...
6606 6 6

W”

anti—numn—unumnuuuumn
6.666666666666666
99999999099999999
UWUUMUWUMUUUU
ommnohwhmoouooo
nmouomuommmo
h“6¢6~6flh~flfl¢h¢fl
BhOOflQWWfiNOI-O6l-
66006 “666.00.“!
Ooocpoooocpooochoooo
InauuN—uuunumuw—num—ru-

“CM'NNOC.C.
H on on
.

noopoaanwncnwomnd
Geomoocnoomnnoooc
Oomacnknccucnnaaa
000.000.00.000...
oncuoonuu

REVALEN

EN
P

6:! 0
ZZZ-ILELZ-l
OMWJ 6
uddrrbflh
r-a ‘saDI-D

.63 <
:22 UNI-l: 22h):
UOUOICUUCOU

¢¢>>>>gqug

VIDA-ADC GUN” U 09) .

~J¢ CID—o.) an
d 12364;:3266416
‘2 06h' 000 U
Dh-Uumahrauun—raun-b
9.; ‘h§1&;¢¢—=::‘&
NU! L16 :33“ A
“MWUUCCBWWUCKKU‘AC
hCCWCZCKWCCKC—C
.' ‘SOJ-dh GOOSE-40°55;

3015062

.33 3

23821E$Sll

31332

ARSD :
IV fl-SOUAREO

U
S

p-n
ADJU

ORIGINAL MODEL)

V A l [~A N C E 0 0 0‘0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

O F

TABLE C-6
ANALYSIS OF VARIANCE

(PERCENT OF JOBS TARDY

186

SIO0 OF F
i

z
E
2
a
a
E
3

0000000000000000
ounhounuaaau
CC.

I

66~COQGOOuOQN660u
OfiuohvnocnvoF6N00
ONMthOnQOOflOO C
udhhnn66n6fl606666
N6066d6¢~06066~60
00000000000000000
Concuoonflhdn6NOOd
0nv¢o~a~nn~o0unuo
«oomoeouonnonu N
Danna a“

m. ,.

NEAN SOUARE

0

’ (

nocuauéovouuooooo
‘3 ' 0- 0-0
‘-

OF

r
O
- I
ODOQOOdooofifioflfllfl
mount-0090000001030"-
newncmcwocmmp
auwhmcoeneoun
nucuo-ouoonunwoun
00000000000000000
n¢N6n00666NquDOO
“NCO ONNO-‘I )CIIOQFFGOB
Cva-omnmoa can
NO fibWWO 00
fink. n
«—

SUN OF SQUARES 1'

LEN

150.2303

3289:3313!

.33'

3285?:23333'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A N A L V 3 I 3
IESYS OF SIGNIFICANCE FOR PERIAR USING SEQUENIIAL SUNS OF SQUARES

SOURCE OF VAPIAIION

VA
8' PREVALEN

(66 C
IZZUUUIIZU:
UOUOZCUUOOU
bu44QkPFN4P
Q“ 0‘00 6
6L6 6666;; 66¢
:0” man: mm UGO!

c Int-00.; 0-
22224523266486
UOL- UUO U

6h h~4>>>hbuppbbb
34 0—0-nx¢¢—= :11;
-m A66

“Q
mazmuuzzxmmuxxcgz

l0- OG~3¢13¢m3¢33
03c54nu6005400380

NO

0°

0‘
00

SOUAREC =
J SIEO R-SOUAREO =

0.
AD

187

TABLE D-l

SUMMARY TABLES FOR WORK—IN-PROCESS
(INVERSE MODEL: 10 OBSERVATIONS)

1002 Prevalence Order ReviegLRelease Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.

Front FCFS .0035 .0037 .0035 .0034 .0034 .0035
SPT .0068 .0069 .0068 .0066 .0068 .0068
SOPN .0038 .0040 .0039 .0038 .0038 .0039

Exit FCFS .0015 .0017 .0015 .0020 .0017 .0017
SPT .0051 .0051 .0050 .0056 .0052 .0052
SOPN .0019 .0021 .0021 .0031 .0023 .0022

Mixed FCFS .0014 .0018 .0015 .0019 .0017 .0017
SPT .0056 .0058 .0056 .0059 .0057 .0057
SOPN .0023 .0028 .0025 .0031 .0026 .0026

 

Avg. .0035 .0038 .0036 .0039 .0037 .0037

50% Prevalence Order Review/Release Mechanism
Loca. Diap. NOR ART . ARL ‘ BRT BRL Avg.

Front FCFS .0032 .0033 .0034 .0031 .0032 .0032
SPT .0073 .0075 .0074 .0066 .0069 .0071
SOPN .0041 .0040 .0042 .0035 .0038 .0039

Exit FCFS .0020 .0023 .0021 .0027 .0023 .0023
SPT .0057 .0059 .0057 .0063 .0060 .0059
SOPN .0026 .0028 .0027 .0035 .0032 .0030

Mixed FCFS .0018 .0023 .0019 .0025 .0020 .0021
SPT .0061 .0065 .0062 .0062 .0061 .0062
SOPN .0027 .0031 .0029 .0031 .0031 .0030

 

Avg. {6646* .0042 .0041 .0042 .0041 .0041

188

TABLE D-2

SUMMARY TABLES FOR MEAN FLOW TIME IN THE SHOP

(INVERSE MODEL:

1002 Prevalence

10 OBSERVATIONS)

Order Review/Release Mechanism

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS .0058 .0084 .0061 .0069 .0058 .0066
SPT .0118 .0114 .0110 .0116 .0112 .0114
SOPN .0068 .0077 .0068 .0077 .0067 .0071
Exit FCFS .0054 .0063 .0056 .0076 .0062 .0062
SPT .0116 .0115 .0113 .0120 .0115 .0116
SOPN .0068 .0069 .0067 .0077 .0072 .0071
Mixed FCFS .0051 .0067 .0051 .0067 .0057 .0058
SPT .0108 .0113 .0107 .0116 .0111 .0111
SOPN .0061 .0069 .0062 .0074 .0066 .0066
Avg. .0078’ .0086 .0077: .0088 .0080 .0082
502 Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS .0061 .0081 .0066 .0079 .0068 .0071
SPT .0119 .0121 .0116 .0118 .0116 .0118
SOPN .0073 .0078 .0074 .0079 .0077 .0076
Exit FCFS .0063 .0071 .0063 .0080 .0070 .0070
SPT .0122 .0121 .0119 .0121 .0120 .0121
SOPN .0081 .0080 .0079 .0073 .0080 .0079
Mixed FCFS .0056 .0071 .0057 .0077 .0066 .0066
SPT .0114 .0118 .0113 .0116 .0114 .0115
SOPN .0069 .0074 .0070 .0071 .0073 .0071
Avg. .0084 .0091 .0084 .0090 .0087 .0087

189

TABLE D-3

SUMMARY TABLES FOR VARIANCE OF FLOW TIME IN THE SHOP
10 OBSERVATIONS)

1002 Prevalence

(LOGARITHMIC MODEL:

Order Review/Release Mechanism

 

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 12.07 10.43 11.67 11.44 11.97 11.52
SPT 9.72 9.42 9.71 9.01 9.56 9.48
SOPN 9.76 8.88 9.52 9.18 9.60 9.39
Exit FCFS 12.20 11.70 12.03 10.95 11.66 11.71
SPT 9.78 9.75 9.80 9.13 9.65 9.62
SOPN 9.70 9.38 9.72 .8.52 9.26 9.32
Mixed FCFS 12.34 11.51 12.31 11.54 12.09 11.96
SPT 10.34 9.97 10.24 9.41 9.91 9.98
SOPN 9.87 9.10 9.69 9.04 9.49 9.44
Avg. 10.64 10.02 10.52 9.80 10.35 10.27
502 Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 12.00 10.93 11.83 10.89 11.73 11.48
SPT 9.91 9.56 9.85 8.95 9.41 9.54
SOPN 9.63 9.03 9.45 9.02 9.17 9.26
Exit FCFS 11.62 11.30 11.54 10.64 11.21 11.26
SPT 9.50 9.46 9.52 8.96 9.29 9.35
SOPN 9.52 9.33 9.56 8.84 9.09 9.27
Mixed FCFS 12.23 11.62 12.19 10.90 11.73 11.73
SPT 10.24 9.88 10.21 9.16 9.62 9.82
SOPN 9.83 9.37 9.75 9.12 9.25 9.46
Avg. 10.50 10.05 10.43 9.61 10.35‘ 10.13

190

TABLE D-4
SUMMARY TABLES FOR MEAN TARDINESS
(LOGARITHMIC MODEL: 10 OBSERVATIONS)

1002 Prevalence Order Review/Release Mechanism

 

 

 

 

 

 

Loca. Disp. NOR ART ARL BRT BRL Avg;
Front FCFS 4.44 4.75 4.37 4.17 4.44 4.44
SPT 1.82 2.13 2.19 2.33 2.18 2.13
SOPN 1.78 3.04 2.62 2.68 2.62 2.55
Exit FCFS 4.52 4.28 4.50 4.25 4.35 4.38
SPT 1.83 2.14 2.17 2.17 2.17 2.10
SOPN 1.22 2.55 2.39 3.81 2.44 2.48
Mixed FCFS 4.62 4.46 4.69 4.39 4.56 4.54
SPT 2.40 2.46 2.53 2.84 2.61 2.57
SOPN 2.03 3.22 2.73 3.38 2.81 2.83
Avg. 2.71* 3.23 3.13 3.34 3.13 3.11
502 Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 4.33 4.46 4.27 4.39 4.44 4.38
SPT 1.92 2.33 2.14 3.40 2.85 2.53
SOPN 1.59 3.16 2.47 3.68 2.98 2.78
Exit FCFS 4.18 4.05 4.25 4.68 4.14 4.26
SPT 1.44 1.77 1.77 2.33 1.94 1.85
SOPN 0.78 2.19 1.82 4.50 2.31 2.32
Mixed FCFS 4.46 4.41 4.50 4.85 4.54 4.55
SPT 2.14 2.41 2.31 3.39 2.94 2.64
SOPN 1.84 3.06 2.57 4.44 3.26 3.04
Avg. 2.52 3.09 2.90 3.96 3.27 3.15

1002 Prevalence

191

TABLE D-5

SUMMARY TABLES FOR VARIANCE OF TARDINESS
10 OBSERVATIONS)

(LOGARITHMIC MODEL:

Order Review/Release Mechanism

 

 

 

 

 

 

Loca. Disp, NOR ART ARL BRT BRL Avg;
Front FCFS 11.88 10.38 11.49 11.24 11.81 11.36
SPT 8.48 8.30 8.59 7.84 8.46 8.33
SOPN 5.90 7.22 6.81 6.89 6.81 6.72
Exit FCFS 11.95 11.42 11.79 10.67 11.40 11.44
SPT 8.36 8.50 8.54 7.71 8.36 8.29
SOPN 4.83 6.24 6.13 7.93 6.24 6.27
Mixed FCFS 12.09 11.33 12.09 11.32 11.89 11.75
SPT 9.53 9.11 9.37 8.61 9.04 9.13
SOPN 6.18 7.43 6.93 7.71 7.04 7.05
Avg. 8.80 8.88 9.08 8.88 9.01 8.93
50% Prevalence Order Review/Release Mechanism
Loca. Disp. NOR ART ARL BRT BRL Avg.
Front FCFS 11.78 10.79 11.64 10.81 11.59 11.32
SPT 8.73 8.51 8.74 8.55 8.56 8.62
SOPN 5.83 7.40 6.80 8.21 7.31 7.11
Exit FCFS 11.29 10.97 11.23 10.61 10.92 11.00
SPT 7.69 7.88 7.88 7.61 7.67 7.75
SOPN 4.63 6.30 5.93 8.70 6.30 6.37
Mixed FCFS 11.98 11.42 11.99 10.93 11.58 11.58
SPT 9.27 9.01 9.29 8.69 8.94 9.04
SOPN 6.27 7.49 7.13 8.86 7.62 7.47
Avg. 8.61 8.86 8.96 9.22 8.95

8.92

192

TABLE E-l

POWER OF THE F—TEST

 

 

Source of Variation WIP MFT VFT MTA VTA PTA
JOBSET >.99 >.99 >.99 >.99 >.99 >.99
ORR >.99 >.99 >.99 >.99 >.99 >.99
DISPATCHING >.99 >.99 >.99 >.99 >.99 >.99
LOCATION >.99 >.99 >.99 >.99 >.99 >.99
PREVALENCE >.99 >.99 >.86 >.OO >.00 >.OO
WHERE WIP : WORK-IN-PROCESS

MFT : MEAN FLOW TIME IN THE SHOP

VFT : VARIANCE OF FLOW TIME IN THE SHOP

MTA : MEAN TARDINESS

VTA VARIANCE OF TARDINESS

PTA : PERCENT OF JOBS TARDY

193

Appendix F presents a multiple comparison test for the
significant interaction effects for work-in-process using
the Duncan procedure at the .05 protection level. Each group
is compared schematically with other groups. Groups
underlined by a common line do not differ from each other;
groups not underlined by a common line do differ.

In addition, a probability associated with the F ratio
and a homogeneity of variance test (Cochran's C) are also
provided for each multiple comparison analysis.

Appendix G through K present the Duncan procedure for
mean flow time in the shop, variance of flow time in the
shop, mean tardiness, variance of tardiness, and percent of
jobs tardy, respectively.

b.

f.

194

APPENDIX F: DUNCAN PROCEDURE FOR WORK-IN-PROCESS

Dispatching Rule * Location * Prevalence

Dispatching Rule for the Front Location and the 1002
Prevalence
(F Prob. . .0000; Cochran's C a .4307, P - .126)

FCFS SOPN SPT

Dispatching Rule for the Exit Location and the 100%
Prevalence

(F Prob. - .0000; Cochran's C - .6537, P - .000)
FCFS SOPN SPT

Dispatching Rule for the Mixed Location and the 100%
Prevalence

(F Prob. - .0000; Cochran's C a .6506, P a .000)
FCFS SOPN SPT

. Dispatching Rule for the Front Location and the 50%

Prevalence
(F Prob. a .0000; Cochran's C a .4922, P = .008)

FCFS SOPN SPT

Dispatching Rule for the Exit Location and the 50%
Prevalence

(F Prob. a .0000; Cochran's C a .5796, P a .000)
FCFS SOPN SPT

Dispatching Rule for the Mixed Location and the 50%
Prevalence

(F Prob. - .OOOO; Cochran's C = .4998, P - .006)
FCFS SOPN SPT

Location for the FCFS Rule and the 1002 Prevalence
(F Prob. . .0000; Cochran's C - .5218, P - .002)

Mixed Exit Front

 

Location for the SPT Rule and the 1001 Prevalence
(F Prob. a .0000; Cochran's C a .5055, P a .004)

Exit Mixed Front

1.

Location
(F Prob.

Exit

 

. Location

(F Prob.
Mixed

Location
(F Prob.

Exit

Location
(F Prob.

Exit

195

for the SOPN Rule and the 100% Prevalence
- .0000; Cochran's C a .4524, P - .054)

Mixed Front

for the FCFS Rule and the 50% Prevalence
- .0000; Cochran's C . .3507, P - 1.000)

Exit Front

for the SPT Rule and the 50% Prevalence
- .0000; Cochran's C - .4041, P . .304)

Mixed Front

for the SOPN Rule and the 50% Prevalence
. .0000; Cochran's C - .3498, P - 1.000)

Mixed Front

II.

196
Order Review/Release Mechanism * Location

Order Review/Release Mechanism for the Front Location
(F Prob. - .7110; Cochran's C . .2050, P - 1.000)

BRT BRL NOR ARL ART

Order Review/Release Mechanism for the Exit Location
(F Prob. - .0492; Cochran's C - .2511, P - .812)

NOR ARL ART BRL BRT

 

Order Review/Release Mechanism for the Mixed Location
(F Prob. . .6292; Cochran's C . .2189 P . 1.000)

NOR ARL BRL ART BRT

Location for the NOR Mechanism

(F Prob. - .OOOO; Cochran's C a .3682, P .719)

Exit Mixed Front

. Location for the ART Mechanism

(F Prob. - .OOOO; Cochran's C a .3526, P a 1.000)

Exit Mixed Front

. Location for the ARL Mechanism

(F Prob. - .OOOO; Cochran's C s .3674, P a .732)

Exit Mixed Front

. Location for the BRT Mechanism

(F Prob. - .0442; Cochran's C . .3562, P a .951)

Exit Mixed Front

 

. Location for the BRL Mechanism

(F Prob. . .0004; Cochran's C a .3645, P .788)

Exit Mixed Front

197
APPENDIX G: DUNCAN PROCEDURE FOR MEAN FLOW TIME IN THE SHOP

I. Order Review/Release Mechanism * Dispatching Rule

Order Review/Release Mechanism for the FCFS Rule
(F Prob. - .OOOO; Cochran's C - .3403, P 2 .OOO)

NOR ARL BRL ART BRT

Order Review/Release Mechanism for the SPT Rule
(F Prob. - .3649; Cochran's C - .2680, P . .125)

ARL BRL NOR ART BRT

Order Review/Release Mechanism for the SOPN Rule
(F Prob. - .3978; Cochran's C - .2807, P . .054)

 

 

 

NOR ARL BRL ART BRT

d. Dispatching Rule for the NOR Mechanism
(F Prob. - .OOOO; Cochran's C a .4374, P s .065)
FCFS SOPN SPT

e. Dispatching Rule for the ART Mechanism
(F Prob. - .OOOO; Cochran's C - .5039, P = .002)
FCFS SOPN SPT

f. Dispatching Rule for the ARL Mechanism
(F Prob. . .OOOO; Cochran's C a .4470, P a .042)
FCFS SOPN SPT

g. Dispatching Rule for the BRT Mechanism
(F Prob. - .OOOO; Cochran's C a .4196, P a .138)
FCFS SOPN SPT

h. Dispatching Rule for the BRL Mechanism

(F Prob. - .OOOO; Cochran's C - .4603, P s .022)
FCFS SOPN SPT

II.

198

Order Review Release Mechanism * Location

Order Review/Release Mechanism for the Front Location
(F Prob. - .0479; Cochran's C . .2933, P - .022)

NOR ARL BRL BRT ART

 

Order Review/Release Mechanism for the Exit Location
(F Prob. . .5272; Cochran's C - .2508, P a .336)

ARL NOR BRL ART BRT

Order Review/Release Mechanism for the Mixed Location
(F Prob. - .1287; Cochran's C - .2556, P s .259)

NOR ARL BRL ART BRT

. Location for the NOR Mechanism

1.000)

(F Prob. a .3559; Cochran's C a .3429, P
Mixed Front Exit

Location for the ART Mechanism
(F Prob. . .0475; Cochran's C = .4183, P = .145)

Mixed Exit Front

Location for the ARL Mechanism

(F Prob. - .4137; Cochran's C a .3610, P .855)

Mixed Front Exit

. Location for the BRT Mechanism

(F Prob. . .5889; Cochran's C a .3510, P = 1.000)
Mixed Front Exit

Location for the BRL Mechanism
(F Prob. - .5397; Cochran's C a .3376, P = 1.000)

Mixed Front Exit

199

APPENDIX H: DUNCAN PROCEDURE FOR VARIANCE
OF FLOW TIME IN THE SHOP

I. Order Review/Release Mechanism * Dispatching Rule

a. Order Review/Release Mechanism for the FCFS Rule
(F Prob. - .OOOO; Cochran's C - .3207, P - .002)

BRT ART BRL ARL NOR

 

 

b. Order Review/Release Mechanism for the SPT Rule
(F Prob. - .OOOO; Cochran's C - .2957, P - .018)

BRT BRL ART ARL NOR

c. Order Review/Release Mechanism for the SOPN Rule
(F Prob. - .OOOO; Cochran's C - .3153, P - .004)

BRT ART BRL ARL NOR

d. Dispatching Rule for the NOR Mechanism

(F Prob. - .OOOO; Cochran's C - .4848, P .006)

SOPN SPT FCFS

e. Dispatching Rule for the ART Mechanism
(F Prob. - .OOOO; Cochran's C n .5395, P a .000)

SOPN PT FCFS

f. Dispatching Rule for the ARL Mechanism
(F Prob. . .OOOO; Cochran's C . .4961, P - .003)

SOPN SPT FCFS

g. Dispatching Rule for the BRT Mechanism
(F Prob. . .OOOO; Cochran's C . .4724, P a .011)

SOPN SPT FCFS

h. Dispatching Rule for the BRL Mechanism
(F Prob. - .OOOO; Cochran's C s .5432, P - .OOO)

SOPN PT FCFS

II.

200
Order Review Release Mechanism * Location
Order Review/Release Mechanism for the Front Location
(F Prob. - .0005; Cochran's C - .2690, P u .117)
ART BRT BRL ARL NOR

Order Review/Release Mechanism for the Exit Location
(F Prob. - .0006; Cochran's C - .2491, P - .368)

BRT BRL ART ARL NOR

Order Review/Release Mechanism for the Mixed Location
(F Prob. - .0004; Cochran's C - .2491, P - .366)

ART ART BRL ARL NOR

 

 

Location for the NOR Mechanism

 

 

 

 

(F Prob. . .2534; Cochran's C a .3613, P . 1.000)
Exit Front Mixed

Location for the ART Mechanism

(F Prob. - .0187; Cochran's C a .4156, P . .161)
Front Exit Mixed

Location for the ARL Mechanism

(F Prob. - .2033; Cochran's C a .3865, P a .434)
Front Exit Mixed

Location for the BRT Mechanism

(F Prob. - .1944; Cochran's C . .3754, P . .597)
Exit Front Mixed

Location for the BRL Mechanism

(F Prob. - .3791; Cochran's C - .3726, P . .642)

Exit Front Mixed

201

APPENDIX I: DUNCAN PROCEDURE FOR MEAN TARDINESS

Order Review/Release Mechanism * Dispatching Rule
Order Review/Release Mechanism for the FCFS Rule
(F Prob. - .9911; Cochran's C - .2807, P = .054)
ART BRL NOR ARL BRT

Order Review/Release Mechanism for the SPT Rule
(F Prob. - .0003; Cochran's C . .2959, P - .018)

NOR ARL ART BRL BRT

 

 

Order Review/Release Mechanism for the SOPN Rule
(F Prob. - .OOOO; Cochran's C a .3054, P a .009)

NOR ARL BRL ART BRT

 

Dispatching Rule for the NOR Mechanism
(F Prob. - .OOOO; Cochran's C - .7877, P = .000)

SOPN SPT FCFS

Dispatching Rule for the ART Mechanism

(F Prob. - .OOOO; Cochran's C = .7130, P = .000)
SPT SOPN FCFS

. Dispatching Rule for the ARL Mechanism
(F Prob. a .0000; Cochran's C s .7373, P = .000)

SPT SOPN FCFS

Dispatching Rule for the BRT Mechanism
(F Prob. - .OOOO; Cochran's C - .5742, P 2 .OOO)

SPT SOPN FCFS

Dispatching Rule for the BRL Mechanism

(F Prob. . .OOOO; Cochran's C - .6702, P .000)

SPT SOPN FCFS

 

II.

202

Order Review Release Mechanism * Prevalence

Order Review/Release Mechanism for the 100% Prevalence
(F Prob. - .0428; Cochran's C = .3184, P - .OOO)

NOR BRL ARL ART BRT

 

 

Order Review/Release Mechanism for the 502
(F Prob. - .OOOO; Cochran's C - .2884, P a

NOR BRL ART BRL BRT

 

 

Prevalence for the NOR Mechanism

(F Prob. - .4446; Cochran's C - .5165, P

100% 50%

Prevalence for the ART Mechanism

(F Prob. - .5597; Cochran's C - .5563,

100% 50%

Prevalence for the ARL Mechanism

(F Prob. s .2887; Cochran's C a .5365,

100% 50%

Prevalence for the BRT Mechanism

(F Prob. - .0034; Cochran's C = .5448,

100% 50%

Prevalence for the BRL Mechanism

(F Prob. . .5399; Cochran's C a .5680,

100% 50%

Prevalence
.006)

.757)

.492)

.398)

.198)

203

III. Location * Prevalence

Location for the 1002 Prevalence

(F Prob. - .1315; Cochran's C - .3828,

Exit Front Mixed

Location for the 50% Prevalence

(F Prob. - .0072; Cochran's C - .3658,

Exit Front Mixed

Prevalence for the Front Location

(F Prob. - .2879; Cochran's C - .5345,

100% 50%

 

Prevalence for the Exit Location

(F Prob. - .3656; Cochran's C s .5426,

100% 50%

Prevalence for the Mixed Location

(F Prob. - .6051; Cochran's C a .5856,

100% 50%

.182)

.455)

.400)

.299)

204

APPENDIX J: DUNCAN PROCEDURE FOR VARIANCE OF TARDINESS

I. Order Review/Release Mechanism * Dispatching Rule

f.

Order Review/Release Mechanism for the FCFS Rule
(F Prob. - .OOOO; Cochran's C - .3203, P a .002)

BRT ART BRL ARL NOR

Order Review/Release Mechanism for the SPT Rule
(F Prob. - .3949; Cochran's C - .2613, P - .187)

NOR ARL ART BRL BRT

Order Review/Release Mechanism for the SOPN Rule
(F Prob. - .OOOO; Cochran's C . .3235, P - .002)

NOR ARL BRL ART BRT

 

Dispatching Rule for the NOR Mechanism
(F Prob. - .OOOO; Cochran's C a .6244, P a .000)

SOPN SPT FCFS

Dispatching Rule for the ART Mechanism
(F Prob. - .OOOO; Cochran's C - .6016, P a .000)

SOPN SPT FCFS

Dispatching Rule for the ARL Mechanism
(F Prob. a .0000; Cochran's C . .4980, P a .002)

SOPN SPT FCFS

. Dispatching Rule for the BRT Mechanism

(F Prob. = .0000; Cochran's C s .6223, P = .000)
SOPN SPT FCFS

Dispatching Rule for the BRL Mechanism
(F Prob. - .OOOO; Cochran's C - .5825, P = .000)

SOPN SPT FCFS

205

II. Dispatching Rule * Prevalence

a. Dispatching Rule for the 100% Prevalence
(F Prob. - .OOOO; Cochran's C = .5627, P

SOPN SPT FCFS

b. Dispatching Rule for the 50% Prevalence

(F Prob. a .0000; Cochran's C - .6338, P

SOPN SPT FCFS

c. Prevalence for the FCFS Rule
(F Prob. - .0807; Cochran's C a

100% 502

d. Prevalence for the SPT

P

(F Prob. . .5520; Cochran's C = .5227, P

100% 50%

e. Prevalence for the SOPN Rule

(F Prob. - .2898; Cochran's C a .5914, P

100% 50%

.000)

.000)

.861)

.580)

.025)

206

APPENDIX K: DUNCAN PROCEDURE FOR PERCENT OF JOBS TARDY

Order Review/Release Mechanism * Dispatchigg Rule *

Location

Order Review/Release Mechanism for the FCFS Rule and
the Front Location
(F Prob. - .OOOO; Cochran's C a .5299, P - .OOO)

NOR ARL BRL BRT ART

 

Order Review/Release Mechanism for the SPT Rule and
the Front Location
(F Prob. . .OOOO; Cochran's C . .4830, P - .OOO)

NOR ARL ART BRL BRT

 

 

. Order Review/Release Mechanism for the SOPN Rule and

the Front Location
(F Prob. - .0427; Cochran's C - .2704, P - .582)

NOR ARL BRL BRT ART

 

 

Order Review/Release Mechanism for the FCFS Rule and
the Exit Location
(F Prob. - .OOOO; Cochran's C I .8691, P a .000)

NOR ART ARL BRL BRT

 

Order Review/Release Mechanism for the SPT Rule and
the Exit Location
(F Prob. - .OOOO; Cochran's C - .7399, P . .OOO)

NOR ART ARL BRL BRT

Order Review/Release Mechanism for the SOPN Rule and
the Exit Location
(F Prob. - .OOOO; Cochran's C - .2450, P - 1.000)

NOR ARL ART BRL BRT

Order Review/Release Mechanism for the FCFS Rule and
the Mixed Location

(F Prob. - .OOOO; Cochran's C a .4357, P a .001)

NOR ARL BRL ART BRT

 

207

Order Review/Release Mechanism for the
the Mixed Location
(F Prob. - .OOOO; Cochran's C - .5884,

SPT Rule and
P - .OOO)

NOR ARL ART BRL BRT

 

 

Order Review/Release Mechanism for the
the Mixed Location
(F Prob. . .0029; Cochran's C n .2870,

NOR ARL BRL ART BRT

 

SOPN Rule and

P - .376)

 

Dispatching Rule for the NOR Mechanism
Location (F Prob. - .0001; Cochran's C

SPT FCFS SOPN

 

Dispatching Rule for the ART Mechanism
Location (F Prob. - .OOOl; Cochran's C

SPT SOPN FCFS

Dispatching Rule for the ARL Mechanism
Location (F Prob. - .0001; Cochran's C

SPT FCFS SOPN

. Dispatching Rule for the BRT Mechanism

Location (F Prob. - .2834; Cochran's C
SPT FCFS SOPN

Dispatching Rule for the BRL Mechanism
Location (F Prob. - .0452; Cochran's C

SPT FCFS SOPN

 

. Dispatching Rule for the NOR Mechanism

Location (F Prob. - .0005; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the ART Mechanism
Location (F Prob. - .OOOO; Cochran's C

SPT FCFS SOPN

and the Front
I .9867, P I .000)

and the Front
8 .4686, P - .202)

and the Front
. .8542, P - .000)

and the Front
2 .4244, P a .454)

and the Front
2 .4943, P s .116)

and the Exit
. .9907, P - .000)

and the Exit
. .9848, P . .OOO)

208

Dispatching Rule for the ARL Mechanism
Location (F Prob. . .0002; Cochran's C

SPT FCFS SOPN

 

Dispatching Rule for the BRT Mechanism
Location (F Prob. - .OOOO; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the BRL Mechanism
Location (F Prob. - .0015; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the NOR Mechanism
Location (F Prob. - .OOOO; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the ART Mechanism
Location (F Prob. - .0002; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the ARL Mechanism
Location (F Prob. - .OOOO; Cochran's C

SPT FCFS SOPN

Dispatching Rule for the BRT Mechanism
Location (F Prob. = .0190; Cochran's C

SPT FCFS SOPN

 

Dispatching Rule for the BRL Mechanism

and the
- .9910,

and the
- .4809,

and the
- .8326,

and the
- .9846,

and the
. 06316,

and the
. .9370,

and the
a .4791,

and the

Exit
Pa

Exit
P:

Exit
P:

Mixed
P-

Mixed
Pa

Mixed
Pa:

Mixed
Pa

Mixed

.000)

.156)

.000)

.002)

.000)

.162)

Location (F Prob. - .0259; Cochran's C - .5961, P a .007)

SPT FCFS SOPN

 

209

II. Order Review/Release Mechanism * Prevalence

Order review/Release Mechanism for the 100% Prevalence
(F Prob. - .OOOO; Cochran's C - .3200, P - .OOO)

NOR ARL BRL ART BRT

 

Order review/Release Mechanism for the 50% Prevalence
(F Prob. - .OOOO; Cochran's C . .3506, P - .OOO)

 

 

 

 

NOR ARL ART BRL BRT
Prevalence for the NOR Mechanism

(F Prob. - .1117; Cochran's C s .6554, P = .003)
100% 50%

Prevalence for the ART Mechanism

(F Prob. - .5342; Cochran's C - .5002, P a .997)
100% 50%

Prevalence for the ARL Mechanism

(F Prob. - .0920; Cochran's C - .5765, P - .148)
100% 50%

Prevalence for the BRT Mechanism

(F Prob. - .0009; Cochran's C - .6164, P = .026)
100% 50%

Prevalence for the BRL Mechanism

(F Prob. - .0413; Cochran's C a .5680, P = .198)

100% 50%

TABLE L-l

ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: BOTTLENECK JOBS)

I A R I A N C E 0 :m! 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

T

F
TESTS OF SIGNIFICANCE FOR SUIF USJNO SEQUENTIAL SUNS OF SQUARES

 

A u_g_;_v s 1 s

00.00000000000000000

210

NEAN SQUARE

..--..-.-.- .. ..

-4-—.- ...... ...d—

0-6.‘

SUM OF SQUARES

OF F

SIG.

F

OF

SOURCE OF VAPIATION

96.36.0660 to
cc 0-

0.9208339!
.025

”0'6."—
WO —

 

I
R! LOCATION

F I H
A I N
T L CA ION
P T M

398
E O
S A C

w I-
286419
00 U

P~>p~fi
‘F53‘;

.21 m

382221

33029156

21112

112::

44
U‘

:0-
--

 

211

ll. . I «I- I . v I I.-.

“coon. 0 02.3.5»... upmatac
note. a a «nasal.

.I .IIIG 6"- ll €.II|I'II.II¢' .II1 It 'Ol 1'» All: I III.

 

 

. .32.: Sun. a.” m. 11mins" «max “ ”a..."
mmmmou .«nwnu ------ ..«nuwow I- us-:; :. 1:... cup. «I... zo.».uo :uo.c umwanm.mu»w;¢uw
is... ”A...” giant??? . .-%§ ,. . __ use in mm.
am... mmmmmm. . ...... a.“ 3......

. Azania... ; magnum ---- . .....mm.

A 3 .2». . A. .. 2.33 ...! ariiimwfiolulwotxmmll'; - , - 22:2: ... 3%..»
augaaua .o .ua» 4‘...uaou. oz.m: Angus: so. uuz.u_t.zo.a to “pa“.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 m-..0:m...0..-fllw¢m.i81d.1ml.¢n!mume h 6 'Idxmlmqm-fliadlui 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

AmQOH nouzuqhfiom .mo=m m=5 2H mane scam z<m=v
moz<Hm<> ma mHm>4<z<

N14 m4m<h

TABLE L-3

ANALYSIS OF VARIANCE
(VARIANCE OF FLOW TIME IN THE SHOP: BOTTLENECK JOBS)

V A 8'! A N C E 0 0 0 0 0'0 0 0 0 0 0 0 0 0 0 0 0 0

O

p

0 00 0... 00 00 00 00 oargllA LV'SI S

21J2

IVSVS 0F STEVIEICAVCE FOR BVARFLSp USINQ SEQUENTIAE SUNS OF SQUARES

SIS. "‘ F

F

MEAN SQUARE

0?

SUM OF SQUARES

or VARIAVIGN

SIUNC’

VHDC' ”0'0. 96
N"! WVnt-CC
0“ 00‘78’.
0f: h0—0.
0Ci13090fli
00 00000

”"900 C",

\EnOVDFOU‘n

0001-0000

ann0mwo -
M

~~*m
4000MNW000¢I
0.09.6...
hMflmUUhflfidU

ooouwcocd
:; .u

'MWNONflWnONI
“W
000000000
0 O 6 O O O O 9 O
UUUUUUUUU
0NN0000NN
000-000 000
TaflhflO‘flfl'
NOONOObo-t
000*."0000‘

0000¢b0000
lfitfimn~OF~mn

uv LUCAIIOM

AYIOU

L Haw—P ’90—‘3-
53?:49-c-

3037???

Zétfltl

'0

$§l

O.
CO.

”0‘
no

Eéifiii

CO

3%

O.
00
N'-

En «Iconanrn

A ‘3 MH'Q‘Z’)
1 II?!

’ I).

BOTTLENECK JOBS)
U’AR-IA "Cit. 00 .0 00 00 00 00 00 0

TABLE L-4
ANALYSIS OF VARIANCE

(MEAN TARDINESS

0 00 00 00 .0 00 00 00 00U00 0..“A.LV 81 S'

213

0" 000‘“ “‘1‘
0

(W F

SIG.
S0555305-3

fiF—ontmfl".
0. 0000010
adccocwc
mango-00:006.
hcccnnms
0 o 0 o 0 0 0 o
moaning-o
C on
0'.

p

Q‘GFOFMFN
“CDQMHNN
\QIflOOOC‘O‘BU‘
Ono-0000000
00000.0(“—
0 o o 0 0 0 0 0 0
#00800050

QflNanQFn
0OF~D¢IO
N O

NEAN SQUARE

QOONNQOOO
s; 00

0F

\

0MOH'9050
0‘0000000

OuNOOOC-uu
0 o 0 0 0 0 0 0 0
00000500!!!

SQUARES
8
3
q
1
1
0
6
9
9

SUN OF
R
B
1
l

SIS 0F SISNIFICANCE FDR BNEANIAR USING SEQUENIIAL SUNS 0F SQUARES

2
0
I-
b
C
' U
C
2.!
’ C
C —’
O- b:
P C
c :20!
c ban-Ju-
0 GI- C
’ QCfia
(”UK 6’
'6 0-C .-
C .0 2734?:
C U: U
I. :0- -—>>¢-b
U 21.; ‘F-=¢:
B 1‘! z
3 M23 MUCO’AOQ’
u r. we -c-ur-x-::
t- t" 3".“46‘0‘

13008532

 

63A07.18830
11631062066

3
9

‘0

OS

AOJUSIEO R-SQHAREO

Q'S'NHRC')

214

..l- I . l1 I211Il11111l.

I. I

5 no .cnn

000‘.“ N0 0

B

0000000000000000..0u08¢~¢¢3 to

- Iflll'l' 11.1... .. I.“ 011-14.

---.z...§-m-lmi. 5.3% ..
Emma“ m an“
3 . ..mmm.

www.m«mmxém- .. . .mmmumm

accauu z‘ux an Qua-30a t: tan.

I 10.10. ll"! . .1.'-I I I'

GUI .-.V Ill I

m.

an.“
meow»

zanbsuaao »0
can

u Guadzumuc awhmafiag
u Qu¢<aamtc

tempt—cc) so uucaom

. nu¢¢aou so .03“ Atupzuaoua 08—”: ¢¢h¢c’o can mango—unso—w 5: «pump

1 '1..- l I 0' ..Ilv)

 

I'll! 2! II. I.. -1 ll-.. 1'

 

Ammon Momzmqhhom ”wmmzHam<h mo moz<Hz<>v

moz<Hm<> mo mHm>q<z<
ml; udm<b

n~nra<z<0000nl0idfilm

.
.
C '

215

..-llllll' '10

. -.. .. . . . . l. .. II . .
U - . - U U . . - - - - - . - . - - . - - ' - ' . - . - - ' - - - - - . . . . . . .

15...! I:

.1. LI

I. 'lI'A-

 

. .5... a a"? m.
noaau. opnomu.-...-.z.nnmowwnn....-mw.
mam max”. mama»: u
as“. ..“m. -....-zfimw...“

“ mam“ 3%.“ .
. ooou .0. -:-..mmm¢pummwm .. won
a no ooun 5

u¢¢aca 80H: 59

.I...I.'I..OI"II . ..‘l1l’.-I11ll'll.I

muccaon to ”tan a¢-2uaouu exam:

 

0 0 0 0 0 0 0 0 0 0 0 0 r 0 m 0 0 0|“ u u I C n c c :

c..."

L o

n
o

J t

‘1' II|OI 'llAll‘IA‘Il -101

a
w
n~*!l-:,

auscaou 56 0:0.

.
..-III".'-I II III. I‘IIII I . I

III.

MflMOOo a au¢<aamuc Ou—mafiaa
- 000. u ou3030m0¢
add a».

...»...

o zoubauoa an :u—cmu—o p: «:9
o zaunnuaa pw subczmna
0 ZGM~¢ we >2 mac
w .tlli!I-- -- - :0 (am a be “cw
to—pc o

h tartamua
. .3.
C

a is...

zu-<~¢¢a be buxaom

¢¢b¢uso con uuaco~u~z¢~m a: «pay»

a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Amman Momzmqhhom uwnm<9 meow he Bzmommmv
uoz<Hm<> mo mHm>4<z<

on; mqm<b

TABLE M-l

ANALYSIS OF VARIANCE
(WORK-IN-PROCESS: NON-BOTTLENECK JOBS)

A N c E 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 o 0

V A R I

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9“ N A L V 8 I S

2115

1:519 nr stcuxrxcaucc son uuxr usxuo sanucutxAL subs or saunas:

1: r

5160

;

NEAN SQUARE

OF

SUN 0F SQUARES

«wuncr 0‘ VARIATION

000NO~C 00
“no 6

000- 0-
050 6'
0"“; Ir
0 I D Q

cmocnnnw
uhv Inc—0N
0 communal!-
ov-cocoan
anrc0wuno
0 0 0 0 0 0 0 0
:15on
cub-0 0i
'-

“FONNNONF

WOnUanfik
O O C O O O O C O
OFOON¢O~Q
OFC‘CFNONO
"“00““?!
human 0
.fl ‘ '.
N

mocuunooa
S u

CFOCCNOQIO

0 0 0 0 0 0 0 0 0
(woman-con
CON‘ONndQ
nah—amend!
OONODOCQD
00000 N
«04 0

ON

LNCAIION
trH d1 LOCATION

ICH
I

00"

AL
a
nu
n
L
N
n

:h punt-5-)

I.
0-(0 a 1
menu (0028036
| .A, _Pc~ _h

éeecarvc?

A1005715

10969.89A9A
2089062009

‘7.

a ”timid «Isrmnm

“‘31UARF”

217

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u.u z.¢ u c < ’ u o

0

c c—coooow
rates. (ouwnou

c cccccofiu
wwacm. onwon.
macaw—mnunou “0009.0
ounce. 0¢oop.o

o oafioc.o—0
o sec—no.0
o ounncoon
u u: ow—m u

.-------'-'l-"----'------"-"""-----'

0 o 0 0 o 0 0 0 o
nor-Inna- dcoe 00¢
2 beau—udflmb uub
I,

U ONHDU-flflnb an
3 coma-weave m7-
9 ~F~Q¢0N00 DO
O‘U‘NOMNGF‘ NF
tat-2'00! Q

a.. uuwn..n.en.n
nr hoax..nn~o.~
cu .«.oo.-cn

. m e~o. who.
a ou...°...

c padun.¢emo

a n*nn¢..nen

m n a.~..~om..
. magma..roo~
a «oao.n¢-o
can o -n...ooo
no auccaom me :a»

2c—b19c4 >z :Lpeav_c >: :
’c-_co:4 >3 tu.e:mm
q...—b¢.u: .- s. a:

rcp04n—2 .: :.

re.»eu

:u.v:m

up. u ru¢¢:rrue :u.r:t.a
ac. u :.z«:rr-e

def: .— m ..m.
2fnbc—9d, k9 :Uazfv

. mu¢¢=om no wzzm 4¢~pzuacum ¢z_m: amauzr cog uuzcu.u_rc_» .. r.v..

m u m h J < 8 d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .

Amman uomzmgppom-zoz "mozm was 2H mzHa scam zcmzv
moz<~m<> mo mHm»q<z<

NI: m4m<9

C

TABLE M—3

ANALYSIS OF VARIANCE
(VARIANCE OF FLOW TIME IN THE SHOP: NON-BOTTLENECK JOBS)

 

V A R I A N c t 0 0 0 0 0 0 0 0_0 0 0 0 0 0 0 0 0 .

 

A“! .-!-..

0
IESIS 0F SIQAIFICANCE FOR NVARFLSR USINI SEQUENIIAL SENS 0F SQUARES

Q
- -’—_.fi

__.;-=
a

218

NEAN SQUARE

..-. “.--.

 

SUP 0F SQUARES

SIG. OF F

F

0F

SOURCE OF VARIAIICN

Hum-m QM
OOH con-mum
mm

 

ION
V LOCAIION

*3

IL Cfia
Luann”

.l 813:3;
d 09

:0- hunt-anna-
DU ChCL‘C

8500-10695

gamma

250A1DSA

.. m—.

p

F.

M
0.

-SQUAREE =
ADJUSIEO R-SQUAREO 3

--.... . .—--. ---

. -.-...—_-.._... ..

.. ...-.-

TABLE M-A

ANALYSIS OF VARIANCE

NON-BOTTLENECK JOBS)

(MEAN TARDINESS

V A'I I A fl‘c [ 0 0 0 0 0 0.0 0 0 0 0 0 0 0 0 0 0 0 0

-.-—- ---_.0-_—_—.- ———-.--. ——..—..———-— .

o.

------...- .

0 . 0

219

IISIS 0F SIGNIFICANCE FOR NNEANIAR USINQ SEQUENIIAL SLNS QF SQUARES

 

SUN QF SQUARES

. - .—.—-..--—.. —— .- .-..

SI00 0' F

F

0F

SOURCE OF IARIAIICN

:REAN sauna:

|

alnnnouwn
woman-83.!
QWI'DND-I-O-

woman-.00
luncmumncwuv
000:00mcb0.
FMfl-GMV
NDHOOM'M'I
WOMODOOO
“00.00.1600
Cfllmoonqwuu.
luu¢u0.—
uu '
I I I
. I
I
2
O
n
h
¢
U
0
8.0
G
On»
0-0
C
:20:
0009
uu-J—n
Ch- 1
(Lt an;
«uflhm
O

0‘ II.
.I tZDJIO
C DO U
3&- but-00h)-
OhJ1i—ch‘z
0.0) 3‘ a
anxmucxmz
UGC-DCI-E
33¢ 0’.‘ 4°C 00

9056906

3....

s...

. _.—_— ..-- .-- .- _ -..

”O
n.

q

--..—_._-_ ,

to nzsouantn

R-SQUAREC
IDJUSI

TABLE M-S

ANALYSIS OF VARIANCE
(VARIANCE OF TARDINESS: NON-BOTTLENECK JOBS)

V A R I A a C E 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A N A L V S I 3,.

220

SISNIFICAMCE FOR NVARIAR USING

"F

V'51:

SEQUENIIAL SUNS OF SQUARES

SIG. "F F

p

OF NEAN SQUARE

SUN OF SQUARES

3‘ VARIAVIJN

\UIF'

OOOU’V-ut.‘
0-600
2001‘ Q
0000‘
00000

0 0 0 0 0

00"“5650' ‘0
dffimfflc0
o-cwnnnmw
000050-00?
QCU‘OU‘Ko—C‘
Q C Q Q C Q O O
00Nflnnt
N819

H

FOOQQQOFNUU!
000000000
“0000“)000
h 9 Q 0 015000
“UUU 0 O 0 00)
oflOmOI-l'hb 0
GFOFFFOC‘u
000001-0000
ODFOnFQQC
WWII-”MN“
0 0 0 050.6!"
HNQdOFOON
N 0N0.“
. "AGING
flfitflflflnfd‘
s; 04

0000-50660
.flnn—uuuaaar
606606600
0 0 O 00*. 0 O O
UUUUKUNUU
00900 000601
mar-nonnat-
610000060"-
Onhhm—h6
01600-00000”
0 0 0 0. 0 0 0 0
nu—nguwnu

H
O

"V LJCAIION

PIQPAICN

"V L'iclII 'IN
RV LOCAIIIV

“ISpA'FM

tlsmtcu
'nc1vvnq
)IS'Vt|F I
we m

17.55205

'III’.|€F‘I

\HJHern R-QGUARPW

I-S

.----------P--------0-------0000

TABLE M-6

ANALYSIS OF VARIANCE
(PERCENT OF JOBS TARDY: NON-BOTTLENECK JOBS)

VARIANC£0000000000000000000

0000000000ANA'LVSIS

OOQQQQOQQ

2221

WP SIGNIFICANCE FOR NPERIAR USING SEQUENIIAL SUNS OF SQUARES

t"Sl§

as r

SIS.

NEAN SQUARE

OF

0F VARIATION

.SI'NAL

:4u»t"

lvpttr
QR

nvwnr

SUN OF SQUARES

000..”0‘.
050010-05
00C-NN
000N‘D
00000

0 0 0 0 0

«Iv-O CO‘I‘.’
«Onflhnfl‘h
c—hnnow-
FQKU’cOI'IQFd
0ND 00050-00

6001-86009!!!“
nmmwownnh
Mn¢¢h6n0
«mncemmoo
00000050500
0 0 0 0 0 0 0 0 0
ho0wlhnl‘00
COmctO-OQO
“ONO“OM
0000-00-1
Nu

OOCNNOCO‘D
a 0!

NF “00‘0th

tcu n1 LJCAIION

14M
anatlau

PA
AI
V

PA

P

17.20001

("WW I. ,
”III ALI

\wnnwvtn nlcquaorw

.:..¢;.m1pcjn

LIST OF REFERENCES

 

LIST OF REFERENCES

Aggarwal, S.C., "MRP. JIT, OPT, FMS?," Harvard Business
Review, September-October, 1985, 8-16.

Ahn, Y.J., S.A. Melnyk, and G.R. Ragatz, "Managing the
Bottleneck Job Shop Through the Use of Dispatching
Rules," 1987 Midwest DSI Conference Proceedings, 99-

101.

Anderson, V.L. and R.A. McLean, Design of Experiments: A
Realistic Approach, Marcel Dekker, Inc., 1975.

 

Baker, C.T. and B.P. Dzielinski, "Simulation of a Simplified
Job Shop," Management Science, Vol. 6, No. 3, 1960,
311-323.

 

Baker, K.R., Introduction To Seguencing and Scheduligg, John
Wiley & Sons., 1974.

Baker, K.R., "The Effects of Input Control In a Simple
Scheduling Model," Journal of Operations Management,
V010 4, N00 2’ 1984, 99-112

Baker, K.R. and J.W.M. Bertrand, "A Comparison of Due Date
Selection Rules," AIIE Transactions, Vol. 13, No. 2,
1981, 123-131.

 

Bechte, W., "Controlling Manufacturing Lead Time and Work—
in-Process Inventory by Means of Load-Oriented
Release," 1982 APICS Conference Proceedings, 67-72.

Bertrand, J.W.M., "The Use of Workload Information to
Control Job Lateness in Controlled and Uncontrolled

Release Production Systems," Journal of Operations
Management, Vol. 3, No. 2, 1983, 79-92.

 

Billington, P.J., "Cost Implications of a Bottleneck in
Multilevel Production Systems," 1985 AIDS Proceedings,
803-805.

Billington, P.J., J.O. McClain, and L.J. Thomas, "Heuristics
For Multilevel Lot-Sizing With A Bottleneck,"
Management Science, Vol. 32, No. 8, 1986, 989—1006.

 

222

223

Blackstone, J.H., D.T. Phillips, and G.L. Hogg, "A State-of-
the-Art Survey of Dis atching Rules for Manufacturing
Job Shop Performance,’ International Journal of
Production Research, Vol. 20, No. 1, 1982, 27-45.

Cochran W.G. and G.M. Cox, Experimental Desigg, Second
Edition, John Wiley 8 Sons., 1957.

Conway, R.W.. "Some Tactical Problems in Digital
Simulation," Manegement Science, Vol. 10, No. 1, 1963,
47-61 0

Conway, R.W., "Priority Dispatching and Work-In-Process

Inventory in a Job Shop," Journal of Industrial
Engineering, Vol. 16, No. 2,—1965, 123-130.

Conway, R.W.. and W.L. Maxwell, "Network Dispatching By The
Shortest Operation Discipline," Operations Research,
Vol. 10, No. 1, 1962, 51-73.

Conway, R.W.. W.L. Maxwell, and L.W. Miller, Theory of
Schedulin , Reading, Massachusetts: Addison-Wesley,
1967.

Davis, E. W., "Project Scheduling under Resource Constraints
— Historical Review and Categorization of Procedures,"
AIIE Transactions, Vol. 5, No. 4, 1973, 297- 312.

 

Deane, R.H. and C.L. Moodie, "A Dispatching Methodology for
Balancing Workload Assignments in a Job Shop Production
Facility," AIIE Transactions, Vol. 4, No. 4, 1972, 277-
283.

Elvers, D.A., "Job Shop Dispatching Rules Using Various
Delivery Setting Criteria," Production and Inventqey
Management, Vol. 14, No. 4, 1973, 62-69.

 

Elvers, D.A., "The Sensitivity of the Relative Effectiveness
of Job Shop Dispatching Rules with Respect to Various
Arrival Distribution," AIIE Transactions, Vol. 6, No.
1, 1974, 41—49.

Fishman, G.S., "Grouping Observations in Digital
Simulation," Management Science, Vol. 4 No.5, 1978,

510-521.

Fogarty, D.W. and T.R. Hoffmann, Production and Inventory
Manegement, South-Western Publishing Co., 1983.

 

Fox, R.F., "MRP, Kanban, or OPT: What's Best?", Inventories
and Production Magazine, July-August, 1982a.

 

Fox, R.F., "OPT An Answer for America: Part II," Inventories
and Production Magazine, November-December, 1982b.

224

Goldratt, E.M. and J. Cox, The Goal: Excellence In
Manufacturing, North River Press, Inc., 1984.

 

Harty, J.D., "Controlling Production Capacity," 1969 APICS
Conference Proceedinge, 60-64.

Huang, P.Y., L.P. Rees, and B.W. Taylor, "A Simulation
Analysis of the Japanese Just-In-Time Technique (with
Kanbans) for a Multiline, Multistage Production
gzztem," Decision Sciences, Vol. 14, No. 1, 1983, 326-

Irastorza, J.C. and R.H. Deane, "A Loading and Balancing
Methodology for Job Shop Control," AIIE Transactions,
v01. 6, N00 4’ 1974’ 302-3070

Irastorza, J.C. and R.H. Deane, "Starve the Shop: Reduce
Work-in-Process," Production and Inventory Manegement,
Vol. 17, No. 2, 1976, 20-25.

Jacobs, F. R., "The OPT Scheduling System: A Review of a New
Production Scheduling System," Production and Inventory
Management, Vol. 24, No. 3, 1983, :47- 51.

Kaczka, E.E., "Computer Simulation," Decision Sciences, Vol.
1, N00 1, 1970’ 174-1920

Kempthorne 0., The Design and Analyeis of Experiments, John
Wiley & Sons, Inc., 1966.

Kleijnen, J.P.C., Statistical Techniques in Simulation, New
york: Marcel Dekker, 1974.

Lundrigan, R., "What Is This Thing Called OPT?", Production
and Inventogy Management, Vol. 27, No. 2, 1986, 2-12.

Meleton, M.P., "OPT-Fantasy or Breakthrough?," Production
and Inventory Management, Vol. 27, No. 2, 1986, 13-21.

Melnyk, S. A. and P. L. Carter, The Principles and Practices
of Shop Floor Control. iThe Second Stege Lessons From
The "Leadin ng Edge, A Report Submitted to The
Educational and Research Foundation of The APICS,1987.

Melnyk, S.A., P.L. Carter, D.M. Dilts, and D.K Lyth, Shop
Floor Control, Homewood Illinois: Dow&Jones-Irwin,
1985.

Meter J. and W. Wasserman, Applied Linear Statistical
Models, R.D. Irwin, Inc., 1974.

 

225

Nicholson T.A.J. and R.D. Pullen, "A Practical Control
System for Optimizing Production Schedules,"

International Jourael of Production Research, Vol. 9,
No. 2, 1971, 219-227.

Ow, P.S., "Focused Scheduling in Proportionate Flowshops,"
Management Science, Vol. 31, No. 7, 1985, 852-869

 

Prather, K.L., "Seven Deadly Sins of Production Control",
1983 APICS Conference Proceedinge, 218-220.

Pritsker, A.A.B., lptroduction to Simulation and SLAMII, New
York: Halsted Press Division of John Wiley and Sons,
Inc., 1984.

Ragatz, G.L., An Evaluation_ef Order Releaee Mechanisms for
Job Shops, Unpublished Dissertation, Indiana
University, 1985.

 

Sandman, W.E. and J.P. Hayes, How Te Win Productivity in
Manufacturing, Yellow Book of Pennsylvania, 1980.

Shannon, R.E., Systems Simulation: The Art and Science,
Prentice-Hall, Inc., 1975.

Scheffe, H., The Analysis of Variance, New York: John Wiley,
1959.

Schonberger, R.J., "Clearest-Road-Ahead Priorities For Shop
Floor Control: Moderating Infinite-Capacity loading
Uneveness," Production and Inventoneranagement, Vol.

20, No. 2, 1979, 17-27.

Solberg, J.J., "Capacity Planning with a Stochastic Workflow
Model," AIIE Transactions, Vol. 12, No. 2, 1981, 116-
122.

Vollmann, T.E., "OPT As An Enhancement To MRP II,"
Production and Inventory Management, Vol. 27, No. 2,
1986, 38-46.

Walker, H.M. and J. Lev, Statistical Inference, Henry Holt
and Company, 1953.

Wallace, T.F., APICS dictionary, Fifth Edition, American
Production and Inventory Control Society, Inc., 1984.

 

Wight, O.W., "Input/Output Control: A Real Handle on Lead
Time," Production and Inventory Management, Vol. 11,
No. 3, 1970, 9-31.

Wight, O.W., Production and Inventory Manegement in the
Computer Age, Van Nosyrand Reinhold Company, 1974.

 

226

Winer, B.J., Statistical Principles In Experimental Design,
McGraw-Hill Book Co., I97f.