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This is to certify that the

dissertation entitled

The Effects of Variability and Disruption
On
Project Stability, Duration, and Net Present Value

presented by

Stephen M. Swartz

has been accepted towards fulfillment
of the requirements for

 

 

Ph.D. degree in Business Administration

jam flam—

ajor esso

Date (76/!2 ’T/i7

MSU i: an Affirmariw Action/Equal Opportunity Institution 0- 12771

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINE return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

MAY 2 9 2003 JUN 1 1 2003
JUN 242003 UL 2 2 2003

JUL 0 8 2.003 3031:9625 5’00‘3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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THE EFFECTS OF VARIABILITY AND DISRUPTION
ON
PROJECT STABILITY, DURATION, AND NET PRESENT VALUE
VOLUME I

By

Stephen M. Swartz

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Marketing and Supply Chain Management

1 999

ABSTRACT

THE EFFECTS OF VARIABILITY AND DISRUPTION
ON
PROJECT STABILITY, DURATION, AND NET PRESENT VALUE

By

Stephen M. Swartz

It has been demonstrated that the performance of scheduling heuristics for the
Resource Constrained Project Scheduling Problem (RCPSP) can be affected by the use of
alternative project execution strategies. This current work seeks to expand our
understanding of the relationship between planning (scheduling) and execution
procedures. The relative performance of a selected group of “high performing”
scheduling heuristics on project total duration, Net Present Value (N PV), and a new class
of stability measures under four different execution strategies is examined. A benchmark
set of RCPSP cases were scheduled and then simulated through execution and the results
are compared. The research findings indicate that relative performance is affected by the
execution strategy in some cases but not in others; and that these relative standings are
sensitive to the presence of variability in task duration. A new heuristic is also proposed

and evaluated.

Copyright by
STEPHEN MERLE SWARTZ

1999

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ACKNOWLEDGEMENTS

Many people have assisted in this effort, and I would like to take some time to

recognize their contributions and extend my sincerest and deepest thanks.

First, I’d like to thank my fellow graduate students at Michigan State University.
Particularly Mark Pagell, from whom I stole the idea for measuring Project Stability and
who got me stated down this path in the first place. Mark gave me plenty of ideas and
encouragement along the way, and I hope to collaborate with him again in the future.
Thanks also to my long suffering office partner, Bob Marsh, who put up with my
incessant whining whenever I hit the invariable committee snag or had a piece of code
misbehave. And I’d certainly like to thank all of the seminar partners and conference co-
presenters along the way who tried (sometimes unsuccessfully!) to keep me focused on

the things that really mattered in refining my research.

Next, I need to thank my colleagues at the Air Force Institute of Technology, and
all of the people who made this endeavor possible in the first place. Special thanks to Dr.
Craig Brandt, my department chair, for giving me the opportunity for doctoral study. Dr.
Brandt also employed great patience in insulating me from excessive workload when I
arrived at my new assignment ABD. Without his efforts on my behalf I would never
have been able to complete the dissertation. Thanks also to those colleagues who had to
pick up the slack for me when I was unable to dedicate more time to faculty service

obligations. I trust that my debt will soon be repaid, with interest!

I certainly owe a debt of gratitude to my committee, who guided me through the
shoals and rapids of designing, conducting, and reporting research. Dr. Gary Ragatz, Dr.
Roger Calantone, Dr. Paul Rubin, Dr. Rob Handfield, and Dr. Morgan Swink all pitched
in to help me develop my skills and attitude to that of a contributing member of
academia. Their mentoring and guidance made all the difference in the world, and I hope
that I can someday live up to their high expectations. They opened my eyes to the joy
and hard work of conducting rational inquiry through the application of the scientific

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method, and for that I am truly blessed. Special thanks are in order for Dr. Gary Ragatz,
my committee chair, who invested time and effort “above and beyond the call of duty” to
steer me from the shoals when I needed it. He had the unenviable task of helping me sort
through the mass of data I created, and convert the best parts into information. As the

punchline goes, “ . . . you shoulda seen what went in the other end!”

Saving the best for last, I must extend a special thanks to my family. To my wife,
Leslie; and our children Jenniffer, Cassandra, and Mikel I can only say “Dad’s back!” I
would never have been able to tackle a PhD program without their Herculean support and
encouragement. Leslie in particular took up the slack; acting as Social Director, Chief of
Services, Chief Financial Officer, and Director of Logistics, she did it all. I offer my
deepest thanks, and hope the missed ballgarnes, recitals, and parent-teacher conferences
did not weigh heavily. I hope their surrogate experience of what it’s like to struggle at
the higher echelons of academia do not sour them from tasting the experience first hand.

In that regard, my parting shot to Leslie is “Tag, You’re It!”

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TABLE OF CONTENTS
VOLUME I
LIST OF TABLES ............................................................................................................. x
LIST OF FIGURES ....................................................................................................... xiv

CHAPTER 1 INTRODUCTION

1.1 Overview ................................................................................................................. 1
1.2 Research Problem and Questions ........................................................................... 2
1.3 Importance of Research .......................................................................................... 6

CHAPTER 2 SIGNIFICANT PRIOR LITERATURE

2.1 General Reviews of the Literature ....................................................................... 13
2.2 Planning Approaches ........................................................................................... 18

2.2.1 Exact Approaches .................................................................................... 18

2.2.2 Heuristic Approaches .............................................................................. 21
2.3 Execution Approaches ......................................................................................... 34
2.4 Measures of Stability ........................................................................................... 38
2.5 Environmental Variables ..................................................................................... 43
2.6 Summary .............................................................................................................. 48

CHAPTER 3 METHODOLOGY

3.1 Introduction ......................................................................................................... 50
3.1.1 Theoretical Model .................................................................................... 50
3. l .2 Hypotheses .............................................................................................. 52
3.2 Dependent Variables ............................................................................................ 53
3.2.1 Net Present Value .................................................................................... 53
3.2.2 Stability .................................................................................................... 55
3.3 Independent Variables: Treatments .................................................................... 58
3.3.1 Planning Methods .................................................................................... 58

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3.4 Independent Variables: Moderating ................................................................... 62
3.4.1 Characteristics of the Problem ................................................................. 62
3.4.2 Characteristics of the Environment ......................................................... 64
3.5 Experimental Design ........................................................................................... 66
3.5.1 Experimental Factors ............................................................................... 66
3.5.2 Problem Set ............................................................................................. 67
3.5.3 Data Generation ....................................................................................... 70
3.6 Data Analysis Issues ............................................................................................ 73
3.7 Limitations and Key Assumptions ...................................................................... 73

CHAPTER 4 RESULTS AND ANALYSIS

4.1 Introduction ......................................................................................................... 76
4.2 Planning Method Performance under Deterministic Assumptions ..................... 76
4.2.1 Comparison Tables .................................................................................. 77
4.2.2 Formal Test Results ................................................................................. 81
4.2.3 Expectations of Performance under Stochastic Conditions ..................... 83
4.2.4 A Note About the Sensitivity of NPV to rt .............................................. 84
4.3 Exploratory Analysis ........................................................................................... 87
4.3.1 Summary Statistics of Key Variables ...................................................... 87
4.3.2 Treatment Cell Means ............................................................................. 90
4.3.3 Treatment Cell Normality and Homoscedasticity ................................... 92
4.4 Covariation .......................................................................................................... 96
4.4.1 Biserial Correlation ................................................................................. 96
4.4.2 ANOVA Results .................................................................................... 103
4.5 Differences of Means ......................................................................................... 109
4.5.1 Scheduling Method Performance by Execution Method ....................... 112
4.5.2 Execution Method Performance by Scheduling Method ....................... 124
4.6 Tests of Hypotheses ........................................................................................... 130
4.6.1 H1: Stability Measures vs. Traditional Measures ................................. 130

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4.6.2 H2: Project Performance by Planning Method ..................................... 131
4.6.3 H3: Project Performance by Execution Method ................................... 133
4.6.4 H4a: Relative Planning Performance by Variability ............................ 134
4.6.5 H4b: Relative Planning Performance by Disruption ............................ 134
4.6.6 H4c: Relative Execution Performance by Variability .......................... 135
4.6.7 H4d: Relative Execution Performance by Disruption .......................... 136
4.7 Summary of Data Analysis ................................................................................ 136

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS

5.1
5.2
5.3
5.4

5.5

5.6

Introduction ....................................................................................................... 138
Research Questions ............................................................................................ 139
Additional Notes on the Effects of Variability and Disruption ......................... 144
Conclusions ....................................................................................................... 149
5.4.1 Theoretical ............................................................................................. 150
5.4.2 Practical ................................................................................................. 152
Recommendations ............................................................................................. 1 53
5.5.1 Future Research ..................................................................................... 153
5.5.2 Managerial Recommendations .............................................................. 155
Summary ............................................................................................................ 156

viii

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APPENDIX A Histograms of Aggregate Statistics ....................................................... 160
APPENDIX B Treatment Means ................................................................................... 167
APPENDIX C Graphical Treatment Means .................................................................. 179
APPENDIX D Histograms of Normality and Homoscedasticity .................................. 191
APPENDIX E Biserial Scatterplots ............................................................................... 203
APPENDIX F AN OVA Residual Plots ......................................................................... 221
APPENDIX G Nonparametric Comparisons ................................................................. 233
APPENDIX H Differences in Ranked Performance ...................................................... 256
APPENDIX I Project Problem Networks ...................................................................... 261
APPENDIX J GPSS/H Simulation Listings .................................................................. 270
APPENDIX K PASCAL Listings ................................................................................. 292
APPENDIX L NPV vs. rt .............................................................................................. 313
APPENDIX M Degradation (Percent Change) .............................................................. 321
BIBLIOGRAPHY .......................................................................................................... 326

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Table 2.1 Weighting Rules ............................................................................................... 33
Table 2.2 Problem Characteristics .................................................................................... 47
Table 3.1 Problem Characteristics Studied ....................................................................... 63
Table 3.2 Problem Set Characteristics .............................................................................. 70
Table 3.3 Pilot Run Data ................................................................................................... 72
Table 4.1 Schedules by Problem (SDUR) ........................................................................ 78
Table 4.2 Schedules by Problem (SNPV) ......................................................................... 80
Table 4.3 Nonparametric Comparison of Scheduling Methods (SDUR) ......................... 82
Table 4.4 Nonparametric Comparison of Scheduling Methods (SNPV) .......................... 82
Table 4.5 NPV vs. rt (OPT) .............................................................................................. 86
Table 4.6 Percent Slopes, NPV vs. rt ................................................................................ 87
Table 4.7 Summary Statistics of Key Variables ............................................................... 88
Table 4.8 Means: ADUR by Scheduling, Execution, Disruption, Variability ................. 91
Table 4.9 Treatment Statistics: Assessment of Normality and Homoscedasticity .......... 93
Table 4.10 Biserial Correlations: Parametric (Pearson’s) ................................................ 97
Table 4.11 Biserial Correlations: Nonparametric (Spearman’s) ...................................... 97
Table 4.12 AN OVA Results ........................................................................................... 104
Table 4.13 Scheduling Method Performance by Execution Method (ADUR) ............... 111
Table 4.14 Relative Top Rankings (Scheduling Methods) ............................................. 113
Table 4.15 Summary of Multiple Comparisons (Scheduling by Execution) .................. 114

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Table 4.17 Summary of Multiple Comparisons (Overall) .............................................. 137
Table 5.1 Percent Change (variability none—some) ......................................................... 145
Table B-1 Means: ADUR by Scheduling, Execution, Disruption,Variability ............... 168
Table B-2 Means: RDUR by Scheduling, Execution, Disruption,Variability ............... 169
Table B-3 Means: ANPV by Scheduling, Execution, Disruption,Variability ............... 170
Table B-4 Means: RNPV by Scheduling, Execution, Disruption,Variability ............... 171
Table B-5 Means: WADE by Scheduling, Execution, Disruption,Variability .............. 172
Table B-6 Means: WADL by Scheduling, Execution, Disruption,Variability .............. 173
Table B-7 Means: WADC by Scheduling, Execution, Disruption,Variability .............. 174
Table B-8 Means: POIC by Scheduling, Execution, Disruption,Variability ................. 175
Table B-9 Means: POIR by Scheduling, Execution, Disruption,Variability ................. 176
Table B-lO Means: POOC by Scheduling, Execution, Disruption,Variability ............. 177
Table B-ll Means: POOR by Scheduling, Execution, Disruption,Variability ............. 178
Table 6-1 Scheduling Method Performance by Execution Method for ADUR ............. 234
Table 6-2 Scheduling Method Performance by Execution Method for RDUR ............. 235
Table G-3 Scheduling Method Performance by Execution Method for AN PV ............. 236
Table G—4 Scheduling Method Performance by Execution Method for RNPV ............. 237
Table G-S Scheduling Method Performance by Execution Method for WADL ............ 238
Table 6-6 Scheduling Method Performance by Execution Method for WADE ............ 239
Table 6-7 Scheduling Method Performance by Execution Method for WADC ............ 240
Table 6-8 Scheduling Method Performance by Execution Method for POIC ............... 241
Table 6-9 Scheduling Method Performance by Execution Method for POIR ............... 242

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Table G-ll Scheduling Method Performance by Execution Method for POOR ........... 244

Table G-12 Execution Method Performance by Scheduling Method for ADUR ........... 245

Table G-13 Execution Method Performance by Scheduling Method for RDUR ........... 246
Table G-l4 Execution Method Performance by Scheduling Method for ANPV ........... 247
Table G-l 5 Execution Method Performance by Scheduling Method for RNPV ........... 248

Table 6-16 Execution Method Performance by Scheduling Method for WADL .......... 249
Table G-17 Execution Method Performance by Scheduling Method for WADE .......... 250

Table G-18 Execution Method Performance by Scheduling Method for WADC .......... 251

Table G-19 Execution Method Performance by Scheduling Method for POIC ............. 252
Table G-20 Execution Method Performance by Scheduling Method for POIR ............. 253
Table G-21 Execution Method Performance by Scheduling Method for POOC ........... 254
Table 6-22 Execution Method Performance by Scheduling Method for POOR ........... 255

Table H-l Tally of Differences in Ranks: Scheduling by Execution (Traditional) ....... 257
Table H—2 Tally of Differences in Ranks: Scheduling by Execution (Stability) ........... 258

Table H-3 Tally of Differences in Ranks: Execution by Scheduling (Traditional) ....... 259

Table H-4 Tally of Differences in Ranks: Execution by Scheduling (Stability) ........... 260
Table L-l NPV vs. rt: OPT ............................................................................................ 314
Table L-2 NPV vs. rt: SLK ............................................................................................ 315
Table L-3 NPV vs. rt: LFT ............................................................................................ 316
Table L-4 NPV vs. rt: RSO ............................................................................................ 317
Table L—S NPV vs. rt: LSC ............................................................................................ 318
Table L-6 NPV vs. rt: DCF ............................................................................................ 319

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Table M-l Percent Change (variability none-some) ....................................................... 322
Table M-2 Percent Change (disruption none-frequent/short) ......................................... 323
Table M-3 Percent Change (disruption none-infrequent/ long) ....................................... 324
Table M-4 Percent Change (disruption frequent/short-infrequent/long) ........................ 325

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Figure 3.1 Theoretical Model ........................................................................................... 51
Figure 3.2 Resource Profile Offset ................................................................................... 57
Figure 3.3 Experimental Design ....................................................................................... 67
Figure 4.1 Sensitivity of NPV to rt (OPT) ........................................................................ 86
Figure 4.2 Histogram of Aggregate Statistics (ADUR) .................................................... 88
Figure 4.3 ADUR Treatment Means ................................................................................. 92
Figure 4.4 Distributions, P Normality and Variance (ADUR) ......................................... 94
Figure A-l: Aggregate Histogram, ADUR ..................................................................... 161
Figure A-2: Aggregate Histogram, RDUR ..................................................................... 161
Figure A-3: Aggregate Histogram, ANPV ..................................................................... 162
Figure A-4: Aggregate Histogram, RNPV ...................................................................... 162
Figure A-5: Aggregate Histogram, POIC ....................................................................... 163
Figure A-6: Aggregate Histogram, POIR ....................................................................... 163
Figure A-7: Aggregate Histogram, POOC ...................................................................... 164
Figure A-8: Aggregate Histogram, POOR ...................................................................... 164
Figure A-9: Aggregate Histogram, WADE .................................................................... 165
Figure A-lO: Aggregate Histogram, WADL .................................................................. 165
Figure A-l 1: Aggregate Histogram, WADC .................................................................. 166
Figure C-l: Graphical Means, ADUR/NRN ................................................................... 180
Figure C-2: Graphical Means, ADUR/FRN ................................................................... 180

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Figure C-4: Graphical Means, ADUR/FRW .................................................................. 180
Figure 05: Graphical Means, RDUR/NRN ................................................................... 181
Figure C-6: Graphical Means, RDUR/FRN .................................................................... 181
Figure C-7: Graphical Means, RDUR/NRW .................................................................. 181
Figure C-8: Graphical Means, RDUR/FRW ................................................................... 181
Figure C-9: Graphical Means, ANPV/NRN ................................................................... 182
Figure 010: Graphical Means, ANPV/F RN .................................................................. 182
Figure C-11: Graphical Means, ANPV/NRW ................................................................ 182
Figure C-12: Graphical Means, ANPV/FRW ................................................................. 182
Figure C-13: Graphical Means, RNPV/NRN ................................................................. 183
Figure 014: Graphical Means, RNPV/F RN .................................................................. 183
Figure C-15: Graphical Means, RNPV/NRW ................................................................ 183
Figure C-16: Graphical Means, RNPV/FRW ................................................................. 183
Figure C-l7: Graphical Means, WADE/NRN ................................................................ 184
Figure C-18: Graphical Means, WADE/F RN ................................................................. 184
Figure C-19: Graphical Means, WADE/NRW ............................................................... 184
Figure 020:. Graphical Means, WADE/FRW ................................................................ 184
Figure 021: Graphical Means, WADL/NRN ................................................................ 185
Figure C-22: Graphical Means, WADL/F RN ................................................................. 185
Figure C-23: Graphical Means, WADL/NRW ............................................................... 185
Figure C—24: Graphical Means, WADL/FRW ................................................................ 185
Figure C-25: Graphical Means, WADC/NRN ................................................................ 186

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Figure C-26: Graphical Means, WADC/F RN ................................................................ 186
Figure C-27: Graphical Means, WADC/NRW ............................................................... 186
Figure C-28: Graphical Means, WADC/FRW ................................................................ 186
Figure C-29: Graphical Means, POIC/N RN ................................................................... 187
Figure C-30: Graphical Means, POIC/F RN .................................................................... 187
Figure C-31: Graphical Means, POIC/NRW .................................................................. 187
Figure 032: Graphical Means, POIC/FRW ................................................................... 187
Figure C-33: Graphical Means, POIR/NRN ................................................................... 188
Figure C-34: Graphical Means, POIR/FRN .................................................................... 188
Figure 035: Graphical Means, POIR/NRW .................................................................. 188
Figure 036: Graphical Means, POIR/FRW ................................................................... 188
Figure C-37: Graphical Means, POOC/NRN ................................................................. 189
Figure C-38: Graphical Means, POOC/F RN .................................................................. 189
Figure C-39: Graphical Means, POOC/NRW ................................................................ 189
Figure C-40: Graphical Means, POOC/FRW ................................................................. 189
Figure C-4l: Graphical Means, POOR/N RN ................................................................. 190
Figure C-42: Graphical Means, POOR/FRN .................................................................. 190
Figure C-43: Graphical Means, POOR/NRW ................................................................ 190
Figure C-44: Graphical Means, POOR/FRW ................................................................. 190
Figure D-l: Normality, ADUR ....................................................................................... 192
Figure D-2: Variance, ADUR ......................................................................................... 192
Figure D-3: Normality, RDUR ....................................................................................... 193
Figure D-4: Variance, RDUR ......................................................................................... 193

xvi

Figure D-5: Normality, ANPV ....................................................................................... 194
Figure D-6: Variance, AN PV .......................................................................................... 194
Figure D-7: Normality, RNPV ........................................................................................ 195
Figure D-8: Variance, RNPV .......................................................................................... 195
Figure D-9: Normality, WADE ...................................................................................... 196
Figure D-10: Variance, WADE ...................................................................................... 196
Figure D-l 1: Normality, WADL .................................................................................... 197
Figure D-12: Variance, WADL ...................................................................................... 197
Figure D-l3: Normality, WADC .................................................................................... 198
Figure D-14: Variance, WADC ...................................................................................... 198
Figure D-15: Normality, POIC ....................................................................................... 199
Figure D-16: Variance, POIC ......................................................................................... 199
Figure D—17: Normality, POIR ....................................................................................... 200
Figure D-18: Variance, POIR ......................................................................................... 200
Figure D-19: Normality, POOC ...................................................................................... 201
Figure D-20: Variance, POOC ........................................................................................ 201
Figure D-21: Normality, POOR ...................................................................................... 202
Figure D-22: Variance, POOR ........................................................................................ 202
Figure E-l: Scatterplot, ADUR-RDUR .......................................................................... 204
Figure E-2: Scatterplot, ANPV-RNPV ........................................................................... 204
Figure E-3: Scatterplot, RNPV-RDUR ........................................................................... 205
Figure E-4: Scatterplot, ANPV-RNPV ........................................................................... 205
Figure E-5: Scatterplot, ANPV-ADUR .......................................................................... 206

xvii

 

Figure E-6: Scatterplot, RNPV-ADUR ........................................................................... 206
Figure E-7: Scatterplot, WADE-ADUR ......................................................................... 207
Figure E-8: Scatterplot, WADE-RDUR ......................................................................... 207
Figure E-9: Scatterplot, WADE-ANPV .......................................................................... 208
Figure E-lO: Scatterplot, WADE-RNPV ........................................................................ 208
Figure E-11: Scatterplot, WADL-ADUR ....................................................................... 209
Figure E-12: Scatterplot, WADL-RDUR ....................................................................... 209
Figure E-13: Scatterplot, WADL-ANPV ........................................................................ 210
Figure E-14: Scatterplot, WADL-RNPV ........................................................................ 210
Figure E-15: Scatterplot, WADC-ADUR ....................................................................... 211
Figure E-16: Scatterplot, WADC-RDUR ....................................................................... 211
Figure E-17: Scatterplot, WADC-ANPV ....................................................................... 212
Figure E-18: Scatterplot, WADC-RNPV ........................................................................ 212
Figure E-19: Scatterplot, POIC-ADUR .......................................................................... 213
Figure E-20: Scatterplot, POIC-RDUR .......................................................................... 213
Figure E-21: Scatterplot, POIC-ANPV ........................................................................... 214
Figure E-22: Scatterplot, POIC-RNPV ........................................................................... 214
Figure E-23: Scatterplot, POIR-ADUR .......................................................................... 215
Figure E-24: Scatterplot, POIR-RDUR .......................................................................... 215
Figure E-25: Scatterplot, POIR-ANPV ........................................................................... 216
Figure E-26: Scatterplot, POIR-RNPV ........................................................................... 216
Figure E-27: Scatterplot, POOC-ADUR ......................................................................... 217
Figure E-28: Scatterplot, POOC-RDUR ......................................................................... 217

xviii

Figure E-29:
Figure E-30:
Figure E-3 1:
Figure E-32:
Figure E-33:

Figure E-34:

Figure F-l:
Figure F-2:
Figure F -3:
Figure F-4:
Figure F -5:
Figure F-6:
Figure F-7:
Figure F-8:

Figure F-9:

Figure F-10:
Figure F-ll:
Figure F-12:
Figure F-13:
Figure F-14:
Figure F-15:
Figure F-16:

Figure F-l7:

Scatterplot, POOC-ANPV ......................................................................... 218
Scatterplot, POOC-RNPV ......................................................................... 218
Scatterplot, POOR-ADUR ......................................................................... 219
Scatterplot, POOR-RDUR ......................................................................... 219
Scatterplot, POOR-ANPV ......................................................................... 220
Scatterplot, POOR-RNPV ......................................................................... 220
Predicted ADUR .......................................................................................... 222
QQ ADUR ................................................................................................... 222
Predicted RDUR .......................................................................................... 223
QQ RDUR .................................................................................................... 223
Predicted AN PV .......................................................................................... 224
QQ ANPV .................................................................................................... 224
Predicted RNPV ........................................................................................... 225
QQ RNPV .................................................................................................... 225
Predicted WADE ......................................................................................... 226
QQ WADE ................................................................................................. 226
Predicted WADL ........................................................................................ 227
QQ WADL ................................................................................................. 227
Predicted WADC ....................................................................................... 228
QQ WADC ................................................................................................ 228
Predicted POIC .......................................................................................... 229
QQ POIC .................................................................................................... 229
Predicted POIR .......................................................................................... 230

xix

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Figure F-20
Figure F-21
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: QQ POIR .................................................................................................... 230
: Predicted POOC ......................................................................................... 231
: QQ POOC .................................................................................................. 231
: Predicted POOR ......................................................................................... 232
: QQ POOR .................................................................................................. 232
Heur013 ........................................................................................................ 262
Heur048 ........................................................................................................ 263
Heur056 ........... 264
Heur014 ........................................................................................................ 265
Heur015 ........................................................................................................ 266
Heur105 ........................................................................................................ 267
Heur107 ........................................................................................................ 268
Heur110 ........................................................................................................ 269

Sensitivity of NPV to rt (OPT) .................................................................... 314
Sensitivity of NPV to rt (SLK) ..................................................................... 315
Sensitivity of NPV to rt (LFT) ..................................................................... 316
Sensitivity of NPV to rt (RSO) ..................................................................... 317
Sensitivity of NPV to rt (LSC) ..................................................................... 318
Sensitivity of NPV to rt (DCF) ..................................................................... 319
Sensitivity of NPV to rt (BCP) ..................................................................... 320

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Chapter 1

INTRODUCTION

1.1 Overview

 

This research investigates the effects of variability and disruption upon the
management of projects. The purpose of this effort is to explore the usefulness of various
techniques in reducing the negative effects of variability and disruption. A project
consists of a series of tasks or activities that must be performed by resources, in a specific
order, to achieve a desired result. Variability refers to uncertainty in the project task
times. Disruptions to the project consist of the unplanned unavailability of resources.
When a project is subject to variability and disruption, the project may begin to take
longer, cost more, and achieve less than planned. These negative effects are very
important, and the issue has received much study by academics and practitioners alike.

Coping mechanisms to avoid the consequences of variability and disruption can
generally take two forms. The first is to schedule or plan the resources and activities
carefully in order to make the project less sensitive. The second is to execute the
schedule in such a way as to mitigate the damage done as it occurs. It is proposed that
some scheduling techniques generate plans that are less sensitive to variability and
disruption (more stable) than others. In addition, it is proposed that some execution
techniques are more effective at absorbing or dampening the effects of disruption than
others. The stability of the project may come at the expense of other desirable project
outcomes, however. A more stable project may take longer to complete, or be more

costly. These issues have not yet been investigated to any detail. This research will

address and begin to resolve some of the fundamental questions and problems
surrounding the performance and stability of projects, subject to variability and
disruptions, under a variety of conditions.

As will be explained in greater detail in the sections to follow, this paper describes a
research effort employing discrete event, dynamic system simulation of a benchmark set
of projects. These simulation experiments were designed around the issues just raised.
Appropriate statistical techniques were applied to the simulation output in order to
explore the relationships between the variables of interest. The following sections will
present in further detail what this research set out to do, how it was done, and why the
research results are important. First, we will discuss the Research Problem and
Questions (section 1.2). This chapter will end with a discussion of why the work is

important and potentially useful in the Importance of Research (section 1.3).

1.2 Research Problem and Questions

Managers calculate and use project schedules to control activities and resources in
projects. Schedules are developed using a variety of methods, and the same project or
group of projects could be scheduled in many different ways using these different
approaches. Each schedule represents a different set of predictions and choices about
how best to manage the resources available to complete the project. For a given project,
each unique schedule (solution) establishes relationships between activities and resources.
These relationships will ultimately determine the performance of the project when

managed using that schedule. Overall performance outcomes of particular interest to

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managers are total project duration and total project cost (or net present value). Other
measures of interest have traditionally included total, peak, and average resource
utilization and other measures of resource efficiency. Individual scheduling techniques
have been developed which generally provide solutions that perform best against one or
the other of these criteria; no single method has been found that provides a "best" answer
on all criteria.

In theory, the manager applies the more successful scheduling technique in order to
optimize the most important project performance criterion. The trade-offs between
criteria implicit in using one scheduling technique over the others are considered when
selecting which scheduling method is considered "best" for a particular application. For
example, some techniques offer better total cost performance, and others offer shorter
total project duration.

In practice, however, the effects of variability and disruptions complicate the
anticipated relationship between the scheduling technique and the performance of the
schedule. "Variability" occurs when the actual task duration times do not equal
scheduled times. "Disruptions" occur when resources (ofien critical) become unavailable
for a period of time, preventing work on some activities from starting as scheduled. For
example, a resource disruption may occur as a result of a mechanical breakdown of a
piece of equipment. Another type of resource disruption may occur when a resource is
taken away by another project, making it unavailable for the current task. These effects
interfere with the ability of the project schedule to accurately predict outcomes and guide

correct decisions as project activities are completed.

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Once variability and/or disruptions cause a deviation from the schedule, additional
choices must be made as to how a particular project will be executed. While the original
schedule represents a plan (and the scheduling technique is a planning method), once the
project is actually begun, the execution method may also determine how well the project
performs. Both the planning method and the execution method contribute to overall
project performance. Given the nature of the project itself (the technical precedence and
resource requirement characteristics which establish the potential performance bounds),
the planning and execution methods used to manage the effort will affect the actual
results of the completed project against the desired results (e. g., total cost, total duration,
net present value).

Under these conditions, an additional concern regarding the performance of a project
may be how "stable" it is. The relative "stability" of a project refers to how immune to
disruption (stable) or sensitive to disruption (unstable) the activities and resources are
under conditions of uncertainty. For the purposes of this research, stability will represent
the degree of deviation from schedule for the resources and activities in the project. A
project that is executed very closely to the schedule will be considered to be more stable.
A project that is executed with numerous (and/or large) deviations from the schedule will
be considered to have been (relatively) less stable.

As will be discussed in section 1.3, Importance of Research, the loss of stability in a
project may indicate an upcoming increase in costs, complexity, and confiision
encountered as the project executes. Project stability may therefore be an important,
desirable outcome for the project manager. It is anticipated that stability will share some

of the same characteristics of other project criteria. To a certain degree, the technical

 

precedence and resource relationships within the projects themselves may impose bounds
on the degree of stability a project may exhibit. Also, certain scheduling and execution
techniques may contribute to or detract from the stability of the project.

Project stability has not yet been studied explicitly; nor has the role of disruption.
This research investigates the performance of both planning and execution techniques in
the single project, constrained resource environment, under conditions of uncertainty,
when subject to disruptions. Planning techniques include several of the most popular and
successful heuristics for project planning and scheduling in the literature today.
Similarly, execution techniques include a representative collection of allocation and
decision making methods. A known, benchmark set of project scheduling problems
representing a broad spectrum of situations have been simulated at multiple levels of
variability and disruption. The performance of each combination of planning and
execution technique has been measured with respect to time, net present value, and
stability. Basic questions surround this issue:

- What is the nature of the tradeoff (if one exists) between schedule stability and

schedule performance with respect to the traditional measures in the project?

- How are planning methods affected by variability and disruption?

- How are execution methods affected by variability and disruption?

- Are schedules developed by certain heuristics/scheduling rules more sensitive to

variability?

- Are schedules developed by certain heuristics/scheduling rules more sensitive to

disruption?

- Do certain execution techniques help minimize the effects of variability?

 

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The procedures employed to answer the research questions posed will be covered in
greater detail in Chapter 3, Methodology. Chapter 3 will include the refinement of these
questions into specific research hypotheses, as well as thorough descriptions of the

variables used to define the theoretical constructs.

1.3 Importance of Research

 

New product development, equipment installation, real property acquisition and
construction, public works, military campaigns, and shop floor design are all examples of
complex endeavors that are managed and controlled through the use of project
management techniques. Virtually any large-scale non-sequential human undertaking
that consists of the accomplishment of order-dependent tasks or activities by people or
machines using resources to achieve a desired result can (and, more properly, should) be
organized and controlled using project management/resource scheduling. Problems
within this field can have severe cost and performance implications (locally); the study
and solution of these problems have broad application (globally). A recent review of
academic literature in this research area (Ozdamar & Ulusoy, 1995) identified over 80
"major" contributions since the 1970's; an automated search of the ProQuest/ABI Inform
database search on the key phrase "Project Management" turned up over 1,270 references
for the time period January 1994 through August 1996 alone! This indicates a high level

of interest in the subject. The problems surrounding the proper allocation of resources to

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tasks in projects, and the scheduling of those tasks, are of great practical and academic

significance.

In order to synchronize the performance of multiple, interdependent activities in a
large project, a schedule is developed. The schedule represents the planned start and stop
times for the activities and provides instructions for the resources needed to perform the
activities. Schedules are developed in order to achieve some set of objectives, while
satisfying various constraints imposed upon the project. On a basic level, performance to
the schedule is important in order to ensure that the objectives are met and the constraints

are satisfied.

Once the project begins, however, variability in the duration of the activities and
disruptions to the resources begin to occur. Variability and disruption cause deviations to
the schedule. These deviations, in turn, may cause other deviations to future scheduled
events. These deviations in the timing of activities or the allocation of resources indicate
instability in the execution of the project. This instability represents a loss in the

synchronization of the project.

Loss of synchronization in the activities and resources in the project may result
in a degradation of project performance. For example, construction projects ofien
experience resource disruptions and activity variability. A key piece of equipment may
fail, or weather conditions may extend the planned duration of an activity. Either of these
events may delay the start time of a subsequent activity. Some resources may only be
available for a finite period of time. If an activity is delayed, a resource needed to

perform it may no longer be available. Additional units of the resource may need to be

secured (increasing cost) or substitute resources may need to be used. As a result, the

project may fail to meet cost or time performance objectives.

During the development and launch of a new product, the activities of the marketing
and design teams may need to be synchronized through adherence to a schedule. The
early completion of graphical layout for a visual ad campaign (ahead of final product
design work) may result in the need to rework the advertisements or embarrassing
misrepresentation of the product. The late completion of customer focus group research
may result in the product being designed with (easily avoidable) undesirable

characteristics.

In a project like a military campaign, there may be a heavy price to pay for an
activity being performed either too early or too late. Supplies delivered to a marshaling
point in advance of schedule may expose those supplies unnecessarily to enemy action,
resulting in the destruction or capture of the supplies. The destruction of a bridge ahead
of schedule may prevent friendly forces from using that bridge to advance into enemy
territory. Similarly, the late performance of activities may have undesirable effects on the
military project. Resources like aircraft and armored vehicles, if allocated to certain
activities either early or late, may be unavailable for higher priority activities or be less

effective than if used at the scheduled time.

Both late and early activity starts or stops can degrade project performance.
Deviations in the start and finish times of activities or deviations in the allocation of

resources represent instability in the project. This instability may result in a loss in the

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synchronization of the schedule. This loss of synchronization can be triggered by

resource disruption or by variability in activity duration.

It is anticipated that the stability of a schedule would be related to the traditional
measures of project cost and time performance. On a basic level, if activities incur a
setup cost (in time or dollars), or if multiple resources must be simultaneously scheduled
in order to perform an activity, then disruptions in the availability of a resource could
directly affect cost performance. If resources are rented from outside sources, cost
premiums may be incurred as a result of schedule deviations. Extra charges may be
incurred for either the early use or late return of rented or leased equipment.

Recent articles in the cost/schedule performance literature (Lee & Gatton, 1994; Just
& Murphy, 1994) focus on the "unavailability of resources" as a key determinant in
project cost performance. Lee & Gatton approach the issue as a productivity problem. In
their study of the construction industry, they identified material unavailability, equipment
unavailability, and unreasonable schedules as the main causes of job inefficiency. They
attribute the source of these problems to the widespread use of current naive scheduling
approaches that assume unlimited or unconstrained resources. An unstated assumption of
their perspective is that resource unavailability (disruption) is not a problem as long as
excess resource capacity is present (and vice versa). Just & Murphy take a similar
approach, focusing on the negative effects of building project plans without regard to the
availability of resources. In their paper, they demonstrate that a failure to plan for

resource unavailability can extend the project length, reduce project efficiency, increase

 

project costs.

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project costs, and result in failures to meet contractual obligations— potentially turning a
profitable project into an unprofitable one.

Deviations from the project schedule may influence the financial evaluation of the
project by the company or its investors. The performance of large projects is often
tracked through the accomplishment of milestones. A milestone represents the
culmination of a key set of activities. In financial terms, schedule variance refers to
deviations from the cash flow schedule associated with the project milestones (Wysocki,
et. al., 1995). Financial managers track the progress of the project by comparing the
variance between the scheduled cost of the work performed and the actual costs incurred
as of the milestone completion date. Instability in the project will have a direct effect
upon the financial variance measures. Resource use ahead of or behind schedule will
affect the actual costs incurred. Task completion ahead of or behind schedule will affect
the costs that should have been incurred according to the schedule. Significant
differences between the scheduled and actual costs incurred are a source of concern for
the financial managers. Confidence in the project can be shaken, and the investors may
alter the financing of the project and demand corrective actions from the project
managers.

In summary, instability in a project may lead to many negative effects. First, the loss
of a resource (or a delay in its availability) may idle other resources, and result in a direct
loss in productivity or efficiency. Second, the project could experience a loss of
synchronization of the activities and resources, resulting in a degradation of the

effectiveness of the project. Third, disruptions to resources may incur additional costs,

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degrade project efficiency, or lead to late completion. Finally, project instability can
result in deviations in the accomplishment of project milestones, which may affect the
financial evaluation of the project or the firm responsible for the project. Disruptions
could spread throughout the system, resulting in many of the negative effects described
previously. An apparently minor disruption to an apparently minor resource could lead to
grave effects on the project as a whole. The degree to which this "ripple effect" creates
overall problems is a reflection of the stability of the project as scheduled and executed.

This research seeks to extend the concept of the effects of resource unavailability and
activity duration variability into the realm of schedule and resource stability. It has been
mentioned that certain factors shape the ultimate performance of the project with respect
to the desired outcomes. Technical and resource dependencies serve to limit or bound the
potential achievement of the project. Variability in activity durations and disruptions in
resources will influence the degree of achievement of project goals. The planning and
execution methods used to schedule and perform the project activities have also been
noted to have a significant effect on the overall project performance. While these factors
have been studied with respect to their effects on the traditional project performance
outcomes, no study has investigated these factors as they relate to project stability.

As a first step, this research defines several project management stability measures.
Next, the study tries to provide insight into the relationships between the traditional
factors of project performance. These traditional factors include the characteristics of the
projects, the nature of the project environment (activity variability and resource
disruption), and the scheduling and execution methods used to manage the project.

Hopefully, insight is provided into the nature of the relationships between these factors

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and project stability. Finally, the knowledge gained in studying both project stability and
the relationships between project stability, other outcome measures, and the traditional
factors of project performance are extended into practical significance for the
management of projects. Ultimately, it is hoped that the descriptive theories built
initially will be translated into prescriptions to assist managers in achieving higher levels

of performance from the projects under their control.

12

Chapter 2

SIGNIFICANT PRIOR RESEARCH

The importance and complexity of problems in project management have led to a
great deal of research activity in this area. Project management/scheduling has been
studied and reported upon extensively in the literature for many years. The basic
questions have been analyzed in many different ways. However, the intractability of
some of the fundamental questions in the field continues to present opportunities. The
following review of previous literature will attempt to establish the conceptual structure
of the field and the position of this research in it. In addition, specific subsections will
establish the state of existing knowledge on (1) Planning Approaches, (2) Execution
Approaches, and (3) Stability Measures. Finally, the role of the exogenous or moderating

considerations in past research will be described.

2.1 General Reviews of the Literature

The domain of project management and project scheduling research is incredibly
diverse. A large volume of published literature on many different aspects of the problem
exists. Many works predate even the formal reports on the initial techniques of the
Program Evaluation and Review Technique (U. S. Department of the Navy, 195 8) and the
Critical Path Method (Kelly and Walker, 1959). Several taxonomic schema have been
used over the years to organize this vast body of literature. Major criteria have been

developed for the purpose of classifying problem and research types within these schema.

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These criteria include: the nature of the constraints, the objectives sought, the solution
approach, how the resources are utilized, and whether single or multiple projects are
solved simultaneously.

An early effort (Davis, 1966) used some primary characteristics of the problem under
study as criteria for logically organizing the literature. Davis noted that there existed
fundamental differences between research investigating the resource constrained problem
type and the resource unconstrained type. In the resource constrained project scheduling
problem, the resources required for the performance of tasks are considered finite and
available at levels below what would be needed to complete all activities in the minimal
amount of time. In the resource unconstrained type, the solution approach assumes that
infinite resources are available on demand. As noted by Davis, both the desired solution
outcome and method of solution are very different for the two types of problems. The
fundamental nature of this split has led to the recognition of the taxonomic characteristic
of resource constrainedness by many other researchers in this field. The resource
constrained class of problems, perhaps by virtue of having higher practical application,
has become the dominant class of problem type in project scheduling research.

Researchers refined the classifications based on the nature of the constraints.
Problems can now be classified (Ozdamar & Ulusoy, 1995) as having only technical or
precedence constraints (Davis's resource unconstrained); or can have resource constraints
which are renewable, nonrenewable, or doubly constrained. Renewable resources are
available for a certain amount of time over a given time period (e.g., 8 hours of
availability over a 24 hour day for personnel shifis). When a new time period begins, the

renewable resources are available once more for the new time period. Non-renewable

14

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resources are available in a finite amount over the duration of the project. Finite
resources such as raw materials or budgeted capital may fall into this category. Doubly
constrained resources can be consumed only for a limited time in given time periods (like
renewable resources) and have only a finite amount of availability over the total project
duration (like nonrenewable resources).

It must be noted that even in 1966 there were several criteria proposed for the
categorization of problems within the two broad types of resource constrained and
unconstrained. Primary among them was the division of problems based on the desired
optimization outcome (Davis, 1966). Outcomes being sought at the time included the
minimization of total project duration, the minimization of total project cost, the
minimization of resource consumption (resource leveling), and the description and
analysis of total time and total cost tradeoff curves. Obj ective(s) sought continued to be
used as a classification criterion by later researchers, and in some cases was used as the
primary criterion (Ozdamar & Ulusoy, 1995). While the time minimization outcome has
consistently received the bulk of attention, the minimization of cost and the maximization
of net present value (NPV) have received considerable attention in the last twenty years.
There is also a class of problems that attempt to simultaneously optimize for multiple
objectives.

The third major taxonomic criterion for the organization of the project
management/scheduling literature was also first noted by Davis in his 1973 follow-up
work. While retaining the problem characteristics of resource constrained vs. resource
unconstrained, and the desired optimization outcome, he divided the literature along a

new axis: the characteristics of the solution method employed. Davis noted that solution

15

methods were either fundamentally exact or heuristic in nature. Exact approaches employ
numerical analysis methods to determine best schedules or allocations of resources in
order to achieve an optimum result on some desired project performance measure.
Heuristic approaches employ inexact rules of thumb or decision rules in order to achieve
good (but not necessarily the best) result on some desired project performance measure.

The exact approaches, while promising, have been limited in their application by the
size and complexity of problems that are tractable in a realistic sense. The implications
of this limitation will be discussed in more detail in a later section of this proposal. The
current research applies several previously successful heuristic procedures to a subset of a
benchmark set of project scheduling problems (the Patterson Set; Patterson, 1984). These
resource constrained project scheduling problems have known, exact solutions for the
deterministic case (found by Patterson's modification of an enumerative procedure
employed by Talbot in 1976). The known, exact solutions provide project schedules or
plans that achieve best results under deterministic conditions.

By the early 1970's, the nature and behavior of the resources and the interaction
between the resources and the activities began to be recognized as forming unique
problem classes. Davis (1973) began the trend by differentiating between single resource
and multiple resource cases. He used three classes of resource utilization types: first, one
resource type, common to all jobs; second, multiple resource types, but only one type
required for each activity; and third, multiple resource types, that are required in a variety
of combinations for the activities in the project. The multiple resource cases were soon
expanded to consider flexible situations where the duration of an activity changed based

on the amount (and perhaps the type) of resources that were assigned to it. This

16

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recognition of implicit time-resource functions established a classification of problems
based on the resource employment mode (Ozdamar & Ulusoy, 1995). Single mode
resource employment exists when each activity requires a fixed amount of resources (by
type) for its accomplishment. Multi-mode resource employment allows the application of
multiple combinations of resources (by type) for the accomplishment of tasks.

A final major taxonomic criterion for the classification of project scheduling research
is the separation of single project problems from multiple project problems. In the single
project cases, researchers attempt to schedule the activities and resources of a single
project. These problems are distinct from the set that attempt to schedule a set of
resources against activities in multiple projects. While much more complex, the multi-
project setting has great practical application to large firms that must attempt to manage
the successful completion of multiple projects (e.g., construction). Due to the simplicity
of the single project case, researchers often initially investigate new issues or techniques
in this environment and then expand their efforts into the multi-project case if initial
results warrant further effort.

Several taxonomic schema have been used over the years to organize the vast body
of project management and project scheduling literature. The domain of this research is
incredibly diverse. Major criteria have been developed for the purpose of classifying
problem and research types within these schema. These criteria include: nature of the
constraints, the objectives sought, the solution approach, how the resources are utilized,
and whether single or multiple projects are solved simultaneously.

The current research effort studies those problems which can be classified as:

resource constrained, considering multiple objectives, solved beuristically, with single

17

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mode resource-activity functions, applied to single projects in isolation. The remainder
of this literature review will concentrate on those works which have focused on this
particular formulation of project scheduling problems. Problem classes outside of this
type will be discussed only as they apply to or lend understanding to this narrower type of
problem. In the following sections of the literature review, discussions cover (in turn):
the planning or scheduling approaches used, the execution approach or decision rules
employed, measures of stability, and the environmental or exogenous variables tracked in

this study.

2.2 Planning Approaches

 

The fundamental goal in solving the resource constrained project scheduling problem
(RCPSP) is to develop a plan for the allocation of resources to the activities in the project
in order to achieve some overall project performance objective(s). This plan generally
takes the form of a schedule of which resources perform which activities and when. The
next two sections of the literature review discuss the limitations, assumptions, and the
applicability of both exact and heuristic approaches. The best specific techniques within
each class are identified and discussed.

2.2.1 Exact Approaches

 

Exact approaches use numerical optimization methods to determine best schedules or
allocations of resources. The definition of best is defined by a desired result on some
project performance measure. For example, a project may need to be scheduled in such a
fashion as to complete all tasks in the shortest time possible (minimize total duration of

the project). An exact approach would formulate a mathematical model of the problem

18

(e.g. an integer, linear program) and solve this model for minimum duration. The exact
approaches promise (when all of the methodological assumptions are met) to provide a
single, best answer to the problem as formulated.

Because of this promise of achieving a best, exact answer, researchers have been
attempting to apply exact methods to the RCPSP since the early days (19503) of research
on the problem. These attempts have achieved mixed success for a variety of reasons.
Two limitations of the exact approaches to the RCPSP are: first, the assumptions
inherent in the exact approaches do not match the realities of the project management
problem, leading to a loss of solution fidelity; and second, the size and complexity of
realistic RCPSPs put them beyond the capabilities of many of the exact methods.

Patterson (1984) reviewed the state of the art in the use of exact procedures. He
noted that the early attempts at finding exact solutions relied on mathematical
programming (integer) models. These models required that the problem be formulated in
very specific and unrealistic ways, and could only model very simplistic problem
characteristics. These attempts were therefore of limited practical use (Davis, 1973). A
more recent mathematical programming model (Slowinski, 1981) formulated the RCPSP
as a Multiple Objective-Integer Linear Program designed to be attacked using Khachian's
algorithm. Such a formulation promised to solve the RCPSP in polynomial time;
however, this and subsequent attempts based on Slowinski's formulation have not been
borne out.

Due to the failures and limitations of the earlier LP models, specialized formulations
were developed, usually relying on an enumerative/search based approach. In the 1984

article Patterson noted that three of these approaches performed best in a wide variety of

19

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situations for the RCPSP: Davis & Heidorn's (1971) Bounded Enumeration procedure,
Stinson's (1976) Branch & Bound, and Talbot's (1976) Implicit Enumeration method.
Two additional Branch & Bound (depth first) procedures have been developed since
1984; the Christofides et. al. work of 1987 and that of Demeulemeester & Herroelen
(1992).

While these exact approaches still require that time be considered in discrete values,
and activity times be integer values, the assumptions required by the model are more
realistic than the mathematical programming approaches tried initially. However, these
exact approaches are still limited in their applicability by the problem size and
complexity. Using these enumerative formulations, linear growth in problem size leads
(generally) to geometric growth in solution time. The RCPSP is combinatorial and NP
complete (Karp, 1972).

The search for efficient analytical exact approaches applicable to practical-sized
projects continues. Recently, Simpson & Patterson (1996) used a parallel processing
approach on an enumerative search algorithm in order to take advantage of recent
advances in computer hardware technology. While representing an improvement in
speed on smaller problems, and a potential expansion in the size and complexity of
projects tractable within a reasonable amount of time, this technique has not yet been
fully developed. Even with the ongoing refinements to the exact approaches, two main
problems still persist in trying to use these methods in practice. Currently, exact
approaches seem to be generally limited to 50 activities and 3 resources or fewer
(Simpson, 1991) in order to produce solutions in a reasonable amount of time. This

significantly limits the application of exact approaches to realistic projects. Also, all

20

exact approaches (to date) have relied upon the assumption of deterministic activity
times. Real project activities deviate from deterministic estimates to varying degrees.
The validity of any exact, deterministic approach is threatened by the stochastic, variable
nature of project management in reality. Therefore, this study concentrates on the
performance of heuristic methods. However, the performance of the exact, deterministic
solutions in the stochastic, variable environment is used as a reference for the
performance of the heuristics. The benchmark set of RCPSP's used in this study, the
Patterson Set, are solvable using Patterson's (1984) implicit enumeration algorithm and
exact time-minimizing solutions for the deterministic cases are known.

2.2.2 Heuristic Approaches

 

Heuristic approaches use inexact rules of thumb or decision rules in order to achieve
a good (but not necessarily the best) result on the desired project performance measure.
The technical precedence (network structure) constraints are inviolate; the decisions
generated by the heuristic techniques involve only the ordering and prioritizing of
activities. The resources, when they become available, are assigned to eligible activities.
Activities become eligible when their precedence or technical constraints have been
satisfied. The order in which the eligible activities are completed determines the
eligibility of additional activites through the technical or precedence constraints. This
flow of activities through the eligible list ultimately determines the completion sequence
of every activity in the project.

Heuristic techniques are further divided by how the method operates. Generally, the
heuristics are either serial or parallel. Serial routines will assign priorities to tasks (for the

purpose of dedicating resources to tasks) in a separate step before sequencing the tasks in

21

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the schedule. Parallel routines prioritize and sequence the tasks at the same time. Due
primarily to the inherent efficiency of the parallel routines, with no loss in applicability or
quality of solution, the parallel routines have generally come to dominate the approaches
in use today. The parallel heuristics have been further subdivided based on the desired
project outcome they have been designed to provide good solutions for (Ozdamar &
Ulusoy, 1995). This is analogous to the specific formulation of each exact approach in
order to optimize a desired project outcome. The main classes of desired outcome are the
minimization of project duration, the minimization of cost/maximization of net present
value, and the satisfaction of multiple objectives. Selected best performers in each class
are discussed below.
2.2.2.1 Heuristics Seeking Minimum Project Duration

Davis & Patterson (1975) offered a comprehensive review in "A Comparison of
Heuristic and Optimum Solutions in Resource-Constrained Scheduling." A general
conclusion in the literature at this point was that there was little basis a priori for making
a choice among the (at that time) literally hundreds of published heuristics. Davis and
Patterson's effort was designed to provide a more definitive answer to the question of
which heuristics perform better. A problem set of 83 multiple resource, resource
constrained projects with 20—27 activities were solved to minimize total project duration
using nine scheduling techniques. First, optimal solutions were found using a bounded
enumeration exact technique (OPT). The calculation of the optimal schedules was
possible due to the small size and limited complexity of the problem set. Second,

schedules were generated using a heuristic approach that assigned activities to resources

22

randomly (RN D). These two approaches, OPT and RND, provided two important
benchmark comparisons for the remaining seven techniques investigated.

The results of this investigation were instructive. First, no single heuristic was found
to be consistently best on every problem. Second, four of the popular heuristics
consistently performed worse than random assignment. The remaining three
outperformed random assignment and performed well enough overall to merit further
consideration as a useful technique by the investigators.

The highest performing heuristic was the Minimum Slack (MINSLK) approach.
MIN SLK assigns the highest priority to those tasks that exhibit the least slack (difference
between the earliest possible start time and the latest possible start time on the
unconstrained, deterministic CPM formulation of the problem). MINSLK demonstrated
only a 5.6% average increase in total project duration over the OPT schedule and found
the same solution as the OPT solution in 24 of the 83 total problems.

The second best performing heuristic was the minimum Late Finish Time (LF T)
method. The LP T method assigns higher priorities to tasks which have the earliest late
finish time in the deterministic CPM formulation of the network. LF T schedules
represented a 6.7% average increase over the optimum schedules, and found the OPT
solution in 17 cases.

A method that performed closely to LFT was the Resource Scheduling Method or
RSM. RSM considers both the current task and any subsequent (dependent) task that
relies on its completion in the deterministic CPM network. When evaluating technically
feasible activities for the next activity start, the eligibles list is composed of activity pairs.

The pairs consist of all currently feasible activities plus each of its follow-on activities.

23

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RSM schedules first those activities that have the smallest delay factor. The delay factor
is calculated as the difference between the earliest finish time of the current task and the
latest start time of its subsequent task in the pair. In a sense, the delay factor represents
the amount of local slack between each task and any task that follows it. The current-
next pair with the least slack will receive the highest scheduling priority (for the currently
eligible task). RSM achieved a 6.8% mean increase in total task duration, and found the
OPT solution for 12 cases.

The RND or random assignment method came in fourth; displaying an 11.4% mean
increase in total duration and finding the OPT answer in only 4 cases. All other heuristics
evaluated performed worse than RND on at least one of the performance criteria (number
of cases where shortest duration solution was found, percentage of times the shortest
solution was found, percentage average increase over shortest project duration).

While not contradicting the previous studies, Davis and Patterson's 1975 effort
provided a comprehensive comparison of many different and popular methods. The
MINSLK technique became established as "the method to beat" for many firture
comparisons.

In 1982, Talbot performed a comparison similar to that of Patterson but with the
addition of some of the more recent heuristics. In his work (Talbot, 1982), he expanded
the complexity of the problem set to include multi-mode resource-task activity functions
(applying more resources shortens activity durations). A set of 100, lO-activity, 3-
resource problems was solved as a benchmark using a 0-1 Integer Linear Programming
formulation and the random assignment rule. Eight different heuristics were then applied

to the problem and the results were compared.

24

 

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While RSM and MINSLK were not tested, LF T was and ranked first for the highest
percentage of best heuristic solutions (84%) and third place for the number of OPT
solutions (33). Two heuristics were tied for first rank for the number of OPT solutions
(34): Min(L-D) and Min(L-Davg). Min(L-D) assigns the highest priority to activities
with the minimum value of late finish time minus the shortest duration. This is
equivalent to using the earliest late start time for the fastest resource loading of the
activity. Min(L-Davg) is a variation of the formulation that uses the average task
duration instead of the shortest (most resources assigned) duration. Both of these
methods are specific and peculiar to the multi-mode resource-activity duration problem
formulation.

In 1990, Boctor performed another comparison, again using OPT and RN D
procedures for performance bounding. Boctor's test employed 36 small (5-20 activities)
and 30 medium (38-111 activities) problems. OPT solutions were obtained for the small
problems, and the deterministic critical path lengths (unconstrained) for the medium
problems were used as best achievable benchmarks. Eight parallel and five serial
heuristics were applied to the problem set. MIN SLK, LF T, and RSM performed best, in
that order. Generally, the serial heuristics were poor performers (only two of the five
outperformed RN D). MIN SLK was again found to be the top performer in Oguz &
Bala's 1994 comparison.

MIN SLK, LF T and RSM have been the top performers in virtually any comparison
test in which they have been tried, with one notable exception. In 1994 Ozdamar &
Ulusoy introduced a new and promising heuristic, Local Constraint-Based Analysis

(LCBA). LCBA is a parallel heuristic that assigns priority to tasks based on an analysis

25

of resource contention amongst the activities on the eligibles list. They tested LCBA
against four other heuristics (Ozdamar & Ulusoy, 1995) in both a single-pass mode of
operation and a multi-pass mode, using the 110-problem Patterson Set. In the multi-pass
mode of operation, the heuristics operate a single, forward pass as they would normally
be used. A backward pass is then performed. First, all activity latest finish times are
changed to reflect the difference between the (just scheduled) start times and the total
project duration. The project completion time is now set to 0 and the scheduling
procedure is repeated in reverse, and activities become eligible when their (in the original
formulation) successor activities are complete. Forward and backward iterations are
repeated until the project duration does not improve.

Ozdamar & Ulusoy reported the results of the heuristics in both the single and multi-
pass versions. Generally, the LCBA outperformed both MINSLK and LFT; with a
greater difference in the multi-pass approach. Also, the Weighted Resource Utilization
and Precedence (WRUP; from an earlier work by Ulusoy & Ozdamar, 1989) technique
which formed the earlier LCBA approach also outperformed LF T but not MINSLK.

2.2.2.2 Heuristics Seeking Maximum Net Present Value

 

While much of the interest in the RCPSP has focused on the minimization of total
project duration (by over a 3 to 1 margin according to Ozdamar & Ulusoy's 1995 review
of the literature), the maximization of Net Present Value (N PV) has also received some
attention. One of the earliest works specifically dedicated to forming and solving the
NPV variant is Russell's 1970 "Cash Flows in Networks." Russell notes that "The use of
critical path or network techniques in cost control has lagged behind other variations of

the basic scheduling technique such as resource allocation for the smoothing or leveling

26

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of resources, although the cost aspects of project control must be basically of more
importance."

While this early work was an attempt at an exact approach to the resource
unconstrained case, it is instructive in the way Russell formulated the problem. He
described the basic cash flow problem as a network of activities, connected by time arcs,
each with an associated pay event or cash flow which could be either positive (a receipt)
or negative (a payment). Generally, in order to maximize NPV, the schedule should
attempt to bring forward positive pay events and push back negative pay events. Often,
in large, complex projects, these two outcomes are in conflict; bringing a positive pay
event forward may result in the inability to push back several much larger negative pay
events and vice versa. Russell's solution was to calculate the marginal costs of each
activity (by duration) and use these costs to formulate a non-linear program (of the "fluid
flow" variety) which could be solved iteratively through successive approximation.

A later work (Russell, 1986) specifically compared the performance of six heuristics
on a set of 80 problems. One of the heuristics was based on the random selection of
activities (RN D), and two were demonstrated to have good track records with respect to
minimizing project duration (MIN SLK and LF T). Four new heuristics were developed in
order to specifically address the characteristics of the NPV RCPSP. The Target
Scheduling (TS) rule uses the optimal finish times from the unconstrained NPV optimal
solution. This rule assigns the highest priority to those activities with the largest
difference between their current earliest finish time and the optimal finish time. TS
essentially prioritizes activities based on the degree of their deviation from the

unconstrained optimal formulation. In the DUAL heuristic, Russell uses information

27

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from the solution of a sequence of network flow (transshipment) problems. He
formulates the (fundamentally non-linear) NPV problem as a series of simpler resource
unconstrained transhipment problems in which only the supply/demand levels at the
nodes change (the method used by A. H. Russell, 1970). The are flow values are
measures of the marginal values of delaying the activity associated with the cash flow at
that node. The DUAL rule assigns the highest priority to those activities with the highest
arc flow value (marginal cost of delay) from the resource unconstrained optimal (cash
flow) solution. The Lowest Activity Number (LAN) rule assigns the highest priority to
those tasks with the smallest index number when activities are numbered from earliest to
latest earliest start time in the unconstrained, deterministic CPM network.

Russell combined these basic decision rules into pairs of primary and tie-breaking
importance: TS, LAN; DUAL, TS; TS, DUAL; MINSLK, LAN; LFT, LAN; and RAN.
One interesting (and unanticipated) result was noted overall. As the probability of
resource contention increased (projects become "more constrained"), the differences in
NPV performance became greater. For relatively unconstrained projects, the performance
of the heuristics was relatively equivalent. Under these conditions, the performance
rankings were: MINSLK, LAN > TS, DUAL > TS, LAN > LFT, LAN > DUAL, TS >
RAN. For projects with greater resource tightness, the differences became more acute.
The relative performance rankings changed significantly: TS, DUAL > TS, LAN >
DUAL, TS > RAN > MINSLK, LAN > LFT, LAN. The duration minimizing heuristics,
under tightly constrained resources, were actually worse in maximizing NPV than the

random assignment rule.

28

Shortly afier the publication of Russell's heuristics, Smith-Daniels and Aquilano
(1987) compared the performance of optimum, early start and late start procedures in
achieving higher levels of project NPV. Using five different cash flow profiles for
Patterson's 110 problem set, the authors tested the methods on 550 problems. Using the
optimal (to minimize time) schedule as a baseline (OPT), the researchers constructed an
earliest possible start schedule (ESCR) then used a variety of rules to shift non-critical
activities later in time to create a late-start constrained resource schedule (LSCR). This
shifi (delay) of non-critical activities should have the effect of delaying cash outflows
(improving NPV) while not delaying project completion. These right-shifting rules were
based on the earlier work of Weist (1964).

The results of this experiment were mixed. Generally, there was no definitive
improvement in NPV for all cases for any one the three methods. The NPV for the OPT
method was higher in 292 of the cases, the NPV was higher for the LSCR for 248 cases,
and in 10 cases the NPVs were equal. The ESCR schedules generally produced inferior
NPV results. The researchers noted that the nature of the payment schedule was an
important factor in the performance of the heuristic approaches. While the OPT schedule
clearly produced the shortest project durations (as expected), the differences in duration
between the ESCR and LSCR were slight.

Overall, Smith-Daniels and Aquilano concluded that while right-shifting of non-
critical (slack) tasks did result in an improvement in NPV in many cases, the time-
minimizing approaches performed well for both time minimization and NPV
maximization. A related work (Smith-Daniels & Smith-Daniels, 1987) demonstrated that

solutions which maximized NPV were indeed different from solutions that minimize time

29

 

 

in many cases. Perhaps more importantly, this work introduced material ordering costs
into the NPV-maximizing RCPSP and concluded that these solutions differed
significantly from the time minimizing solutions. When viewed together, the results from
these two 1987 studies appear contradictory, at least in the claims of how dissimilar the
time minimizing and NPV maximizing solutions are. This matter was clarified somewhat
in 1990 by Blrnaghraby & Herroelen. In this study, the authors included the concept of
time dependent payments (bonus schedules). Their general finding was that when project
bonus payments (higher cash receipt for earlier completion) were present, a project
schedule that first constructed a minimum duration schedule and then right-shifted non
critical activities produced the best results. Using a 0-1 Integer Linear Programming
method, they demonstrate that their heuristic does indeed find the optimal solution for
some small problems. A wider test of the approach was not reported.

Perhaps the most interesting and complete analysis of the NPV maximizing RCPSP
is the study performed by Padman and Smith-Daniels in 1993. Based primarily on
Russell's (1970) approach, the authors use the dual formulation of the linear
approximation to the non-linear NPV maximizing mathematical program to assign
earliness costs and tardiness penalties for each activity. While Russell's approach
iteratively manipulated target times for activity completion until all marginal costs were
equal (implying optimality), Padman used the preliminary marginal costs from Russell's
preparation step to guide the performance of selected heuristics. The shadow prices are
calculated initially, and scheduling proceeds until resource contention is encountered.
Shadow prices are then recalculated, priorities are reassigned, and scheduling continues

until the next resource contention occurs and the process repeats.

30

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Eight new heuristics were applied to 144 projects of varying size, complexity and
resource constrainedness. As no optimal solutions were available, the heuristics were
compared to each other on the basis of best vs. percent performance below best. Two
general findings are noteworthy. First, at low and medium levels of resource
constrainedness, there were very small differences among the heuristics. Performance
differences only became significant at high levels of contention (2.0 Average Utilization
or higher). Second, as the projects became larger and more complex, the performance
differences went away. The heuristics seemed to make a big difference only for the
smaller (50 or less activities) projects.

The two best performing heuristics in this complex, multiple iteration technique were
the Immediate Release of the Opportunity Cost of Scheduling (IOCS) and Immediate
Release of the Cash Flow Weight - Opportunity Cost of Cash Flow (ICFW-OCC)
methods. In IOCS, highest priority for scheduling is given to those activities with the
highest opportunity cost of not being scheduled (based on Russell's dual formulation). In
ICFW-OCC, the priority is given to those activities with the highest calculated difference
between their cash flow of completion and their opportunity cost of completion. The
overall conclusion of this research was that an effective strategy for scheduling the NPV-
maximizing RCPSP was to apply a multi-heuristic approach. Schedule the project using
a family of heuristics, then select the best schedule for each project. Another overall
conclusion was that there was found to be a definite trade-off between the postponement
of expensive activities and the possible additional resource contention that this delay may

create.

31

 

   
  

A Illt
good (in t.
b) Finder
ortimizati

COFtS-TJCI S

 

“rank

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That"; 5.

AA

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10 2'16 relax,

A more recent work included several new and promising heuristics for developing
good (in terms of NPV) schedules (Pinder and Marucheck, 1996; based on previous work
by Pinder and Marucheck, 1989). In their research, Pinder and Marucheck used one
optimization-guided heuristic, six established heuristics, and ten new heuristics to
construct schedules. A randomly generated set of problems with desired characteristics
was created. The scheduling methods were applied to each problem, and the NPV of the
resulting schedule was then calculated. The amount of (planned) NPV was then used as
the criterion for success for comparing the scheduling methods.

Each of the scheduling methods employed a parallel, multi-pass algorithm to assign
start times to activities based on priority rules. The optimization guided heuristic was
used as a benchmark for NPV performance for the remaining scheduling techniques. It
performed consistently best on all problems. This method formulates and solves the dual
to the relaxed (resource unconstrained) NPV maximization LP problem using the
procedure of Padman and Smith-Daniels (1993). The marginal costs (N PV reductions) of
delaying each activity are then used to prioritize activities on the eligibles (technically
feasible) list. The established heuristics used were the MINSLK, EDD, SPT, and GRD
rules described earlier. Also used were the greatest number of successors (GNS) and
greatest succeeding processing time (GSPT) rules. GNS assigns priority to those
activities with the greatest number of following activities. GSPT schedules first those
activities with the largest total of processing time for all following activities.

Ten new heuristics (five pairs) were developed, each based on some form of
discounted cash flow weights. Each heuristic used a different weighting factor w; (based

on the cash flow, discount rate, and duration) to calculate the scheduling priority of the

32

activities. There are five weighting schemes for calculating w as indicated in Table 2.1,
Weighting Rules. Each weighting scheme includes two basic variations of w,
comprising a pair. The first case of the pair simply assigns priority based on min[1/w,-].
The second case of the pair assigns priority based on min[d,'/w,-], where d; is the duration

of the activity being considered.

Table 2. l: Weighting Rules

 

 

 

 

 

 

Acronym Weight wi Prioritization Statistic
DCF D, DCFDW CFiexp(—adi) l/Wi di/wi
DCFEF, DCF EF W CF,exp(-aEF,) l/wi ‘ di/wi
DCFLF, DCFLFW CFiexp(-aLFi) l/Wi y di/wi
ZDCFEF, ZDCFEF W (‘23,,Es CF k)exp(-orEFi) l/wi , d,./wi
ZDCFLF, ZDCFLFW (2kEs CFk)exp(-orLFi) l/W. , di/W.

 

 

 

 

 

where CFi Cash Flow as a result of activity i

at = Discount Rate

LFi Late Finish time of activity i

EFi = Early Finish time of activity i

kes = The set of activity i and all of it's successors

The most successful of all methods tested was the optimization guided heuristic. The
XDCFLF heuristic consistently performed next best. The performance of the remaining
new and traditional heuristics was mixed. Generally, the ZDCFEF (new) and GSRR,
GSPT (traditional) prioritization rules performed well also. The SPT, ZDCFEFW, and
ZDCFLFW rules consistently returned the poorest performance.

In a similar study, Yang, Tay, and Sum ( 1995; based on the 1989 work by Pinder and
Marucheck) added a random prioritization of activities to the set of traditional heuristics,
and Sllbstituted simulated annealing for the optimization guided approach used by Pinder

and Marucheck. The results were similar. The simulated annealing method consistently

33

 

provided the best performance. Out of the new and traditional rule based heuristics, they

found that the ZDCFLF rule worked almost as well as the simulated annealing method,
and better than the remaining heuristics. These results are completely consistent with

those found by Pinder and Marucheck in 1989 and 1996.

2.3 Execution Approaches

 

While extensive research has been performed on the development of schedules or
plans for the RCPSP, very little work has been done on the use of decision rules or
techniques for the execution of the schedule once the project has actually begun. The
schedule represents a series of predictions about the behavior of the resources and
activities involved in the project. The degree to which these predictions come true in
reality (or don't) may affect the degree to which this schedule remains valid over the
lifetime of the project. Variability which is not taken into account, and disruptions to
resources which are not planned for, will each contribute to deviations from the schedule
during project execution.

An execution approach represents a mechanism for coping with the real-world
deviations from the model-world schedule predictions. The effectiveness of the
execution approach may determine the outcome of the project to a greater degree than the
planning approach used. As the conditions (in reality) depart from what was planned for,
the issue of how these departures and uncertainties are handled becomes increasingly

important.

34

  
  
  
  

Art .-
'Plarztt';
notes the
practice; 't
atallabilrt

prtorjtres a

 

um} use

13916315 u:
Emeline a;

An early work recognizing the problems inherent in the execution of schedules is
"Planning and Dynamic Control of Projects Under Uncertainty" (Burt, 1977). Burt first
notes the absence of network optimization techniques in the management of projects in
practice; he attributes this to uncertainty in task durations, the variability in the
availability of resources, and the dynamism inherent in managers intervening to reallocate
priorities and resources. These factors conspire to make even the best "optimal" schedule
utterly useless fi'om a practical standpoint.

Burt proposed four dispatching or execution rules to assist in the management of
projects under conditions of dynamic uncertainty. First, the static approach represents a
baseline attempt to adhere to the original schedule. Next, dynamic rules behave in the
same manner as static, but the project is rescheduled using the original algorithm every
time an activity is completed. Third, lag first uses dynamic scheduling, but allocates
higher levels of resources at the end of the project (the withholding of resources at the
beginning of the project with a sudden increase in the middle). Finally, seq lag is similar
to the lag first approach, but smoothly increases resources applied to tasks from the
beginning to the end.

These approaches were tested using a discrete event, dynamic simulation. General
results from this investigation demonstrated that dynamic updating (of all types) did
indeed improve the performance of the projects. Larger projects benefited the most from
this effect. Also, the backloading of resources (lag first and seq lag) improved the
duration of many of the projects tested. This improvement was most pronounced in
projects with a higher degree of variability in individual task durations. This could be the

result of the increased resources having a smoothing effect on the negative roll-up of

35

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residual activity delays toward the end of the project (some delays early on would be
smoothed by the effect of shorter activities following them).

A more recent work by Partovi and Burton (1993) focused on rescheduling intervals.
Using concepts developed in the production scheduling literature, Partovi and Burton
used simulation to investigate various monitoring and control techniques for project
scheduling. They simulated five different project networks, with 25 to 48 activities,
managed using five rescheduling intervals. The frequencies for rescheduling were: no
rescheduling, five equal intervals, front-loaded intervals, end-loaded intervals, and
random intervals.

Some general conclusions were reached. First, all of the rescheduling schemes were
better than the baseline no rescheduling case. Second, while all of the techniques
improved the performance of the projects, there was no clear always best method. A
related result was that rescheduling seemed to be more helpful for some problems than
for others. While shorter projects with fewer activities seemd to benefit more than longer
projects with more activities, no specific analysis was performed in order to determine the
key characteristics of projects which would benefit the most or least from the different
rescheduling methods. More general results indicated that if you can only reschedule
occasionally, rescheduling later is better than rescheduling earlier in the project life.
Also, more fi'equent rescheduling is better than less frequent rescheduling.

The application of production scheduling and rescheduling concepts to the project
management environment seems to be a promising approach. An interesting recent work
(Yang, 1996) uses the concepts of scheduling and dispatching from the production

scheduling literature to investigate the effect of variance from predicted activity times

36

used d:
tyrant;
dispatch;

m‘rernm

Simu

 

in
"fifth?
u ‘4
“
31):“
\‘L

(used during scheduling) on project performance during execution. Yang also used a
dynamic simulation to evaluate the performance of deterministic scheduling and
dispatching rules in the execution of resource constrained projects in stochastic
environments.

Simulated annealing was used to build near optimal schedules, by searching the tree
of potential scheduling decisions for improvement in the total project time. Three other
dispatching rules were used to build schedules. Once the initial schedule was found,
activities were assigned priorities based on their scheduled start times. These priorities
were then used to order activities on the precedence feasible list as the project was
executed. The dispatching heuristics tested were the cumulative resource requirement
(CRR), MINSLK, and first come, first served (FCFS). The CRR method is a resource-
weighted variation of the cumulative cash flow NPV maximizing rule discussed earlier.
Once the schedules were built using the four methods (SA and the heuristics), the projects
were simulated and execution rules were applied to the updated priority-eligibles list in
order to make the actual resource assignment decisions.

Two execution rules were examined: full reservation (FR) and no reservation (NR).
FR attempts to execute activities strictly according to their priority ranking on the
eligibles list. If the highest priority activity on the list cannot be executed (due to the
unavailability of a needed resource), then those resources which are needed and available
are reserved by the high priority activity until all resources needed become available. The
NR rule, conversely, does not reserve resources. If the highest priority activity cannot be
executed, the next lower priority activity is evaluated and executed if resources are

available. While the FR rule tends to ensure that the activities are executed in roughly the

37

311116 0?;

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same order as the updated priority list, the NR rule tends to ensure that resources are
more fully utilized.

Some general conclusions were reached. First, the author noted that the SA
technique produced results superior to CRR, MIN SLK, and F CFS. Specific results were
affected by interaction with the type of execution rule used. When FR was used,
MINSLK and CR produced results only slightly better than FCFS (with SA much
better). Under NR execution rules, MINSLK and CR produced results much better than
FCFS, almost as short as SA. Also, the NR rule produced better project results than FR
in all but a few cases. In addition, the author explored several rescheduling frequencies
and timing schemes using the SA scheduling approach. The results generally matched
the earlier conclusions of Partovi and Burton (1993). Project completion times are helped
by rescheduling, with more frequent rescheduling producing more improvement. The FR
rule is helped by rescheduling more than NR. One interesting general finding was that
highly constrained (in resources and precedence relationships) and loosely constrained
projects did not seem to benefit much from rescheduling, while moderately constrained

projects benefited greatly.

23 Measures of Stability

 

Scheduling stability (the particular concept of stability being studied here) refers to
the ability of the schedule to resist or absorb unplanned variance or events. Stability will
represent the degree of deviation from schedule for the resources and activities in the

project. A project that is executed very closely to the schedule will be considered to be

38

more st;
schedule
Stir

earetullt

hf “Win
ttttdesira'f

SCl’tt‘LlLilfi ;

.. t- .
151941110.

    
   
  
 

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(101111 01 it

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reg-June‘s

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more stable. A project that is executed with numerous (and/or large) deviations from the
schedule will be considered to have been (relatively) less stable.

Stability is an important issue in scheduling when resources are limited and must be
carefully managed. The schedule represents a plan for how to best use the resources
available in order to achieve some set of objectives within the constraints imposed upon
the project. When the schedule or plan cannot be met, several direct and indirect
undesirable consequences may result. First, the desired objectives toward which the
schedule is optimized may not be achieved. If the schedule is unable to resist an
unplanned variation, or loses validity when a disturbance occurs, the resources may not
be put to their best use from that point forward. In addition, when the schedule breaks
down or loses validity, resources that must be secured from outside the system may be
brought in (and paid for) too early or too late, resulting in idle time and additional costs.
Learning and unlearning, as well as other tangible set up costs, may take place when
resources are set up and broken down as priorities change. When the schedule loses
validity, local decisions (based on the invalid schedule) may no longer integrate well with
the global objectives. As the plan breaks down the activities and resources may be
misdirected and misused, resulting in both a loss of effectiveness and an increase in costs
(Steele, 1975; Mather, 1977; Kropp, Carlson, and Jucker, 1979).

While no direct study of the stability issue for project scheduling has been provided
in the literature (a gap the current research hopes to fill), some related work has been
performed. The issue of stability has been addressed in the production scheduling
literature; particularly with respect to the generation of schedules in MRP systems.

Steele (1975) defines "A 'nervous MRP' system is one that generates excessive changes to

39

   

lob-l6) L
negame
'Nothirt,
change fl
believe.‘

Mail

 

low-level requirements when there are no major changes in the master schedule." The
negative effects of this instability in the schedule are further described by the author:
"Nothing is more disconcerting to the new MRP owner than to have his system priorities
change faster than he can respond to them, or worse, to a degree more than he can
believe."

Mather (1977) also examined the instability problem in MRP schedules, focusing on
causes and outcomes of frequent rescheduling. He identified six causes of rescheduling:
changes in lot size, lead time, or safety stock; changes in product design or configuration;
errors in records; and unplanned transactions. These are correctly considered to be
sources of variability or disruptions unaccounted for by the scheduling logic. His
recommendations to address the causes mention variance reduction (attacking the source
of the unpredictability) as the best way to reduce the instability of the MRP schedules.
However, the majority of his comments focused on dampening mechanisms to reduce the
sensitivity of the schedule and make it less responsive to change. This, he noted, has the
negative side effect of reducing the effectiveness of the schedule in achieving best results
for the desired system outcomes- potentially negating the very reason why the MRP
system was installed in the first place!

The variation source reduction approach to reducing MRP nervousness has been
studied in detail at the level of addressing specific sources of variation (Sridharan, Berry,
Udayabhanu, 1988; F edergruen and Tzur, 1994; Metters, 1993). These studies advocate
a non-response strategy to cope with variability and disruption. An example of this
strategy is the freezing of input variables to the schedule; refusing to accept changes a

priori, e.g., not accepting demand inputs within a certain time window. A second

40

 

without

10 pk“ t‘f‘,

 

 

 

'3‘
cl.\‘

K;
5:.“ ’3‘ 0“
bim~§ L]

e

example involves the dampening of changes. By refusing to respond to changes post hoc,
managers can attempt to limit the damage. For example, if the lead time for an item
changes due to a delay in processing, simply accept the delay in that one end item
(without examining the affect on other items or rescheduling around that change) in order
to prevent the disruption from spreading through rescheduling.

As study progressed on MRP nervousness (schedule instability) and the negative
effects of it, more formal definitions and measures were developed. Two measures of
nervousness were the number of unplanned orders in the present time period and the
number of times the planned orders in the present period were altered (Blackburn, Cropp,
and Millen, 1986). The first measure captures the level of disruption, and the second
captures the response of the system to these disruptions.

Extending this work, Sridharan et a1. noted that those measures only dealt with the
current effects of past changes, providing a static snapshot at a single point in time. They
developed a measure of nervousness that was based on a weighted moving average of the
absolute values of the schedule deviations (Sridharan, Berry, Udayabhanu, 1987). This
measure allows the capture of the longitudinal effects of nervousness, appropriately
weighted. The concept of instability (nervousness) has been expanded into DRP
(logistics) systems as well (Ho, 1992).

In project scheduling, the concept of stability is not as well studied. Willis (1985),
while mainly concerned about activity float (critical and non-critical), as an aside defined
a stable schedule as one that does not drastically alter activity start and stop times. Pagell
(1995) refined the concept of stability to include a more formal definition, proposing a

stability metric:

41

there

 

mt .
5114:.

 

$051), — ASD,|

_ i=x

 

(n—x)-DL

where n = number of activities in project
x = sequence number of first delayed activity
DL = total project Delay Length
OSDi = Original Start Date of activity i
ASDi = Adjusted (actual) Start Date of activity i

Stability (Pagell's formula) calculates the average absolute value of the activity start
time deviations for all activities after the first deviation. This average deviation of post-
shock activities is then divided by the total project delay length. In this respect, stability
captures the "effect size" of the disruptions upon the total project length. A value greater
than 1 indicates that the average deviation of all post-shock activities was greater than the
total project delay length. This could represent the tapering off of an initial disruption, or
the spread of the disruption to non-critical (as opposed to critical) activities. Similarly, a
value of less than 1 indicates that the disruption had a greater effect on the total project
than on the average post-shock activity.

While the measure is intuitively appealing in that it attempts to capture the "effect
size" (in a sense) of disruptions, and generally appealing because it is filling a void, the
Pagell measure has some shortcomings. In a practical sense, the measure is problematic
because it is unbounded. If a schedule were to execute with no delay, the measure would

be undefined (division by zero). Small overall delays, in conjunction with disruptions

occurring first toward the end of the project, cause the measure to become large

42

lpOltttI.

I3
CL.
E?

A“? Jr“
mud-5..

TM.

'1.»

schedti.
me'rtes .-

 

Etta-“.‘g.
“‘M

be their

(potentially very large). In addition, the measure does not differentiate between late starts
and early starts. Depending upon the circumstances, late or early starts may have very
different practical consequences for the project manager.

There is no commonly accepted definition of nor metric for stability in project
scheduling. A number of approaches might therefore be considered. Some alternative
metrics are presented and discussed in Chapter 3, Methodology. The usefulness and

relevance of these metrics are explored in this research.

2.5 Environmental Variables

 

Several characteristics of the problem itself and the environment in which the
problem is scheduled and executed have been investigated for their moderating effects
upon the performance of the planning and execution methods. Patterson (1976) found
that the nature of the problem itself can affect the performance of scheduling heuristics.
He proposed that 12 key characteristics of the problem influenced the performance of
various heuristics in achieving schedules of shorter duration. This list of problem
characteristics that "matter" has been altered by other researchers, and Patterson's own list
has changed. The problem characteristics are listed and categorized in Table 2.2,
Problem Characteristics, at the end of this section.

Patterson (Patterson et al., 1990) found in a recent study that the performance of both
the heuristics and exact approaches can be affected by the characteristics of the problems
themselves. His recognition of the influence of problem characteristics upon the
performance of the scheduling method indicated the need to identify and control for the

(indirect) effects of these variables when studying the (direct) affects of the methods

43

themselves. His more recent list was updated to refine some definitions and included
cash flow measures reflecting NPV concerns. Overall size and complexity characteristics
include the number of activities, network complexity ratio (ratio of arcs/nodes), and mean
number of activity modes (for projects which allow multiple modes for activity duration).
Project length characteristics were measured using minimum, mean and maximum
activity durations; standard deviation of activity durations, and critical path length (based
on deterministic minimum activity durations). Project resource utilization was captured
using the average fraction of resources used by activity mode. Finally, cash flow
characteristics were represented by mean per-period cash out, number of positive cash
payments, and mean magnitude of positive cash payments. His 1990 study noted that the
performance of many heuristics and exact approaches alike can be influenced by these
problem characteristics.

Russell (1986) sought to identify the individual contributions to performance of
eighteen problem characteristics as a subsection of his exploration of the performance of
scheduling rules. He characterized the problems in his problem set using Patterson's
original (1976) twelve and six additional cash flow measures. Russell formulated the
problem using simple linear regression. The dependent variable was calculated as an
NPV performance score derived by taking the difference between the best and worst
performing heuristics for each problem (the TS-DUAL and MIN SLK-LAN procedures,
respectively). The independent variables were the respective problem characteristics.
Russell was measuring the performance degradation between the two scheduling
heuristics as predicted by problem characteristics. Measures of resource constrainedness

were found to be particularly powerful, accounting for over 74% of all variation. These

44

measures included the average percent of demand for resources, maximum resource
utilization, maximum resource constrainedness, and maximum resource constrainedness
over time. Another significant measure was the average utilization factor (R2 = .75).
This is unsurprising, as the average utilization factor is another form of the concept of
resource constrainedness. Average resource constrainedness was also found to be a
valuable (although less so) resource measure (R2 =.15). While not an intrinsic project
characteristic per se, the makespan delay factor was also strongly related to NPV
performance (R2 = .78). The makespan delay factor is calculated as the ratio of the
constrained critical path length over the unconstrained critical path length; this represents
the growth in project completion time due to the unavailability of resources. The
measure therefore reflects both the nature of the problem itself (based on interactions
between the technical and resource constraints) and the efficiency of the scheduling
method. Because of this, it can be inferred that the makespan delay factor is not
particularly useful a priori in a practical sense with respect to the selection of a
scheduling method. However, once the schedule has been developed, or after alternate
schedules have been developed, the makespan delay factor information may be useful in
predicting the performance of execution methods or the anticipated performance of the
schedule itself. In summary, the key point of Russell is the identification of resource
utilization and constrainedness as key factors affecting the NPV performance of
scheduling heuristics.

Another comprehensive analysis of the effects of problem characteristics on the
performance of scheduling heuristics was performed by Smith-Daniels and Aquilano in

1987 ("Using a Late-Start Resource-Constrained Project Schedule to Improve Project Net

45

‘T‘.’
3"“.

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lllt It ‘
£03151}; ‘ .
and rot.
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Present Value"). In addition to regression analyses of characteristics (eighteen in this
case), the authors performed a principle components, varimax-rotated factor analysis.
The first factor to be strongly related to NPV performance consists of resource
constrainedness and utilization measures. Average and maximum resource utilization,
and total and average resource obstruction were included in this factor. The second factor
consisted of maximum and average resource constrainedness, and average and maximum
resource constrainedness over time. Resource constrainedness is represented by the
resource loading (requirement) divided by the resource availability over the
unconstrained CPM formulation of the problem. Total project duration and three cash
flow measures (total cash outflow, present value of cash outflows, and the present value
difference between early start and late start schedules) made up the third factor. The
coefficient of network complexity and the coefficient of network density stood alone as
the fourth and fifih factors. Network complexity was defined as the ratio of arcs to nodes
in the activity on are representation of the problem.

As characteristics of the project, the following five factors have been demonstrated to
contribute significantly to the performance of heuristics attempting to maximize net
present value: resource utilization, resource constrainedness, cash flow structure,
problem complexity, and problem density. Three additional project characteristics have
been contributed by Yang (1996). First, Yang uses a modified version of resource
utilization, calculating resource availability as the ratio of the total resources required
(over time) divided by the total resources available (over time). Yang also includes a
version of network density termed order strength. Order strength is calculated as the total

number of actual precedence relationships divided by the total number of possible

46

ESE: a : SEES.

 

precedence relationships, including redundant arcs. Finally, he studies error estimation as

a problem characteristic. Error estimation is a measure of the variation in actual activity

times from the estimated activity times used for building the schedule. Yang found each

of these characteristics to be significantly related to the total duration of the projects.

Table 2. 2: Problem Characteristics

 

Category

Metric

Duration

NPV

 

Size/Scope

Number of Activities

3

 

Network Density Ratio

3

1,2

 

Network Complexity Ratio

 

Order Strength

 

Error Estimation

 

Mean Number of Activity Modes

 

Length

Minimum Activity Duration

 

Mean Activity Duration

 

Maximum Activity Duration

 

Standard Deviation of Activity Durations

~H-H

 

Critical Path Length

wwwwwuph

\O

 

Constrainedness

Average Resource Constrainedness

 

Maximum Resource Constrainedness

\O

 

Maximum Resource Constrainedness Over Time

t—tu—It—tu—t
NNNN

 

Total Resource Obstruction

 

Average Resource Obstruction

 

Makespan Delay Factor

 

Utilization

Average Fraction of Resources Used by Activity
Mode

-~NN°

 

Average Percent Resource Demand

 

Average Resource Utilization

 

Maximum Resource Utilization

1,2

 

Average Utilization Factor

 

Resource Availability

 

Cash Flows

Mean Per-Period Cash Out

 

Number of Positive Cash Payments

 

Mean Magnitude of Positive Cash Payments

 

Total Cash Outflow

 

 

Present Value of Cash Flows

 

 

NNWWW

 

 

Key: 1. Russell, 1986 2. Smith-Daniels&Aquilano,1987 3. Patterson, 1990 4. Yang, 1996

47

 

 

 

 

 

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lamb;
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2.6 Summary

 

Several key areas in the study of project scheduling emerge from the literature which
have direct relevance to the current research. First, the nature of the planning approaches
used must be considered carefully, as the performance of the different methods can vary.
Second, the execution approaches must also be considered. Under the conditions of
variability, with resource disruptions, it may not be possible to follow the schedule and
the means of execution begins to influence performance outcomes. Finally, several
environmental variables must be considered as possible moderating influences upon
performance. These considerations will each be discussed in turn as they relate to the
current research. They are mentioned briefly here and described in greater detail in
Chapter 3, Methodology.

Two planning heuristics have been used to represent methods that perform well in
finding the shortest project duration: MINSLK and LFT. These are compared to the
known optimal (shortest time) solution referred to as OPT. Also, two of the better
performing NPV maximizing methods were used to construct schedules. These are the
LSCR and ZDCFLF heuristics. The NPV performance of these methods are compared to
a right shifted version of the optimum (RSOPT) solution. The RSOPT schedule uses the
latest start times from the known optimal shortest duration schedule. While it was
expected that the solution methods would perform well on their target performance
measures, their performance with respect to the stability measures was unknown.

Two primary execution methods were tested: the reservation (full and no) and the

release (waiting and no waiting) types. This resulted in four combinations: full

48

 

remix.
torrid."

1110663..

CORSET
meme
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“with:

 

reservation, waiting; full reservation, no waiting; no reservation, waiting; and no
reservation, no waiting. The full and no reservation rules were as described by Yang
(1996). The waiting and no waiting rules refer to the release of technically eligible
activities with respect to their scheduled start times. The activities, while technically
feasible, were either forced to wait until their scheduled start times before being
considered eligible, or released immediately upon becoming technically feasible. These
procedures are discussed in greater detail in Chapter 3, Methodology.

Several problem characteristics related to problem size, duration, complexity,
constrainedness, and utilization were tracked. The number of activities was used to
measure problem size, and the minimum-duration critical path length measured duration.
Problem complexity was represented by the network density ratio and network
complexity ratio. The level of constrainedness was represented by average and maximum
resource constrainedness, as well as the overall makespan delay factor. Problems for the
experiment were selected to represent a broad and balanced spectrum of these

characteristics.

49

Chapter 3

METHODOLOGY

3.1 Introduction

 

As previously mentioned (refer to section 1.2, Research Problem and Questions) the
purpose of this research was to investigate the performance of both planning and
execution techniques in the single project, constrained resource environment, under

conditions of uncertainty, when subject to disruptions.

3.1.1 Theoretical Model

 

The theoretical model proposes that the choice of both a planning and execution
method has an effect upon the performance of the project. Further, the model posits that
the effects of the planning and execution methods on performance are moderated by the
characteristics of the project and environment in which the project is performed (see
Figure 3.1, Theoretical Model). The selection of a planning and execution method
represent policy decisions that would be actively taken by the manager of a project.
These choices would be made against the backdrop of the situation; the characteristics of
both the project and the environment in which the project exists. Decisions taken by
managers under these conditions would benefit from an understanding of how these

factors interact.

The planning and execution methods represent the two primary constructs of interest
in this study. Previous research has already established that the planning method can play

a role in determining project outcomes. The influence of the execution method, while not

50

 

 

studied as extensively, has

   

Environment
- Disruption
- Variability

   

also been established. The

    

relationships between these
constructs and the project
performance construct has a
solid theoretical basis in the
literature (as described in
Chapter 2, Significant Prior

Figure 3. 1: Theoretical Model Research, sections 2.2 and

 

 

2.3). The current research seeks to extend these relationships to include stability as a new

class of performance measure affected by planning and execution method.

Two moderating constructs were included in this study. The environmental
moderator construct includes the factors of task duration variability and resource
disruption. This construct was manipulated as part of the experiment. The problem
moderator construct includes factors that are characteristics of the problem itself. While
not manipulated explicitly during the experiment, an appropriate range of values were
employed through the selection of representative problems. Characteristics selected for
inclusion in this study were those which either have already demonstrated or are
suspected to demonstrate significant effects on the performance of the planning and
execution methods. The moderating effects of the problem characteristics are also well-

grounded in the literature (Chapter 2, Significant Prior Research, section 2.5).

51

 

 

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3.1.2 Hypotheses

 

In the theoretical model (see Figure 3.1: Theoretical Model), it is proposed that the
choices of which planning and execution methods are used to manage the project will
determine, to a large degree, the overall performance of the project. These relationships
are moderated by several key characteristics of both the project problem itself and the
environment in which the project is managed. Project performance includes the duration,
NPV, and stability of the projects measured upon completion. Specific hypotheses

include:

H1: Stability measures are positively correlated with traditional project performance
measures.

H2: Project performance is significantly affected by the planning method used.
H3: Project performance is significantly affected by the execution method used.

H4: Relative planning & execution method performance is significantly affected by
environmental characteristics.

H4a: Relative planning performance is significantly affected by the presence of
activity duration variability.

H4b: Relative planning performance is significantly affected by the nature of the
resource disruptions (longer, less frequent vs. shorter, more frequent
disruptions).

H4c: Relative execution performance is significantly affected by the presence of
activity duration variability.

H4d: Relative execution performance is significantly affected by the nature of the
resource disruptions (longer, less frequent vs. shorter, more frequent
disruptions).

The remainder of this chapter describes the methodology used to test these
hypotheses. The discussion includes descriptions of the variables used (sections 3.2

through 3.4), the experimental design (section 3.5), how the data analysis was performed

52

(section 3.6), and finally a discussion of the limitations and key assumptions inherent in

the research.

3.2 Dependent Variables

 

Three main performance variables of interest were investigated in this study: project
length, project NPV, and stability. Project length is quite simply measured as the total
duration of the project, from the start of the first activity to the completion of the last
activity. This has traditionally been considered the most important overall measure of
performance. In project scheduling, financial aspects of project performance are also
considered (especially by practitioners) to be important. Primary among these is project

Net Present Value (NPV).

3.2.1 Net Present Value

 

The NPV was calculated for each project at the termination of the simulation as the
sum of all cash flows, discounted for when they were realized following the definition
(Russell, 1970):

NPV=:C ,-e"’r'

i=1

where CFi = Cash Flow realized as a result of completing activity i

or = Discount Rate
Ti = Time at which activity i is complete
n = Number of activities

53

Each activity in the project, from the initial (i = l) to the terrrrinal (i = n), has a cash
outflow (CF, < 0), cash inflow (CF, > 0), or cash neutral (CF, = 0) event associated with it
and a specific time T, at which it is realized. The sum of all negative and positive cash
flows for each activity, discounted for when they occurred, represents the value of the

project as a whole.

The projects in this study were modeled as being composed entirely of negative cash
flow events for each activity, with a single large positive cash flow upon completion.
The specific negative flow (cost) for each activity was calculated as the total resource
time used by the activity times an arbitrary cost constant (in this case, $25). The T,
realization time of the cost was established as the completion time of the activity. All
times are incremented in units of days. The discount rate or (internal rate of return; hurdle
rate) was selected to be .15, corresponding to a typical investment rate of return expected

from a Standard & Poors 500 corporation (Laderman, 1996).

The terminal positive cash flow was calculated to be representative of a completion
payment as formulated by a firm bidding for the project as a contract. This value
includes all costs and a profit. The payment was based on anticipated costs and timing as
projected by the schedule. First, the present value of all costs (scheduled) was calculated.
This was multiplied by the arbitrary factor of 1.5 to allow for profit and cost overruns.
The cost plus profit value was then time adjusted using the NPV formula. The calculated
payment would therefore cover all costs and result in a positive total NPV for the project

as long as the project was completed according to schedule.

54

The project duration and NPV were calculated as an actual value, expected value,
and an actual/expected ratio. The actual value calculations were based upon the activity
start and stop times as simulated during the experiment. The expected value calculations
were based upon the activity start and stop times as programmed by the scheduling

method used.

3.2.2 Stability

 

The final dependent variable, stability, was measured in several different ways.
Some basic precepts were followed when designing and selecting the stability measures
used. One precept was that the measures should capture some level of deviation from the
schedule. This can represent a deviation in activity timing (start and stop times) or a
deviation in resource use, or a combination of the two. Each of the following measures
was designed to capture activity deviation, resource deviation, or a combination of the

two.

3.2.2.1 Weighted Activity Deviation

.. SS, —As,. » AS, —ss,.
w, ~Zmax|:0 ] w, . zmax[0 ]

WADE: "=' , WADL: "'

 

 

 

where i = index number of activity
n = index number of last activity
AS, = Actual Start time of activity i
SS, = Scheduled Start time of activity i
wL = weight for late activities
wE = weight for early activities
ASAD = Average Scheduled Activity Duration

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Weighted Activity Deviation (WAD) calculates the mean magnitude of deviation
from scheduled start time for all activities, weighted according to earliness or lateness,
and scaled for scheduled project size. In Weighted Activity Deviation, Earliness
(WADE) the numerator captures the total earliness of all activities that started before their
scheduled times. Weighted Activity Deviation, Lateness (WADL) captures the total
lateness of all activities that started after their scheduled times. The distribution of
weight between wL and wE assigns a penalty based on the relative importance of earliness
vs. lateness for the management of the project. The denominator scales the deviations by
the size of the project as represented by the number of activities times the average

scheduled activity deviation. This is equivalent to the total scheduled activity time.

For this initial study, the earliness and lateness penalties were set equal wL = wE = l.
A composite measure WADC (Weighted Activity Deviation, Composite) was calculated
as the sum of the earliness and lateness numerators divided by the denominator used for
the individual measures. In each of the three measures, a larger value represents less

stability.

3.2.2.2 Resource Profile Offset

 

 

 

 

 

. ”SR, -AR,' 4 AR, -SR,
:(t. -t._ )-max 20, —t,._,)-max
0 I l I O ’_0 O
POIR = " , - ~ p00R = - . , ,
:0, - z,_, ) - SR, 20,. — t,_, ) -SR,
I=0 (=0

where t, = time at which a level of resource use changes; scheduled or actual
tn = time at which terminal activity ends
SR, = scheduled resource use over the interval [t,,,, t,)
AR, = actual resource use over the interval [t,,,, t,)

56

 

 

 

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These two measures compare the profile of scheduled resource use to the profile of

actual resource use over time. These measures capture resource use deviations without

regard for activities. In other words, these variables measure resource use deviations

without considering whether the resources are being used for the "right" (scheduled) or

"wrong" activities.

The POIR (Profile Offset, Idleness Ratio) measure sums the amount of resource use

 

 

—— Scheduled
- - - - Actual

 

Units of Resource

 

 

 

Time
Figure 3. 2: Resource Profile Offset

 

 

over time when the
actual resource use is
less than the scheduled
resource use. This is
unscheduled idleness.
The POOR (Profile
Offset, Overuse Ratio)
measure captures the
amount of resource use

over time when the

actual resource use is greater than scheduled resource use. This is unscheduled overuse.

The formula represents the discrete integral (since the resource profile functions are step

functions) of the area between the two profiles with respect to time. This is then divided

by the total area under the scheduled resource profile (these relationships are depicted

graphically in Figure 3.2: Resource Profile Offset). Note that each resource type used by

the project will have its own profile. The measure in use for this research will sum the

57

areas across the resources equally. Weighted formulations could be constructed,

assigning different weighting "penalties" to various resource types.

A composite measure was not constructed. In each of the two measures, a larger
value represents less stability. POIR is bounded by [0, 1]. A value of 0 implies no
unplanned idleness. A value of 1 implies that all resources were idle during the
scheduled length of the project. POOR is bounded by [0, 00). A value of 0 implies that
no resource was used outside of the scheduled usage profile. Larger values imply that
unscheduled resource usage occurred. As a practical matter, it is anticipated that values
would not greatly exceed 1.0 (virtually all resource usage is over use and project duration
not much greater than twice scheduled). “Raw” measures were calculated by assigning

variables POIC and POOC to the values of the numerators.

3.3 Independent Variables: Treatments

Two main treatments, the methods for planning and execution, were applied in the
study. The planning method generated the project schedule. The execution method was
the set of rules used to assign resources to activities as the project was simulated. Most
of the planning and execution methods have been discussed in detail in Chapter 2,

Significant Prior Research. Exceptions are discussed in detail as required.

3.3.1 Planning Methods

Planning methods were used to construct the original schedule for each project.

First, two benchmark planning methods were chosen to provide a basis for comparing the

58

performance of the remaining methods. The OPT method generates the known optimal
(time) solution for the deterministic case. The "right-shifted" version of the OPT (the
R80) was used as a benchmark approach oriented toward improved NPV. RSO
constructs a schedule by right-shifting all activities in the OPT schedule to zero slack.
Other planning heuristics used were Minimum Slack (SLK), Late Finish Time (LF T),
Late-Start Constrained Resource (LSC), and the Sum of Discounted Cash Flow of Future
Activities at Late-Finish Times (DCF) (previously discussed in Chapter 2). The SLK and
LFT methods are representative of good time-minimizing procedures, and the LSC and

DCF methods represent good NPV-maximizing methods.

Finally, an experimental method (a new heuristic) was used. This heuristic was
based on a combination of Greatest Resource Demand and Bowers' resource-constrained
MINSLK (Bowers, 1995). It schedules first the activity which has the least slack along a
resource-constrained critical path, with virtual ties being settled by assigning priority to

the activity that uses the most heavily tasked resource.

Stage 1 of the algorithm uses the Bowers definition of criticality (Bowers, 1995) to
establish the initial MINSLK priority. The problem starts with a typical unconstrained
CPM formulation, then considers resource constraints on a second set of passes as

follows:

Step 1: Forward pass, yielding earliest start and finish times (technical precedence).
Step 2: Backward pass, yielding latest start and finish times (technical precedence).

Step 3: Forward pass, resolving resource contention by assigning resources to CPM
priority activities (minimum CPM slack), yielding earliest start and finish
times (technical and resource precedence).

59

Step 4: Backward pass, applying resource precedence links from previous step to
update the latest start and finish times (technical and resource precedence).

Step 5: Calculate Resource Critical float (slack) as the difference between earliest
and latest start times for each activity.

Slack (latest start - earliest start) is now based on the contention-free start and finish
times. The critical path (zero slack path) flows along both technical and resource
dependency arcs. These slacks are used in the classical MINSLK method in order to
construct the schedule. The second stage of the algorithm adjusts this schedule by
considering the resource loading in the project. "Virtual Ties" are determined and solved

in the following manner:

Step 1: Establish the sensitivity constant, 5 (arbitrarily use 5 = 1.0 times average
activity duration).
Step 2: Identify the currently unscheduled activities with the highest priority (based

on Bowers-MINSLK resource critical float value above) and determine
virtual ties: a virtual tie is defined as a situation where two activities have

amounts of resource critical float that are within 5 of each other.

Step 3: Assign priority (break the virtual tie) by scheduling first the activity that uses
more of the most heavily utilized resource (over the remainder of the project);
if each activity uses the same amount, break tie using the next-most heavily
utilized resource until the tie is broken. If the tie can't be broken on the basis
of resource utilization, break the tie using the original resource-critical float

priority.
Step 4: If, in the previous steps, the schedule has changed, reschedule the remaining
activities using the Bowers-MINSLK method.

Step 5: Continue to loop through Steps 2-5 of this stage until the terminal activity
has been scheduled.

It was anticipated that this heuristic would develop schedules that while not
necessarily "optimal" in a deterministic sense will nevertheless be robust to disruption

and stable during the simulation. This heuristic is designed to trade project duration and

60

   

NPV away for an increase in stability. The sensitivity constant 8 has been set to an
arbitrary value (equal to the average activity duration). This constant represents the

degree of "separation" between slack values that will be allowed before rescheduling
based on resource utilization is forced. Higher values of 6 will result in more frequent

virtual tie conditions; and smaller values of 8 will result in less frequent virtual tie
conditions. Obviously, any future research considering the use of this new heuristic must

consider alternative rationales for the assignment of values for 8. This heuristic will be

referred to as the Bowers-Critical Path method (B-CPM).

3 .3.2 Execution Methods

 

The execution methods are the decision rules used to assign resources to activities as
the simulation progresses. Two primary dimensions of execution method were tested:
the Reservation (Full and No) and the Release (Waiting and No Waiting) types. This
resulted in four combinations: Full Reservation, Waiting (FR-W); Full Reservation, No
Waiting (F R-N); No Reservation, Waiting (NR-W); and No Reservation, No Waiting
(NR-N).

The Full and No Reservation rules were as described by Yang (1996). Under Full
Reservation, an activity reserves the resources it needs as soon as the activity is
technically feasible. Reserved resources can not be used by any other activity. Resources
are reserved on a FCFS basis in order of priority each time a completing activity releases
the resources it was using. This execution method sacrifices resource utilization in order
to achieve stricter activity completion by priority order. The No Reservation rule does

not allow activities to tie up any resources until all resources needed are available and the

61

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activity begins. Under No Reservation, a lower priority activity (which is otherwise
technically feasible) that uses fewer resources can start before a higher priority activity
which uses more resources. The higher priority activity may now have to wait until the

lower priority activity is complete.

The Waiting and No Waiting rules refer to the release of technically eligible
activities with respect to their scheduled start times. Under Waiting, a technically
feasible activity is forced to wait until its scheduled start time before being considered
fully eligible (to seize resources). Under No Waiting conditions, an activity may begin

vying for resources immediately upon becoming technically feasible.

3.4 Independent Variables: Moderating

Two main classes or types of moderating variables were investigated: the
Characteristics of the Problem and the Characteristics of the Environment. Most of these
characteristics have been previously discussed in Chapter 2, Significant Prior Research.
While these characteristics were not explicitly manipulated in the experiment, a set of
problems was used which represent an appropriate range of values for these

characteristics.
3.4.1 Characteristics of the Problem

The characteristics of the problem are those relevant descriptive aspects unique to
each problem in the problem set. Several specific problem characteristics were tracked

(see Table 3.1: Problem Characteristics).

62

Table 3. 1: Problem Characteristics Studied

 

Problem Characteristic

Measure

 

Size

Number of Activities

 

Critical Path Length (scheduled)

 

Complexity

Network Complexity Ratio

 

Network Density Ratio

 

Constrainedness

Makespan Delay Factor

 

Average Resource Constrainedness

 

Maximum Resource Constrainedness

 

Utilization

Average Resource Utilization (scheduled)

 

Maximum Resource Utilization (scheduled)

 

Average Resource Utilization (actual)

 

 

 

Maximum Resource Utilization (actual)

 

First, problem size was measured using the Number of Activities and the Critical

Path Length (duration of critical path). The complexity of the problem was assessed

using two separate measures: the Network Complexity and Density Ratios. The

Network Complexity Ratio is the ratio of arcs (dependencies) over the nodes (activities).
The Network Density Ratio is defined here as the ratio of actual precedence arcs over the
total possible arcs. The measure used here includes redundant arcs. The number of total
possible arcs is determined by finding the sum of the series 1 + 2 + 3 + . . . + (n-l) where
n is the total number of activities (or by using the formula [n(n-1)]/2 which is equivalent).
This definition is consistent with the “Order Strength” measure of Yang (Yang, 1996) and

differs from the classical definition of density used in network analysis which does not

count the redundant or duplicate arcs.

63

 

The degree to which the project is "resource constrained" was tracked using three
separate numbers. First, constrainedness was measured fairly directly by the Average and
Maximum Resource Constrainedness, based on the simultaneous or overlapping demand
for a resource by project activities. Constrainedness was calculated as the ratio of total
planned resource requirements (nmnber and duration for all activities) divided by the
resource availability over the unconstrained CPM critical path length (unconstrained
duration). The Makespan Delay Factor is a similar measure of constrainedness. It
reflects the growth in project schedule length to account for resource dependencies. The
Makespan Delay Factor was calculated as the ratio between the constrained duration

(provided by the specific scheduling technique) to the unconstrained CPM duration.

The final group of problem characteristics measured were those relating to the
utilization of the resources. The Average Resource Utilization and Maximum Resource
Utilization were measured for the problem; for both scheduled and actual use. These
measures were calculated as the requirement for or use of the resources (load) over the
availability (capacity) of the resources over the duration of the project. Utilization was
calculated for both planned and actual project execution. The utilization measures
should, of course, show a close and direct relationship to the constrainedness measures

(higher constrainedness should generally result in higher utilization).
3.4.2 Characteristics of the Environment

Key characteristics of the project execution environment were also accounted for.
Two of these were explicit to the design of the experiment. First, the variability

(uncertainty in duration of activity/task times) was set at two levels: None (deterministic

64

activity times), and Some (distribution range 30% of activity time). The "actual" activity
durations were selected randomly from a Beta(1.5, 3) distribution with a mean equal to
the "planned" duration and a spread as described above. The distribution was thus offset
such that the endpoints reside approximately 1/3 of the spread below and 2/3 of the

spread above the mean.

The second environmental characteristic was the Disruption Level (disruptions in
resource availability). Each project has between 1 and 3 total types of resources used,
and each resource type has between 1 and 15 units available. The types and numbers of
resources required are a fixed part of the problem. A disruption will be modeled as the
unplanned shutdown or loss of availability of a resource during idle time. While shut
down, the resource is unavailable for use by any project activity. The frequency and
duration of the disruptions were established at reasonable (but arbitrary) levels.
Disruptions were set at three levels: None (no interruptions in resource availability),

F requent-Short (F -S), and Infrequent-Long (I-L). The F-S and LL disruptions occurred
randomly, according to sampling from an exponential distribution. Disruptions to each
resource occur independently. The length of the shutdown was also sampled from an
exponential distribution. The parameters for the distributions were selected to result in
approximately the same total amount of disruption over the same length of time. F -S
generated shutdowns of each resource expected once every 5 days, expected to last 1 day.
The IL schedule generated exponential shutdowns expected every 15 days, each

expected to last 3 days. Over the same length of simulated time, the total disrupted time

65

 

 

would be about the same for each resource type. This expectation was investigated

during the pilot runs of the model and was found to be reasonable.

3.5 Experimental Design

 

The experimental design used in this research was selected in order to address the
research questions (section 1.2, Research Problem and Questions) by testing the
hypotheses (section 3.1, Introduction and Hypotheses) using data provided through an
analysis of the behavior of the variables just described. The remainder of this section will
describe the research design by presenting the theoretical model, experimental factors,

problem set, and generation of the data.

3.5.1 Experimental Factors

 

The main experimental factors are the methods of planning (7 levels) and execution
(4 levels). In addition, there are the moderating factors related to the environment. These
include the variability (2 levels) and disruption (3 levels). The characteristics of the
problem (11 variables plus the problem name as a categorical variable) are experienced as

"naturally occurring" over the 18 problems in the benchmark set.

Figure 3.3: Experimental Design, shows a simplified diagram of the treatment
variables and the environmental moderators. Each cell of the diagram represents an
experimental combination of the variables. Each of the 18 problems in the reduced
problem set were simulated for multiple replications in each cell. Output values of the

dependent variables were recorded along with the values of all dependent variables.

66

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'8 Var, lnfq Dis
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Planning combinations were

Figure 3° 3‘ Experimental Design simulated for each of the 18

 

 

problems in the set, yielding a total of 3,240 experiments conducted. Each experiment
(of the 168 combinations of the 18 problems) was conducted multiple times in order to
produce estimates of the 11 outcome variables (two Duration, two NPV, and the seven

Stability variables).

3.5.2 Problem Set

 

A subset of problems from a known, benchmark set of resource constrained project
scheduling problems (the "Patterson Set") were used. This subset has been selected to
represent a broad spectrum of problem types to provide an appropriate level of variation
on the problem characteristics identified. The Patterson Set is an accepted benchmark set
of 110 basic project scheduling problems for which optimal solutions (in the
deterministic case) have already been derived. This set of 110 problems includes three
different levels of resource constrainedness (comprising 330 total problems), and
problems of various sizes (7 to 51 activities), complexity, resource type, and duration (6

to 189 time units duration).

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Generalizability of the benchmark set comes from the variation of the problems
themselves. Over time, problems with unique characteristics have been added to this
benchmark set in order to provide a wide range of variation in problem types. In a very
real sense, this approach increases the validity of the research in terms of comparability to
previous theoretical work, but makes the results un-generalizable to any specific real-
world, practical project scheduling environment. For this exploratory study into the
behaviors of projects with respect to stability, this loss of specificity in external validity
was considered to be appropriate. It is anticipated that more practical, follow-on research

will increase the extensibility of any general concepts or theories developed here.

The characteristics of the reduced problem set is compared to the full Patterson set in
Table 3.2, Problem Set Characteristics. The first grouping of characteristics to be
compared relates to problem size. Along the characteristic Number of Activities (N Act),
the reduced set differs from the full set by not including the smallest problems. It seemed
unlikely that problems with fewer than 22 activities would offer any useful insights into
the nature of stability. Many of the statistical differences between the full and reduced
problem sets are a result of this decision to not include the smaller problems. This shows
up in the characteristic Critical Path Length (CPL), which refers to the duration of the
project as scheduled. The full set CPL is based on the Optimum (minimum duration)
schedules as provided in the Patterson set of problems. The exclusion of the smaller
problems from the reduced set has resulted in a loss of the shorter duration (smaller CPL)

cases.

68

The next grouping of characteristics to be compared relate to problem complexity.
Along the characteristics Network Complexity Ratio (N CR) and Network Density Ratio
(NDR), the reduced set offers acceptable comparability. Most of the statistics are either
identical or similar. The notable exception is the difference in range (at the high end) for
NDR. The reduced set does not offer the same level of density as the full set, with a
reduction of about 30%. While the impact of this loss in range is unclear, it is considered

to be acceptable for the purposes of this study.

The next set of characteristics to be discussed are those related to constrainedness.
The characteristics Makespan Delay Factor (MDF), Average Resource Constrainedness
(ARC), and Maximum Resource Constrainedness (MRC) all seem to be comparable
between the full and reduced problem sets. The ranges are all either identical or very

close. The means and medians do not show any disparate central tendencies.

The final grouping of characteristics describe the utilization of the problems. Both
Average Resource Utilization (ARU) and Maximum Resource Utilization (MRU) show a
slightly restricted range at both the high and low ends in the reduced set. The means and
medians are comparable. It was decided that in an overall sense, the reduced set of 18
problems could be considered to be a fairly representative sample of the full set of 330
problems as compiled by Patterson. The restriction in range as a result of the exclusion
of very small problems was not considered to be troublesome for the purposes of this
study. The restriction in range along the utilization and density characteristics was

considered small enough to be acceptable.

69

Table 3. 2: Problem Set Characteristics

 

 

 

 

 

 

 

 

 

 

 

 

 

Full NAct CPL MDF NCR NDR ARC MRC ARU MRU
Low 7 6 1.00 1.09 0.05 0.40 0.42 0.38 0.39
Mean 26 59 1.99 1.55 0.14 1.43 1.54 0.70 0.77
SD 9 32 0.66 0.31 0.06 0.54 0.56 0.08 0.09
Median 25 60 2.13 1.52 0.12 1.49 1.64 0.70 0.76
High 51 189 3.77 3.09 0.39 2.75 2.85 0.96 1.00
Reduced

Low 22 20 1.00 1.09 0.05 0.44 0.44 0.43 0.43
Mean 36 75 1.87 1.69 0.11 1.28 1.39 0.67 0.72
SD 12 44 0.77 0.53 0.07 0.63 0.67 0.09 0.11
Median 35 67 1.92 1.57 0.10 1.25 1.30 0.67 0.73
High 51 189 3.85 3.09 0.29 2.75 2.85 0.84 0.90

 

 

 

 

 

 

 

 

 

 

3.5.3 Data Generation

 

Dynamic, discrete-event system simulation was used to generate the data for the

experiment in order to address the research questions. The experiment was conducted as

a firll-factorial simulation of project scheduling and execution over the appropriate levels

of experimentally manipulated variables and the "naturally occurring" variation in the

problems themselves. Each run of the simulation model represented an independent,

terminating execution of the planned schedule with "actual" events (task variability and

disruptions) occurring randomly. Four versions of the model were used, each

representing the individual execution methods required by the experimental design. The

schedule generated by the planning method was read into the model during model

initialization.

7O

 

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enVHi

 

 

Through the management of simulation parameters, a range of values for key
environmental characteristics (levels of variability and disruption) was provided. Each
parameter requiring random sampling used an independent random number stream, and
the random number streams were synchronized between the four model versions. The
performance of each combination of planning and execution technique was measured
with respect to time, NPV, and stability under a range of variability and disruption for the
different types of projects as described under the experimental design. Programs were
written and run under the GPSS/H modeling language on a variety of IBM-PC
compatible desktop computers using the 386 and 486 chipsets. The simulation output
consisted of matrices of the start and stop times ("actual") for all activities in the project,

and a listing of the values of all experimental parameters used in the simulation.

The simulation output matrices were converted into lines of data using conversion
routines written in Turbo Pascal 6.0 and executed on the same 386 and 486 desktop
platforms. The conversion routines calculated and tabulated the primary statistics of
interest for the study, including all independent and dependent variables as well as the

environmental and problem characteristics referenced in the experimental design.

Pilot runs of the models and conversion routines were conducted for the purposes of
model validation and run size estimation. Debugging and primafacie validation was
conducted with small runs (n=5) for each cell of the experimental design and each
individual problem (scheduling method x execution method x variability x disruption x
problem). Based on a cursory examination of the initial data, sequential sampling was

selected as the simulation management procedure. Successive batches of runs were

71

C02".

512 L”

Wt? T

“'11:

conducted and analyzed until the desired level of precision was achieved. The initial run
size was selected to be n=40 per cell. Parameter estimates and their confidence intervals
were then analyzed for sufficiency of n (see Table 3.3, Pilot Run Data). This analysis

was performed on the parameter Duration.

Table 3. 3: Pilot Run Data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Factor Level Mean CI (99%) SD N 1
SKED lfi 118.8596 3.73 178.1763 17280]
rso 119.7431 3.81 181.6762 17289
opt 119.8072 3.81 181.6928 17280]
slk 121.4167 3.78 180.3401 17280]
bcp 124.8155 4.10 195.7626 17280|
dcf 129.2070 4.09 195.1381 17280]
lsc 129.2070 4.09 195.1381 17280]
EXEC fm 76.4474 0.69 43.5456 3024a
frw 79.0979 0.71 44.6163 3029
nrw 164.4700 3.81 240.3958 3024a
nt-n 173.1596 4.19 264.4338 30240]
DIS none 76.7464 0.60 43.7062 40320|
long-infreq 113.0239 1.60 116.4872 40320|
short-freq 180.1109 3.97 289.7730 40370]
SPD none 122.9814 2.10 187.6725 60480]
beta 123.6061 2.09 186.3968 60480|

 

The confidence interval half widths indicate that overall, the initial run size should be
sufficient to provide discriminating precision between the dependent variables. For the
durations, the data indicate that means within the factor Scheduling method (SKED) can
be separated into groups. Means within the factors Execution method (EXEC) and
Disruption level (DIS) can be separated. It appears as though there was inadequate
precision to separate means within the factor Variability (SPD). Based on an examination

of the existing sample size and estimates of standard deviation (N and SD), it would seem

72

that the sample size would have to become very large- to the point of impracticality-

before any differences could be established with confidence.

3.6 Data Analysis Issues

 

The methods used to analyze the data were appropriate for the experimental design
and selected in order to address the research issues, problem, questions, and hypotheses.
AS a designed, full factorial experiment, the selection of Analysis of Variance (AN OVA)
as a primary analytical technique was indicated. However, nonparametric comparison
techniques were also used where warranted. These will be discussed as needed in
Chapter 4, Results and Analysis. The ANOVA and other subsequent statistical tests were
conducted using SPSS 8.0 for Windows running on IBM-PC compatible desktop

computers employing Pentium 11 type chipsets.

3.7 Limitations and Key Assumptions

 

Several limitations were imposed upon the scope and nature of this research effort.
The primary limitations included: single projects, single mode resource use, no
preemption of activities, and small (51 activities or less) projects. Due to the exploratory
nature of this investigation into the unexplored topical area of project schedule stability, a
subset of well understood examples from a benchmark problem set and a restricted

number of behaviors was studied.

73

While there is a great deal of interest and research into the scheduling of multiple
projects simultaneously, many new concepts have been tested in the single project
environment first. The reasons for this are several; primarily, when multiple RCPSP
projects are studied simultaneously, the subtle or secondary behaviors of the planning
methods may become "lost" in the complexity of the problem. Interactions between
"problem characteristics" and "execution methods," for example, may be overwhelmed
by delays induced into smaller projects by the presence of the larger problems in the same
scheduling mix. In order to avoid this potential source of behavior masking, this research
effort considered only single, independent projects for the time being. It is anticipated
that the more interesting findings of this study will be extended into the multiple-project

case in the future.

Second, while "multi-mode resource use" cases are of some interest (due to higher
fidelity to certain real world situations), only single mode behaviors will be studied here.
The assumption underlying the use of the single mode is that each activity requires a
fixed number and type of resources for its completion, and that the completion generally
takes a certain amount of time. This characterization has been used more ofien in the
literature than the multi-mode scenario. The Patterson Set is formulated following this
assumption. Currently, for the purposes of comparing the results of this study to other
studies and aligning the assumptions with the benchmark set of problems, only the single
mode operationalization will be used. Once more, it is anticipated that future extensions

of this work will include the study of multi-mode behaviors.

74

While it may be noted that the preemption of activities and the accrual of "set-up
costs" are primafacie of great interest in any study formulated around the issues of
variability, disruption, and stability, preemption will not be studied here. This is also
planned for inclusion into future research. The additional complexity of including
various preemption rules and set-up cost structures into the experimental design (above
and beyond the more basic variables and levels currently proposed) is deemed beyond the

scope of this initial study on the current items of interest.

Fourth, only relatively "small" projects (as contained in the benchmark set of
problems) will be studied. It is important for an initial study of this type to be able to
perform some reasonable comparisons to known phenomena that have been previously
studied. This can be achieved in two ways: first, by using any standards or benchmarks
that have been used before (like the problem set itself); and second, by manipulating the
relevant variables in similar ways and at similar levels. The use of small problems also
allows us to use known, optimal solutions (for the deterministic case, minimizing
duration). The known, optimal solutions provide a "best case" schedule to compare the

performance of the other heuristics.

75

Chapter 4

RESULTS AND ANALYSIS

4.1 Introduction

 

This chapter presents the results of statistical tests and analysis of the data created by
the procedures outlined in Chapter 3, Methodology. This presentation is performed in
five sections.

First, the schedules created by the different scheduling methods are compared. The
next three sections compare the performance of the schedules when executed under the
simulated environmental conditions. The first of these presents exploratory analyses of
the key variables. The second presents analyses of covariation. The final section of the
three compares treatment means.

The fifth section of this chapter draws inferences from the statistical results with
respect to the hypotheses and theoretical model under study. The chapter closes with a

brief summary of the data analyses.

4.2 Plannifl Method Performance under Deterministic Assumptions

This section compares the schedules created prior to simulation. Each of the 7
scheduling methods was applied to each of the 18 problems in the problem set.
“Scheduled Duration” and “Scheduled NPV” performance measures were then calculated

for each schedule. These measures were calculated assuming no schedule variation. The

76

values correspond to relative levels of performance that represent optimistic bounds on
potential actual performance. Often, this potential performance is used by managers to

select a schedule, and is also used as a basis for predictions of actual performance.

4.2.1 Comparison Tables

 

The scheduling results are presented in Table 4.1, Schedules by Problem (SDUR)
and Table 4.2, Schedules by Problem (SNPV). For each problem in the problem set, the

performance level (duration or NPV) is listed. Each scheduling method that achieved that
level of performance is listed on the same row. Identical schedules are those with the
same start and stop times for every activity. Identical schedules are separated by
commas. Schedules that achieve the same level of overall duration or NPV performance,
but are not identical, are separated by semicolons. In instances where many schedules
achieve the same level of overall performance, the row is continued on the next line with
no entry in the performance column. The percent range between the highest and lowest

values for each problem (range/midpoint) is given under the problem identifier.

The scheduling methods create schedules that differed by duration in the majority of
cases. Three of the problems were solved with 6 different durations, 4 were solved with
5, 2 were each solved with 4, 3, and 2 different durations, and only 5 of the 18 problems
were solved with the same overall duration. Among those problems that were solved
with the same overall duration, schedule activity timing differed. Each of these problems

were solved with at least 5 unique activity timing schedules. It is interesting to note that

77

 

llllll

 

\n

1113

Table 4. l: Schedules by Problem (SDUR)

H15A ' °
S ° LSC 17% SL LFT' BCP
LFT DCF

H15B '
BCP 13% LFT

S LSC' LFT DCF S 'LSC

SLK S ° LSC

BCP BCP

DCF DCF

OPT, RSO; SLK, LSC;

- - OPT' LSC

OPT, BCP; SLK, LFT;
- SLK

DCF BCP

OPT, RSO; SLK, LSC;
- - OPT, RSO; SLK, LSC;

45 BCP RSO'LSC
47 DCF LFT

° OPT, RSO; SLK, LSC;
78 BCP . .

91 DCF LSC

95 LF T LFT
98 BCP BCP
100 LSC DCF
OPT, RSO; SLK, LSC;

 

106 DCF
in all of these cases, the scheduling methods grouped together the same way: OPT and
R80, SLK and LSC, then LFT, DCF, and BCP. This is not unexpected, however. It is

noted that in cases where the problem network has diminishing non-critical slack, the
“right shifting” methods (RSO and LSC) will converge on their respective non-shifted

versions (OPT and SLK). Inspection of the 5 problem networks involved will indicate

78

Ct"

 

Wt

53?

 

that this is indeed the case. It would be a surprising result if the methods involved did not

come up with identical schedules.

While the duration differences between the schedules exist, the question remains as
to how great the differences were. Of course, in five cases the differences in duration
were 0; corresponding to the problems where the scheduling methods came up with the
same duration. In two cases the greatest difference between the durations was 1 time unit
(day). In percentage terms, these one day differences amounted to 2% and 4% of the
midrange duration. For these problems, the differences between scheduled durations
were practically negligible. The remaining 11 problems all had differences between the
shortest and longest scheduled duration of 4 days or more. Percent differences for three
of these were less than 10% (4 days/9%, 8 days/8%, and 6 days/7%). The remaining
eight problems all had differences that could be considered Significant, spanning either
over 15 days or 30% or both. This is to be considered in light of the total durations which

range from 20 days to 189 days.

The scheduling methods created schedules that differed by NPV in the majority of
cases. Five of the problems were solved with 5 different NPVS, 6 with 4 different NPVS,
5 with 3, and 2 problems were solved with 2 different NPVS. No problem existed where
all scheduling methods came up with the same NPV. General patterns in the grouping of
performance by method can be noted here as well, although not as sharply defined as for
duration. OPT and RS0 again came up with the same NPV in 12 cases. SLK and LFT
(instead of LSC) came up with the same result in 7 cases. Scheduling method

performance on NPV were mixed for the remainder of the problems.

79

Table 4. 2: Schedules by Problem (SNPV)

H15B
SL FT - 1 715 LFT
BCP 1 705 BCP
LSC DCF l 697 SLK

LFT LSC DCF 16493 SLK
SLK 16474 BCP DCF LSC
S LFT 19 85 LFT RSO

BCP 19 83 SLK
LSC DCF 19 56 BCP

LSC DCF 48 027 BCP S LSC

R80 20 184 LFT

LFT BCP 20161 LSC DCF

3 R80 LSC DCF 51619 LFT
7741 BCP 51609 BCP

7 2 LFT l 642 SL LFT
7720 LSC DCF 1 636 BCP

9 960 BCP 3 619 OPT R80
9 952 SLK 3 617 BCP
9938 DCF LSC 3 616 LSC DCF

 

445 R80 LSC DCF

While NPV differences existed for all problems, the size of the differences was
slight. Seventeen of the problems reflected an NPV difference of $43 or less. The
remaining problem showed a scheduled NPV difference of $205. These differences must
be considered slight when compared to the NPV totals; which range fi'om a low of $5,906

to a high of $48,028. None of the NPV differences reached a level equal to 1% of the

80

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mqv‘

midrange NPV for that problem (indicated by a — in Table 4.2). The nature of these
differences is a function of the total durations and discounting rate as programmed into
the model under study. It is unlikely, with the discounting rates used (15%) and the
durations expected (20 to 189 days), that any great differences in NPV would be seen.
The sensitivity of NPV to time and discounting rates will be discussed in a later section in

this chapter.

4.2.2 Formal Test Results

 

A nonparametric multiple comparison method (Conover, 1980) was used to test for
differences between the scheduling methods on the scheduled duration and NPV
performance measures. This method extends the Friedman’s Rank Sum test to the
situation where multiple comparisons need to be made. The comparison is analogous to a
multiple differences of means test, but uses the rank sums instead of the actual mean
values. The comparisons are shown in Table 4.3, Nonparametric Comparison of
Scheduling Methods (SDUR) and Table 4.4, Nonparametric Comparison of Scheduling
Methods (SNPV). The overall significance (that at least one rank sum score differs from
another) of the test is indicated in the heading of the table. Individual comparisons were
performed at the 0.05 level of significance in all cases. The actual mean values
(performance of the scheduling method on all 18 problems) are provided for comparison

against the rank sums.

Overall, it can be seen that the relative duration performance between the scheduling
methods against all 18 problems can be statistically separated into groups. RSO and OPT

were generally the best performers, and DCF was the worst. OPT, LSC, LFT, and SLK

81

could be considered part of the “top middle” group of performers, and LF T, SLK, and
BCP fell into the “bottom middle” group. The OPT, SLK, and LFT methods were
selected to represent the “high performers” on duration. Putting aside the performance of
the two benchmarks (OPT and RS0), the SLK and LFT methods comprise the highest
performing group, along with LSC. The hybrid heuristic BCP came in near the bottom of

the rankings against scheduled project duration. Only DCF performed worse.

Table 4. 3: Nonparametric Comparison of Scheduling Methods (SDUR)

 

 

 

 

 

 

 

 

 

 

 

 

SDUR (0-0000)

.Mean Method—Juli Sum
73.3 RSO 44.5 A
73.3 OPT 46.0 A B
74.8 LSC 67.0 B
74.7 LFT 76.0 B C
75.2 SLK 78.5 B C
76.2 BCP 83.5 C
79.7 DCF 108.5 D

Table 4. 4: Nonparametric Comparison of Scheduling Methods (SNPV)

SNPV (0.00001

Mean Method—Bank Sum
17279.44 OPT 103.5 A
17266.89 RSO 87.5 A B
17275.67 LFT 86.0 B
17271.67 BCP 73.0 B
17273.78 SLK 72.0 B
17254.56 DCF 41.0 C
17254.56 LSC 41.0 C

 

 

 

 

It is also apparent that the relative NPV performance between the scheduling
methods against the 18 problems can be statistically separated into groups. Again, OPT
and R80 form the top performing group. LSC and DCF (the two methods selected
because of their strong track record on NPV) formed the poor performing group. RSO,
LFT, BCP, and SLK were all grouped in the middle range. The RSO, LSC, and DCF

methods were selected to represent the “high performers” on NPV. Ignoring the two

82

benchmark methods (OPT and R80), the LSC and DCF methods comprise the lowest
performing group. All of the other heuristics performed better. Even the hybrid heuristic

BCP out-performed LSC and DCF.

4.2.3 Expectations of Performance under Stochastic Conditions

 

Central to this current research is the theory that the predicted performance of
various scheduling methods can be changed significantly by the presence of
environmental variability (disruptions and task time deviations) and execution
procedures. A key issue to be investigated in the current study is to what degree the
scheduling methods come up with robust or stable plans that continue to achieve high

levels of performance in spite of the environmental factors and execution methods.

It is expected that both the relative and absolute performance of the various
schedules will change as a result of adding environmental uncertainty and differing
execution policies. It is also presumed that the highest-performing schedules under the
deterministic assumptions may suffer the most under stochastic conditions; certainly in an
absolute sense, but perhaps also in a relative sense. The better schedules
(deterministically) are generally “tighter,” with less non-critical slack. Less slack should
make the schedule less able to absorb variability without causing some type of
performance degradation. More slack in a schedule should allow the schedule to
experience variability and still perform reasonably close to what was predicted. It is thus
surmised that the “looser” (less efficient under deterministic assumptions) schedules may
actually outperform the “tighter” schedules when variability and disruptions are added.

Whether or not the ability of a particular schedule to use slack in absorbing variability

83

 

 

 

(and remain on schedule) in the absolute sense is enough to counteract the superiority of

another schedule in a relative sense remains to be seen.

4.2.4 A Note About the Sensitivity of NPV to rt

It was previously noted that the magnitude of the differences in NPV between
scheduling methods for each problem were a function of (in large part) the duration and
discount rate used by the model. Either a small discount rate or a short duration (or both)
will result in small values of the product rt (r iS the discount rate, as a fraction; t is the
fraction of time in years). The basic discounting procedure used in calculating NPV
discounts the value of a cash flow by e raised to the rt power (as described in Chapter 3,
Methodology). The model in use here assumes a negative cash flow for each activity,

then a single positive cash flow upon completion.

Schedules can achieve different NPVs for each problem in two ways. First, the
timing of activities can change the timing of the negative cash flows. This effect would
probably be slight. Second, the total duration will affect the timing of the single positive
cash flow. This effect would probably be a greater differentiator between schedules than
the effect of different negative cash flows. In addition, if all activities and the project

Completion are generally all “early” or all “late,” the effects on NPV of either accelerating
0r delaying negative flows and accelerating or delaying the positive flow have
Complementary effects that may further reduce the impact of schedule deviations on
NPV. If cash outflows are early (late), and the cash inflow is late (early), the effect on

NPV would be enhanced. These situations would seem to be unlikely.

84

 

 

 

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A simple investigation was conducted into the sensitivity of NPV to changes in the
discount rate r and total duration t. NPV was calculated for four different levels of rt (1,
2, 3, and 4 times the scheduled rt), for each schedule and problem in the problem set. An
rt value of 1 corresponds to an r of 0.15 (as used in the study) and a total duration equal to
the scheduled duration. Values of 2, 3, and 4 correspond (respectively) to an rt factor of
two, three, or four times the baseline value. In this sense, 2 would correspond to either
the same r but double the duration, or the same duration and double the discount rate. As
the rt factor increases, the project value would decrease. Representative data for
scheduling method OPT is given in Table 4.5, NPV vs. rt (OPT). This table includes a
calculation of the slope and percent slope of the NPV-rt curve for each problem. The
slope is calculated as the dollar change in NPV for each factor increase in rt. The percent
slope is calculated as the slope as a percentage of the average NPV over the range of rt
values from one to four. These results are depicted graphically in Figure 4.1, Sensitivity
of NPV to rt (OPT). Full tables and figures for all scheduling methods are provided in

Appendix L, NPV vs. rt.

From Table 4.5 and Figure 4.1, no great differences in NPV were seen even for
relatively large increases in rt. As expected, the shorter (smaller) project problems were
much less sensitive to changes in rt than the larger (longer) projects. As a percentage rt,
no problem exhibits greater than a 4% decrease in NPV for an increase in rt from one to
fOur times greater than that used in the study (a 3.73% decrease for Heur107C under

OPT). The greatest sensitivity (3.78%) was exhibited by Heur107C under the scheduling

method BCP. A summary table of all percent slopes, with the average percent slopes and

85

F1:

 

 

 

NPV vs. rt: OPT

60000

 

E 30000 .- ,: --:---:-— ~—:-..-:
2

20000 t -_.- a,” 5:, - .

 

 

10000 -.

 

 

 

 

 

Figure 4. 1: Sensitivity of NPV to rt (OPT)

 

 

ranges for all scheduling methods
and problems is provided in Table

4.6, Percent Slopes, NPV vs. rt.

It is expected that differences in
NPV in the data would be very
small. Any detectable differences, if
statistically significant, would be

surprising. It would be even more

surprising if any practically significant differences were to be found. If a pattern of

statistically significant differences in NPV were present, this would indicate an effect

strength powerful enough to overcome the slight nature of differences in NPV

explainable by small changes in rt alone.

Table 4.5: NPV vs. rt (OPT)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rt Factor
2 4 Slope %s|ope
HEUR01 3A 5910 5882 5854 5827 -28 -0.47
HEURO13C 13285 13147 13011 12877 -136 -1.04
HEURO48A 6664 6628 6592 6557 -36 -0.54
HEUR04BC 16624 16426 16232 16040 -195 -1.19
HEUROSGA 6660 6620 6580 6541 -40 -0.60
HEUROSGC 19677 19445 19217 18992 -228 -1.18
HEUR014A 3910 3870 3831 3793 —39 -1.02
HEUR014B 7746 7619 7496 7374 -124 -1.64
HEUR014C 9978 9786 9599 9417 -187 -1.93
HEUR015A 6450 6387 6326 6265 -61 -0.97
HEUR0153 12721 12521 12325 12133 -196 -1.58
HEURO15C 16499 16170 15848 15535 -321 -2.01
HEUR105A 19591 19288 18991 18699 -297 -1.55
H EUR1 05C 48027 46473 44985 43561 -1489 -3.25
HEUR1 07A 20190 19862 19540 19226 -321 -1.63
HEUR107C 51635 49719 47899 46168 -1822 -3.73
HEUR110A 12646 12518 12393 12268 -126 -1.01
HEUR1 1°C 32619 31862 31129 30419 -733 -2.33

 

86

 

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77,. n: n L .8. m a!

 

 

Table 4.6: Percent Slopes, NPV vs. rt

 

OPT SLK LFT RSO LSC DCF BCP av range

HEUR013A -0.47 -0.48 -0.49 -0.47 -0.50 -0.36 -0.50 -0.47 0.14
HEUR013C -1.04 -1.09 -1.08 -1.04 -1.09 -0.72 -1.02 -1.01 0.37
HEUR048A -0.54 -0.59 -0.58 -0.55 -0.58 -0.43 -0.61 -0.55 0.18
HEUR048C -1.19 -1.20 -1.19 -1.19 -1.20 -0.81 -1.19 -1.14 0.39
HEUR056A -0.60 -0.60 -0.60 -0.64 -0.65 -0.41 -0.60 -0.59 0.24
HEUROSSC -1.18 -1.19 -1.18 -1.18 -1.19 -0.79 -1.18 -1.13 0.40
HEUR014A -1.02 -1.02 -1.02 -1.10 -1.07 -0.73 -1.02 -1.00 0.37
HEUR014B -1.64 -1.74 -1.82 -1.65 -1.77 -1.31 -1.70 -1.66 0.51
HEUR014C -1.93 -2.18 -2.08 -1.93 -2.18 -1.56 -2.11 -1.99 0.63
HEURO15A -0.97 -0.96 -0.96 -1.03 -1.04 -0.69 -0.96 -0.95 0.35
HEURO15B -1.58 -1.76 -1.62 -1.59 -1.77 -1.24 -1.70 -1.61 0.54
HEURO15C -2.01 -2.04 -2.01 -2.01 -2.05 -1.44 -2.15 -1.96 0.71
HEUR105A -1.55 -1.59 -1.58 -1.58 -1.61 -1.18 -1.72 -1.54 0.54
HEUR1OSC -3.25 -3.25 -3.25 -3.25 -3.25 -2.19 -3.25 -3.10 1.06
HEUR107A -1.63 -1.63 -1.66 -1.67 -1.67 -1.18 -1.63 -1.58 0.49
HEUR107C -3.73 -3.77 -3.76 -3.73 -3.77 -2.52 -3.78 -3.58 1.26
HEUR110A -1.01 -1.04 -1.04 -1.02 -1.04 -0.75 -1.09 -1.00 0.34
HEUR110C -2.33 -2.31 -2.31 -2.33 -2.31 -1.57 -2.33 -2.21 0.76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.3 Efiloratory Analysis

 

The first set of analyses performed on the simulation output were exploratory in
nature. This section is concerned with an initial analysis of the output variables of
duration, NPV, and stability. Specifically, the next three subsections will report
aggregate statistics, a presentation of mean values in the treatment cells, and an
assessment of the likelihood of normality and homoscedasticity within and between

treatment cells.
4.3.1 Summary Statistics of Key Variables

A standard set of statistics were calculated for each output variable and are presented
in Table 4.7, Summary Statistics of Key Variables. While the results are unsurprising,

some items of interest can be noted.

87

Table 4.7: Summary Statistics of Key Variables

 

Actual durations (ADUR) range from a low of 19.44 days to a high of 226.84 days.

This is reasonable, given the scheduled durations (SDUR) from 20 days to 189 days. In

addition, the durations appear to be clustering in the “short, medium, and long” categories

as designed in to the problem set (see Figure 4.2, Histogram of Aggregate Statistics

(ADUR) and histograms for the remaining variables in Appendix A). The mean ADUR

 

 

 

   
  
 

ADUR
Std. Dov = 4554
Mean = 781
N = 120960 00

 

 

 

 

20.0 60,0 100,0 1 .0 - 220 0
40.0 50 0 120.0 160 0 2000

Figure 4. 2: Histogram of Aggregate Statistics (ADUR)

 

 

88

of 78.1106 is larger than the
average SDUR of 75.3 143.
Combined with the mean RDUR
of 1.0371, and an ADUR
skewness of 1.1 15, this indicates
that there is more “lateness” than
“earliness” being experienced in
the problem set. The NPV

statistics indicate a

corresponding reduction from what was scheduled. The actual NPV (AN PV) mean of
$17,130.00 is lower than the scheduled mean of $17,268.08, and the average ratio of
actual to scheduled NPV (RNPV) is less than unity (0.9934). The minimum and
maximum values are reasonably close to the minimum and maximum scheduled values.
The ratio variables RDUR and RNPV appear relatively symmetrical around 1.0 which is

also expected.

A footnote to the NPV statistics must be made. The large variance (30% of the
mean) of the aggregate measure reinforces the expectation that differences in NPV
between treatments for the same problem will be undetectable. Once more it is noted that
any underlying effect on NPV as a result of differing treatment would have to be very
consistent and powerful if it is to be detected. However, these differences are still
expected to be practically insignificant even if statistically significant. Conversely, an
examination of the NPV histograms indicates that some clustering is occurring and this

may indicate some underlying relationships betWeen NPV and the treatments.

Each of the stability measures should be bounded by zero, and this is reflected in the
actual minimum values. The measures are unique in this. When the disruption and
variability levels are set to “none,” the stability measures will respond as 0. The stability
measures should generally appear left-peaked and right tailed (similar to an exponential
distribution), and each histogram shows a spike at O and a long tail to the right at least

partially as a result of the left-bounded characteristic.

It was also expected that the ratio forms of resource profile offset (POIR and POOR)

would be less than unity, and the maximum values reflect this. Another interesting thing

89

”r

 

to note is that the resource profile offset measures are quite similar. The resource profile
offset “idleness” (POIC) and “overuse” (POOC) statistics, as well as the ratio statistics,
are quite similar. This was somewhat expected, as a shortening or lengthening of the
project duration would most probably be associated with accelerated or delayed activity
start and stop times. This, in turn, will compress or expand the resource profile evenly,
and for every unit of overuse (accelerated start) we would expect a unit of idleness

(accelerated stop) and vice versa.

The weighted activity deviation stability measures appear to be behaving as
expected. Earliness (WADE) happens less than lateness. The contribution of earliness to
the composite measure (WADC) is small. Each measure displays a long tail to the right
(mean much closer to the minimum than the maximum level, and the skewness statistics
indicate long tails in the positive direction. The histograms also display this

characteristic.

4.3.2 Treatment Cell Means

 

Table 4.8, Means: ADUR by Scheduling and Execution Method, by Disruption and
Variability contains the mean values of ADUR within each treatment combination. The
complete set of tables for all performance measures is included in Appendix B. The
columns in the table separate the treatments by variability (top header) and disruption
type (bottom header). The rows in the table separate the treatments by scheduling

method (left header) and execution method (right header).

This information is presented graphically in Figure 4.3, ADUR Treatment Means.

The complete set of figures for all performance variables is included in Appendix C,

90

Table 4.8: Means: ADUR by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR some none
Sched Exec none freq Infq None freq infq
OPT FRN 74.53 76.03 79.79 73.33 74.91 78.84
FRW 75.45 76.51 79.64 73.33 74.93 78.29
NRN 75.40 77.21 78.70 74.44 76.39 78.49
NRW 75.35 77.02 79.37 73.33 75.39 78.31
SLK FRN 76.22 77.74 81.57 75.17 76.82 80.67
FRW 77.23 78.32 81.46 75.17 76.78 80.00
NRN 76.12 77.77 79.53 75.22 77.13 78.87
NRW 76.94 78.49 81.00 75.17 77.26 79.80
LF T F RN 75.75 77.23 80.89 74.72 76.38 80.12
FRW 76.74 77.83 81.10 74.72 76.39 79.58
NRN 75.47 77.45 78.69 74.83 76.83 78.31
NRW 76.58 78.13 80.23 74.72 76.81 79.19
RSO FRN 74.55 75.99 79.70 73.28 74.84 78.73
FRW 75.58 76.61 79.78 73.28 74.90 78.26
NRN 75.34 77.00 78.76 74.56 76.30 78.13
NRW 75.40 76.96 79.48 73.28 75.38 78.00
LSC F RN 75.78 77.31 81.03 74.78 76.40 80.20
F RW 76.99 78.08 81.24 74.7 8 76.48 79.83
NRN 75.94 77.58 79.1 1 75.22 76.61 78.40
NRW 76.73 78.31 80.99 74.78 76.92 79.66
DCF FRN 80.45 81.86 85.49 79.67 81.14 84.91
FRW 81.62 82.57 85.74 79.67 81.20 84.47
NRN 79.57 81.07 83.65 79.00 80.64 83.25
NRW 81.13 82.62 84.99 79.67 81.64 84.35
BCP F RN 77.26 78.56 82.22 76.22 77.70 81.41
FRW 78.28 79.25 82.32 76.22 77.79 80.90
NRN 76.69 77.99 79.76 76.28 77.53 79.57
NRW 77.95 79.64 82.03 76.22 78.30 80.82

 

 

Graphical Treatment Means. The graphs present the mean values within a treatment
combination for each variable. Each variable is represented by four graphs, one for each
execution method. On any individual graph, separate series are used for each scheduling
method. The x axis captures the 6 different combinations of spread (variability; none and

some) and disruption (none, frequent-short, and infrequent-long). Values 1-3 indicate no

91

variability and none, frequent, and infrequent disruption (in that order). Values 3-6
indicate the same disruption pattern but with variability. The y axis captures the value of

the performance variable.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADURbyVARandUS: NRN ‘ WRVSVARandDS: FRN
00.00 850° +
“'m + 4. DW? 84.01) E”:
0200 031k 82.00 + 0""
+ + , m ‘ o- + i; . IR
¢ woo _ {7 .. t x 31w ' U + .3 1
3 7a a + p 0"o 3 ,8 00 - n 0'”
( 00 g 6 J lsc < ' ’ o ... lac
7000 ii — U +00! l 70.00 0 5 ~ ‘5 +dd
‘ 0
74 m a -bcp 74.00 a? i U :bq:
’ a
72.00 72.00
1 2 3 4 5 e 1 2 3 4 5 0
VAR and us VAR no as
AUJRbyVARandUS: NRW AWRVSVARandDIS: FRW
00.00 + 00.00 +
.1. i L W:
04.00 001* 04.00 i 0091
&.w + _ + oslk 32m ._ + I 05*
<- .9 m ‘- + m
g 00.00 a + - x 00.00 0 ~
3 : a .- Ono g — + 05°
< 731” - D g E; I” < 781!) 7 — II 130 .
70.00 t: .. 7* +001 76113 *‘ '3 ~ 5- +001
II o D ‘ 13 o C
74.00 ~ be? 74.00 J”
n c
72.00 72.00
1 2 3 4 5 6 1 2 3 4 5 s
VAR no as J VAR and us

 

 

4.3.3 Treatment Cell Normality and Homoscedasticity

 

The next step in the exploratory analysis was to assess the data for suitability for
more formal statistical testing. Each of the 3,024 treatment cells (168 factor
combinations and 18 problems in the problem set) was tested for normality, and the skew,

kurtosis, and standard deviation values were calculated. These metrics were deemed

92

 

essential to establishing normality and equality of variance within the treatment cells;
assumptions that must be met in order to claim strong inference for a wide variety of

parametric tests (Cohen and Cohen, 1983; Neter et. al., 1996).

The SAS procedure UNIVARIATE was used with the NORMAL option to generate
summary statistics within each treatment cell, to include measures of kurtosis, skewness,
and standard deviation. A statistic (the Shapiro-Wilk statistic, W) was generated to
conduct a formal test for normality. Small values of W lead to a rejection of the
hypothesis that the data are sampled from a normal distribution (SAS Institute, 1985).
These results are all summarized in Table 4.9, Treatment Statistics: Assessment of
Normality and Homoscedasticity. The normality and standard deviation data are

summarized graphically for ADUR in Figure 4.4 and for the rest of the variables in

Appendix D.

Table 4.9: Treatment Statistics: Assessment of Normality and Homoscedasticity

 

93

Table 4.9 generally indicates significant levels of skewness and kurtosis in many
treatment cells. This is unsurprising; many of the variables are bounded on one side and
have the potential to exhibit extreme values on the other. The wide spread in levels of
skew and kurtosis (noted by the high standard deviations relative to mean values) also
suggest that the shapes of the distributions between treatment cells for the same variable
differ significantly. These characteristics may present problems in meeting the

assumptions of parametric statistical tests.

Meeting the assumption of normality is also unsupported. The mean probabilities (of
values less than W) are less than .4 for all variables, and less than .3 for all but two of
them. The standard deviations of the probabilities indicate that a wide range of values is
present for each variable. A closer examination of the values for ADUR (presented
graphically in Figure 4.4) explains both the low means and wide ranges. It is known a
priori that the treatment cells corresponding to the No Variability and No Disruption

combinations will have no variance; the values will all be identical. These treatment

 

 

 

1 000 1400 ‘
ADUR (P<W) ADUR (VAR)
800 Std. Dev = .28 120° 3” Dev = 3,54
' Mean = .24 1000 Mean = 5.2
600 N = 2510-00 800 N = 3024.00

600

400 ,
400 ',

 

200

  

200

4 -. T? 0 *
0.0 .20 .40 .60 .80 1.00 0 10 20 30 40 50 60 70 80
l‘Tigllre 4. 4: Distributions, P Normality and Variance (ADUR)

 

 

 

 

 

 

 

94

combinations represent 504 out of the 3024 possible combinations. In addition, some of
the variables may be relatively immune to task time variability or resource disruption.
No Disruption and Some Variability represent an additional 504 combinations; No
Variability and either F requent-Short and Infrequent-Long represent another 504
combinations each. It would be anticipated (and this is borne out by the charts) that the
distribution of probabilities less than W would be heavily weighted on the left. This is
the case for ADUR as shown, and is also present to a similar degree for RDUR, AN PV,
RNPV, POIC, POIR, POOC, and POOR. WADE, WADL, and WADC exhibit a much
greater left-shifting than the rest. At this point, normality of the data is in question. A
reduced data set (excluding all of the no variability/no disruption cases) was examined.

Even afier excluding these cases, it was unreasonable to assume normality.

A similar problem exists with the assumption of equal variance. The amount of
“spread” of the standard deviation values is indicated in Table 4.9. For every variable,
the standard deviation (of the standard deviations) is greater than the mean. Graphically,
We see (on Figure 4.4) that the values again are left-shifted around zero. This is due to
the previously mentioned deterministic treatment cells. The spread of values imply that
the assumption of equal variances would not be met by the data. This effect is present for

all of the performance variables. Unequal variances were prevalent in the reduced data

Set as well.
Parametric statistical testing requires data to be relatively normal (or at least mound

Shaped) and the variances of comparison sets to be approximately equal in order to draw

the strongest inferences from sampled data (Cohen and Cohen, 1983; Neter et. Al., 1996).

95

Summary statistics relating to normality and homoscedasticity were generated, and
indicate that the data may have trouble meeting these assumptions. Therefore, while

parametric data analysis methods may be employed, caution must be exercised in

drawing inferences from the results. The following analyses will take this into account.

4.4 Covariation

In order to assess the behaviors of and relationships between the variables in the
study, two analyses of covariation were performed. First, relationships between and
among the outcome variables were assessed using biserial correlations. This information
should help determine how unique or similar the individual measures are; and whether or
not the proposed stability measures offer information that is significantly different from
the existing, traditional measures. Also, a classical Analysis of Variance (ANOVA) was
Performed assessing the degree of covariation between levels of the factors (independent
Variables) and the outcome variables. This information should help determine which
faetors are more or less important to the outcomes, and whether or not a selection of

Combinations of factors would result in better performance levels.

4-4- 1 Biserial Correlation

 

Two biserial correlations were performed in order to assess the degree to which the

onteome variables responded in concert with one another. Table 4.10 (Biserial

Correlations: Parametric) and Table 4.11 (Biserial Correlations: Nonparametric) present

96

 

Table 4.10: Biserial Correlations: Parametric (Pearson's)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR RDUR ANPV RNPV WADE WADL TVADC rorc Poi?! rooc POOR
‘Anun -
RDUR .077 -
(.000)
ANPV .897 .051 -
(.000) (.000)
RNPV -.064 -.452 .009 -
(.000) (.000) (.002)
WADE .005 -.123 .001 .146 -
(.108) (.000) (.851) (.000)
WADL .456 .723 .402 -295 -009 -
(.000) (.000) (.000) (.000) (.002)
WADC .443 .670 .390 -249 .245 .967 -
(.000) (.000) (.000) (.000) (.000) (.000)
Pore .649 .494 .655 -.111 .092 .845 .842 -
(.000) (.000) (.000) (.000) (.000) (.000) (.000)
Porn .099 .621 .061 -.130 .305 .640 .698 .623 -
(.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)
Pooc .643 .543 .635 -.255 .062 .865 .854 .982 .613 -
(.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)
\Poon .100 .693 .045 -.400 .246 .663 .705 .597 .961 .627 -
(.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)
Table 4.11: Biserial Correlations: Nonparametric (Spearman's)
ADUTR RDUR ANPV RNPV WADE WADL WADC POIC POIR POOC POOR
ADUR -
m .121 -
(.000)
\—
ANPV .773 .043 -
(.000) (.000)
\—
RNPV -.l65 -.596 -009 -
w\ (.000) (.000) (.001)
ADE -.010 -.044 -.029 .01 1 -
w\~ (.001) (.000) (.000) (.000)
ADL .388 .832 .299 -524 .063 -
'w\ (.000) (.000) (.000) (.000) (.000)
ADC .373 .716 .289 -459 .332 .917 -
W (.000) (.000) (.000) (.000) (.000) (.000)
'C .487 .607 .513 -.336 .246 .837 .898 -
W (.000) (.000) (.000) (.000) (.000) (.000) (.000)
IR .152 .698 .080 -.330 .309 .782 .877 .833 -
\ (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)
0°C .477 .669 .473 -.483 .230 .872 .917 .979 .823 -
P (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)
00R .157 .769 .051 -.542 .278 .821 .891 .806 .957 .849 -
(.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000) (.000)

 

97

 

 

the correlation coefficients and significance levels for the combinations of variables. A

graphical presentation of the data is included in Appendix E, Biserial Scatterplots.

In general, the results found on the parametric and non-parametric tables are similar.
The following discussion will refer to the non-parametric correlation matrix. First, the
significance levels (values above the diagonal) were all 0.001 or less; indicating a high
degree of statistical confidence in the correlations. Three main categories of correlations

will be discussed: within the traditional measures, within the stability measures, and
between the traditional and stability measures.

Traditional Measures. Within the traditional measures, the correlation between

 

ADUR and ANPV (0.773) was strong, indicating that long durations are associated with
high levels of NPV. This is unsurprising, as the model calculated the cash flows based on
a “cost plus” method, which would generally make the larger (longer) projects more
Profitable. Between ADUR and RDUR, the low correlation (0.121) indicates that longer
Projects did not necessarily experience longer delays (as a percentage of scheduled
duration) than shorter projects, but that this effect was mildly present. An even lower and

negative (-0.009) correlation between ANPV and RN PV indicates no relationship

b(it"veen actual NPV and changes in NPV from scheduled. Similarly, no relationship
(0.043) was detected between RDUR and ANPV. A mild and negative (-0.165)
colTelation was observed between ADUR and RNPV. This suggests that for projects with
10Tiger actual durations, the actual NPV decreased compared to the scheduled NPV. This
relationship maycome from two distinct sources. “Higher” values of ADUR may result

from either longer schedules, or delays in any schedule. On the other hand, “smaller”

98

values of RNPV can result only from reductions in anticipated NPV on a project of any
size. The relationship may be the result of longer projects being more susceptible to
reductions in NPV (vice planned values), or may be the result of delays in a project of
any size resulting in reductions in NPV. A strong and negative relationship (-0.596) was
found between RDUR and RNPV. This indicates that when a project is delayed beyond
schedule, the NPV is reduced below schedule. This phenomenon would lend credence to

the idea (just discussed) that the source of the negative relationship between ADUR and
RNPV could be the result of delayed projects.

Stability Measures. The next set of correlations to be discussed are those among the

 

stability measures. In general, strong, positive correlations were found between the

Stability measures. The lowest relationships were found between WADE and anything
else (0.063 with WADL to 0.332 with WADC). As anticipated, the relationship between
WADE and WADL was slight (0.063). Therefore, activity lateness was not found to
coexist with activity earliness. WADE was correlated more strongly with WADC
(0.332); since WADC is a measure consisting of the sum of WADE and WADL this is
not surprising. The vast majority of the WADC variable came from WADL. WADC and
WADL share a 0.917 correlation coefficient. WADE was correlated mildly with the
reSource overuse and idleness measures (POOC, POOR, POIC, and POIR); slightly more
With the ratio variables than the raw amounts. WADL and WADC exhibit strong
relationships with the resource measures, with WADC consistently showing higher
coI‘I‘elations. These values range from 0.877 (POIR) to 0.917 (POOC). Also, strong

col‘relations were present between the resource measures themselves. As expected, the

99

relationships were stronger within the idleness and overuse forms themselves. The
coefficient values were all above 0.806, with a 0.979 between POIC and POOC and a
0.957 between POIR and POOR. These findings indicate that while simple activity
earliness was not related to the other measures, activity lateness, lateness and earliness,

and the resource idleness and overuse measures were all closely related.

Traditional Measures vs. Stability Measures. The final set of correlations to be
discussed are those between the traditional measures and the stability measures. The first
striking result is that WADE and RNPV are negatively correlated with all of the other
measures, and are positively related only to each other. Higher amounts of simple
activity earliness is associated with lower ADUR, RDUR, and ANPV (-0.010, -0.044, -
0.029). Higher amounts of lateness, lateness and earliness combined, resource idleness
and idleness vs. schedule, and resource overuse and overuse vs. schedule are all

associated with lower NPV vs. scheduled (-0.524, -0.459, -0.336, -0.330, -0.483, -O.542).

It is unsurprising that lateness measures would be associated with lower RNPV, as
Previously discussed. However, there is no a priori reason to suspect that high levels of
reSource offset would necessarily be strongly (negatively) correlated with RNPV. Indeed,
high amounts of resource offset (either idleness or overuse) would be present in either
high (project early) or low (project late) RNPV situations. In this case, it has already
been established that the high levels of resource offset are associated with lateness (high
WADL; ~0.8 correlation). The range restriction on duration (and NPV) “built-in” to the
experiment may be more responsible for this relationship than any underlying effect,

1'IOWever. For any given project, the amount of “earliness” that can be experienced is

100

bounded by the dependencies (resource and task) in the network. The amount of
“lateness,” on the other hand, is virtually unbounded. In general, the amount of resource
offset and earliness would be relatively small, and the amount of offset and lateness
would be relatively large, across all problems in the problem set and across all levels of
factors and treatments. Perhaps, therefore, the apparent association between resource
offset and RNPV is more artifactual than actual. Additional evidence for this can be

found in analysis of the next correlations to be discussed, between the duration and offset

measures.

Raw idleness (POIC) and overuse (POOC) show a strong correlation with raw
duration (ADUR; 0.487 and 0.477 respectively). The correlations drop below 0.2 for the
idleness and overuse ratios. All correlations are strong between the raw and ratio offset
measures and the duration ratio measure; each above 0.6 (and POOR-RDUR at 0.769).
High levels of offset are associated with project lateness. The associations between the
Offset measures and RDUR indicate that even when the scheduled durations of the

Projects are set aside, offset (instability) and delays are closely related. This, in turn,

leads to reductions in NPV (vice scheduled).

It should also be noted that the correlations between offset and AN PV are sirrrilar to
thOse between offset and ADUR; with higher values for the raw measures and lower
Values for the ratio measures. It is proposed that the same phenomenon is at work in both
instances. The longer projects have higher NPVs (as previously discussed) and more
activities by design. A longer project, with more activities, would show higher raw

Values for offset than a shorter project with fewer activities even if the “rate” of offset

101

were the same for both. The ratio measures were included in the study specifically to

account for this. When the ratio variables are used, a truer picture of the relationship
(without the confound of project size) is possible.

The final set of relationships to be discussed in this section are those between
WADL/WADC and the traditional duration and raw NPV measures. The behaviors of
WADL and WADC are very similar; of course, WADL comprises the vast majority of
the composite WADC measure. The term “lateness” will be used to refer to both WADL
and WADC. Lateness is strongly correlated positively with duration; both raw (ADUR,
0.373) and ratio (RDUR, 0.716). This is to be expected. Lateness is also mildly
correlated with ANPV (0.289). This seems surprising, as it appears to suggest that higher

amounts of lateness correspond to higher levels of NPV. Once more this appears to be an
artifactual result of the design of the problems in the problem set. Larger, longer projects

will necessarily accumulate more lateness over time, as well as having higher scheduled

NPV amounts.

Summa_ry. Some general conclusions can be drawn from an analysis of the biserial
Con‘elations (Appendix E, Biserial Scatterplots and Table 4.10, Biserial Correlations:
Nonparametric). First, the traditional measures clearly measure two distinct concepts:
duration and value. This finding is consistent with previous research into duration and
NPV. The raw values ADUR-ANPV and the ratio variables RDUR-RNPV show strong

col‘l‘elations. When adjusted to take into account the project size (through the use of the
1mic variables), this correlation is negative. While not explicitly recognized in the

literature, this result is consistent with previous general findings. The stability measures

102

divide into two distinct groups, the offset measures and the deviation measures. Idleness
and overuse appear to behave similarly; they covary both in raw and ratio form. The
activity deviation measures seem to consist of a trivial earliness component, and a much
more prevalent lateness component. Between and among the traditional and stability
measures, two phenomena seem to suggest that the two types of measures indeed
constitute different classes of project performance characteristics. First, while the
traditional and stability measures exhibit strong covariation in some areas, in others the
relationships are weak. Second, the overall correlations between the types of measures
are lower than those within each type of measure, indicating that perhaps there are
differing degrees of commonality or overlap between and among the types of measures.
Overall, it can be said that duration, stability, and value are distinct aspects of project
performance; and that these aspects are related to each other. The characteristics of and
relationships between the project performance measures must be considered when

analyzing the remainder of the research results.

51.12 ANOVA Results

The next step in the analysis of the data was to perform Analysis of Variance
(AN OVA) procedures in accordance with the experimental design. The factors (project
identifier, disruption level, and variability level) and treatments (scheduling and
exe=eution method) were used in a model to predict project performance along each of the
measures. Table 4.12, ANOVA Results, indicate the degree of success (adjusted R2) and
Significance of each model. These will be discussed in a later section. First, a discussion

0f AN OVA model assumptions and how well the data fit the assumptions is in order.

103

Table 4.12: AN OVA Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 3 a. a B a‘ 8 e e 8 e
9. a .2. 5 E E E 2 2 2 §
Levene .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
Adj. R2 .994 .355 .997 .022 .435 .465 .482 .648 .469 .625 .434
Model .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
lntcpt .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
N .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
S .000 .000 .898 .41 7 .000 .000 .000 .000 .000 .000 .000
E .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
D .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
V .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
SE .000 .000 1 .000 .999 .000 .000 .000 .000 .000 .000 .000
SD .007 .000 1.000 1 .000 .000 .000 .000 .000 .000 .000 .000
SV .000 .000 l .000 .999 .000 .029 .000 .000 .000 .000 .000
ED .000 .000 .000 .320 .000 .000 .000 .000 .000 .000 .000
EV .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
DV .000 .000 .000 .750 .000 .000 .000 .000 .000 .000 .000
SED .003 .000 l .000 1 .000 .000 .000 .000 .002 .000 .015 .000
SDV .946 .789 1.000 1 .000 .1 18 .793 .704 .075 .000 .151 .000
SEV .778 .01 1 1.000 1.000 .000 .980 .131 .000 .000 .000 .000
EDV .000 .000 .060 .997 .000 .730 .000 .206 .032 .691 .089
SEDV 1.000 1 .000 1.000 1 .000 .140 1 .000 1 .000 .999 .224 1 .000 .529

 

Model Assumptions. In order to draw strong inferences from ANOVA results, the

 

data must satisfy several assumptions (Neter, et. al., 1996; Cohen and Cohen, 1983; and

Otl’lers). As the data increasingly violates these assumptions, the ANOVA model departs

from its intended purpose and the validity of the model falls apart. Moderate levels of

departure may be acceptable for the interpretation of strong results, but cast doubt upon

Subtle results. High levels of departure tend to jeopardize even strong results. Before

PlaCing trust in the ANOVA results, or drawing inferences from these results, the

departures of the model from the assumptions must be checked.

104

 

Five departures have been identified as critical to the interpretation and acceptance of

ANOVA results (Neter, et. al., 1996):

1.

Nonconstancy of error variance: the ANOVA model requires that the error
terms (model estimate minus actual value) have constant variance for all
treatment levels. Two types of tests were used to check this assumption, formal
tests and an informal test. The formal test used on the error terms was the
Levene test, reported as a probability or likelihood that the variances of the error
terms are equal. These results are shown as the top row in Table 4.12, ANOVA
Results. Also, the raw data was tested formally as already discussed in section
4.3.3, Treatment Cell Normality and Homoscedasticity. It is noted at this time
that all AN OVA models and the raw data failed the formal tests. The informal
test was a visual examination of scatterplots of the error variance (standardized
residuals) versus the predicted values. Most of the models failed the informal
test as well. The informal tests generally indicated that variance increased in
direct proportion to the predicted values. Scatterplots for models are provided in
Appendix F . Most models also failed this informal test, with two exceptions.
The models RDUR and RN PV did not appear to depart radically from the
assumption of equivariance. All other models displayed a troubling level of

departure.

Nonindependence of error terms: time series data are susceptible to
autocorrelation between elements in the time series. This departure is not

applicable to the current study or models. Statistical independence is built in to

105

the experimental design and the conduct of the simulation experiments

themselves.

Outliers: the presence of extreme values can bias and complicate appropriate
analysis of results. An informal test was used here; a visual inspection of the
scatterplots of error terms vs. predicted values (refer to previous figure). It
should be noted that the nature of the distributions of the variables (left-
bounded, and right-tailed distributions with high levels of skew) would lend
themselves to the creation of extreme values as a matter of course. No unusual

or significant presence of outliers was observed.

Omission of important explanatory variables: unaccounted for sources of
variance, which exist primarily in empirical studies. The departure of a model in
a designed laboratory experiment is dependent upon the completeness and
validity of the experimental design itself. As long as the theoretical model is
valid, and accounts for the relevant variables to be studied, the design and
conduct of a full factorial experimental simulation mitigates against this
departure. From a purely statistical and analytical sense, within the current
experiment, all relevant explanatory variables have been identified and carefully

managed.

Nonnormality of error terms: the ANOVA models used are essentially
parametric tests; they rely on an assumption of normality. Normality of the data
itself was tested formally, and the surrogate normality of the error terms was

tested informally. The results of the formal tests have already been discussed in

106

section 4.3.3, Treatment Cell Normality and Homoscedasticity. The informal
test on the error terms consisted of a visual inspection of scatterplots of the
standardized residuals vs. expected normal values (see Appendix F, AN OVA

Residual Plots). Departures from normality were observed for all models.

Departures from the AN OVA model assumptions were observed both in the formal
and informal tests. The departures from normality and equivariance are particularly
troubling, as these assumptions are considered vital to having confidence in ANOVA
results and the validity of their interpretation. Remedial efforts were considered and
attempted. Transformations of the variables did moderate the departures somewhat, but

additional problems in interpreting the ANOVA results caused the remediation efforts to

be abandoned.

Results. Based on the departures of the ANOVA models from the assumptions, the
results must be viewed with some caution. While in some cases these departures were
mOderate, in others they were quite large. This realization must be balanced against the

aPparent statistical significance of the results presented in Table 4.12, ANOVA Results.

For each project performance variable, the ANOVA model used the project problem
identifier (“Name,” N) as a blocking factor. The main effects of this blocking factor was
acCounted for by the model first, and this blocking factor was not used in any of the

interactions tests. The remaining factors and treatments were each considered for both
main and interaction effects according to the full factorial experimental design. The
SCheduling Method (S, 7 levels), Execution Method (B, 4 levels), Disruption Type (D, 3

levels) and Variability (V, 2 levels) were all entered into the model.

107

The explanatory power of the AN OVA models on the traditional performance
measures was high in the case of ADUR and ANPV (adjusted R2 of 0.994 and 0.997,
respectively). While the overall model significance appears to be better than 0.000 in
each case, the model departed quite significantly from the assumptions. Ironically, in the
case of the ratio versions of these variables (RDUR and RNPV), the explanatory power
was much lower (0.355 and 0.022) but the departures were much less. Interpretation of
these results is firrther confounded by the significance levels of many higher-order
interactions. ADUR, RDUR, and AN PV each have significant two- and three-way
interactions. ADUR and RDUR show all factors and interactions to be significant down
to the two-way level, and at least two of the three-way interactions to be significant.
ANPV shows about half of the two-way and one of the three-way interactions to be
significant. This seriously complicates any interpretation of the results, above and

beyond the departures of the data from the model assumptions. For RNPV, the
assumptions aren’t violated as much as the others, and the interactions are less of a

PFOblem as well, but the explanatory power is quite low (model adjusted R2 of 0.022).

Results for the stability measures were similar. Adjusted R2 values range from 0.434
to 0.648, indicating that the models provide a fairly high degree of explanatory power.
HO’W'ever, interpretation of these results are complicated by the departures of the models
from the assumptions, and the presence of interactions between factors. With one

eKeatption, all variables showed interactions significant at 0.000 or better for all two-level

interactions, and at least two three-way interactions significant at 0.05 or better.

108

Overall, the ANOVA results are uninforrnative with respect to either the traditional
or stability variables. However, the AN OVA did detect interactions between factors.
Even with the departures from the assumptions, the presence of interactions would
complicate additional testing. A weak inference could be drawn that the significance of
the interactions supports the idea that each of the factors is important, and selection or
“fitting” of scheduling and execution method to the appropriate environmental condition
is indicated. While the assumptions of the ANOVA analysis were violated, there is
evidence that significant interactions exist between the factors in the study. The focus of
analysis needs to include an assessment of the nature and importance of these

interactions. Multiple comparisons are indicated in order to evaluate interactions.

3 Differences of Means

Due to the insurmountable problems with the ANOVA analyses, nonparametric
differences of means tests were performed. A multiple comparison version of the
Friedman nonparametric rank sum test (Conover, 1980) was used to detect differences in
ratlked performance between the scheduling and execution methods for each factor level
Combination. For each treatment of interest (either the scheduling or execution method),
Performance was ranked using the problem identifier as the blocking factor. This
cOrliparison is performed independently for each combination of the remaining treatment

(eXecution or scheduling method, respectively) and environmental factors. The results of
these multiple comparisons are included in Appendix G, Nonparametric Comparisons. A

Satnple is presented in Table 4.13, Scheduling Method Performance by Execution Method

109

(ADUR). These results correspond to the graphical information previously seen in

Appendix C, Graphical Treatment Means.

Before presenting the multiple comparison results, a brief description of the tables is
in order. Referring to the sample table (Table 4.13), the performance variable is indicated
in the upper left hand comer (ADUR in this case). In the second column of the header
row, the factor of interest used for the comparison is given next. Since this table reports
the rankings of the scheduling methods within each execution method, the headers are
F RN, FRW, NRN, and NRW. At the next level of headings, the disruption type (none,
freq, infq) is given. This header is not repeated for each execution method type, but all
entries in the respective column belong to that disruption type category. Finally, the
variability level (some or none) is indicated, along with the overall significance of the
multiple comparison test. For every comparison, a significance level of 0.05 was used to
differentiate between groups within each comparison set. Finally, the critical treatment

members (scheduling, in this case) are listed according to their rank scores, and
Significant differences in ranks are indicated by grouping similar scores alphabetically.
For example, under F RN-NONE-none for ADUR, there was no significant difference
betvveen scheduling methods RSO and OPT (group A), but they both differed

Significantly from LSC (group B). In turn, LSC was ranked differently from SLK (group

D) and so on. This format was used for all multiple comparisons.

The following sections present comparisons between scheduling methods for each

eXecution method, and then comparisons between execution methods within scheduling

110

method. In each case, a discussion of results for the traditional measures is presented

first, followed by a discussion of the results for the stability measures.

Table 4.13: Scheduling Method Performance by Execution Method (ADUR)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR FRN
NON—E FREQ INFQ

none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A RSO A RSO A RSO A RSO A
OPT A RSO A OPT A OPT A OPT A OPT A
LSC B LSC B LSC B LSC B LSC B LSC B
LFT C LFT C LFT C LFT B LFT C LFT B
SLK D SLK C SLK D SLK C SLK D SLK C
BCP E BCP D BCP E BCP D BCP E BCP D
DCF F DCF E DCF F DCF E DCF F DCF E

FRW
none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A OPT A OPT A OPT A OPT A
OPT A RSO A RSO A RSO A RSO A RSO A
LSC B LSC B LSC B LSC B LSC B LSC B
LFT C LFT BC LFT C LF T BC LF T B LFT B
SLK D SLK C SLK C SLK C SLK B SLK B
BCP E BCP D BCP D BCP D BCP C BCP C
DCF F DCF E DCF E DCF E DCF D DCF D

NRN
none .000 some .000 none .000 some .000 none .000 some .000
OPT A RSO A RSO A RSO A RSO A RSO A
RSO B OPT A OPT AB OPT AB LSC B OPT A
LSC C LFT B LSC B LFT BC OPT B LFT AB
SLK D LSC C LFT C LSC C LFT B LSC BC
LFT D SLK C SLK D SLK C SLK C SLK C
BCP E BCP D BCP E BCP D BCP D BCP D
DCF F DCF E DCF F DCF E DCF E DCF E

19in
none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A OPT A OPT A RSO A OPT A
OPT A RSO A RSO A RSO A OPT A RSO A
LSC B LSC B LSC B LSC B LFT B LFT B
LF T C LFT B LFT C LF T B LSC B SLK C
SLK D SLK B SLK D SLK B SLK B LSC C
BCP E BCP C BCP E BCP C BCP C BCP D
DCF F DCF D DCF F DCF D DCF D DC F E

 

111

 

While complete information is presented for all variables in the tables and figures,
when the performance against individual variables is presented, the discussion of the
results will be limited to ADUR, WADC, and POOC. The ratio variables RDUR and
POOR will be discussed in a limited fashion, only when they behave in interesting ways.
Results with respect to the NPV measures will be presented only when interesting or
unanticipated behaviors are present. The WADC measure reflects most of the behaviors
of WADL and WADE, and will represent the family of “deviation based” stability
measures. POOC is selected to represent the “resource based” stability measures. The
behavior of POOC and POIC are similar, and as POOC represents an “overage” or
overuse type of measure, this indicator is probably more relevant to project management

practitioners.

4.5.1 Scheduling Method Performance by Execution Method

 

Multiple comparisons were performed on the rank performance of the scheduling
methods within each execution method and combinations of disruption type and
variability level. An aggregate presentation of the multiple comparison rank data is
presented in Table 4.14, Relative Top Rankings (Scheduling Methods). This table
presents tallies of how many times each scheduling method was found in the top
performing group for each performance variable. The tallies are broken down by
disruption type (left column; none, frequent-short, and infrequent-long) and variability

level (right column; none and some).

112

Table 4.14: Relative Top Rankings (Scheduling Methods)

t
G
a:
'1"
«a
H
9
5
3'
J:

Infrequent-long

 

A more detailed breakdown of the multiple comparison rank data is shown in Table
4.15, Summary of Multiple Comparisons (Scheduling by Execution). For each variable,
the table indicates the ability of the multiple comparison procedure to discriminate
between individual methods (Discriminate Ability). Numbers in the columns represent
the number of times (out of the total comparisons made) that the methods were separated
into 1, 2-3, 4-5, or 6-7 distinct groups. A high tally of the numbers toward the low end

indicates a weak ability to discriminate between the scheduling methods (a large number

113

of comparisons which were unable to discriminate). Higher counts in the high end

indicate a much stronger ability to discriminate between scheduling methods.

Table 4.15: Summary of Multiple Comparisons (Scheduling by Execution)

 

 

 

 

 

 

 

 

 

 

 

 

 

Discrim. Ability (24) Rank Rank Diff
Var 1 2-3 4-5 6-7 Top 2 Ratio Bottom 2 Ratio var dis
ADUR 0 0 l6 8 OPT RSO 47/48 BCP DCF 48/48 2/ 12 2/8
RDUR 3 7 l 1 3 DCF BCP 41/42 OPT RSO 31/42 4/ 12 2/8
ANPV 12 1 7 4 LF T OPT l9/24 LSC DCF 21/24 0/ 12 4/8
RNPV l4 4 3 3 DCF BCP 16/20 RSO LSC 17/20 0/12 3/8
WADE 12 4 4 4 OPT DCF 12/24 RSO LSC 24/24 2/ 12 3/8
WADL 3 1 1 9 l LSC BCP DCF 37/42 OPT RSO 26/24 7/ 12 6/8
WADC 2 l3 7 2 DCF BCP 27/44 RSO LSC 33/24 5/ 12 4/8
POIC 2 8 l4 0 LFT BCP RSO 29/44 RSO LSC 24/44 6/ 12 7/8
POIR 2 7 15 0 LF T BCP RSO 29/44 RSO LSC 24/44 6/ 12 7/8
POOC 2 13 9 0 BCP RSO LFT 30/44 RSO LSC 24/44 5/12 6/8
POOR 2 l3 9 0 BCP RSO LFT 30/44 RSO LSC 24/44 5/ 12 6/8

 

 

 

 

 

 

 

 

 

 

 

 

 

The “Top 2” and “Bottom 2” columns indicate which specific methods are found
most often in the top (or bottom) two positions in the rankings. Membership in the top
(bottom) two rank positions is tallied, and the top two scheduling methods (three in the
event of a tie for second place) are listed along with the total number of times they are
found in the top (bottom) two positions. This information indicates the relative
superiority (inferiority) and consistency of performance of the scheduling methods. A
high count (ratio) indicates that the top (bottom) two methods were found in the top
(bottom) two positions for many individual comparisons. Complete results are presented

in Appendix G, Nonparametric Comparisons.

The “Rank Differences” columns indicate the number of times that the rank order
performance between multiple comparisons (Appendix G) differed. For each variable,

the rank performance lists were compared within each combination of treatments and

114

factors. If the ranked lists could not be made equal across variability (some or none), or
if any one of the ranked lists could not be made identical to the others across disruption
(none, frequent, or infrequent), the comparison was scored as a “difference.” If ranked
lists being compared could be made identical, by shifiing equivalent methods within their
significant difference bands, then the lists were considered to be “not different.” The
differences were tallied in tables contained in Appendix H, Differences in Ranked
Performance. If the ranked lists differed significantly, then this would support the
proposition that the relative performance of the scheduling methods were sensitive to
variability (or disruption, respectively). A somewhat arbitrary rule was developed to
classify the dependence of the variable upon the factor. For any individual variable, if
greater than 75% of the cases show a difference, then it is inferred that the relative rank
performance is highly dependent upon the factor. Strong dependence is inferred for
between 50% and 75% of cases, and moderate dependence for 25% to 50%. No or weak
dependence is inferred if fewer than 25% of cases exhibit different relative rank

performance order. This arbitrary rule is used to simplify interpretation of results.

Traditional Measures. For the ADUR variable, a pattern is observed across all

 

treatment-factor combinations. The RSO and OPT methods are clearly superior, and the
DCF and BCP methods are clearly inferior. RSO and OPT are ranked either first or
second in 47 of the 48 cases, and BCP and DCF are ranked sixth and seventh in 48 of 48
cases. LSC, LFT, and SLK (mainly in that order) fall into the middle. The rank sum
comparison method showed a strong ability to discriminate between scheduling methods,

separating the seven methods into five or six statistically significantly different groups in

115

most cases. This provides strong evidence that performance on ADUR is dependent upon
the scheduling method used. As the pattern is consistent across all levels of variability
and disruption, no evidence is provided that relative schedule performance on ADUR is
dependent upon these factors. In addition, the number of cases where the relative
rankings differed (2/ 12 for variability, and 2/8 for disruption) were too low to support this

proposition.

This ability to discriminate is reduced sharply for the RDUR measure. In many
cases, the ranking procedure is only able to separate the methods into three groups (or
less). Even in cases where the methods can be differentiated into five or more groups,
there is overlap between members of the different groups. This is due in large part to the
narrow range of values for RDUR (vice ADUR), as well as a lack of consistency in the
performance of the methods. In three striking examples, the rank sums were exactly
equal. When either Full Reservation or Waiting conditions were present, and there was
no variability and no disruptions, the ADUR was exactly equal to SDUR; and RDUR was
therefore unity. If, however, the execution method is changed to No Reservation-No
Waiting (NRN), this allows individual tasks to seize resources out of order. When this
happens, the schedule effectively disrupts itself and differences in performance become
apparent. In total, this provides only moderate evidence that performance on RDUR is

dependent on the scheduling method.

An additional phenomenon is observed in the ranked performance order under
differing execution protocols for RDUR. At the bottom end of the performance ranking,

separate patterns are observed between F RN/N RN and FRW/NRW. The presence or

116

absence of the Waiting discipline changes which scheduling methods perform worst.
Under a No Waiting system, OPT and RSO are usually last (19 out of 22 instances).
Under a Waiting system, OPT improves slightly and LSC takes it’s place (RSO and LSC
in last two places; 17 out of 20 cases). This evidence suggests that the relative

performance of the scheduling methods is sensitive to the execution method.

The most striking observation from an analysis of the ADUR and RDUR scheduling
method comparisons is that the rank order is almost completely reversed between the two
measures. Where RSO and OPT are the highest performing schedules on ADUR, they
are poor performers on RDUR. Similarly, DCF and BCP perform last on ADUR but
score very highly on RDUR, filling the top two positions 41 out of 42 times. LSC, LF T,
and SLK continue to fill the middle positions on the rank list. This finding suggests that
scheduling methods that result in shorter SDUR may also achieve shorter ADUR, but
much larger (proportionally) differences between ADUR and SDUR. RSO and OPT
deliver shorter actual durations, but promise scheduled durations much shorter than they
can deliver. BCP and DCF promise and deliver longer durations, but they are more able
to meet those promises. This suggests the existence of a trade-off between duration and
the ability to meet schedule. Two feasible schedules of dissimilar duration may provide
countervailing ability to meet their respective scheduled durations. No clear pattern
exists across and between the variability and disruption levels; indicating that the
evidence is unable to suggest that relative scheduling performance on RDUR is

dependent upon these factors. This lack of support is reflected in the number of cases

117

where ranked lists differ (4/ 12 for variability and 2 out of 12 for disruption). The

variability score (4/ 12) indicates a “moderate” level of dependence.

A similar phenomenon is observed between ANPV and RNPV; however, as
predicted in section 4.2.4 (A Note About the Sensitivity of NPV to rt), difficulty is
encountered in establishing significant differences between the performance of the
competing methods. Whenever variability is present, differences are not large enough
between the scheduling methods to be detectable for both the AN PV and RNPV measures
(all methods ranked in the same group). This is seen in the low overall significance of the
Comparisons, and the inability of the comparison to differentiate between scheduling
methods. In the majority of comparisons, the test was unable to separate the ranked
performance into more than 1 group (all methods were equal). When variability is
present, there is no evidence that performance on AN PV is dependent upon the

scheduling method used.

When variability is “none,” however, some discriminatory power exists and patterns
emerge. Including only those 12 cases, 11 of the comparisons separate the methods into
at least 4 groups. This provides strong evidence that performance on ANPV is dependent
upon scheduling method when variability is absent (or perhaps low). This phenomenon
also suggests the relative performance of the scheduling methods is dependent on the
variability level. The rank order pattern is consistent across the disruption levels. This
SUggests that there is no evidence that the relative scheduling method performance is

dependent upon the disruption level.

118

Also similar to RDUR, the execution method affects the ability to discriminate
between scheduling methods for RNPV. When a Waiting system is used (FRW and
NRW), and Disruption and Variability are none, ANPV is equal to SNPV and RNPV
becomes unity. When activities are allowed to seize available resources ahead of
schedule, however (N 0 Waiting), differences in ANPV are possible and the performance
of the scheduling methods can be differentiated. Patterns are similar between ANPV and
RNPV (but with different methods). Under no variability, discriminatory power exists
and this provides evidence that the RNPV performance is dependent upon scheduling
method. When variability is present, the evidence fails to support this conclusion. This,
in turn, suggests that the relative performance of the scheduling methods is dependent
upon the variability level. The pattern is consistent across all levels of disruption,
suggesting that the relative scheduling performance is not dependent upon disruption.
This lack of evidence is clear from an inspection of the relative rank differences (0 out of
12 for relative differences due to variability). Some evidence suggests that the relative
performance of scheduling methods on ANPV could be moderately dependent upon
disruption type, however. The count of cases where the relative ranked performance

differed (4 out of 8) indicates a moderate level of dependence.

In general, for AN PV the best performing methods are OPT and LF T when the
execution method used is F RN , F RW, and NRW. Under NRN, the performance of OPT
drops and BCP replaces it in the first or second ranking. At the other end of the
Spectrum, LSC and DCF are the poorest performers under FRN, FRW, and NRW. Under

NRN, the performance of DCF improves, and RS0 replaces it at the bottom of the

119

rankings. When either a Full Reservation system or a Waiting system are in effect, the
ranked performance of the various scheduling methods follow a pattern. When neither a
Reservation system nor a Waiting system is used, the ranked performance of the various
scheduling methods follows a different pattern. This phenomenon suggests that the

relative performance of the scheduling methods is sensitive to the execution method used.

The ranked performance of the scheduling methods on RNPV differs significantly
from the ranked performance of ANPV. Unlike the phenomenon observed between
ADUR and RDUR, the rankings are not necessarily reversed. For RNPV (when
variability is absent and differences are detectable), patterns in ranked performance are
observed, but not to the same consistency as noted previously for ADUR, RDUR, and
ANPV. Generally, DCF and BCP occupy the top two rank positions (16 out of 20 cases),
and RSO and LSC occupy the two bottom rank positions (17 out of 20 cases).
Exceptions are due to the movement of OPT (2 out of 20 top and 2 out of 20 bottom),
SLK(1 out of 20 top), and LFT (1 out of 20 bottom). The cases where the relative
ranked performance differed indicated no support for a relative dependence on variability
(0 out of 12 cases). Moderate relative dependence is indicated for disruption type, with 3

out of 8 cases being different.

Stabilifi Measures. One interesting overall result is noted regarding the performance

 

of the RSO scheduling method on the resource profile offset measures (POOC, POOR,
POIC, and POIR). RSO consistently places both in the “Top 2” and the “Bottom 2”
categories. This is explained by an examination of the specific scheduling method

performance by execution method tables in Appendix G. First, inability to discriminate

120

creates somewhat broad categories at both the top and bottom of the rankings. Second,
many of the other scheduling methods do not follow consistent or distinct patterns in their
placement on the rankings. Against this backdrop, the RSO method ranks very highly
when combined with the F RN and NRN execution methods. RSO ranks very low when

applied under the F RW and NRW execution disciplines.

This can be explained by the nature of the RSO method. RSO involves the right-
shifting of non-critical tasks until the schedule contains no slack. Under a “no waiting”
discipline (FRN and NRN), these tasks would be performed ahead of schedule, creating
potential instability. Conversely, under a “waiting” discipline (FRW and NRW), tasks
which may be technically feasible would wait until their right-shifted scheduled time,
reducing the potential instability. This phenomenon would not be present for the other
schedules, as (by default) tasks are commonly scheduled as soon as they become feasible,
in effect creating a left-shifted schedule. This implies that either a waiting discipline or
left-shifting may prevent some instability; however, under left-shifting, each task is
subject to instability induced by the late finishes of predecessor tasks. This in turn may
suggest an approach to protecting a schedule from instability by properly allocating
schedule slack on the non-critical tasks. A strategy of using a waiting execution
discipline in conjunction with scheduling tasks “in the middle” between right and left

shifted options may reduce the exposure of the schedule to instability.

The ability to discriminate for the combined earliness-lateness variable WADC was
marginally better than the individual WADE and WADL. One of the comparisons moved

from the 1 group into the 2-3 groups category, and one moved from the 4-5 groups

121

category into the 6-7 groups category. This was offset by one of the 4-5 groups
comparisons moving down into the 2-3 groups category. This provides moderate
evidence that WADC performance is dependent upon the scheduling method used. DCF
and BCP were the top performers, occupying the top two ranks 27 out of 44 times. RSO
and LSC were the bottom performers, ranked in the last two positions 33 out of 44 times.
These rankings varied somewhat; LF T, SLK, and LSC rose to the top 14 times but no
discernible pattern was present with respect to either variability or disruption. The rank
orders were different under variability in 5 out of 12 cases; and different under disruption

in 4 out of 8 cases, showing moderate levels of dependence upon these factors.

Rank patterns for the overuse stability measures POOC and POOR were virtually
identical, with the exception of minor differences in the ability to discriminate. General
patterns were similar to those for POIC and POIR, except for the specific rank
performances of the various scheduling methods. Both variables showed a moderate to
strong ability to discriminate, providing evidence that project performance on POOC and
POOR was dependent upon the scheduling methods. BCP, RSO and LFT were high
performers 30 out of 44 times, and RSO and LSC were the lowest performers 24 out of
44 times. The many deviations to this pattern showed only a moderate consistency
between and across variability and disruption type. Evidence for the rank order of
scheduling methods being dependent on variability and disruption was therefore mixed.
Interestingly, RSO and LSC were consistently in the bottom two positions for F RN and
NRN, but not for FRW or NRW. When the waiting discipline was in use, no clear

pattern existed. This suggests at least a mild dependence of the rank scheduling

122

performance upon the execution method. The rank differences indicate that the relative
performance of the scheduling methods was moderately dependent upon variability level

(5 out of 12 cases), and strongly dependent upon disruption level (6 out of 8 cases).

Summa_ry. Overall, the multiple comparisons provide some evidence that the
performance outcomes are dependent upon the scheduling methods. This evidence is
strong for ADUR, and strong for ANPV and RNPV (when variability is “none”) and
strong for WADE (under no waiting). For the remaining variables, the ability to
discriminate suggests a moderate amount of support for the hypothesis that performance

outcomes are dependent upon scheduling method.

Evidence also indicates that in many cases, the relative rank performance of the
scheduling methods is dependent on the level of variability present. Scheduling method
performance shows a strong dependence on variability for WADL. Moderate dependence
is apparent for RDUR, WADC, POIC, POIR, POOC, and POOR. The relative rank order
performance of scheduling methods for ADUR, ANPV, RN PV, and WADE do not

appear to exhibit a dependence on variability.

More evidence supports the premise that the relative rank performance of the
scheduling methods is dependent on the type of disruptions present. Relative scheduling
performance is highly dependent upon disruption type for POIC and POIR. Strong
dependence is evident for WADL, POOC, and POOR. Moderate evidence exists for
ANPV, RNPV, WADE, and WADC. No or slight evidence appears for the remaining

variables (ADUR and RDUR).

123

Two additional weak inferences can be drawn as a result of an analysis of the rank
performance comparisons of the scheduling methods. First, the stability measures and
the traditional measures do indeed seem to react differently to the various treatment and
factor combinations. The performance of the methods differs slightly between the
traditional and stability measures. Second, it has been noted that for some of the
variables, the rank performances differ across the different execution methods. This

premise will be tested more directly in the next section.

4.5.2 Execution Method Performance by Scheduling Method

 

Multiple comparisons were performed on the rank performance of the execution
methods within each scheduling method and combinations of disruption type and
variability level. Summary results are given in Table 4.16, Summary of Multiple
Comparisons (Execution by Scheduling). The format of the table used is similar to that
of the previous table, with two exceptions: first, instead of tallying the Top (Bottom) 2
methods, the table reports membership in the first (last) position. The top (bottom) two
vote-getting methods are still given as before, but a tally is recorded only for membership
in the absolute first (last) position on the multiple comparison. Second, the discriminate
ability is tallied for the individual number of groups found, instead of tallies within a
range of values. Complete results are presented in Appendix G, Nonparametric

Comparisons.

As before, the “Rank Differences” columns indicate the number of times that the
rank order performance between multiple comparisons (Appendix G) differed. For each

variable, the rank performance lists were compared within each combination of

124

treatments and factors. If the ranked lists could not be made equal across variability
(some or none), or if any one of the ranked lists could not be made identical to the others
across disruption (none, frequent, or infrequent), the comparison was scored as a
“difference.” If ranked lists being compared could be made identical, by shifting
equivalent methods within their significant difference bands, then the lists were
considered to be “not different.” The differences were tallied in tables contained in
Appendix H, Differences in Ranked Performance. If the ranked lists differed
significantly, then this would support the proposition that the relative performance of the
execution methods were sensitive to variability (or disruption, respectively). Once again,
for any individual variable, if greater than 75% of the cases show a difference, then it is
inferred that the relative rank performance is highly dependent upon the factor. Strong
dependence is inferred for between 50% and 75% of cases, and moderate dependence for
25% to 50%. No or weak dependence is inferred if fewer than 25% of cases exhibit

different relative rank performance order.

Table 4.16: Summary of Multiple Comparisons (Execution by Scheduling)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discrim. Ability (42) Rank Rank Diff

Var 1 2 3 4 Top 1 Ratio Bottom 1 Ratio var Dis

ADUR 0 13 19 10 NRN FRN 41/42 FRW NRW 28/42 12/21 10/14
RDUR 0 13 19 10 NRN FRN 41/42 FRW NRW 28/42 12/21 10/ 14
ANPV 0 21 19 2 NRN FRN 32/42 FRW F RN 27/42 15/21 5/14
RNPV 0 22 18 2 NRN FRN 33/42 FRW FRN 27/42 15/21 5/14
WADE 0 15 27 0 FRW FRN 42/42 NRN 42/42 0/21 0/14
WADL l 12 18 ll FRN NRN 39/4] NRN FRN 34/41 15/21 12/14
WADC 0 l4 l4 l4 NRW FRN 34/42 NRN 42/42 0/21 5/14
POIC 0 12 20 10 FRN NRW 31/42 NRN FRW 36/42 3/21 13/14
POIR 0 12 21 9 FRN NRW 31/42 NRN FRW 36/42 3/21 13/ 14
POOC 0 17 16 9 NRW FRN 33/42 NRN FRN 35/42 4/21 13/14
POOR 0 16 18 8 NRW FRN 33/42 NRN FRN 35/42 4/21 13/14

 

125

 

Traditional Measures. The duration variables ADUR and RDUR display identical

 

ranked performance for execution methods within each scheduling method. This is in
contrast to the reversed rankings between ADUR and RDUR observed for the scheduling
methods previously noted. The no waiting (FRN and NRN) protocols were clearly
superior to the waiting (FRW and NRW) methods. This suggests that allowing activities
to seize resources as soon as they are technically feasible may result in decreased total
project duration. While the choice of a reservation system (full or none) is equivocal (21
for none and 20 for full), this implies that a less structured approach to execution may be
superior in terms of duration than the more structured strategies. This clear ability to
separate the performance of the execution methods supports the hypothesis that project

performance is dependent upon the execution method used.

Some additional (but inconclusive) patterns emerged (see Appendix G). In every
case, the rank performance order changes across either disruption, variability, or both. In
one case (LSC), the rank performance of the execution methods appears to change across
disruption level. In the remaining cases, the performance order changes arbitrarily. This
is supported by consideration of the rank difference tallies. For both ADUR and RDUR,
the relative rank order was dependent upon variability in 12 out of 21 cases; and
dependent upon disruption type in 10 out of 14 cases. This suggests a strong level of

dependence for both variables and for both factors.

The time value of money variables (AN PV and RNPV) also behaved very closely to
each other. The performance rankings were identical, except that in two cases the

groupings and significance levels were different. Ability to discriminate was strong

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(although weaker than for ADUR and RDUR), indicating that rank performance is
dependent upon execution method. FRN and NRN were ranked in first place 32 out of 42
times (similar to ADUR and RDUR). Surprisingly, FRN was also ranked in last place 12
times. FRN was ranked first when variability was “none” and disruptions were equal to
“none” or “freq” (7 out of 14 times). FRN was not ranked last under these conditions.
When disruption was “infq,” F RN was not ranked first at all but was ranked last 11 out of
14 times (regardless of variability). This indicates that relative ranked performance
depends in some part upon variability, and to a larger degree on disruption type.
Similarly, NRN is ranked first when variability is “some” 17 times out of 25 (and never
last), and only 8 times when variability is “none” (and ranked last 11 times out of l 1).
This suggests that for NRN, relative performance is dependent upon variability. In
general, the relative rankings differed 15 out of 21 times under differing levels of
variability, suggesting a strong dependence. The ordering was different 5 times out of 14

under varying disruption type, indicating a moderate level of dependence.

Stability Measures. WADE, WADL, and WADC do not behave in a cohesive

 

manner. They each display at least a moderate ability to discriminate, indicating that
performance is to some degree dependent upon execution method. This ability is weakest
for WADL, and strongest for WADC. For WADE, the top performers were FRW and

F RN , occupying the top rank 42 out of 42 times. In every case where FRN was the top
performer, it’s performance was statistically indistinguishable from that of NRW. NRN
was the worst performer 42 out of 42 times. These results provide no evidence that

relative rank performance is dependent upon either variability or disruption. This is also

127

the case for the rank difference counts. For WADE, no differences were shown out of all

cases for either variability or disruption.

For WADC, NRW or FRN were ranked first 34 out of 42 times, and NRN was
ranked last 42 out of 42 times. When variability was none, and disruptions were none,
FRN was ranked first 5 out of 7 times (NRW first 0 times). When variability was some,
and disruptions were none, NRW was ranked first 7 out of 7 times (FRN first 0 times).
This would suggest that the relative performance of the execution methods are sensitive
to variability level; at least when disruptions are none. When disruptions were frequent,
FRN was ranked first 10 out of 14 times (N RW first 0). When disruptions were
infrequent, NRW was ranked first 12 out of 14 times (FRN first 0). The striking
difference between relative rank order between the infrequent and frequent disruption
levels suggests that the relative rank performance of the execution methods is dependent
upon disruption. The rank difference counts indicate that while relative perforamcne is
not dependent upon variability (0 out of 21 cases), at least a moderate level of

dependence is indicated for disruption level (5 out of 14 cases).

The rank performance of the execution methods on POOC and POOR are very
similar, with some minor differences in the ability to discriminate. While the actual ranks
are identical, in two cases there was more discriminatory power for POOR. Overall, the
ability to discriminate was fairly strong, suggesting that project performance is dependent
upon execution method. When disruptions are none, and variability is none, F RN is
ranked first 5 out of 7 times (NRW first 0). When variability is some, NRW is ranked

first 7 times out of 7 (FRN first 0). This suggests that (at least when disruptions are none)

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relative ranked performance is dependent upon variability level. Again, as in the case of
POIC and POIR, this is not supported by the rank difference counts (4 out of 21). When
disruptions are frequent, FRN is ranked first 10 out of 14 times (NRW 2). When
disruptions are infrequent, NRW is ranked first 9 of 14 times (FRN 0). This suggests that
relative rank performance is dependent upon disruption level. This receives strong
support from the rank different counts. POOC and POOR show that when disruption
type varies, the relative rank performance order differs in 13 out of 14 cases. This

suggests a high level of dependence.

Summa_ry. Overall, the multiple comparisons provide some evidence that the
performance outcomes are dependent upon the execution methods. This evidence is
strong for the duration variables (ADUR and RDUR), and weak or equivocal for AN PV
and RNPV. For the stability variables, the ability to discriminate is strong in all cases

except for the earliness variable WADE (which shows a moderate or equivocal level of
support).

Evidence also indicates that in many cases, the relative rank performance of the
execution methods is dependent on the level of variability present. This evidence is
strong under ADUR, RDUR, ANPV, RNPV, and WADL. Weak or no dependence is

apparent for the remaining variables (WADE, WADC, POIC, POIR, POOC, and POOR).

Stronger evidence supports the premise that the rank performance of the execution
methods is dependent on the type of disruptions present. A high degree of dependence is

observed for WADL, POIC, POIR, POOC, and POOR. Strong dependence is inferred for

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ADUR, and RDUR. AN PV, RNPV, and WADC each show moderate levels of

dependence on disruption type. Weak or no dependence is observed only for WADE.

One additional inference is supported as a result of an analysis of the rank
performance comparisons of the execution methods. As previously noted for the
scheduling method comparisons, the stability measures and the traditional measures do
indeed seem to react differently to the various treatment and factor combinations. The
performance of the methods differs slightly between the traditional and stability

measures.

4.6 Tests of Hypotheses

 

The data generated by the experiment and the subsequent analysis of that data has
provided information relevant to the original research hypotheses. The following sections

will address each hypothesis in turn, and propose conclusions about them.

4.6.] H1: Stability Measures vs. Traditional Measures

 

The first hypothesis concerns the relationships between the traditional measures and
the stability measures. Specifically, hypothesis 1 states “Stability measures are positively
correlated with traditional measures.” This hypothesis has been addressed in section
4.4.1, Biserial Correlations. In general, we find that while the data supports the

hypothesis, several noteworthy characteristics are also observed.

First, the traditional measures clearly measure two distinct concepts: duration and

value. The raw values ADUR-ANPV and the ratio variables RDUR-RNPV show strong

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correlations. When adjusted to take into account the project size (through the use of the

ratio variables), this correlation is negative.

Second, the stability measures divide into two distinct groups, the offset measures
and the deviation measures. Idleness and overuse appear to behave similarly; they covary
both in raw and ratio form. The activity deviation measures seem to consist of a trivial

earliness component, and a much more prevalent lateness component.

Third, between and among the traditional and stability measures, two phenomena
seem to suggest that the two types of measures indeed constitute different classes of
project performance characteristics. First, while the traditional and stability measures
exhibit strong covariation in some areas, in others the relationships are weak. Second, the
overall correlations between the types of measures are lower than those within each type
of measure, indicating that perhaps there are differing degrees of commonality or overlap

between and among the types of measures.

Overall, it can be said that duration, stability, and value are distinct aspects of project
performance; and that these aspects are related to each other. In general, higher stability

is associated with higher NPV and shorter (better) duration.

4.6.2 H2: Project Performance by Planning Method

 

Hypothesis 2 posits that “Project performance is significantly affected by the
planning method used.” Evidence relevant to this hypothesis was presented in section
4.5.1, Scheduling Method Performance by Execution Method. Multiple comparisons

were used to distinguish between the performance of the scheduling methods under all

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combinations of the remaining treatments and factors. For a given test, if the
performance between the scheduling methods was found to be significantly different, this
would support the hypothesis. The dependence of a variable upon the planning method
used is represented by the ability of the multiple comparison method to discriminate

between them based on ranked performance against that variable.

“Highly dependent” cases were characterized by variables which had an ability to
discriminate into 4 or more (out of 7) performance groups in more than 75% of all cases
(18 out of 24), and fewer than 10% of the cases where performance was unable to be
separated (3 out of 24). “Strongly dependent” cases were characterized by variables
which had an ability to discriminate into 4 or more (out of 7) performance groups in more
than 50% of all cases (12 out of 24), and fewer than 25% of the cases where performance
was unable to be separated (6 out of 24). “Moderately dependent” cases were
characterized by variables where fewer than 25% of all cases were unable to be

discriminated (6 out of 24).

While the hypothesis was generally supported by the data, the variables responded
differently to the influence of the scheduling methods. ADUR performance was highly
dependent upon scheduling method. RDUR, POIC, and POIR were strongly dependent,
and WADL, WADC, POOC, and POOR were moderately dependent. ANPV, RNPV, and
WADE were only moderately dependent upon scheduling method; and only under certain

circumstances.

132

4.6.3 H3: Project Performance by Execution Method

 

Hypothesis 3 posits that “Project performance is significantly affected by the
execution method used.” Evidence relevant to this hypothesis was presented in section
4.5.2, Execution Method Performance by Scheduling Method. Multiple comparisons
were used to distinguish between the performance of the execution methods under all
combinations of the remaining treatments and factors. For a given test, if the
performance between the execution methods was found to be significantly different, this
would support the hypothesis. The dependence of a variable upon the execution method
used is represented by the ability of the multiple comparison method to discriminate

between them based on ranked performance against that variable.

“Highly dependent” cases were characterized by variables which had an ability to
discriminate into 3 or more (out of 4) performance groups in more than 75% of all cases
(32 out of 42), and fewer than 10% of the cases where performance was unable to be
separated (4 out of 42). “Strongly dependent” cases were characterized by variables
which had an ability to discriminate into 3 or more (out of 4) performance groups in more
than 50% of all cases (21 out of 42), and fewer than 25% of the cases where performance
was unable to be separated (11 out of 42). “Moderately dependent” cases were
characterized by variables where fewer than 25% of all cases were unable to be

discriminated (11 out of 42).

This hypothesis was consistently and strongly supported by the data. All variables

except for RDUR were strongly dependent upon execution method. RNPV was

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moderately dependent upon the choice of execution method, and missed being

characterized as strongly dependent by only 1 case out of 42.

4.6.4 H4a: Relative Planning Performance by Variability

 

This hypothesis posits that “relative planning method performance is significantly
affected by the presence of activity duration variability.” Evidence to support this
hypothesis would take the form of differences in rank order performance of the planning
methods across the levels of the variability factor, within combinations of the other

treatments and factors.

The evidence is presented in (previously discussed) Table 4.15, through an
examination of the number of cases where the relative rank performance order was
significantly different. Strong evidence in support of the hypothesis was indicated for the
variable WADL. Only moderate evidence was seen for RDUR, WADC, POIC, POIR,
POOC, and POOR. Weak or no support was indicated for ADUR, ANPV, RNPV, and
WADE. It would seem that the overall evidence in support of this hypothesis is

equivocal and variable-specific.

4.6.5 H4b: Relative Planning Performance by Disruption

 

This hypothesis posits that “relative planning method performance is significantly
affected by the type of resource disruption.” Evidence to support this hypothesis would
take the form of differences in rank order performance of the planning methods across the

types of the disruption factor, within combinations of the other treatments and factors.

134

The evidence is presented in (previously discussed) Table 4.15, through an
examination of the number of cases where the relative rank performance order was
significantly different. Strong evidence in support of the hypothesis (highly dependent or
strong dependence) was indicated for the variable WADL, POIC, and POIR. Only
moderate evidence was seen for ANPV, RNPV, WADE, and WADC. Weak or no
support was indicated for ADUR, and RDUR. It would seem that the overall evidence in
support of this hypothesis is moderately strong and general in nature- with the exception

of the duration variables.

4.6.6 H4c: Relative Execution Performance bLVariability

 

This hypothesis posits that “relative execution method performance is significantly
affected by the presence of activity duration variability.” Evidence to support this
hypothesis would take the form of differences in rank order performance of the execution
methods across the levels of the variability factor, within combinations of the other

treatments and factors.

The evidence is presented in (previously discussed) Table 4.16, through an
examination of the number of cases where the relative rank performance order was
significantly different. Strong evidence in support of the hypothesis was indicated for the
variable ADUR, RDUR, ANPV, RNPV, and WADL. Weak or no support was indicated
for the remainder of the stability variables. The overall evidence in support of this
hypothesis is strong for the traditional variables of duration and value; but nonexistent for

the stability measures.

135

4.6.7 H4d: Relative Execution Performance by Disruption

 

This hypothesis states that “relative execution method performance is significantly
affected by the type of resource disruption.” Evidence to support this hypothesis would
take the form of differences in rank order performance of the planning methods across the

types of the disruption factor, within combinations of the other treatments and factors.

The evidence is presented in (previously discussed) Table 4.16, through an
examination of the number of cases where the relative rank performance order was
significantly different. Strong evidence in support of the hypothesis (highly dependent or
strong dependence) was indicated for the variables ADUR, RDUR, WADL, POIC, POIR,
POOC, and POOR. Moderate evidence was seen for ANPV, RNPV, and WADC. Weak
or no support was indicated only for WADE. It would seem that the overall evidence in

support of this hypothesis is strong and general in nature, across variables of all types.

4.7 Summary of Data Analysis

 

A summary of the analysis of the multiple comparison tables with respect to the
research hypotheses is presented below in Table 4.17, Summary of Multiple Comparisons
(Overall). For each variable, inferences are drawn with respect to the level of support

provided to hypotheses 2, 3, and 4 as previously discussed in sections 4.4 through 4.6.

Additionally, evidence was found to support H1; but while the traditional variables

and the stability variables covaried as expected, the relationships were not clear. The

136

stability variables seemed to be measuring something “intrinsically different” from either
duration or value. The implications of this evidence will be discussed in Chapter 5,

Conclusions and Recommendations.

Table 4.17: Summary of Multiple Comparisons (Overall)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H2 H3 H4a H4b H40 H4d

ADUR ++ + - - + +
RDUR + + ~ - + +
ANPV -‘ + — ~ + ~
RNPV 3 ~ - ~ + ~
WADE -2 + - ~ - -
WADL ~ + + + + «1+
WADC ~ + ~ ~ - ~
POIC + + ~ ++ - ++
POIR + + ~ 4+ _ ++
POOC ~ + ~ + - ++
POOR ~ + ~ + - ++

Support: ++ very strong + high ~moderate - weak or none

 

 

 

l 2

supported under variability = none supported under no waiting

137

Chapter 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 Introduction

 

This research investigated the effects of variability and disruption upon the
management of projects. The purpose of this effort was to explore the usefulness of
various techniques in reducing the negative effects of variability and disruption. A
project consists of a series of tasks or activities that must be performed by resources, in a
specific order, to achieve a desired result. Variability refers to uncertainty in the project
task times. Disruptions to the project consist of the unplanned unavailability of
resources. When a project is subject to variability and disruption, the project may begin
to take longer, cost more, and achieve less than planned. These negative effects are very
important, and the issue has received much study by academics and practitioners alike.

Coping mechanisms to avoid the consequences of variability and disruption can
generally take two forms. The first is to schedule or plan the resources and activities
carefully in order to make the project less sensitive. The second is to execute the
schedule in such a way as to mitigate the damage done as it occurs. It is proposed that
some scheduling techniques generate plans that are less sensitive to variability and
disruption (more stable) than others. In addition, it is proposed that some execution
techniques are more effective at absorbing or dampening the effects of disruption than
others. The stability of the project may come at the expense of other desirable project

outcomes, however. A more stable project may take longer to complete, or be more

138

costly. These issues have not yet been investigated in any detail. This research has
addressed and started to resolve some of the fundamental questions and problems
surrounding the performance and stability of projects, subject to variability and

disruptions, under a variety of conditions.

5.2 Research Questions

 

Several questions were asked at the beginning of this effort, and they have been
addressed through the collection and analysis of the data with respect to the hypotheses
(specific hypotheses addressed in Chapter 4, Results and Analysis). The questions are
presented here again, and answered.

What is the nature of the tradeoff (if one exists) between schedule stability and
schedule performance with respect to the traditional measures in the project?

This research question was most directly associated with hypothesis H1, “Stability
measures are positively correlated with traditional measures.” Evidence in support of this
hypothesis was presented and discussed in section 4.4.1, Biserial Correlation, and
summarized in section 4.6.1, H1: Stability Measures vs. Traditional Measures.

The evidence indicated that while the stability measures were related to the
traditional measures, these relationships were complex. Duration and Net Present Value
were negatively correlated when correcting for schedule differences. Among the stability
measures, the task deviation measures and resource deviation measures were correlated
strongly within themselves, and somewhat less so between them. Activity earliness was
an exception to this, not being correlated strongly with any of the other stability

measures. Between the stability and traditional measures, several additional relationships

139

were noted. Lateness measures were inversely related to RNPV, and positively related to
RDUR. The resource deviation measures were positively related to ADUR, and less so
with RDUR. In conjunction with the biserial scatterplots (Appendix E) this information
indicates that the stability, duration, and value variables capture distinct but related
concepts. The duration and stability variables covary, and are inversely related to value.
The evidence also suggests that stability is somewhat multi-dimensional.

How are planning methods affected by variability and disruption?

This research question was most directly associated with hypothesis H2, “Project
performance is significantly affected by the planning method used.” Evidence in support
of this hypothesis was presented and discussed in sections 4.2.2, Formal Test Results,
4.3.2, Treatment Cell Means, 4.5.1, Scheduling Method Performance by Execution
Method, and 4.6.2, H2: Project Performance by Planning Method.

While the hypothesis was generally supported by the data, the variables responded
differently to the influence of the scheduling methods. ADUR performance was highly
dependent upon scheduling method. RDUR, POIC, and POIR were strongly dependent,
and WADL, WADC, POOC, and POOR were moderately dependent. AN PV, RNPV, and
WADE were only moderately dependent upon scheduling method; and only under certain
circumstances. The value measures were dependent upon scheduling method when
variability was “none.” When variability is present, the effect of scheduling method on
NPV was overwhelmed by the “background” variance. WADE was dependent only
under “no waiting” (as would be expected- earliness would be prevented under a waiting

discipline). Project performance on duration and resource idleness is dependent upon

140

scheduling method used, and performance on other stability measures is weakly
dependent.

How are execution methods affected by variability and disruption?

This research question was most directly associated with hypothesis H3, “Project
performance is significantly affected by the execution method used.” Evidence in
support of this hypothesis was presented and discussed in sections 4.2.2, Formal Test
Results, 4.3.2, Treatment Cell Means, 4.5.2, Execution Method Performance by
Scheduling Method, and 4.6.3, H3 .' Project Performance by Execution Method.

This hypothesis was consistently and strongly supported by the data. All variables
except for RDUR were strongly dependent upon execution method. RNPV was
moderately dependent upon the choice of execution method, and missed being
characterized as strongly dependent by only 1 case out of 42. Project performance on
virtually all measures was dependent upon choice of execution method; perhaps more so
than by choice of scheduling method.

Are schedules developed by certain heuristics/scheduling rules more sensitive to
variability?

This research question was most directly associated with hypothesis H4a, “Relative
planning method performance is significantly affected by the presence of activity
duration variability.” Evidence in support of this hypothesis was presented and discussed
in sections 4.3.2, Treatment Cell Means, 4.5.1, Scheduling Method Performance by
Execution Method, and 4.6.4, H4a: Relative Planning Performance by Variability.

Strong evidence in support of the hypothesis was indicated for the variable WADL.

Only moderate evidence was seen for RDUR, WADC, POIC, POIR, POOC, and POOR.

141

Weak or no support was indicated for ADUR, AN PV, RNPV, and WADE. It would
seem that the overall evidence in support of this hypothesis is equivocal and variable-
specific. The relative performance of the scheduling methods is apparently not dependent
upon task time variability.

Are schedules developed by certain heuristics/scheduling rules more sensitive to
disruption?

This research question was most directly associated with hypothesis H4b, “Relative
planning method performance is significantly affected by the nature of the resource
disruptions.” Evidence in support of this hypothesis was presented and discussed in
sections 4.3.2, Treatment Cell Means, 4.5.1, Scheduling Method Performance by
Execution Method, and 4.6.5, H4b: Relative Planning Performance by Disruption.

Strong evidence in support of the hypothesis (highly dependent or strong
dependence) was indicated for the variable WADL, POIC, and POIR. Only moderate
evidence was seen for ANPV, RNPV, WADE, and WADC. Weak or no support was
indicated for ADUR, and RDUR. It would seem that the overall evidence in support of
this hypothesis is moderately strong and general in nature- with the exception of the
duration variables. The relative performance of the scheduling methods on value and
stability is dependent upon disruption type, but not duration.

Do certain execution techniques help minimize the effects of variability?

This research question was most directly associated with hypothesis H4c, “Relative
execution method performance is significantly affected by the presence of activity

duration variability.” Evidence in support of this hypothesis was presented and discussed

142

in sections 4.3.2, Treatment Cell Means, 4.5.2, Execution Method Performance by
Scheduling Method, and 4.6.6, H4c: Relative Execution Performance by Variability.

Strong evidence in support of the hypothesis was indicated for the variable ADUR,
RDUR, ANPV, RNPV, and WADL. Weak or no support was indicated for the remainder
of the stability variables. The overall evidence in support of this hypothesis is strong for
the traditional variables of duration and value; but nonexistent for the stability measures.
The relative performance of the execution techniques on duration and value is dependent
upon variability, but not stability.

Do certain execution techniques help minimize the effects of disruption?

This research question was most directly associated with hypothesis H4d, “Relative
execution method performance is significantly affected by the nature of the resource
disruptions.” Evidence in support of this hypothesis was presented and discussed in
sections 4.3.2, Treatment Cell Means, 4.5.2, Execution Method Performance by
Scheduling Method, and 4.6.7, H4d: Relative Execution Performance by Disruption.

Strong evidence in support of the hypothesis (highly dependent or strong
dependence) was indicated for the variables ADUR, RDUR, WADL, POIC, POIR,
POOC, and POOR. Moderate evidence was seen for ANPV, RNPV, and WADC. Weak
or no support was indicated only for WADE.. It would seem that the overall evidence in
support of this hypothesis is strong and general in nature, across variables of all types.
The relative performance of the execution methods against duration, value, and stability

measures is dependent upon disruption type.

143

5.3 Additional Notes on the Effects of Variability and Disruption

 

It has been established that project duration and stability are degraded by the
presence of variability and disruption. What has not been presented in any detail is how
significant this degradation may be. It would be instructive to examine the percent
changes in key variables between the no variability and some variability cases, and
between the three disruption types.

ADUR is a uni-dimensional variable (a simple measure of time). A percent change
between two values would be calculated as the ratio of the differences over the initial
value. To calculate the percent change between “none” and “some” variability, ADUR
under “some” was subtracted from ADUR under “none” to get a difference. This
difference was divided by ADUR under “none” and multiplied by 100 to calculate a
percent change in ADUR. A similar calculation was performed to get the percent change
between the three disruption types.

WADC is already a multi-dimensional (ratio) variable. From Chapter 3, WADC is
calculated as the ratio of earliness and lateness to the total time scheduled. WADC
already represents a percentage; the percentage of lateness and earliness out of total time.
To calculate a WADC “percent change” would be problematic in cases where the initial
value in the ratio were small (or zero). The percent change would approach infinity as the
initial value approached zero. As WADC under “none” variability and “none” disruption
was zero, and as WADC is already a ratio variable, the percent change for WADC was
calculated as the difference between the two values. The percent changes between the

three different types of disruption were calculated in the same way.

144

The percent change for POOR was calculated in the same way as WADC. POOR is

also a ratio variable; the ratio of resource overuse to scheduled resource use. POOR is

already a percentage; the percentage of resource overuse out of total use.

Table 5.1: Percent Change (variability none-some)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR egg WADC alg POOR avg

OPT FRN -1.9 -2.2 -29.8 -28.3 -5.3 -4.9
FRW -2.9 -31.2 -5.5
NRN -1.3 -23.5 -3.8
NRW -2.7 -28.5 -4.9

SLK FRN -1.6 -1.9 -29.8 -22.9 -5.3 -5.1
FRW -2.7 -31.7 -5.6
NRN -1.1 -27.5 -4.6
NRW -2.2 -27.6 -5.0

LFT FRN -1.5 -3.8 -28.2 -27.8 -5.1 -4.9
FRW -2.6 ~30.6 -5.4
NRN -9.0 -24.9 4.2
NRW -2.2 -27.3 -4.9

RSO FRN -2.1 -3.8 -26.1 -25.8 -2.9 -3.4
FRW -3 .2 -31.4 -5.1
NRN -l.3 -17.2 -1.3
NRW -2.9 -28.4 -4.4

LSC FRN -1.6 -2.1 -24.0 -25.9 -2.5 -3.4
FRW -2.8 -30.0 -5.0
NRN -1.5 -23.8 -1.9
NRW -2.6 -25.6 -4.3

DCF FRN -1.1 -3.0 -28.0 -25.4 -5.9 -5.3
FRW -2.2 -28.5 -5.9
NRN -7.2 -20.8 -4.4
NRW -1.5 -24.4 -5.0

BCP FRN -1.5 -2.9 -31.9 -30.2 -5.6 -5.3
FRW -2.6 -32.8 -5.8
NRN -5.2 -28.0 -4.6
NRW -2.1 -28.4 -5.1

 

 

 

Table 5.1, Percent Change (variability some-none) presents the percent differences

between the “none” variability and “some” variability cases. Cases were paired

according to none and some variability along all other factors including scheduling

145

method, execution method, disruption type, project problem, and run number. Results
were grouped by scheduling and execution method.

The results indicate that the presence of variability increases ADUR by 1.1
(DCF/F RN or SLK/NRN) to 9.0 (LFT/N RN) percent, with most values near 2.0 percent
(median value 2.2; half of all values between 1.5 and 2.5). With respect to the scheduling
and execution methods, two patterns emerge. First, LFT and RSO experience the greatest
degradation in duration (3.8 percent). SLK appears least sensitive to variability, at 1.9
percent increase in ADUR. Second, for most scheduling methods (OPT, SLK, RSO, and
LSC), the execution methods from least to most sensitive follow the order NRN-FRN-
NRW—FRW. Rank order placement of the four methods follows waiting policy first, into
the top two (no waiting) vs. bottom two (waiting) places. This implies that a “waiting”
policy is more sensitive to variability in terms of overall project duration growth. Within
the waiting policy, the reservation policy also seems to matter. Within each waiting
policy, no reservation seems to provide better results than full reservation. A
“reservation” policy also appears sensitive to variability, but the waiting policy has more
of an effect than the reservation policy.

The exceptions to this execution method sensitivity pattern occur for scheduling
methods LFT, DCF, and BCP. For each of these, the (least to worst) pattern is F RN-
NRW-FRW-NRN. F RN is the least sensitive, and NRN is the most sensitive. NRN was
the least sensitive (best choice) for OPT, SLK, RSO, LSC; and is here the worst choice.
FRN, on the other hand, was the second best choice for OPT, SLK, RSO, and LSC and is

the best choice here.

146

Overall, the implications for the decision maker are somewhat less than clear. The
top two combinations are SLK-NRN and DCF-FRN. The best scheduling method is
SLK. For most scheduling methods, the best execution method is NRN, but this is the
worst choice for the others; where F RN is the best. This would suggest that selection of
the scheduling and execution method combination is highly situational. However, the
difference between the best combination and the 13th best combination (out of the 28
total) is only 1 percent. A general conclusion that may be reached here is that variability
may not actually be that important a criteria to consider when selecting a scheduling and
execution method combination to use when trying to minimize the degradation of actual
duration.

A similar analysis can be performed for the two stability measures WADC and
POOR. When variability is present (vice absent), WADC increases from 17.2 percent
(RSO-NRN) to 32.8 percent (BCP-FRW). The median value is 28 percent, and half of all
values range between 15 and 30 percent. The least amount of average increase (loss of
stability) is experienced under the SLK scheduling method (average 22.9 percent), and
the greatest amount of average increase occurs under BCP (30.2 percent). The
“optimum” schedule (OPT) fared poorly (at 28.3%, in sixth place), while the right-shifted
optimum (RSO) did fairly well (25.8%; third place). Overall performance (least to most
degradation) was ordered SLK-DCF-RSO-LSC-LFT-OPT-BCP.

Performance degradation of the POOR stability measure under the scheduling
methods follows a different pattern from WADC. Overall, when variability is present,
the range of degradation runs from 1.3% (RSO-NRN) to 5.9% (DCF-FRW). The median

value is 5.0%, and half of all values range between 4.3% and 5.3%. The “optimum”

147

schedule (OPT) was placed third overall (4.9%) and the right-shifted optimum (RSO) was
ranked first. Overall rank order was RSO-LSC-OPT-LFT-SLK-DCF-BCP.

With respect to the execution methods, patterns emerge. The dominant pattern in the
increase in WADC from no variability to some variability is (least to most): NRN-NRW—
FRN-FRW. This pattern holds for OPT, SLK, LFT, DCF, and BCP. This pattern
suggests that the reservation policy is the dominant part of the execution method, with
both “no reservation” execution methods being better than the methods with “full
reservation” systems. The waiting policy appears to be less important; with “no waiting”
giving better results than “waiting.” LSC and RSO share a different pattern; NRN-FRN-
NRW-FRW (least to most). For these scheduling methods, the waiting policy appears to
be more important, with “no waiting” providing better results. The “no reservation”
system also seems to be less sensitive to variability (increases in WADC) than the “full
reservation” system under this pattern for LSC and RS0. This pattern was the same for
both the WADC and POOR stability measures.

These findings support and extend the general finding that project performance, and
the performance of the scheduling and execution methods, are affected by the presence of
variability in the task times. Both overall duration (ADUR) and stability (WADC and
POOR) are degraded under the presence of variability. While it appears that stability is
affected more than duration, and the WADC measure is more affected than the POOR
measure, direct comparisons cannot be made due to differences in the way the percent
changes were calculated.

This degradation is worse for some scheduling and execution methods than others.

While some patterns emerge and have been discussed, no clear conclusions can be drawn

148

due to the strong interactions present between the scheduling and execution methods. An
interesting observation can be made, however. Patterns in the sensitivity of the execution
methods with respect to the reservation system and waiting policy were noted. These
patterns were consistent within the stability degradation measures, and differed from the
duration degradation measure. In either case, two patterns emerged. There existed a
“dominant” pattern for the majority of scheduling methods, and a “secondary” pattern for
the remainder of the scheduling methods. No rationale for this is offered at this time, and
this phenomenon merits fiu’ther investigation. It is posited that (currently unidentified)
characteristics of the scheduling and execution methods may provide a more robust “fit”
when used together. Further development of an appropriate “fit” model is warranted.
With respect to the disruption types, tables were constructed and are included in
Appendix M, Degradation (Percent Change). Findings were similar to those for
variability. One additional observation was that the degradation from infrequent/long
disruptions was greater (3% greater for ADUR, 40% greater for WADC, and 3% greater
for POOR) than the degradation from frequent/short disruptions. Patterns among and
between the scheduling and execution methods were observed similar to those seen for

the effect of variability.

5.4 Conclusions

 

Several conclusions can be drawn from the results just summarized. The stability,
duration, and value variables capture distinct but related concepts. The duration and

stability variables covary, and are inversely related to value. Stability may be somewhat

149

multi-dimensional. Project performance on duration and resource idleness is dependent
upon scheduling method used, and performance on other stability measures is weakly
dependent. Performance on virtually all measures was dependent upon choice of
execution method; perhaps more so than choice of scheduling method. The relative
performance of the scheduling methods is apparently not dependent upon task time
variability. The relative performance of the scheduling methods on value and stability
(but not duration) is dependent upon disruption type. The relative performance of the
execution techniques on duration and value is dependent upon variability, but
performance on stability is not. The relative performance of the execution methods
against duration, value, and stability measures is dependent upon disruption type. The
theoretical and practical implications of these conclusions will now be discussed.

5.4.1 Theoretical

 

A review of the literature (Chapter 2, Significant Prior Research) established the
position of this current effort with respect to previous research. Any results must
therefore be considered in the larger context of the resource constrained, project
scheduling problem (RCPSP). The research model was constructed to investigate a
single problem, with multiple, constrained resources; solved heuristically to achieve
multiple objectives, and with single mode resource activity functions. A benchmark set
of well-established problems with known, optimal (for minimum duration) solutions was
used, with specific problems selected to represent a broad spectrum of the most relevant
problem characteristics. The experiment itself was designed to investigate the
performance of various scheduling and execution techniques under varying conditions of

task time variability and resource disruption. In this way, the study was firmly anchored

150

to many previous studies on the performance of scheduling methods. It proposed a new
heuristic (the BCP), and included previously recognized high performers against the
traditional measures of duration and NPV. Research on the scheduling methods has been
extensive; investigation into the role and performance of execution methods has been less
detailed. This research extended and sought to validate the recent research; particularly
the efforts of Partovi and Burton (1993) and Yang (1996).

With respect to the role of the scheduling and execution methods, current theory has
emphasized the role of the scheduling methods in determining project outcomes. This
has been challenged somewhat recently, and indeed, this current research supports the
idea that the execution methods are at least (if not more) important than the scheduling
techniques. Also, the relative performance of the scheduling methods with respect to
project conditions (project characteristics and environmental characteristics) has been
equivocal. Previous studies found no or weak influence from these characteristics on
relative planning method performance. The current research found similar results with
respect to the scheduling methods and the environmental characteristics of variability and
disruption (the problem characteristics were not explicitly studied). However, evidence
was found to suggest that the relative performance of the execution methods is dependent
upon variability (for the duration measures) and disruption type (for both the duration and
stability measures). These findings would suggest the potential to develop a “fit model”
for the use of various execution methods. Certain environmental conditions may
necessitate the use of one type of execution method over another. The influence of the
project characteristics upon execution method may also be an important factor in the

development of a “fit model;” but the current research does not address these factors.

151

In addition to validating and extending the previous research into scheduling and
execution method performance, this effort opened a new avenue into the role of stability
in projects. Evidence suggests that stability represents a distinct class of performance.
Several metrics were developed and studied, and the findings support that the metrics
could be developed and implemented. The stability measures exhibited behaviors that
were both similar to and different from the traditional measures. However, the role of
project stability in the management of projects has not yet been established.

5.4.2 Practical

 

Bearing in mind the issues surrounding the limitations of the model employed in the
study, some of the theoretical conclusions imply practical consequences. First, while the
importance of the scheduling method used to plan the project has historically been
paramount, the contribution of execution policies has not been recognized. Perhaps the
current emphasis on developing and using more sophisticated planning methods is
misguided. Second, practitioners currently employ a host of metrics that can generally be
categorized as related to either “cost, schedule, or performance (quality)” with an
emphasis on total cost and total duration. Key schedule and cost milestones are
established, and closely monitored. Great effort is sometimes taken to ensure that
milestones are met. The assumption seems to be that if the milestones are met, the
overall performance will follow. This research suggests that while intuitively appealing,
the relationship between schedule conformance on the milestone level and performance at
the overall project level might not be as straightforward as it might seem. Measures
related to project stability may eventually fill the role of management to the naive

milestone technique. Finally, it has not been reported that significant time or effort is

152

spent on trying to identify either project or environmental characteristics in order to
improve decisions taken regarding project implementation. While this research has not
challenged that practice with respect to the relative performance of the planning methods,
evidence suggests that the relative performance of execution strategies may be affected
by these characteristics. Conclusions in this area would be premature, as further research

is needed.

5.5 Recommendations

 

As a result of the findings of this research, several recommendations can be made.
The recommendations fall into two general categories: research recommendations and
practical recommendations. They will be presented in that order in the following two
sections.

5.5.] Future Research

 

Several avenues of additional research should be pursued in order to capitalize on
these initial results. This initial study was limited in it’s generalizability (refer to section
3.7, Limitations and Key Assumptions), and additional research should be conducted to
resolve this. Two major limitations were that only small and medium sized projects were
used, and only in a single project environment. While useful for conducting an initial,
exploratory study, these two conditions are somewhat unrealistic in practice. Extending
the generalizability of the findings would require an investigation using larger projects,
and more than one project being executed at the same time. Studies of this nature would
broaden the application of the findings. The findings could change under these more

realistic conditions.

153

The validity of the study was reduced by additional limitations. Validity questions
surround the behavior of the model, and the role of the stability measures. The behavior
of the model did not allow pre-emption of resources by higher priority tasks; reasonable
perhaps in a single project environment but unreasonable in practice. Future research
should include the use of pre-emption; perhaps with several different rules included as
additional execution techniques. Empirical research should be conducted to study
execution policies in greater detail. While the current effort looked at some basic
execution policies, there are a wide variety of potential policies that could be used.
Practioners should be surveyed in order to determine which execution policies are being
used, and to what effect. A more comprehensive family of policies can then be
programmed into the model.

The role of the stability measures should also be investigated. The current effort
proposed some measures, but there are many more in use. Financial measures of stability
(of the budget/cost variance type) should be included in future studies. It would be useful
to survey practitioners for additional stability-type measures that are currently in use.
Similarly, the importance and role of stability measures in managing and controlling
project execution should be investigated. While a certain emphasis on stability seems
reasonable, how important or useful are stability measures in practice?

This research has provided evidence that suggests that the relative performance of the
execution methods may be dependent on environmental characteristics (variability level
and disruption type). If the performance of the execution methods depends on these
factors, it might be possible to develop a model that describes the “best fit” between the

project environment and the method used. The role of problem characteristics in

154

it?!

determining relative performance was not studied, and should be investigated in
conjunction with the environmental characteristics. Future research should be conducted
in order to establish the validity of an execution method selection model.

In order to address the issues of generalizability and validity, future research is
recommended. Empirical studies should be conducted to both establish the role and
importance of stability in managing projects, and refine the definition of stability and the
development of stability measures. Execution policies employed by practitioners should
also be studied, and included in future models. Laboratory studies should be continued,
and should incorporate the findings of the empirical work. The new models should
extend generalizability by using larger, more realistic project problems in a simultaneous
project execution environment. Finally, the role of project and environmental
characteristics on relative execution method performance should be investigated in an
attempt to assess the validity of a “fit model” for use by practioners.

5.5.2 Managerial Recommendations

Additional research is needed before strong recommendations to practioners would
be justified. However, some preliminary judgements can be made. First, managers
should explore the effect of various execution policies on project management. Perhaps
they should select a fast, easy, reasonable heuristic for rough scheduling, then spend a
significant amount of time and energy in a deliberative process of selecting and
employing appropriate execution policies. An understanding of the underlying
characteristics of their projects and environment, and how they interact with the
execution methods, may be a good start. These efforts should, of course be conducted

c00peratively by academics and practioners alike.

155

perfo
consi
apprc
whil
to bi
C-OSl

rele

 

Second, practitioners could balance their reliance on current “cost, schedule, or
performance (quality)” metrics associated with the execution of milestones with a
consideration of better metrics for management. While the current milestone-based
approach is useful for reporting, it may not be as helpful for actually managing the project
while it is being executed. Again, this is an open question, and additional research needs
to be done. The relationships between current measures and overall performance (total
cost and total duration) are not clear. Measures related to project stability may be more

relevant to day-to-day management of projects.

5.6 Summary

 

Project stability has not yet been studied explicitly; nor has the role of disruption.
This research investigated the performance of both planning and execution techniques in
the single project, constrained resource environment, under conditions of uncertainty,
when subject to disruptions. Planning techniques included several of the most popular
and successful heuristics for project planning and scheduling in the literature today.
Similarly, execution techniques included a representative collection of allocation and
decision making methods. A known, benchmark set of project scheduling problems
representing a broad spectrum of project characteristics were simulated at multiple levels
of variability and disruption. The performance of each combination of planning and
execution technique has been measured with respect to time, net present value, and
stability.

In summary, instability in a project may lead to many negative effects. First, the loss

of a resource (or a delay in its availability) may idle other resources, and result in a direct

156

loss in productivity or efficiency. Second, the project could experience a loss of
synchronization of the activities and resources, resulting in a degradation of the
effectiveness of the project. Third, disruptions to resources may incur additional costs,
degrade project efficiency, or lead to late completion. Finally, project instability can
result in deviations in the accomplishment of project milestones, which may affect the
financial evaluation of the project or the firm responsible for the project. Disruptions
could spread throughout the system, resulting in many of the negative effects described
previously. An apparently minor disruption to an apparently minor resource could lead to
grave effects on the project as a whole. The degree to which this "ripple effect" creates
overall problems is a reflection of the stability of the project as scheduled and executed.

This research sought to extend the concept of the effects of resource unavailability
and activity duration variability into the realm of schedule and resource stability. Certain
factors shape the ultimate performance of the project with respect to the desired
outcomes. Technical and resource dependencies serve to limit or bound the potential
achievement of the project. Variability in activity durations and disruptions in resources
will influence the degree of achievement of project goals. The planning and execution
methods used to schedule and perform the project activities have also been noted to have
a significant effect on the overall project performance. While these factors have been
studied with respect to their effects on the traditional project performance outcomes, no
study has investigated these factors as they relate to project stability.

As a first step, this research defined several project management stability measures.
The study tried to provide insight into the relationships between the traditional factors of

project performance. These traditional factors included the nature of the project

157

environment (activity variability and resource disruption), and the scheduling and
execution methods used to manage the project. Hopefully, insight was provided into the
nature of the relationships between these factors and project stability. Finally, the
knowledge gained in studying both project stability and the relationships between project
stability, other outcome measures, and the traditional factors of project performance
could be extended into practical significance for the management of projects. Ultimately,
it is hoped that the descriptive theories built initially can be translated into prescriptions
to assist managers in achieving higher levels of performance from the projects under their

control.

158

THE EFFECTS OF VARIABILITY AND DISRUPTION
ON
PROJECT STABILITY, DURATION, AND NET PRESENT VALUE
VOLUME 11

By

Stephen M. Swartz

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Marketing and Supply Chain Management

1999

APPENDICES

159

APPENDIX A

HISTOGRAMS OF AGGREGATE STATISTICS

160

Figure A-l: Aggregate Histogram, ADUR

 

30000
ADUR
Std. Dev = 45.54
Mean = 78.1
N = 120960.00
20000

1 0000

 

 

 

0 1
20.0 60.0 100.0 140.0 180.0 220.0
40.0 80.0 120.0 160.0 200.0

Figure A-2: Aggregate Histogram, RDUR

FAAAA

 

OUUW
RDUR
40000‘ Std. Dev = .05
ean = 1 03
ii = 120960.00

30000 '

20000 '

10000 ‘

 

 

 

.825 .925 1.025 1.125 1.225 1.325 1.425
.875 .975 1.075 1.175 1.275 1.375 1.475

161

Figure A-3: Aggregate Histogram, ANPV

 

30000
ANPV
Std. Dev = 13239.35
Mean = 17130.
N = 120960.00
20000 ‘

10000

 

 

 

7 I <3 <3 .9 a} t?
00 ‘30 00 ‘90 6‘0 o '90
0 Qb ab qb

Figure A-4: Aggregate Histogram, RNPV

 

70000
RNPV
60000‘
.~._.,-._ Std. Dev = .04
Mean = .993
50000 . N = 120960.00

40000l
300001
20000‘

100001

 

 

 

Figure A—5: Aggregate Histogram, POIC

 

40000 '
POIC
arrears-54
30°00 N = 120960.00

20000

1 0000

 

 

 

0 . . f -
0.0 200.0 400.0 600.0 800.0 1000.0
100.0 300.0 500.0 700.0 900.0 1100.0

Figure A-6: Aggregate Histogram, POIR

 

30000'
POIR
Std. Dev - .07

Me ean- — .080
N- - 120960. 00

20000

1 0000

 

 

 

0
0.000 .050 .100 .150 .200 .250 .300 .350 .400 .450
.025 075 .125 .175 .225 .275 .325 3.75 .425 .475

163

Figure A-7: Aggregate Histogram, POOC

 

 

 

40000‘
POOC
'S/ltd. IDeV1Z6E5>452
ea = .
30°00 N = 120960.00
20000
10000
0
000 7000 {300

 

Figure A-8: Aggregate Histogram, POOR

 

 

 

 

30000 '
POOR
Std. Dev = .07
Mean = .082
N = 120960.00
20000
10000
0 . -
0000 .100 .200 .300 .400 .500
.050 .150 .250 .350 .450

Figure A-9: Aggregate Histogram, WADE

 

 

100000 ‘
, . WADE
80000 35. .1 Mean = .08
N = 120960.00

50000 éf

20000 _

  

 

 

 

0.00 .25 .50 .75 1100' 1:25 1T501T75T2T00 2:25
.13 .38 .63 .88 1.13 1.38 1.63 1.88 2.13 2.38

Figure A-lO: Aggregate Histogram, WADL

 

50000 ‘

WADL

Std. Dev = .75
40000 Mean = .53

N = 120960.00

30000
20000

10000 r‘

 

 

1.00 2.00 3.00 4100' 5100' 6:00' 7:00' 8.00
50 1.50 2.50 3.50 4.50 5.50 5.50 7.50

165

Figure A-l 1: Aggregate Histogram, WADC

 

40000 ‘
WADC
I\Sl‘td. Dev6=1.77
ean = .
30°00 N = 120960.00

20000

 

 

 

00 3.00 4100' 5.007 door {00' 8.00
2.50 3.50 4.50 5.50 6.50 7.50

2.
.50

166

APPENDIX B

TREATMENT MEANS

167

Table B-1:
Means: ADUR by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR some none
Sched Exec none freq infq none freq infq
opt frn 74.53 76.03 79.79 73.33 74.91 78.84
frw 75.45 76.51 79.64 73.33 74.93 78.29
nm 75.40 77.21 78.70 74.44 76.39 78.49
nrw 75.35 77.02 79.37 73.33 75.39 78.31
slk frn 76.22 77.74 81.57 75.17 76.82 80.67
frw 77.23 78.32 81.46 75.17 76.78 80.00
nm 76.12 77.77 79.53 75.22 77.13 78.87
nrw 76.94 78.49 81.00 75.17 77.26 79.80
lfi frn 75.75 77.23 80.89 74.72 76.38 80.12
frw 76.74 77.83 81.10 74.72 76.39 79.58
nm 75.47 77 .45 78.69 74.83 76.83 78.31
nrw 76.58 78.13 80.23 74.72 76.81 79.19
rso frn 74.55 75.99 79.70 73.28 74.84 78.73
frw 75.58 76.61 79.78 73.28 74.90 78.26
nrn 75.34 77.00 78.76 74.56 76.30 78.13
nrw 75.40 76.96 79.48 73.28 75.38 78.00
lsc frn 7 5.78 77.31 81.03 74.78 76.40 80.20
frw 76.99 78.08 81.24 74.78 76.48 79.83
nm 75.94 77.58 79.11 75.22 76.61 78.40
nrw 76.73 78.31 80.99 74.78 76.92 79.66
dcf frn 80.45 81.86 85.49 79.67 81.14 84.91
frw 81.62 82.57 85.74 79.67 81.20 84.47
nm 79.57 81.07 83.65 79.00 80.64 83.25
nrw 81.13 82.62 84.99 79.67 81.64 84.35
bcp frn 77.26 78.56 82.22 76.22 77.70 81.41
frw 78.28 79.25 82.32 76.22 77.79 80.90
nm 76.69 77.99 79.76 76.28 77.53 79.57
nrw 77.95 79.64 82.03 76.22 78.30 80.82

 

 

 

 

 

 

 

168

 

Table B—2:

Means: RDUR by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RDUR some none
Sched Exec none freq none freq infq
opt frn 1.0224 1.0413 1.0827 1.0000 1.0213 1.0653
frw 1.0354 1.0497 1.0850 1.0000 1.0215 1.0606
nm 1.0343 1.0589 1.0780 1.0161 1.0460 1.0702
nrw 1.0322 1.0549 1.0856 1.0000 1.0273 1.0643
slk frn 1.0181 1.0358 1.0794 1.0000 1.0203 1.0636
frw 1.0322 1.0457 1.0812 1.0000 1.0204 1.0576
nm 1.0167 1.03 82 1.0582 1.0025 1.0293 1.0484
nrw 1.0266 1.0453 1.0755 1.0000 1.0254 1.0557
lfl frn 1.0182 1.0345 1.0752 1.0000 1.0197 1.0624
frw 1.0321 1.0450 1.0810 1.0000 1.0212 1.0570
nm 1.0137 1.0385 1.0541 1.0045 1.0299 1.0459
nrw 1.0280 1.047 1 1 .0720 1.0000 1.0260 1.0544
rso frn 1.0244 1.041 1 1.0826 1.0000 1.021 1 1.0648
frw 1.0394 1.0527 1 .0893 1.0000 1.0224 1.0626
nm 1.0342 1.0569 1.0781 1.0193 1.0450 1.0656
nrw 1.0348 1.0560 1.0880 1.0000 1.0284 1.0624
lsc frn 1.0177 1.0368 1.0790 1.0000 1.0206 1.0645
frw 1.0361 1.0499 1.0863 1.0000 1.0230 1.0637
nm 1.0230 1.0443 1.0636 1.0083 1.0295 1.0497
nrw 1.0317 1.0510 1.0851 1.0000 1.0279 1.0625
dcf frn 1.0125 1.0284 1.0672 1.0000 1.0170 1.0576
frw 1.0278 1.0385 1.0725 1.0000 1.0177 1.0532
nm 0.9952 1.01 12 1.0373 0.9876 1.0052 1.0322
nrw 1.0196 1.0353 1.0623 1.0000 1.0222 1.0512
bcp fm 1.0177 1.0316 1.0703 1.0000 1.0176 1.0567
frw 1.0313 1.0427 1.0759 1.0000 1.0195 1.0528
nm 1.0085 1.0223 1.0407 1.0021 1.0172 1.0382
nrw 1.0247 1.0441 1.0701 1.0000 1.0239 1.0525

 

169

 

Table B-3:
Means: ANPV by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANPV some none

Sched Exec none freq infq none freq infq

opt frn 17037.46 17001.37 16900.35 17268.32 17232.59 17129.57
frw 17021.27 16998.79 16917.90 17268.32 17233.97 17147.87
nrn 17154.39 17109.52 17134.54 17257.72 17223.92 17167.16
nrw 17145.51 17101.00 17111.03 17268.32 17221.60 17156.64

slk frn 17032.49 16996.30 16897.60 17262.64 17224.09 17124.68
frw 17015.99 16993.13 16914.93 17262.64 17227.79 17147.55
nrn 17158.50 17117.19 17129.04 17263.34 17228.71 17178.18
nrw 17142.78 17097.51 17100.13 17262.64 17212.38 17153.37

1ft fi'n 17034.88 16998.49 16903 .88 17264.62 17224.70 17129.92
frw 17018.39 16995.00 16910.83 17264.62 17228.42 17148.87
nm 17162.38 17119.11 17145.76 17263.45 17232.40 17189.03
nrw 17144.12 17098.50 17111.68 17264.62 17216.47 17161.62

rso frn 17033.08 16997.38 16897.31 17265.01 17229.21 17127.57
frw 17017.46 16995.24 16914.05 17266.75 17231.91 17146.39
nm 17149.50 17106.78 17124.93 17251.77 17218.17 17169.92
nrw 17142.24 17099.99 17104.06 17266.75 17218.72 17160.08

lsc fi'n 17028.83 16992.86 16895.82 17258.85 17220.98 17122.76
frw 17012.72 16989.82 16911.59 17261.14 17225.19 17144.21
nm 17151.97 17109.95 17133.24 17253.71 17227.01 17177.18
nrw 17139.10 17092.21 17091.67 17261.14 17211.34 17147.58

dcf frn 17027.37 16993.98 16903.57 17254.56 17219.84 17127.07
frw 17010.95 16990.87 16912.65 17254.56 17220.97 17141.89
nm 17160.89 17113.53 17105.07 17261.16 17221.28 17149.46
nrw 17137.88 17092.01 17096.57 17254.56 17206.94 17138.52

bcp frn 17031.54 16996.95 16898.54 17260.64 17224.80 17122.84
frw 17014.51 16992.99 16911.92 17260.64 17225.96 17141.66
nrn 17162.41 17119.18 17130.51 17260.40 17229.71 17170.19
nrw 17140.54 17089.69 17092.25 17260.64 17208.77 17149.44

 

170

 

Table B-4:
Means: RNPV by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RNPV some none
Sched Exec none freq infq none freq
opt frn 0.9866 0.9853 0.9822 1.0000 0.9987 0.9954
frw 0.9859 0.9851 0.9825 1.0000 0.9987 0.9958
nm 0.9940 0.9919 0.9910 0.9990 0.9974 0.9956
nrw 0.9941 0.9922 0.9906 1.0000 0.9983 0.9958
slk frn 0.9867 0.9854 0.9822 1.0000 0.9986 0.9953
frw 0.9859 0.9851 0.9824 1.0000 0.9987 0.9959
nm 0.9949 0.9930 0.9919 1.0000 0.9984 0.9969
nrw 0.9944 0.9926 0.9909 1 .0000 0.9983 0.9962
lfi frn 0.9867 0.9855 0.9825 1.0000 0.9986 0.9955
frw 0.9860 0.9851 0.9824 1.0000 0.9986 0.9960
nm 0.9951 0.9929 0.9922 0.9999 0.9983 0.9970
nrw 0.9943 0.9925 0.9912 1.0000 0.9983 0.9963
rso fm 0.9863 0.9851 0.9820 0.9998 0.9985 0.9952
frw 0.9857 0.9849 0.9822 1.0000 0.9987 0.9958
nm 0.9936 0.9917 0.9906 0.9985 0.9971 0.9955
nrw 0.9940 0.9921 0.9904 1 .0000 0.9982 0.9960
lsc frn 0.9865 0.9852 0.9820 0.9997 0.9984 0.9951
frw 0.9858 0.9849 0.9822 1.0000 0.9986 0.9956
nm 0.9943 0.9924 0.9915 0.9992 0.9981 0.9965
nrw 0.9941 0.9923 0.9904 1.0000 0.9982 0.9959
dcf frn 0.9869 0.9858 0.9828 1.0000 0.9988 0.9957
frw 0.9861 0.9854 0.9828 1.0000 0.9988 0.9961
nm 0.9959 0.9941 0.9924 1.0007 0.9993 0.9971
nrw 0.9947 0.9929 0.9915 1.0000 0.9984 0.9962
bcp frn 0.9867 0.9856 0.9825 1.0000 0.9988 0.9955
frw 0.9860 0.9852 0.9826 1.0000 0.9987 0.9960
nm 0.9954 0.9937 0.9926 1.0000 0.9989 0.9971
nrw 0.9944 0.9924 0.9909 1 .0000 0.9982 0.9961

 

171

 

Table B-5:

Means: WADE by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WADE some none
Sched Exec none freq none freq
opt frn 0.1 136 0.0620 0.0364 0.0000 0.0003 0.0004
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.1968 0.2877 0.2524 0.0802 0.2249 0.1973
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
slk frn 0.131 1 0.0723 0.0368 0.0000 0.0008 0.0005
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.1856 0.3142 0.2725 0.0177 0.2528 0.2106
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1ft frn 0.1247 0.0696 0.0373 0.0000 0.0004 0.0006
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.1721 0.2904 0.2428 0.0195 0.2266 0.1829
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
rso frn 0.1905 0.1391 0.1075 0.1040 0.0972 0.0837
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.3329 0.4137 0.3720 0.2590 0.3852 0.3537
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
lsc frn 0.2401 0.1743 0.1320 0.1462 0.1286 0.1 163
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.3577 0.5018 0.4374 0.2384 0.4489 0.4005
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
dcf frn 0.1375 0.0801 0.0503 0.0000 0.0000 0.0001
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.1959 0.2597 0.2052 0.0890 0.2034 0.1509
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
bcp frn 0.1256 0.0782 0.0474 0.0000 0.0001 0.0005
frw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
nm 0.2107 0.4447 0.3769 0.0067 0.3616 0.3022
nrw 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

 

 

 

 

 

 

 

 

172

 

Table B-6:

Means: WADL by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WADL some none

Sched Exec none freq none freq infq

opt frn 0.2923 0.5139 1.1214 0.0000 0.2837 0.9600
frw 0.3784 0.5925 1.1316 0.0000 0.3008 0.8662
nm 0.4104 0.7907 0.9965 0.1704 0.6225 0.9330
nrw 0.3623 0.6662 1.0526 0.0000 0.3723 0.8542

slk frn 0.2793 0.5080 1.1480 0.0000 0.3009 0.9779
frw 0.3732 0.5965 1.1594 0.0000 0.3088 0.8702
nm 0.2912 0.61 14 0.8346 0.0326 0.4686 0.7017
nrw 0.341 1 0.6333 1.0506 0.0000 0.3768 0.8201

1ft frn 0.2733 0.4879 1.1092 0.0000 0.2992 0.9572
frw 0.3646 0.5818 1.1561 0.0000 0.3057 0.8798
nm 0.2591 0.6760 0.8053 0.0293 0.5227 0.7189
nrw 0.3524 0.6391 1.0139 0.0000 0.3822 0.8046

rso frn 0.2731 0.4822 1.0821 0.0000 0.2709 0.9356
frw 0.3785 0.5839 1.1252 0.0000 0.2939 0.8516
nm 0.3683 0.7108 0.9673 0.1760 0.6084 0.8671
nrw 0.3382 0.6288 1.0414 0.0000 0.3680 0.7869

lsc frn 0.2406 0.4620 1.0864 0.0000 0.2839 0.9403
frw 0.3601 0.5774 1.1406 0.0000 0.3042 0.8735
nm 0.2587 0.5752 0.7769 0.0535 0.4080 0.6443
nrw 0.3179 0.6019 1.0367 0.0000 0.3680 0.8213

dcf frn 0.2554 0.4600 1.0716 0.0000 0.2646 0.9360
frw 0.3523 0.5504 1.1045 0.0000 0.2865 0.8652
nm 0.2106 0.5955 0.9703 0.0274 0.4782 0.8650
nrw 0.3135 0.6161 1.0789 0.0000 0.3880 0.8896

bcp fm 0.2906 0.4808 1.0947 0.0000 0.2655 0.8949
frw 0.3857 0.5846 1.1257 0.0000 0.2917 0.8191
nm 0.2542 0.5247 0.7574 0.0144 0.3858 0.6575
nrw 0.3332 0.6294 1.0393 0.0000 0.361 1 0.7897

 

 

 

 

 

 

173

 

Table B-7:
Means: WADC by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WADC some none

Sched Exec none freq infq none freq infq

opt frn 0.4059 0.5759 1.1578 0.0000 0.2840 0.9604
frw 0.3784 0.5925 1.1316 0.0000 0.3008 0.8662
nm 0.6073 1.0784 1.2489 0.2505 0.8474 1.1303
nrw 0.3623 0.6662 1.0526 0.0000 0.3723 0.8542

slk frn 0.4104 0.5803 1.1848 0.0000 0.3017 0.9783
frw 0.3732 0.5965 1.1594 0.0000 0.3088 0.8702
nm 0.4769 0.9256 1.1071 0.0502 0.7214 0.9123
nrw 0.341 1 0.6333 1.0506 0.0000 0.3768 0.8201

1ft frn 0.3981 0.5575 1.1465 0.0000 0.2996 0.9578
frw 0.3646 0.5818 1.1561 0.0000 0.3057 0.8798
nm 0.4312 0.9664 1.0481 0.0488 0.7493 0.9018
nrw 0.3524 0.6391 1.0139 0.0000 0.3822 0.8046

rso frn 0.4636 0.6213 1.1896 0.1040 0.3682 1.0193
frw 0.3785 0.5839 1.1252 0.0000 0.2939 0.8516
nm 0.7012 1.1245 1.3394 0.4349 0.9936 1.2208
nrw 0.3382 0.6288 1.0414 0.0000 0.3680 0.7869

lsc frn 0.4807 0.6362 1.2184 0.1462 0.4125 1.0567
frw 0.3601 0.5774 1.1406 0.0000 0.3042 0.8735
nm 0.6164 1.0770 1.2143 0.2919 0.8569 1.0448
nrw 0.3179 0.6019 1.0367 0.0000 0.3680 0.8213

dcf frn 0.3929 0.5401 1.1219 0.0000 0.2646 0.9360
frw 0.3523 0.5504 1.1045 0.0000 0.2865 0.8652
nm 0.4064 0.8552 1.1755 0.1163 0.6816 1.0159
nrw 0.3135 0.6161 1.0789 0.0000 0.3880 0.8896

bcp frn 0.4162 0.5590 1.1422 0.0000 0.2656 0.8953
frw 0.3857 0.5846 1.1257 0.0000 0.2917 0.8191
nm 0.4649 0.9694 1.1343 0.0210 0.7474 0.9598
nrw 0.3332 0.6294 1.0393 0.0000 0.3611 0.7897

 

 

 

 

 

174

 

Table B-8:
Means: POIC by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIC some none

Sched Exec none freq none freq

opt frn 83.49 122.75 210.63 0.00 79.47 189.49
frw 85.91 130.93 207.30 0.00 88.33 180.43
am 95.56 149.32 181.12 23.61 123.02 169.02
nrw 83.87 140.13 193.73 0.00 98.15 169.39

slk frn 83.88 121.68 210.47 0.00 82.13 188.69
frw 85.57 129.83 207.27 0.00 86.11 174.86
nrn 88.41 133.82 170.67 5.83 103.78 147.86
nrw 81.93 138.87 197.45 0.00 98.63 164.98

1ft frn 78.62 115.60 204.16 0.00 80.11 182.21
frw 81.57 124.81 204.17 0.00 82.99 172.26
nrn 80.74 135.55 159.70 9.78 105.24 141.31
nrw 78.95 131.18 187.00 0.00 92.03 158.16

rso fm 97.23 134.17 219.44 37.83 107.48 208.18
frw 81.53 125.69 202.97 0.00 85.53 175.61
nrn 111.08 158.39 193.55 65.94 150.56 186.51
nrw 77.03 132.40 187.46 0.00 96.73 158.70

lsc frn 102.42 135.39 221.73 46.06 115.81 212.15
frw 81.42 124.09 202.14 0.00 83.79 172.59
nrn 109.92 153.37 184.20 57.94 133.50 174.61
nrw 75.44 132.74 191.82 0.00 95.10 163.00

dcf frn 90.79 131.06 221.27 0.00 85.03 198.56
frw 91.41 139.05 221.91 0.00 92.35 191.16
nm 91.34 145.30 202.84 13.00 113.59 178.56
nrw 84.46 145.80 210.22 0.00 105.94 181.48

bcp frn 87.84 123.34 205.24 0.00 78.22 180.10
frw 90.36 133.66 205.69 0.00 86.35 170.98
nrn 89.90 137.88 175.70 2.00 107.01 155.39
nrw 85.29 145.76 204.31 0.00 99.41 166.76

 

 

 

 

 

 

 

175

 

Table B-9:
Means: POIR by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIR some none

Sched Exec none freq infq none freq infq

opt frn 0.0673 0.0881 0.1305 0.0000 0.0442 0.1011
frw 0.0679 0.0923 0.1306 0.0000 0.0477 0.0968
nm 0.0836 0.1155 0.1299 0.0271 0.0856 0.1085
nrw 0.0662 0.0956 0.1260 0.0000 0.0518 0.0953

slk frn 0.0678 0.0887 0.1331 0.0000 0.0455 0.1030
frw 0.0674 0.0923 0.1325 0.0000 0.0477 0.0967
nm 0.0759 0.1047 0.1207 0.0083 0.0713 0.0921
nrw 0.0657 0.0945 0.1261 0.0000 0.0525 0.0920

1ft frn 0.0653 0.0850 0.1303 0.0000 0.0445 0.1014
frw 0.0658 0.0900 0.1319 0.0000 0.0479 0.0958
nm 0.0708 0.1067 0.1 172 0.01 17 0.0734 0.0906
nrw 0.0647 0.0923 0.1225 0.0000 0.0507 0.0894

rso frn 0.0890 0.1076 0.1472 0.0524 0.0878 0.1362
frw 0.0620 0.0854 0.1248 0.0000 0.0449 0.0939
nm 0.1074 0.1347 0.1497 0.0874 0.1290 0.1435
nrw 0.0575 0.0866 0.1 178 0.0000 0.0492 0.0867

lsc frn 0.0951 0.1115 0.1538 0.0632 0.0964 0.1453
frw 0.0622 0.0854 0.1273 0.0000 0.0461 0.0974
nm 0.1062 0.1326 0.1454 0.0732 0.1192 0.1371
nrw 0.0570 0.0868 0.1207 0.0000 0.0508 0.0910

dcf frn 0.0764 0.0943 0.1406 0.0000 0.0441 0.1072
frw 0.0725 0.0982 0.1429 0.0000 0.0497 0.1054
nm 0.0757 0.1062 0.1312 0.0193 0.0694 0.1021
nrw 0.0697 0.0981 0.1340 0.0000 0.0520 0.1003

bcp frn 0.0706 0.0878 0.1276 0.0000 0.0417 0.0954
frw 0.071 1 0.0937 0.1306 0.0000 0.0470 0.0917
nm 0.0745 0.101 1 0.1 166 0.0042 0.0674 0.0896
nrw 0.0663 0.0953 0.1259 0.0000 0.0507 0.0893

 

 

 

 

 

 

 

176

 

Table B-10:

Means: POOC by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOC some none

Sched Exec none freq none freq

opt frn 92.25 131.51 219.38 0.00 79.47 189.49
frw 94.68 139.68 216.06 0.00 88.33 180.43
nrn 99.37 153.57 182.75 23.61 123.02 169.02
nrw 87.68 144.38 195.37 0.00 98.15 169.39

slk frn 92.63 130.44 219.21 0.00 82.13 188.69
frw 94.33 138.59 216.02 0.00 86.11 174.86
am 92.22 138.06 172.30 5.83 103.78 147.86
nrw 85.74 143.10 199.10 0.00 98.63 164.98

lft fm 87.37 124.36 212.92 0.00 80.11 182.21
frw 90.33 133.58 212.93 0.00 82.99 172.26
nrn 84.55 139.80 161.33 9.78 105.24 141.31
nrw 82.77 135.42 188.64 0.00 92.03 158.16

rso frn 105.99 142.93 228.20 37.83 107.48 208.18
frw 90.29 134.44 21 1.73 0.00 85.53 175.61
nrn 114.89 162.65 195.20 65.94 150.56 186.51
nrw 80.84 136.65 189.10 0.00 96.73 158.70

lsc frn 111.18 144.16 230.48 46.06 115.81 212.15
frw 90.18 132.85 210.88 0.00 83.79 172.59
nm 113.73 157.62 185.83 57.94 133.50 174.61
nrw 79.25 136.97 193.46 0.00 95.10 163.00

dcf frn 99.55 139.80 230.05 0.00 85.03 198.56
w 100.09 147.71 230.58 0.00 92.35 191.16
nrn 95.14 149.54 204.47 13.00 113.59 178.56
nrw 88.26 150.05 21 1.86 0.00 105.94 181.48

bcp frn 96.60 132.10 214.00 0.00 78.22 180.10
frw 99.1 1 142.42 214.44 0.00 86.35 170.98
nrn 93.71 142.12 177.33 2.00 107.01 155.39
nrw 89.1 1 150.00 205.94 0.00 99.41 166.76

 

 

 

 

 

 

177

 

Table B-1 1:
Means: POOR by Scheduling, Execution, Disruption, Variability

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOR some none

Sched Exec none freq infq none freq infq

opt frn 0.0736 0.0943 0.1367 0.0000 0.0442 0.101 1
frw 0.0742 0.0986 0.1368 0.0000 0.0477 0.0968
nm 0.0858 0.1179 0.1321 0.0271 0.0856 0.1085
nrw 0.0683 0.0981 0.1283 0.0000 0.0518 0.0953

slk frn 0.0740 0.0949 0.1393 0.0000 0.0455 0.1030
frw 0.0737 0.0985 0.1387 0.0000 0.0477 0.0967
nm 0.0781 0.1071 0.1230 0.0083 0.0713 0.0921
nrw 0.0679 0.0969 0.1284 0.0000 0.0525 0.0920

1ft frn 0.0715 0.0912 0.1366 0.0000 0.0445 0.1014
frw 0.0721 0.0963 0.1381 0.0000 0.0479 0.0958
nm 0.0729 0.1091 0.1 195 0.01 17 0.0734 0.0906
nrw 0.0669 0.0947 0.1247 0.0000 0.0507 0.0894

rso frn 0.0952 0.1139 0.1534 0.0524 0.0878 0.1362
frw 0.0682 0.0916 0.1310 0.0000 0.0449 0.0939
nm 0.1095 0.1371 0.1519 0.0874 0.1290 0.1435
nrw 0.0596 0.0891 0.1200 0.0000 0.0492 0.0867

lsc frn 0.1013 0.1177 0.1601 0.0632 0.0964 0.1453
frw 0.0684 0.0916 0.1335 0.0000 0.0461 0.0974
nm 0.1083 0.1350 0.1476 0.0732 0.1192 0.1371
nrw 0.0592 0.0893 0.1230 0.0000 0.0508 0.0910

dcf frn 0.0810 0.1005 0.1469 0.0000 0.0441 0.1072
frw 0.0787 0.1044 0.1491 0.0000 0.0497 0.1054
nm 0.0797 0.1086 0.1335 0.0193 0.0695 0.1021
nrw 0.0691 0.1005 0.1362 0.0000 0.0552 0.1003

bcp frn 0.0768 0.0940 0.1338 0.0000 0.0417 0.0954
frw 0.0774 0.1000 0.1368 0.0000 0.0470 0.0917
nm 0.0767 0.1036 0.1 188 0.0042 0.0674 0.0896
nrw 0.0684 0.0977 0.1281 0.0000 0.0507 0.0893

 

 

 

 

 

178

 

APPENDIX C

GRAPI—IICAL TREATMENT NIEANS

179

 

 

 

 

 

 

 

 

 

 

 

66.00
64.00 + .. “Jon,
I am lostl
. + 1 ,
1 x mm + ‘4'. 1
DO 1
gum a + 10 1
8 a 1x1”,
76.“) - ’4.”
74.00 3 Eff?“
72.00 _ . L I
1 2 3 4 5 6
VARandus
ADURVSVARandDIS: FRN
1
'- 66.00
+ 1
, 34.00 136111
1 + n
1 60.00 14 1
l C U + ’0'”)
2 76.00 - _ .
1 2 .x'”
78.00 a - 8 +ch!"
' 74.00 2 ° l-‘fl‘
D
‘ 72.00 . . . .
1 1 2 3 4 5 6
VARandus
ADleyVARandDS WV
66.00 1
. + A _ g,
,1 84.“) 10°“
. 62.00 + - + ’06-: 1
j i
i ¢60.00 _ g + A“ 1‘
101309
76.00 8 _ ,
6 g ‘X"°!.
1 78m - D l+u ‘
_ 74.00 3 mp1
1 U __
7200 . . .
1 2 3 4 5 8
I VARanles
j MwVARmd“: W
1
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1 64.00 r35")
1 8200 + g loatk‘
+ n
1 60.00 14 ..
1 7600 8 _ 1x391
76.00 0 .. 8 “up
a _
74.00 2 .1899.
l O 1
‘ 72m .1 f 5 . ,
1 2 3 4 5 6 l
l VARandus
LHW _‘ i nv _ ____ __ -____ 7 7 .

Figure C-l
Graphical Means, ADUR/NRN

Figure C-2
Graphical Means, ADUR/FRN

Figure 03
Graphical Means, ADUR/NRW

Figure C-4
Graphical Means, ADUR/FRW

RDURbyVARandDIS: NRN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00917
103111
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0180
xlsc
+9614
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1.0600 6
X
1.0600 9 8
6
3 1.0400 2; x
" a
1.0200 -
+ 8
1.0000 5 +
+
0.9600 ,
1 2 3 4 5 6
VARand us
WNVARUIIII FRN
1.1000
1.0600 .. 2
1.0600 11 :F
I
3 1.0400 ..
-= 1
1.02003 .
1.06001. I
09600 .
1 2 3 4 5 6
VAR-no us
RDURbyVARmd DIS: NRW
1
‘ 1.1000
1.0600l 2
1.0600 .. + 4
a 1000‘ g
1.0600T I
1.0000 .. .
0.9600
1 2 3 4 5 6
VARand as
RDURvaVARandDIS FRW
1.1000
1.06001. 8
:p
1.0a» .. I
g 1.0400 a
1.0200 1’ I
1.0000 l I
0.9600 .
1 2 3 4 s 6
VARandflS

181

Figure C-S
Graphical Means, RDUR/NRN

Figure C-6
Graphical Means, RDUR/FRN

Figure C-7
Graphical Means, RDUR/NRW

Figure C-8
Graphical Means, RDUR/FRW

MWVARNDIS: NRN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1736000
172500) .. n
1720060 .. ‘ A 0°“
17150.00fi 0* '
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5 17000.00 1’ ‘xlac _
1 1mm .. +661 1
, TmIn .. >-IX:p‘
16660001. —-‘
16600.00 5. . ‘
1 3 4 5 6
VARand as
All'VvsVARand as. FRN
, 17300.00
‘ 1735000. I
. 1720000 I 0°“
: 17150.00. l 10"“
‘ > 17100.00. 15" j
. 3 1705000 . .0001
1 1m!” . ixllc {1
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1 3 4 5 6
' VAR-nuns
MbyVARmd' W1!
‘ 1730000
I 17250001. I _
! 1m.m . I .059“
j 17150.00* [0*
l > 1710000 1. g All
. 3 171501111 ‘0130 ll
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‘ 1 3 4 5 6
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’ 1730000
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; 1mm l ' ‘_bcpll
l 16660.00 .. L -——~—;
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1 3 4 5 6
van-nuns

182

Figure 09
Graphical Means, ANPV/N RN

Figure 010
Graphical Means, ANPV/F RN

Figure C-ll
Graphical Means, AN PV/NRW

Figure 012
Graphical Means, ANPV/FRW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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183

Figure C-l3
Graphical Means, RNPV/N RN

Figure C-14
Graphical Means, RNPV/F RN

Figure C-1 5
Graphical Means, RNPV/NRW

Figure 016
Graphical Means, RNPV/FRW

 

 

 

 

 

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1 0.6000
0.5000
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184

Figure C-17
Graphical Means, WADE/NRN

Figure 018
Graphical Means, WADE/F RN

Figure C-l9
Graphical Means, WADE/NRW

Figure C-ZO
Graphical Means, WADE/FRW

WADLbyVARaIleS: NRN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2000
0.6000 T D g
4 8
a 0mm . Q a
0.4000 §
02000 0
0.0000 . l
1 2 3 4 5
VAR and DS
WADL vs VAR aid DIS: FRN
1.2000
1.0000 A a
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WADL vs VAR and DIS: FRW
1.2000 ‘
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3 0.6000 .. .
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185

Figure C-21
Graphical Means, WADL/NRN

Figure 022
Graphical Means, WADL/F RN

Figure 023
Graphical Means, WADL/NRW

Figure 024
Graphical Means, WADL/FRW

WAmbyVARUdUS: IRN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.4000 0
1.2000 8 § 006'
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1 00000 6 Z Z,“ Flgure 025
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‘ 3 0.33m xlsc
l 0“!” O +¢f
1 0.2000 1 5 1-000
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1 2 3 4 5 6
VAR-nu us
WADCvsVARmd DIS: FRN
1.4000 0“
1 2000 100111
mi i M ‘ Figure 026
1 '30 .
§ 0.0000 .. :3, Graphical Means, WADC/F RN
‘ 3 0.6000 . I i+001
0.4000 : ‘_bcp
0.2000 l 5
0.0000 4
1 2 3 4 5 6
VARIMDS
WADC by VAR Hid DIS: NRW
1.4000
1.2000 . .0031”
- 1.00001. 3 0:“ ‘ Figure C-27
1 § ”000 .. I '2.” Graphical Means, WADC/NRW
1‘ 3 0.” J. a 1x30 ‘
l 0.2000 » 1”"
0.0000 k
1 2 3 4 5 6
VAR-Indus
WADCVSVARIIIDIS: FRW
\ 1.4M am
1.20!) 0. ‘ .03“
. 1.0000 .. 1A“ * Figure C-28
. m1 .
‘ § 00000 .. fl 1:.“ 1 Graphical Means, WADC/FRW
‘ 3 0m » . 1+“
0.4000 »-°°P
0.2000 .. .
0.0000 s
1 2 3 4 5 6

VAR and us

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

250.00
200.00 13°“
g ‘oslk
15000 g 0 1A“ 1
2 E °"°
1m.m xlsc
+001
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1 2 3 4 5 6
VARanst
PGCvsVARmles FRN
250.00 ”000‘
200.00 .. 5 1°“ ‘
Am
0 150.0) 0'30
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VARIMDS
l
PGCWVARUKI”: WV
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1 200.00 .. § no“
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150.00 . [Am .1
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PWVOVPRNIJS FM
250.00 "05¢":
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Figure 029
Graphical Means, POIC/N RN

Figure C-3O
Graphical Means, POIC/F RN

Figure 031
Graphical Means, POIC/NRW

Figure C-32
Graphical Means, POIC/FRW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.1600
0.1400 9 1 " ‘
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1 2 3 4 5 6
VARand 015
POIRVBVARNDIS FRN
0.1000 . 055"
01400 2 0"“,
0.1200 4'“
0.1000 5 5 10'”;
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PORVIVARIIIUS: FRW
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0.14mi i 1°“
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‘- 0.0600 111‘”
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1 1 2 3 4 5 6

Figure C-33
Graphical Means, POIR/NRN

Figure C-34
Graphical Means, POIR/FRN

Figure C-35
Graphical Means, POIR/NRW

Figure 036
Graphical Means, POIR/FRW

Poocwvmwms: NRN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

250.00
20000 E :10!)( ‘
oslk 1
15000 g 0 Am 1 Figure 037
10000 g :2: ~ Graphical Means, POOC/NRN
50.00 9 :Z:
0.00 1 g 1
1 2 3 4 5 6
VAR and US
I H 0000 v; 6110;103:010} *
250.00 00m
1 g ‘oslk
20000 An .
15000 orso Figure C-38
§ ' K g 6 x1: Graphical Means, POOC/FRN
a. 100.00 +
50.00 ‘ 25 ‘ :°_°".
0.00 +
1 2 3 4 5 6
uni-110015
Poocwvmmu raw
250.00
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1 3 Oreo 1, Graphical Means, POOC/NRW
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1 2 3 4 5 6
VARandus
i’fl—-w# POOCfifivsVPRIndflS FRW
250m 009'1 ‘
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§ ‘5“ 1 4 x1». 1 Graphical Means, POOC/FRW
a. 100.00 I +001 ‘
5000: -000
0CD 1;
1 2 3 4 5 6
VARInd us

 

189

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.1600
0.1400 s: 9 Bop!
‘3 0
0.1200 0 g x 094k
‘ x 0.1000 ‘ Ann
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0.0000 . . 1
1 2 3 4 5 6
VARInd us
POORVOVAROM [33: PM
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0.0000 . + .

1 2 3 4 5 6
VARmdus
MWVARMUS MW

0.1600 .

0.1400 Dept"

0.1200 .. i .001:

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8 0.0600 .. 0'30 1
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0.0000 4

1 2 3 4 5 6
VAR-M as
MWVARIKIUS FRW
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0.1900 1. 031k

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0.1200 .. 0,301

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8 0.0600 466' p
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0.0400. _,.,- 1

0.0200 .

0.0000 . ,—

1 2 3 4 5 6
VARand 015

Figure C-41
Graphical Means, POOR/NRN

Figure 042
Graphical Means, POOR/FRN

Figure C-43
Graphical Means, POOR/NRW

Figure C-44
Graphical Means, POOR/FRW

APPENDIX D

HISTOGRAMS OF NORMALITY AND HOMOSCEDASTICITY

191

Figure D-l: Normality, ADUR

 

ADUR (P<W)

Std. Dev = .28
800 Mean = .24
N = 2510.00

 

 

Figure D-2: Variance, ADUR

 

1400
1200 ADUR (VAR)
“Satd. Dev5=28.54
ean = .

100° N = 3024.00
800

600

400

200

  

 

 

0.0 10.0 200' 300' 400' 500' 60.0" 700' 90.0
5.0 15.0 25.0 35.0 45.0 55.0 65.0 75.0

192

Figure D-3: Normality, RDUR

 

RDUR (P<W)
80° Std. Dev = .28

Mean = .24

N = 2510.00

 

 

Figure D-4: Variance, RDUR

 

1200 '

1000 RDUR (VAR)
Std. Dev = .00
Mean = .0009

800 N = 3024.00

600

400

200

 

 

0 . . . . . 1
0.0000 .0020 .0040 .0060 .0080 .0100
.0010 .0030 .0050 .0070 .0090

193

Figure D-S: Normality, ANPV

 

700 '

600 ANPV (P<W)
Std. Dev = .34
500 Mean = .38
N = 2520.00

 

Figure D—6: Variance, ANPV

 

ANPV (VAR)

Std. Dev = 1181701
Mean = 5411724
N = 3024.00

 

 

 

 

194

 

Figure D-7: Normality, RNPV

 

700

600

500

400

300

 

2000 ‘

1000

RNPV (P<W)

Std. Dev = .34
Mean = .38
N = 2520.00

 

Figure D-8: Variance, RNPV

 

 

195

RN PV (VAR)

Std. Dev = .00
Mean = .00156
N = 3024.00

 

Figure D-9: Normality, WADE

 

1000

""" WADE (P<W)
800‘; Std. Dev = .17

‘ Mean-2 .06 *

j N = 1102.00
600: f
400i ;
200j'1

A

Ii

Oi”... —

 

 

 

 

 

(100'.10 .20 .302 .404 .50 .60 .70 .99» .90 e

.05 15 .25 .35 .45 .55 .65 .75 .85

Figure D-lO: Variance, WADE

 

3000‘

WADE (VAR)

Std. Dev = .03
Mean = .010

2000 N = 3024.00

 

1000 §{

 

 

 

 

 

.{50 ' .200 ' .250 ' .300
.175 .225 .275

196

.325

Figure D-ll: Normality, WADL

 

2000

WADL (P<W)
.... Std. Dev = .19

E Mean= .10
: 5 N = 2516.00

1000

 

 

 

 

 

Figure D-12: Variance, WADL

 

2000

WADL (VAR)
Std. Dev = .30
":9 Mean = .16

~ N = 3024.00

 

 

 

 

 

 

197

Figure D-l3: Normality, WADC
2000

 

WADC (P<W)
, Std. Dev = .20
Mean = .10

N = 2520.00

1000 Q 3

 

 

 

 

 

Figure D-l4: Variance, WADC

2000

 

WADC AR
1.. (v 1

Std. Dev = .30
Mean = .16

N = 3024.00

1000 ;_5

 

 

 

 

 

 

 

198

Figure D-lS: Normality, POIC

nnn
OUU

POIC (P<VV)

Std. Dev = .28
600 Mean = .26 -.
N = 2520.00

 

 

Figure D-16: Variance, POIC

 

2000
POIC (VAR)
Std. Dev = 3910.18
Mean = 2189.0
N = 3024.00
1000

 

 

 

199

AAA
OUU

600

 

wan -

IUU

600

500

400

300

200

100

 

Figure D-17: Normality, POIR

POIR (P<VV)

Std. Dev = .28
Mean = .26
N = 2520.00

 

Figure D-l8: Variance, POIR

POIR (VAR)

Std. Dev = .00
Mean = .00095
N = 3024.00

 

Figure D-19: Normality, POOC

 

1000
POOC (P<VV)
80° Std. Dev = .27
Mean = .23
N = 2520.00

 

 

Figure D-20: Variance, POOC

 

 

1600
1400 POOC (VAR)
Std. Dev = 5972.52
1200 Mean = 3368.4
N = 3024.00
1000 .
aoo '-
600 ‘ ’
400
200
o . ,
t? t? 7 7, 7 6‘},
‘b q? q?%%.6bq?oo‘b 0%”be 0%

 

 

Figure D-21: Normality, POOR

 

1000
. POOR (P<VV)
800 Std. Dev = .27
r Mean = .23
N = 2520.00

 

 

Figure D-22: Variance, POOR

 

POOR (VAR)

Std. Dev = .00
Mean = .0014
N = 3024.00

 

 

 

202

APPENDIX E

BISERIAL SCATTERPLOTS

203

Figure E-l: Scatterplot, ADUR-RDUR

 

 

 

 

 

 

 

 

ADUR
Figure E-Z: Scatterplot, ANPV-RNPV
1.2 I 9
. i
S
1.01 / //
l I I I
‘ ' U l I
.9 '
ANPV

204

 

 

RDUR

Figure E-3: Scatterplot, RNPV-RDUR

 

 

  

 

 

 

 

 

 

 

1.3 D
U
i“. E u u c a
D
13' B H
a Q
‘3 8
C} a. '
12' %a E
5 E8...-
GB 0
1.1‘ g 0%
toJ m
‘ D
g u
3
,J a an
[3! m D
D D
9 . , - 2
1 s ,9 1.0 H 12
RNPV
Figure E-4: Scatterplot, ANPV-RDUR
u) u
D
1.4-
w1
12‘
141
1.0-
.o'
a I I
0 10000 20000 30000 40000 wow 00000
ANPV

205

Figure E-S: Scatterplot, ANPV-ADUR

 

 

ANPV

ADUR
o

 

 

 

Figure E-6: Scatterplot, RNPV-ADUR

 

 

 

 

 

206

Figure E-7: Scatterplot, WADE-ADUR

 

 

 

 

 

Figure E-8: Scatterplot, WADE-RDUR

 

 

 

 

 

207

Figure E-9: Scatterplot, WADE-ANPV

 

 

 

 

Figure E-lO: Scatterplot, WADE-RNPV

 

 

 

 

 

 

208

Figure E-l 1: Scatterplot, WADL-ADUR

 

 

 

 

Figure E-12: Scatterplot, WADL—RDUR

 

 

 

 

209

 

 

Figure E-l3: Scatterplot, WADL-ANPV

 

ANPV

 

 

 

Figure E-14: Scatterplot, WADL-RNPV

 

 

 

9 ”:3 '
whkcbuuu

 

210

 

 

RDUR

Figure E-15: Scatterplot, WADC-ADUR

 

 

 

 

 

Figure E-16: Scatterplot, WADC-RDUR

 

 

 

 

 

211

[NPV

Figure E-17: Scatterplot, WADC-ANPV

 

 

ANPV

 

 

 

 

Ila-l-

 

 

 

 

212

RDUR

Figure E-19: Scatterplot, POIC-ADUR

 

   
 

    

 

 

 

 

 

 

 

 

 

.5 0 °
um
[I
D
9 o _ . . _ _ _
45D 0 200 400 000 I!) «am 12
POIC
Figure E-20: Scatterplot, POIC-RDUR
“’ u
D
1.4‘
13‘
12‘ u
{I
1.1 ‘
1.0'
.0‘
-Zn 12m
ponc

213

ANPV

NPV

Figure E-21: Scatterplot, POIC-ANPV

 

 

 

 

 

 

 

   
  
 

  

 

cocoo-

W'

W‘

20000-

10000‘

n ' ,7
41!) O 200 can 600 900 'm 12
POIC
Figure E-22: Scatterplot, POIC-RNPV
1‘ on D u
an
m, "1' Ex“DJ-u £

J gm. .
1.1
1.0- H

:‘ 9;. 0 u
.9‘ .
HP 35:: in a
n =8 0 m
DDDODD a ‘b 0

’°‘ "am a
.7 '

~200 O 200 000 000 900 1M 1200

pow

214

 

ADUR

RDUR

Figure E-23: Scatterplot, POIR-ADUR

 

 

 

 

POIR

Figure E-24: Scatterplot, POIR-RDUR

 

 

 

 

 

POIR

215

 

PNPV

RUPV

Figure E-25: Scatterplot, POIR-ANPV

 

 

 

 

POIR

Figure E-26: Scatterplot, POIR-RNPV

 

 

 

 

POIR

216

 

 

ADUR

RDUR

Figure E-27: Scatterplot, POOC-ADUR

 

 

 

 

 

 

 

 

 

217

RNPV

Figure E-29: Scatterplot, POOC-ANPV

 

 

 

 

 

 

 

  

 

 

50000-

0000‘

30000-

W'

iummj

0 v
41'!) O 203 400 000 900 1000 1200 1400
POOC
Figure E-30: Scatterplot, POOC-RNPV

1.‘ .0”

1 1
10‘

D
9.
=5:
Ilm ' @530 D n W D an
an I '3 tar-“3°00 D “b u
.a- a,
D D
7 I v I I I v
‘200 200 400 000 800 1000 12(1) 1400
9000

218

 

Figure E-3 1: Scatterplot, POOR-ADUR

 

 

 

 

 

 

 

 

 

 

:1
2113" a DD
100‘
D
CK
D
9 o _ , , a
1 DO 1 2 3 Q 1|
POOR
Figure E-32: Scatterplot, POOR-RDUR
" u
D
1 4‘
13‘
121
1.1‘
1.0'
,.
[I
D
9 n , a .
1 00 1 2 ,3 4 5
poon

219

 

Figure E-33: Scatterplot, POOR-ANPV

 

 

 

ANPV

 

 

POOR

Figure E-34: Scatterplot, POOR-RNPV

 

 

 

FWPV

 

 

POOR

220

 

APPENDIX F

ANOVA RESIDUAL PLOTS

221

 

Figure F-l: Predicted ADUR

 

8'1

a
g” 8

D

Iii

O 100 2C!) 300

b
A

N
1

O
n

     

 

 

ad Resror AUJR
L

6

 

Pred ADUR

Figure F-2: QQ ADUR

Normal Q-Q Plot of Std Ros for ADUR

 

 

 

Expecbd Norma Wire
5
D

b

 

.o 4 .2 o 2 4 0 a 10

Observed Value

222

 

Figure F-3: Predicted RDUR

 

SdRaeruJR

 

 

 

 

Prod RDUR

Figure F4: QQ RDUR

Normal Q-Q Plot of Std Res for RDUR

 

 

 

~10 0 10 Z)

 

Observed Value

223

30 Res It! ANPV

Figure F-S: Predicted ANPV

 

 

 

 

10
I
04 ' ”I
g
-m V I' V U V
0 10000 20000 30000 40000 50000
PredANPV

Figure F-6: QQ ANPV

Normal Q-Q Plot of Std Res for ANPV

Expected Norma vars

b

 

4+

24

DJ

9'0
L

 

 

 

 

-20

Observed Value

-10

224

10

Figure F -7: Predicted RNPV

 

 

 

scamrararw

 

 

Prod RNPV

Figure F-8: QQ RNPV

Normal Q-Q Plot of Std Res for RNPV

 

N
n

I

4 4 -2 O 2 4 I

 

Expecm Normal Vane
b .

 

 

Observed Value

225

Figure F-9: Predicted WADE

 

 

 

30 Res fa' WADE

.1n

 

 

-.1 DD 1 .2 3 .4 .5 .5

Fred WADE

Figure F-lO: QQ WADE

Normal Q-Q Plot of Std Res for WADE

 

4‘ “In?

9
.

 

Emma Nmna van
5

b

 

 

-10 0 10 20

Observed Value

226

Figure F-l 1: Predicted WADL

 

 

 

 

 

 

3
9 .
Q
E A - _
-.5 0.0 5 10 1.5 21) 2.5
Pred WADL
Figure F-12: QQ WADL
Normal Q-Q Plot of Std Res for WADL
. 5

Expected Norma Vaue
8

 

 

 

-‘ID 0 1O 2!)

Observed Value

227

sweater WADC

Figure F-13: Predicted WADC

 

44

 
 

i...
Damn-1mm D D D

 

 

 

Prod WADC

Figure F-l4: QQ WADC

Normal Q-Q Plot of Std Res for WADC

 

 

 

 

4 4

Observed Value

228

Figure F-15: Predicted POIC

 

 

 

animator POC

 

 

Pred POIC

Figure F-16: QQ POIC

Normal Q-Q Plot of Std Res for POIC

 

 

 

 

U
3?
41
’l
0-
av
>
E
34-
B D
§. . , _ , , ,f
-r 4 .2 o 2 4 e e 10

Observed Value

229

Figure F-17: Predicted POIR

 

32198st POR
.1)

L

 

 

 

-.1

Fred POlR

Figure F-18: QQ POIR

Normal Q-Q Plot of Std Res for POIR

 

 

 

Observed Value

230

 

 

Figure F-19: Predicted POOC

 

 

 

 

 

10
el
0‘
4'
2‘
01
E
9 4‘
E .4 , 1 - . . _
41” .100 0 100 200 300 400 we 000
PmdPOOC

Figure F-ZO: QQ POOC

Normal Q-Q Plot of Std Res for POOC

 

44

24

b
I

no

 

 

Brpeceu Nam Value
5

6

 

be
a
o
3

«4 -2 O 2

6

Observed Value

231

Figure F-21: Predicted POOR

 

 

 

 

 

 

 

 

 

[I
o
a:
£
8 A
.4 0's .2 1
Fred POIR
Figure F -22: QQ POOR
Normal Q-Q Plot of Std Res for POOR
0
4- a n
21
o-l
r
>
E
u
z 4'
B D
Er .
.e 1. .E 6 5 3 5 s
Observed Value

232

APPENDIX G

NONPARAMETRIC COMPARISONS

233

Table G-l:
Scheduling Method Performance by Execution Method for ADUR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A RSO A RSO A RSO A RSO A
OPT A RSO A OPT A OPT A OPT A OPT A
LSC B LSC B LSC B LSC B LSC B LSC B
LFT C LFT C LFT C LFT B LF T C LFT B
SLK D SLK C SLK D SLK C SLK D SLK C
BCP E BCP D BCP E BCP D BCP E BCP D
DCF F DCF E DCF F DCF E DCF F DCF E
FRW
none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A OPT A OPT A OPT A OPT A
OPT A RSO A RSO A RSO A RSO A RSO A
LSC B LSC B LSC B LSC B LSC B LSC B
LFT C LFT BC LFT C LFT BC LFT B ' LFT B
SLK D SLK C SLK C SLK C SLK B SLK B
BCP E BCP D BCP D BCP D BCP C BCP C
DCF F DCF E DCF E DCF E DCF D DCF D
NRN
none .000 some .000 none .000 some .000 none .000 some .000
OPT A RSO A RSO A RSO A RSO A RSO A
RSO B OPT A OPT AB OPT AB LSC B OPT A
LSC C LFT B LSC B LFT BC OPT B LF T AB
SLK D LSC C LFT C LSC C LF T B LSC BC
LFT D SLK C SLK D SLK C SLK C SLK C
BCP E BCP D BCP E BCP D BCP D BCP D
DCF F DCF E DCF F DCF E DCF E DCF E
NRW
none .000 some .000 none .000 some .000 none .000 some .000
RSO A OPT A OPT A OPT A RSO A OPT A
OPT A RSO A RSO A RSO A OPT A RSO A
LSC B LSC B LSC B LSC B LFT B LFT B
LFT C LFT B LFT C LFT B LSC B SLK C
SLK D SLK B SLK D SLK B SLK B LSC C
BCP E BCP C BCP E BCP C BCP C BCP D
DCF F DCF D DCF F DCF D DCF D DCF E

 

 

 

 

 

 

234

 

Table G-2:
Scheduling Method Performance by Execution Method for RDUR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RDUR FRN
NONE FREQ INFQ
none some .000 none .000 some .000 none .000 some .000
A DCF A DCF A DCF A DCF A DCF A
L LSC B BCP A BCP AB BCP A BCP A
L E BCP B OPT B LFT BC LSC B LFT B
Q SLK B RSO B SLK C RSO B LSC BC
U LFT B LSC B LSC CD SLK B SLK BC
A OPT C SLK B RSO DE LFT B RSO C
L RSO C LFT B OPT E OPT B OPT C
FRW
none some .000 none .000 some .000 none .000 some .000
A DCF A DCF A DCF A DCF A DCF A
L BCP B BCP B BCP B BCP AB BCP A
L E LFT BC SLK BC LFT BC SLK BC SLK B
Q SLK BC OPT BCD SLK CD LFT CD LFT B
U OPT CD LFT CD OPT CE OPT DE OPT BC
A LSC DE RSO D LSC EF RSO EF LSC CD
L RSO E LSC E RSO F LSC F RSO D
N RN
none .000 some .000 none .000 some .000 none .000 some .000
DCF A DCF A DCF A DCF A DCF A DCF A
BCP B BCP B BCP B BCP B BCP B BCP A
LFT C LFT C LSC C SLK C LFT C LFT B
SLK C SLK C LF T C LFT C SLK C SLK BC
LSC D LSC D SLK C LSC D LSC C LSC C
OPT E RSO E RSO D RSO E RSO D RSO D
RSO F OPT E OPT D OPT E OPT E OPT D
NRW
none some .000 none .000 some .000 none .000 some .000
A DCF A DCF A DCF A DCF A DCF A
L BCP B BCP B BCP B BCP B BCP B
L E SLK BC SLK BC SLK B SLK B LF T B
Q LFT C OPT BC LFT B LFT B SLK B
U LSC D LFT CD LSC C RSO C OPT C
A OPT D RSO DE OPT C OPT C LSC C
L RSO D LSC E RSO C LSC C RSO C

 

235

 

Table G-3:
Scheduling Method Performance by Execution Method for ANPV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANPV FRN
NONE FREQ INFQ
none .000 some .389 none .000 some .66] none .000 some .879
OPT A OPT A OPT A OPT A OPT A OPT A
LFT B LFT A LFT B LFT A LFT B LFT A
RSO C BCP A BCP BC BCP A BCP B BCP A
BCP D SLK A RSO C SLK A SLK B SLK A
SLK D RSO A SLK C RSO A RSO C RSO A
LSC E LSC A LSC D DCF A DCF D DCF A
DCF F DCF A DCF E LSC A LSC D LSC A
FRW
none .000 some .336 none .000 some .645 none .000 some .816
OPT A OPT A OPT A OPT A OPT A OPT A
LFT B LFT A RSO B LFT A LFT B BCP A
RSO C BCP A LFT B BCP A SLK B LFT A
BC P D RSO A SLK B SLK A BCP BC SLK A
SLK E SLK A BCP C RSO A RSO C RSO A
LSC F LSC A LSC D DCF A LSC D DCF A
DCF G DCF A DCF E LSC A DCF D LSC A
NRN
none .000 some .094 none .000 some .157 none .000 some .252
LFT A LFT A BCP A BCP A BCP A LFT A
BCP B BCP A LFT A DCF A LFT A BCP A
SLK B DCF A SLK B LF T A SLK B SLK A
OPT C SLK A DCF B SLK A DCF B DCF A
DCF D OPT A OPT C OPT A OPT C OPT A
RSO E LSC A LSC C LSC A LSC C LSC A
LSC F RSO A RSO D RSO A RSO D RSO A
NRW
none .000 some .526 none .000 some .919 none .000 some .859
OPT A OPT A OPT A OPT A LF T A LFT A
LF T B LFT A LFT B LFT A SLK A OPT A
RSO C BCP A SLK BC SLK A OPT A SLK A
BCP D SLK A RSO BC RSO A BCP A BCP A
SLK E RSO A BCP C BCP A RSO B DCF A
LSC F DCF A LSC D DCF A DCF C RSO A
DCF G LSC A DCF E LSC A LSC C LSC A

 

 

 

 

 

 

236

 

Table G-4:
Scheduling Method Performance by Execution Method for RNPV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RNPV FRN
NONE FREQ , IN FQ
none .000 some .786 none .000 some .797 none .000 some .820
OPT A DCF A DCF A DCF A DCF A DCF A
SLK A SLK A BCP AB BCP A BCP AB BCP A
LFT A LFT A OPT BC LFT A LF T B LFT A
DCF A BCP A LFT C SLK A OPT B OPT A
BCP A OPT A SLK C OPT A SLK B SLK A
RSO B LSC A RSO D LSC A RSO C LSC A
LSC C RSO A LSC E RSO A LSC C RSO A
FRW
none some .938 none .000 some .897 none .000 some .925
A DCF A DCF A DCF A DCF A DCF A
L BCP A OPT B BCP A BCP A BCP A
L E SLK A SLK BC LFT A SLK B OPT A
Q LFT A BCP BCD SLK A LF T B SLK A
U OPT A RSO CD OPT A OPT B LF T A
A LSC A LFT D RSO A RSO C RSO A
L RSO A LSC E LSC A LSC D LSC A
NRN
none .000 some .009 none .000 some .009 none .000 some .084
DCF A DCF A DCF A DCF A DCF A BCP A
BCP B BCP A BCP B BCP A BCP B DCF A
SLK BC LFT A LF T C SLK A LFT BC LFT A
LFT C SLK A SLK C LFT A SLK C SLK A
OPT D LSC A LSC D LSC A LSC D LSC A
LSC E OPT A OPT E OPT A OPT E OPT A
RSO F RSO A RSO F RSO A RSO F RSO A
NRW
none some .756 none .000 some .789 none .000 some .647
A DCF A DCF A DCF A DCF A DCF A
L BCP A BCP B SLK A SLK B LFT A
L E SLK A OPT B LFT A BCP B SLK A
Q LFT A SLK B BCP A LFT B BCP A
U OPT A LF T B LSC A OPT C OPT A
A LSC A RSO C OPT A RSO C LSC A
L RSO A LSC C RSO A LSC C RSO A

 

237

 

Table G-S:
Scheduling Method Performance by Execution Method for WADL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDL FRN
NONE FREQ INF Q
none some .000 none .000 some .001 none .000 some .001
A LSC A RSO A LSC A RSO A LSC A
L DCF B LSC A DCF AB LSC AB DCF AB
L E LFT BC DCF AB BC P BC DCF AB BCP AB
Q SLK BC BCP BC RSO BC BC P BC RSO AB
U RSO BC OPT BD LFT BC OPT CD LFT BC
A BCP C LFT DE SLK CD LFT D SLK C
L OPT C SLK E OPT D SLK D OPT C
FRW
none some .075 none .001 some .028 none .001 some .146
A DCF A DCF A DCF A BCP A DCF A
L LSC AB BCP AB LSC AB DCF A BCP AB
L E LF T AB RSO ABC LFT ABC SLK AB LSC AB
Q SLK AB OPT BCD BCP BC RSO AB LF T AB
U OPT B SLK CD SLK BC OPT B SLK AB
A BCP B LSC CD RSO BC LF T B RSO B
L RSO B LF T D OPT C LSC B OPT B
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A DC F A LSC A BCP A LSC A BCP A
LSC B BCP B BCP A DCF A BCP A LSC AB
LF T BC LSC BC DC F B LSC A LFT B LF T ABC
DCF C LFT BC SLK B SLK B DCF B DCF BC
SLK D SLK C LFT B LFT C SLK B SLK C
OPT E RSO D RSO C RSO CD RSO C RSO D
RSO F OPT E OPT D OPT D OPT D OPT E
NRW
none some .024 none .035 some .004 none .001 some .025
A DCF A BCP A LSC A BCP A BC P A
L LSC AB RSO AB DCF A RSO AB LFT A
L E BCP ABC DCF ABC BCP A SLK AB DCF A
Q SLK ABC OPT ABC RSO A LFT AB LSC A
U LF T ABC SLK BC SLK A DCF AB SLK AB
A RSO BC LSC C LFT A LSC BC RSO B
L OPT C LFT C OPT B OPT C OPT B

 

 

 

 

 

 

238

 

Table G-6:
Scheduling Method Performance by Execution Method for WADE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDE FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A OPT A BCP A OPT A DCF A SLK A
SLK A BCP A DCF A SLK AB BCP A OPT A
LFT A LFT AB LFT A LFT AB OPT A LFT A
DCF A SLK AB OPT A BCP AB LFT A BCP AB
BCP A DCF B SLK A DCF B SLK A DCF B
RSO B RSO C RSO B RSO C RSO B RSO C
LSC C LSC D LSC C LSC D LSC C LSC D
FRW
none some none some none some
A A A A A A
L L L L L L
L E L E L E L E L E L E
Q Q Q Q Q Q
U U U U U U
A A A A A A
L L L L L L
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A LFT A DCF A DCF A DCF A DCF A
LFT B SLK AB OPT B OPT B LFT B LFT B
SLK C OPT B LFT B LFT BC OPT B OPT B
OPT D BCP B SLK C SLK C SLK B SLK C
DCF E DCF B BCP D BCP D BCP C BCP D
LSC F RSO C RSO E RSO E RSO D RSO E
RSO G LSC C LSC F LSC F LSC E LSC F
NRW
none some none some none some
A A A A A A
L L L L L L
L E L E L E L E L E L E
Q Q Q Q Q Q
U U U U U U
A A A A A A
L L L L L L

 

 

 

 

 

 

239

 

Table G-7:
Scheduling Method Performance by Execution Method for WADC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDC FRN
NONE FREQ IN FQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A LFT A DCF A DCF A DCF A BCP A
SLK A DCF A BC P AB LF T A BCP AB DCF AB
LFT A OPT A OPT BC BCP A OPT BC LFT B
DCF A SLK A LFT C D SLK A LFT C SLK B
BCP A BCP A SLK D OPT A SLK C OPT B
RSO B RSO B RSO E RSO B RSO D RSO C
LSC C LSC B LSC F LSC B LSC E LSC C
FRW
none some .075 none .001 some .028 none .008 some .146
A DC F A DCF A DCF A BCP A DCF A
L LSC AB BCP AB LSC AB DCF AB BCP AB
L E LFT AB RSO ABC LFT ABC SLK ABC LSC AB
Q SLK AB OPT BCD BCP BC RSO ABC LF T AB
U OPT B SLK CD SLK BC OPT BC SLK AB
A BC P B LSC CD RSO BC LFT C RSO B
L RSO B LF T D OPT C LSC C OPT B
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A DCF A DCF A DCF A LFT A LFT A
SLK B LF T A SLK B SLK B DCF AB DCF A
LFT B BCP B LFT B LFT B SLK AB SLK B
DCF C SLK B BCP B BCP B BCP B BCP B
OPT D OPT C OPT C OPT C OPT C OPT C
LSC E LSC D LSC D LSC D LSC C LSC C
RSO F RSO E RSO E RSO D RSO D RSO D
NRW
none some .024 none .035 so me .004 none .001 some .025
A DCF A BCP A LSC A BCP A BCP A
L LSC AB RSO AB DCF A RSO AB LFT AB
L E BCP ABC DCF ABC BCP A SLK AB DCF AB
Q SLK ABC OPT ABC RSO A LFT AB LSC AB
U LF T ABC SLK BC SLK A DCF AB SLK AB
A RSO BC LSC C LFT AB LSC BC RSO BC
L OPT C LFT C OPT B OPT C OPT C

 

 

 

 

 

 

240

 

Table G-8:

Scheduling Method Performance by Execution Method for POIC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIC FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A LFT A BCP A LFT A BCP A BCP A
SLK A SLK A DCF AB SLK B LFT AB LFT AB
LFT A OPT A OPT AB BCP B OPT AB OPT AB
DCF A BC P B LFT AB OPT B SLK B SLK B
BCP A DCF B SLK B DCF C DCF B DCF C
RSO B RSO C RSO C RSO D RSO C RSO D
LSC C LSC D LSC D LSC D LSC D LSC E
FRW
none some .000 none .244 some .000 none .004 some .000
A LSC A RSO A LSC A BCP A RSO A
L LFT A LSC AB RSO AB RSO AB LSC AB
L E RSO AB BCP AB LFT AB SLK AB BCP AB
Q SLK AB LFT AB SLK BC LFT AB OPT AB
U OPT B SLK AB OPT C LSC BC LF T B
A BCP C OPT B BCP CD OPT BC SLK B
L DCF C DCF B DCF D DCF C DCF C
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A LFT A BCP A BCP A LFT A LFT A
DCF B SLK B SLK A SLK AB BCP A BCP A
LFT B BCP B LFT A LFT BC SLK A SLK B
SLK B DCF B DCF A DCF C DCF B DCF C
OPT C OPT C OPT B OPT D OPT C OPT C
LSC D LSC D LSC C LSC E LSC D LSC D
RSO E RSO D RSO D RSO E RSO E RSO E
NRW
none some .000 none .055 some .000 none .000 some .000
A LSC A RSO A LSC A RSO A RSO A
L RSO A LFT AB RSO A LFT AB LF T A
L E LFT AB LSC AB LFT AB SLK AB LSC AB
Q SLK BC BCP AB SLK BC BCP AB BCP B
U BCP CD OPT AB BCP CD LSC B SLK B
A OPT CD SLK B OPT CD OPT C OPT B
L DCF D DCF B DCF D DCF C DCF C

 

 

 

 

 

 

241

 

Table G-9:

Scheduling Method Performance by Execution Method for POIR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIR FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A LF T A BCP A LFT A BCP A BCP A
SLK A SLK A DCF AB SLK B LFT AB LFT AB
LFT A OPT AB OPT AB BCP B OPT AB OPT AB
DCF A BCP BC LFT AB OPT B SLK B SLK B
BCP A DCF C SLK B DCF C DCF B DCF C
RSO B RSO D RSO C RSO D RSO C RSO D
LSC C LSC E LSC D LSC D LSC D LSC E
FRW
none some .000 none .245 some .000 none .004 some .000
A LSC A RSO A LSC A BCP A RSO A
L LFT A LSC AB RSO AB RSO AB LSC AB
L E RSO AB BCP AB LFT AB SLK AB BCP AB
Q SLK AB LFT AB SLK BC LFT AB OPT AB
U OPT B SLK AB OPT C LSC BC LF T B
A BCP C OPT B BCP CD OPT BC SLK B
L DCF C DCF B DCF D DCF C DCF C
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A LFT A BCP A BCP A LFT A LFT A
DCF B SLK B SLK A SLK AB BCP A BCP A
LFT B BCP B LFT A LF T BC SLK A SLK B
SLK B DCF B DCF A DCF C DCF B DCF C
OPT C OPT C OPT B OPT D OPT C OPT C
LSC D LSC D LSC C LSC E LSC D LSC D
RSO E RSO D RSO D RSO E RSO E RSO E
NRW
none some .000 none .056 some .000 none .000 some .000
A LSC A RSO A LSC A RSO A RSO A
L RSO A LF T AB RSO A LFT AB LFT A
L E LF T AB LSC AB LF T AB SLK AB LSC AB
Q SLK BC BCP AB SLK BC BCP AB BCP B
U BCP CD OPT AB BCP CD LSC B SLK B
A OPT CD SLK B OPT CD OPT C OPT B
L DCF D DCF B DCF D DCF D DCF C

 

 

 

 

 

 

242

 

Table G-10:
Scheduling Method Performance by Execution Method for POOC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOC FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A LF T A BCP A LFT A BCP A BCP A
SLK A OPT AB DCF AB BCP A LFT AB LFT A
LFT A SLK AB OPT AB OPT A OPT AB OPT A
DCF A BCP B LFT AB SLK A SLK B SLK A
BCP A DCF C SLK B DCF B DCF B DCF B
RSO B RSO D RSO C RSO C RSO C RSO C
LSC C LSC E LSC D LSC C LSC D LSC D
FRW
none some .003 none .244 some .000 none .004 some .000
A LSC A RSO A LSC A BCP A RSO A
L RSO A LSC AB RSO A RSO AB LSC A
L E LFT A BCP AB LFT AB SLK AB BCP A
Q SLK AB LFT AB SLK AB LFT AB OPT A
U OPT AB SLK AB OPT BC LSC BC LFT A
A BCP B OPT B BCP BC OPT BC SLK A
L DCF B DCF B DCF C DCF C DCF B
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A LFT A BCP A BCP A LFT A BCP A
DCF B SLK B SLK A SLK AB BCP A LFT A
LFT B BCP B LFT A LF T AB SLK A SLK A
SLK B DCF B DCF A DCF B DCF B OPT B
OPT C OPT C OPT B OPT C OPT C DCF B
LSC D LSC D LSC C LSC D LSC D LSC C
RSO E RSO D RSO D RSO D RSO E RSO C
N RW
none some .006 none .055 some .000 none .000 some .000
A LSC A RSO A LSC A RSO A RSO A
L RSO AB LFT AB RSO A LFT AB LFT AB
L E LFT ABC LSC AB LFT AB SLK AB LSC AB
Q SLK BC BCP AB SLK BC BCP AB SLK B
U BCP C OPT AB OPT C LSC B BCP B
A OPT C SLK B BCP C OPT C OPT B
L DCF C DCF B DCF C DCF C DCF C

 

 

 

 

 

 

243

 

Table G-l 1:
Scheduling Method Performance by Execution Method for POOR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOR FRN
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
OPT A LF T A BCP A LFT A BCP A BCP A
SLK A OPT AB DCF AB BCP A LFT AB LFT A
LFT A SLK AB OPT AB OPT A OPT AB OPT A
DCF A BCP B LFT AB SLK A SLK B SLK A
BCP A DCF C SLK B DCF B DCF B DCF B
RSO B RSO D RSO C RSO C RSO C RSO C
LSC C LSC E LSC D LSC C LSC D LSC D
FRW
none some .003 none .245 some .000 none .004 some .000
A LSC A RSO A LSC A BCP A RSO A
L RSO A LSC AB RSO A RSO AB LSC A
L E LFT A BCP AB LF T AB SLK AB BCP A
Q SLK AB LFT AB SLK AB LF T AB OPT A
U OPT AB SLK AB OPT BC LSC BC LF T A
A BCP B OPT B BCP BC OPT BC SLK A
L DCF B DCF B DCF C DCF C DCF B
NRN
none .000 some .000 none .000 some .000 none .000 some .000
BCP A LFT A BCP A BCP A LFT A BCP A
DCF B SLK B SLK A SLK AB BCP A LFT A
LFT B BCP B LF T A LF T B SLK A SLK A
SLK B DCF B DCF A DCF B DCF B OPT B
OPT C OPT C OPT B OPT C OPT C DCF B
LSC D LSC D LSC C LSC D LSC D LSC C
RSO E RSO D RSO D RSO D RSO E RSO C
NRW
none some .006 none .056 some .000 none .000 some .000
A LSC A RSO A LSC A RSO A RSO A
L RSO AB LFT AB RSO A LFT AB LFT AB
L E LFT ABC LSC AB LFT AB SLK AB LSC AB
Q SLK BC BCP AB SLK BC BCP AB SLK B
U BCP C OPT AB OPT C LSC B BCP B
A OPT C SLK B BCP C OPT C OPT B
L DCF C DCF B DCF C DCF C DCF C

 

 

 

 

 

 

244

 

Table G-12:

Execution Method Performance by Scheduling Method for ADUR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR OPT
NONE FREQ INF Q
none .000 some .000 none .000 some .000 none .000 some .074
FRN A FRN A F RN A FRN A FRW A FRN A
FRW A NRN B FRW B FRW B FRN AB NRN A
NRW A NRW B NRW C NRN C NRW B FRW AB
NRN B FRW C NRN D NRW C NRN C NRW B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
F RN A NRN A FRN A NRN A NRN A NRN A
FRW A FRN A FRW AB FRN A NRW B NRW B
NRW A NRW B NRN B FRW B F RW B F RN BC
NRN B FRW C NRW C NRW B F RN C FRW C
LFI‘
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRN A FRN A F RN A NRN A NRN A
F RW A FRN B FRW B NRN A NRW B FRN B
NRW A NRW C NRN B FRW B F RW BC NRW B
NRN B FRW D NRW C NRW B F RN C FRW C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
FRN A FRN A F RN A F RN A F RN A NRN A
FRW A NRN B FRW B F RW B NRW AB FRN A
NRW A NRW C NRW C NRN B FRW AB NRW B
NRN B FRW D NRN D NRW B NRN B FRW B
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRN A FRN A FRN A FRN A NRN A NRN A
F RW A NRN A NRN B NRN B FRN B FRN B
NRW A NRW B F RW C FRW C NRW C FRW C
NRN B FRW C NRW D NRW C FRW C NRW C
DC F
none .000 some .000 none .000 some .000 none .000 some .000
NRN A NRN A NRN A NRN A NRN A NRN A
F RN B F RN B FRN B F RN B NRW B NRW B
FRW B NRW C FRW C NRW C FRW C FRN C
NRW B F RW D NRW D FRW C F RN C FRW D
BCP
none .000 some .000 none .000 some .000 none .000 some .000
F RN A NRN A NRN A NRN A NRN A NRN A
FRW A FRN B FRN B FRN B NRW B FRN B
NRW A NRW C FRW C F RW C FRW BC NRW BC
NRN B FRW D NRW D NRW C F RN C F RW C

 

 

 

 

 

 

245

 

Table G-13:
Execution Method Performance by Scheduling Method for RDUR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RDUR OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
FRN A FRN A F RN A FRN A FRW A FRN A
FRW A NRN B FRW A FRW B FRN AB NRN A
NRW A NRW B NRW B NRN C NRW B FRW AB
NRN B FRW C NRN C NRW C NRN C NRW B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRN A FRN A NRN A NRN A NRN A
F RW A FRN A FRW AB F RN A NRW B NRW B
NRW A NRW B NRN B FRW B FRW B F RN BC
NRN B FRW C NRW C NRW B FRN C FRW C
LFT
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRN A FRN A F RN A NRN A NRN A
FRW A FRN B FRW B NRN A NRW B FRN B
NRW A NRW C NRN B FRW B FRW BC NRW B
NRN B FRW D NRW C NRW B FRN C FRW C
RSO
none .000 some .000 none .000 some .000 none .197 some .000
FRN A FRN A FRN A FRN A FRN A NRN A
FRW A NRN B FRW B FRW B NRW AB FRN A
NRW A NRW C NRW C NRN B F RW AB NRW B
NRN B FRW D NRN D NRW B NRN B FRW B
LSC
none .000 some .000 none .000 some .000 none .000 some .000
F RN A FRN A FRN A F RN A NRN A NRN A
FRW A NRN A NRN B NRN B FRN B F RN B
NRW A NRW B F RW C FRW C NRW C FRW C
NRN B F RW C NRW D NRW C FRW C NRW C
DC F
none .000 some .000 none .000 some .000 none .000 some .000
NRN A NRN A NRN A NRN A NRN A NRN A
F RN B F RN B FRN B FRN B NRW B NRW B
F RW B NRW C F RW C NRW C FRW C FRN C
NRW B F RW D NRW D FRW C FRN C FRW D
BCP
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRN A NRN A NRN A NRN A NRN A
F RW A FRN B FRN B FRN B NRW B F RN B
NRW A NRW C FRW C FRW C FRW BC NRW BC
NRN B FRW D NRW D NRW C FRN C FRW C

 

 

 

 

246

 

Table G-l4:

Execution Method Performance by Scheduling Method for ANPV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANPV OPT
NONE FREQ INFQ

none .000 some .016 none .000 some .070 none .000 some .005

F RN A NRW A FRN A NRW A FRW A NRN A

FRW A NRN A F RW A NRN A FRN AB NRW A

NRW A FRN B NRW B FRN AB NRW B F RW B

NRN B FRW B NRN C F RW B NRN C FRN B
SLK

none .000 some .006 none .000 some .027 none .000 some .002

FRN A NRN A F RN A NRN A NRN A NRN A

F RW A NRW A FRW A NRW AB NRW A NRW A

NRW A FRN B NRN A FRN BC F RW B FRW B

NRN B FRW B NRW B FRW C FRN C FRN B
LFT

none .000 some .007 none .000 some .030 none .000 some .001

F RN A NRN A FRN A NRN A NRN A NRN A

FRW A NRW AB F RW B NRW AB NRW B NRW A

NRW A F RN BC NRN B F RN BC FRW B F RW B

NRN B FRW C NRW C F RW C F RN C FRN B
RSO

none .000 some .017 none .000 some .069 none .000 some .006

F RW A NRW A FRW A NRW A NRW A NRN A

NRW A NRN A FRN B NRN AB FRW A NRW A

F RN B FRN B NRW B FRN AB FRN B FRW B

NRN C F RW B NRN C FRW B NRN C FRN B
LSC

none .000 some .010 none .000 some .042 none .009 some .003

F RW A NRN A FRW A NRN A NRN A NRN A

NRW A NRW A FRN B NRW AB NRW A NRW A

F RN B FRN B NRW B FRN BC FRW A FRW B

NRN C F RW B NRN C F RW C FRN B FRN B
DCF

none .000 some .003 none .000 some .016 none .000 some .002

NRN A NRN A NRN A NRN A NRN A NRN A

FRN B NRW AB FRN B NRW AB NRW B NRW A

FRW B FRN BC FRW C FRN BC FRW C FRN B

NRW B F RW C NRW D F RW C FRN C F RW B
BCP

none .000 some .005 none .000 some .026 none .000 some .001

FRN A NRN A NRN A NRN A NRN A NRN A

F RW A NRW A FRN B NRW AB NRW B NRW A

NRW A FRN B FRW C F RN BC F RW BC FRW B

NRN B FRW B NRW D FRW C FRN C FRN B

 

 

 

 

247

 

Table G-lS:

Execution Method Performance by Scheduling Method for RNPV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RNPV OPT
NONE FREQ INFQ
none .000 some .016 none .000 some .070 none .000 some .005
FRN A NRN A FRN A NRW A F RW A NRN A
FRW A NRW A FRW A NRN AB FRN AB NRW A
NRW A FRN AB NRW B FRN AB NRW B FRW B
NRN B FRW B NRN C FRW B NRN C FRN B
SLK
none .000 some .006 none .000 some .028 none .000 some .002
F RN A NRN A FRN A NRN A NRN A NRN A
FRW A NRW AB F RW AB NRW AB NRW A NRW A
NRW A FRN BC NRN B F RN BC FRW B FRW B
NRN B FRW C NRW C FRW C F RN C F RN B
LFT
none .000 some .007 none .000 some .029 none .000 some .001
FRN A NRN A F RN A NRN A NRN A NRN A
FRW A NRW AB FRW B NRW AB NRW B NRW A
NRW A F RN BC NRN B FRN BC FRW BC FRN B
NRN B FRW C NRW C F RW C FRN C FRW B
RSO
none .000 some .017 none .000 some .069 none .000 some .006
FRW A NRW A FRW A NRW A NRW A NRN A
NRW A NRN A FRN B NRN AB FRW A NRW A
F RN B FRN B NRW B F RN AB FRN B F RW B
NRN C FRW B NRN C FRW B NRN C FRN B
LSC
none .000 some .010 none .000 some .042 none .015 some .003
F RW A NRN A FRW A NRN A NRN A NRN A
NRW A NRW A FRN B NRW AB NRW A NRW A
FRN B FRN B NRW B FRN BC F RW A FRW B
NRN C FRW B NRN C F RW C F RN B FRN B
DCF
none .000 some .003 none .000 some .016 none .000 some .002
NRN A NRN A NRN A NRN A NRN A NRN A
FRN B NRW AB F RN B NRW AB NRW B NRW A
FRW B FRN BC FRW C FRN BC F RW C FRN B
NRW B FRW C NRW D F RW C FRN C FRW B
BCP
none .000 some .005 none .000 some .026 none .000 some .001
FRN A NRN A NRN A NRN A NRN A NRN A
F RW A NRW A FRN B NRW AB NRW B NRW A
NRW A FRN B FRW C FRN B FRW BC FRW B
NRN B F RW B NRW D F RW B F RN C F RN B

 

 

 

 

248

 

Table G-l6:

Execution Method Performance by Scheduling Method for WADL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDL OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .026
FRN A F RN A FRN A F RN A FRW A FRN A
FRW A NRN B FRW B FRW B FRN AB NRN A
NRW A NRW B NRW C NRW C NRW B NRW AB
NRN B FRW C NRN D NRN D NRN C F RW B
SLK
none .000 some .000 none .000 some .000 none .024 some .000
FRN A FRN A FRN A F RN A NRW A NRN A
F RW A NRN A F RW A NRN B FRW A FRN B
NRW A NRW B NRW B F RW B NRN A NRW B
NRN B F RW C NRN C NRW B FRN B FRW C
LFT
none .000 some .000 none .000 some .000 none .127 some .000
F RN A NRN A FRN A FRN A NRN A NRN A
FRW A FRN A FRW B F RW B NRW AB FRN B
NRW A NRW B NRW C NRW BC FRW AB NRW B
NRN B FRW C NRN D NRN C F RN B FRW C
RSO
none .000 some .000 none .000 some .000 none .001 some .000
FRN A FRN A FRN A FRN A F RN A NRN A
FRW A NRN B FRW B FRW B NRW AB FRN A
NRW A NRW C NRW C NRW B FRW BC NRW B
NRN B F RW D NRN D NRN C NRN C F RW C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRN A F RN A FRN A FRN A NRN A NRN A
FRW A NRN B FRW B NRN B FRN B FRN B
NRW A NRW C NRW C FRW C NRW C NRW C
NRN B FRW D NRN D NRW C FRW C FRW C
DCF
none .000 some .000 none .000 some .000 none .868 some .000
FRN A NRN A FRN A FRN A F RW A NRN A
FRW A FRN B FRW B NRN B NRN A FRN B
NRW A NRW C NRW C F RW BC NRW A NRW C
NRN B FRW D NRN D NRW C FRN A F RW C
BCP
none .000 some .000 none .000 some .000 none .000 some .000
F RN A NRN A F RN A FRN A NRN A NRN A
FRW A FRN B FRW B NRN B NRW B FRN B
NRW A NRW C NRW C FRW C FRW B NRW B
NRN B FRW D NRN D NRW C FRN B FRW C

 

 

 

 

 

 

249

 

Table G-l7:

Execution Method Performance by Scheduling Method for WADE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDE OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
F RN A FRW A F RW A FRW A F RW A F RW A
FRW A NRW A NRW A NRW A NRW A NRW A
NRW A FRN B FRN A F RN B FRN A FRN B
NRN B NRN C NRN B NRN C NRN B NRN C
SLK
none .000 some .000 none .000 some .000 none .000 some .000
FRN A F RW A F RW A FRW A FRW A FRW A
FRW A NRW A NRW A NRW A NRW A NRW A
NRW A F RN B FRN A FRN B FRN A FRN B
NRN B NRN C NRN B NRN C NRN B NRN C
LFT
none .000 some .000 none .000 some .000 none .000 some .000
F RN A FRW A FRW A FRW A F RW A FRW A
FRW A NRW A NRW A NRW A NRW A NRW A
NRW A FRN B FRN A FRN B FRN A FRN B
NRN B NRN C NRN B NRN C NRN B NRN C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
FRW A FRW A FRW A F RW A FRW A FRW A
NRW A NRW A NRW A NRW A NRW A NRW A
F RN B FRN B FRN B F RN B FRN B FRN B
NRN C NRN C NRN C NRN C NRN C NRN C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRW A F RW A F RW A F RW A FRW A FRW A
NRW A NRW A NRW A NRW A NRW A NRW A
FRN B FRN B FRN B FRN B FRN B FRN B
NRN C NRN C NRN C NRN C NRN C NRN C
DCF
none .000 some .000 none .000 some .000 none .000 some .000
F RN A F RW A F RW A FRW A FRN A F RW A
FRW A NRW A NRW A NRW A NRW A NRW A
NRW A FRN B F RN A FRN B F RW A FRN B
NRN B NRN C NRN B NRN C NRN B NRN C
BCP
none .000 some .000 none .000 some .000 none .000 some .000
F RN A F RW A FRW A F RW A F RW A FRW A
FRW A NRW A NRW A NRW A NRW A NRW A
NRW A FRN B FRN A FRN B FRN A FRN B
NRN B NRN C NRN B NRN C NRN B NRN C

 

 

 

 

 

 

250

 

Table G-18:

Execution Method Performance by Scheduling Method for WADC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WDC OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A F RN A FRN A F RW A NRW A
FRW A FRW A FRW B FRW A FRN A FRN A
NRW A FRN B NRW C NRW B NRW A FRW A
NRN B NRN C NRN D NRN C NRN B NRN B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A F RN A F RN A NRW A NRW A
FRW A FRW B F RW A FRW A FRW A F RN B
NRW A FRN C NRW B NRW A F RN B FRW B
NRN B NRN D NRN C NRN B NRN C NRN C
LFT
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A FRN A FRN A NRW A NRW A
FRW A FRW B FRW B FRW AB FRW A FRN B
NRW A FRN C NRW C NRW B FRN A FRW B
NRN B NRN D NRN D NRN C NRN B NRN B
RSO
none .000 some .000 none .000 some .000 none .000 some .000
F RW A NRW A FRW A F RW A NRW A NRW A
NRW A FRW B NRW B NRW AB FRW A FRW B
F RN B F RN C FRN C FRN B FRN B FRN C
NRN C NRN D NRN D NRN C NRN C NRN D
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A FRW A FRW A NRW A NRW A
NRW A FRW B NRW B NRW A FRW A F RW B
FRN B FRN C FRN C FRN B FRN B FRN C
NRN C NRN D NRN D NRN C NRN C NRN D
DC F
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A F RN A FRN A FRW A NRW A
FRW A FRW B F RW B FRW A NRW A FRW A
NRW A F RN C NRW C NRW A F RN A FRN A
NRN B NRN D NRN D NRN B NRN B NRN B
BC P
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A F RN A FRN A NRW A NRW A
FRW A FRW B FRW B FRW AB FRW A FRN B
NRW A FRN C NRW C NRW B FRN A F RW B
NRN B NRN D NRN D NRN C NRN B NRN C

 

 

 

 

251

 

Table G-l9:

Execution Method Performance by Scheduling Method for POIC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIC OPT
NONE FREQ [NF Q
none .000 some .000 none .000 some .000 none .000 some .086
FRN A FRN A FRN A FRN A NRW A NRW A
F RW A NRW A F RW A FRW B FRW AB FRN AB
NRW A FRW B NRW B NRW C F RN B NRN B
NRN B NRN C NRN C NRN D NRN C FRW B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
F RN A NRW A FRN A F RN A NRW A NRN A
FRW A FRN A FRW A FRW B NRN A NRW B
NRW A FRW B NRW B NRW B FRW A FRN C
NRN B NRN C NRN C NRN C F RN B FRW C
LFT
none .000 some .003 none .000 some .000 none .000 some .000
F RN A FRN A FRN A FRN A NRN A NRN A
FRW A NRW A F RW B FRW B NRW AB NRW B
NRW A NRN B NRW B NRW B FRW BC FRN C
NRN B F RW B NRN C NRN C F RN C FRW C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
F RW A NRW A FRW A FRW A NRW A NRW A
NRW A FRW B NRW B NRW A FRW B FRW B
FRN B F RN C F RN C FRN B FRN C FRN C
NRN C NRN D NRN D NRN C NRN D NRN C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A F RW A F RW A NRW A NRW A
NRW A F RW B NRW B NRW A F RW B FRW B
FRN B F RN C F RN C F RN B NRN C NRN C
NRN C NRN D NRN D NRN C F RN D FRN D
DCF
none .000 some .000 none .000 some .000 none .000 some .000
F RN A NRW A FRN A FRN A NRW A NRN A
FRW A FRN B FRW B FRW B NRN AB NRW A
NRW A FRW B NRW C NRW B F RW B FRN B
NRN B NRN B NRN D NRN C FRN B FRW B
BCP
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A F RN A FRN A NRW A NRN A
F RW A F RN AB FRW B FRW B NRN A NRW B
NRW A NRN BC NRW C NRW BC FRW AB FRN B
NRN B F RW C NRN D NRN C FRN B F RW C

 

 

 

 

252

 

Table G-20:

Execution Method Performance by Scheduling Method for POIR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POIR OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .086
FRN A F RN A FRN A F RN A NRW A NRW A
FRW A NRW A FRW A F RW B F RW AB FRN AB
NRW A FRW B NRW B NRW C FRN B NRN B
NRN B NRN C NRN C NRN D NRN C FRW B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A FRN A FRN A NRW A NRN A
FRW A FRN A F RW A FRW B NRN A NRW B
NRW A FRW B NRW B NRW B F RW A F RN C
NRN B NRN C NRN C NRN C FRN B FRW C
LFT
none .000 some .000 none .000 some .000 none .000 some .000
FRN A F RN A F RN A FRN A NRN A NRN A
FRW A NRW A FRW B FRW B NRW AB NRW B
NRW A NRN B NRW B NRW B FRW BC FRN C
NRN B FRW B NRN C NRN C FRN C FRW C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A FRW A FRW A NRW A NRW A
NRW A F RW B NRW B NRW A FRW B FRW B
FRN B F RN C F RN C FRN B F RN C FRN C
NRN C NRN D NRN D NRN C NRN D NRN C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A F RW A FRW A NRW A NRW A
NRW A FRW A NRW B NRW A F RW B FRW B
FRN B F RN B F RN C FRN B NRN C NRN C
NRN C NRN C NRN D NRN C FRN D FRN D
DCF
none .000 some .000 none .000 some .000 none .021 some .000
FRN A NRW A FRN A FRN A NRW A NRN A
FRW A F RN B F RW B FRW B NRN AB NRW A
NRW A FRW B NRW C NRW B F RW B FRN B
NRN B NRN B NRN D NRN C FRN B FRW B
BCP
none .000 some .000 none .000 some .000 none .059 some .000
FRN A NRW A F RN A FRN A NRW A NRN A
F RW A FRN AB F RW B F RW B NRN AB NRW B
NRW A NRN BC NRW C NRW BC FRW AB FRN B
NRN B F RW C NRN D NRN C FRN B FRW C

 

 

 

 

253

 

Table G-Zl:

Execution Method Performance by Scheduling Method for POOC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOC OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .008
FRN A NRW A FRN A FRN A NRW A NRW A
FRW A FRN B F RW A NRW B FRW AB NRN AB
NRW A FRW B NRW B FRW B F RN B FRN B
NRN B NRN C NRN C NRN C NRN C FRW B
SLK
none .000 some .000 none .000 some .001 none .000 some .000
FRN A NRW A FRN A FRN A NRW A NRN A
F RW A F RN B F RW A NRW AB NRN A NRW B
NRW A F RW B NRW B FRW B FRW A FRN C
NRN B NRN B NRN C NRN C FRN B F RW C
LFT
none .000 some .007 none .000 some .000 none .000 some .000
FRN A NRW A F RN A FRN A NRN A NRN A
FRW A F RN B FRW B NRW B NRW AB NRW B
NRW A NRN B NRW B FRW B FRW BC FRN C
NRN B FRW B NRN C NRN C F RN C FRW C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A FRW A NRW A NRW A NRW A
NRW A FRW B NRW B FRW A F RW B FRW B
FRN A FRN C FRN C FRN B FRN C NRN C
NRN B NRN D NRN D NRN C NRN D F RN C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
F RW A NRW A FRW A NRW A NRW A NRW A
NRW A F RW B NRW B F RW A FRW B FRW B
FRN B FRN C F RN C FRN B NRN C NRN C
NRN C NRN D NRN D NRN C FRN D FRN D
DCF
none .000 some .000 none .000 some .004 none .021 some .000
FRN A NRW A F RN A F RN A NRW A NRN A
FRW A F RW B FRW B NRW A NRN AB NRW A
NRW A NRN B NRW C FRW AB FRW B F RN B
NRN B F RN B NRN D NRN B F RN B F RW B
BCP
none .000 some .000 none .000 some .000 none .060 some .000
FRN A NRW A F RN A FRN A NRW A NRN A
FRW A NRN B FRW B NRW B NRN A NRW B
NRW A FRN B NRW C FRW B FRW AB F RN BC
NRN B FRW B NRN D NRN B F RN B F RW C

 

 

 

 

254

 

Table G-22:
Execution Method Performance by Scheduling Method for POOR

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POOR OPT
NONE FREQ INFQ
none .000 some .000 none .000 some .000 none .000 some .008
F RN A NRW A FRN A FRN A NRW A NRW A
FRW A FRN B F RW A NRW B F RW AB NRN AB
NRW A FRW B NRW B FRW B FRN B FRN B
NRN B NRN C NRN C NRN C NRN C FRW B
SLK
none .000 some .000 none .000 some .000 none .000 some .000
FRN A NRW A FRN A FRN A NRW A NRN A
FRW A FRN B FRW A NRW AB NRN A NRW B
NRW A FRW B NRW B FRW B F RW A FRN C
NRN B NRN B NRN C NRN C FRN B FRW C
LFT
none .000 some .007 none .000 some .000 none .000 some .000
F RN A NRW A FRN A FRN A NRN A NRN A
FRW A FRN B FRW B NRW B NRW AB NRW B
NRW A NRN B NRW B FRW B F RW BC FRN C
NRN B FRW B NRN C NRN C FRN C FRW C
RSO
none .000 some .000 none .000 some .000 none .000 some .000
FRW A NRW A FRW A NRW A NRW A NRW A
NRW A FRW B NRW B F RW A FRW B FRW B
FRN B FRN C FRN C FRN B FRN C NRN C
NRN C NRN D NRN D NRN C NRN D FRN C
LSC
none .000 some .000 none .000 some .000 none .000 some .000
F RW A NRW A F RW A NRW A NRW A NRW A
NRW A F RW B NRW B FRW A F RW B FRW B
F RN B F RN C F RN C FRN B NRN C NRN C
NRN C NRN D NRN D NRN C FRN D FRN D
DCF
none .000 some .000 none .000 some .004 none .021 some .000
FRN A NRW A F RN A FRN A NRW A NRN A
FRW A FRW B FRW A NRW A NRN AB NRW A
NRW A NRN B NRW B FRW AB F RW B FRN B
NRN B FRN B NRN C NRN B F RN B FRW B
BCP
none .000 some .000 none .000 some .000 none .059 some .000
FRN A NRW A FRN A F RN A NRW A NRN A
FRW A NRN B FRW B NRW B NRN A NRW B
NRW A FRN B NRW C FRW B FRW AB F RN BC
NRN B F RW B NRN D NRN B FRN B F RW C

 

 

 

 

255

 

 

APPENDIX H

DIFFERENCES IN RANKED PERFORMANCE

256

Table H-l:
Tally of Differences in Ranks: Scheduling by Execution (Traditional)

NONE 1N NONE SOME

+
+
+
+
+
+
+
+
+

 

257

Tally of Differences in Ranks: Scheduling by Execution (Stability)

Table H-Z:

 

NONE

FREQ

INFQ

NONE

SOME

 

WADE

FRN

+

+

 

FRW

 

NRN

+

+

 

NRW

 

WADL

FRN

 

FRW

++

 

NRN

+++

 

NRW

+ r

+++-

 

WADC

FRN

 

FRW

+ r

+ r

 

NRN

 

NRW

+ r

 

POIC

FRN

 

+++-

+ r

+++++.

 

NRN

 

N RW

+ r

 

POIR

FRN

 

FRW

+++-

+ r

+++-

 

NRN

+++++++++-

 

NRW

+

 

FRN

+++.

 

FRW

 

NRN

 

NRW

++.

 

POOR

 

FRN

 

FRW

+++-

 

NRN

+

 

 

N RW

 

 

+

 

 

+++++++++-

 

+

 

 

258

 

Table H-3:
Tally of Differences in Ranks: Execution by Scheduling (Traditional)

 

NONE FREQ INFQ NONE SOME
FRN - + - - +
FRW - - - - -
NRN + - - +
NRW -
FRN -
FRW -
NRN +
NRW -
FRN -
FRW -
NRN +
NRW -
FRN -
FRW -
NRN +
NRW -
FRN -
FRW -
NRN +
NRW -
FRN -
FRW -
NRN +
NRW -
FRN -
FRW -
NRN +
NRW -

 

 

 

+

 

WADE

 

 

++
++

 

WADL
+ + +

 

+r
+r
+++-

 

 

+r
+r

 

WADC

 

 

 

+++.
+r+r
+++++-

 

POIC

 

+ r

 

 

+++u
+r
+++-

 

POIR

 

+++++++++u

+

 

 

+++-
I

 

 

POOC

++-

 

 

+++.
I

 

POOR
+

 

+
+++++++++u

+
+
+

 

 

 

 

 

 

 

 

 

259

Table 114:
Tally of Differences in Ranks: Execution by Scheduling (Stability)

NONE IN NONE SOME
OPT
SLK
LFT
RSO
LSC
DC F
BC P
OPT
SLK
LFT
RSO
LSC
DCF
BC P
OPT
SLK
LFT
RSO

+++++++n

++-++++++++-

DCF

OPT

++++-

LFT

++++++.++++++.

++++++-

+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

+++.

 

260

APPENDIX I

PROJECT PROBLEM NETWORKS

261

 

          
 
         

4.3.3.1 .
ebWKOVI ’ Q '9 "‘\

4986. «Viv «\J) 9
u I» .x‘ ‘4
A‘s awe/«N

 
 

9

4494 be

 

 

 

 

 

 

 

 

 

APPENDIX J

GPSS/I—I SIMULATION LISTINGS

270

 

*‘k'ki*i‘itiiii'ki'***************************************************************

PR01.GPS — A Project Simulator

i*I'OI'I‘R'I'OI'I'I-I'ii‘fififififiifiififiifi‘fifiil’fi##I-l-Wfl'tfi

*

Planning:
Execution:

>PROl:
PROZ:
PRO3:
PRO4:

Full Reservation—Wait
Full Reservation-No Wait (lock partial resources/go when feasible)
No Reservation-Wait (lock iff fully avail/wait till schedule)

No Reservation—No Wait

Per schedule from POLB (priority based on SST)
Full Reservation (tech feas act's lock resources when avail)
No Waiting (act's advance when feas,

even if SST not expired)

(lock partial resources/wait till schedule)

(lock iff fully avail/go when feasible)

POLB: file containing problem data sets

SIMPOLl:

MH$DAT1=
MBSDATZ:
MLSDAT3:
ML$DT:

RN(1):
RN(2):
RN(3):
RN(4):

&SPD:
&DIS:

&L:
&M:

TECH:
RESO:

PBSANUM:
PBSRESx:
PB$FEZ:
PB$TOT:
PHSSST:
PL$DUR:

BETA

reserved

file written to with simulation results

matrix containing problem data from POLB

sparse matrix representing activity feasibility

matrix containing simulation output to write to SIMPOLl
matrix accumulating downtime

(total time) of resource 1, 2 or 3

duration of activities as sampled by BETA function
down time of activities as sampled by ADVANCE (rvexpo) block

variability (spread) ratio of activity durations
number of expected disruptions to each resource during project

number of individual problems read from the POLB data file
number of simulation repetitions of each individual problem

chain holding technical/time infeasible activities (first stage)
chain holding resource infeasible activities (second stage)

SIMULATE

REALLOCATE
REALLOCATE
REALLOCATE
REALLOCATE
REALLOCATE
REALLOCATE
REALLOCATE
REALLOCATE

INTEGER
INTEGER
REAL
CHAR*8

FUNCTION

FMS,0
FSV,0
GRP,0
HSV,0
LOG,0
QUE,0
TAB,O

COM,25008

number of resources (storage)
number of precedence activities remaining for activity start
"tote" counter for looping and xact management

scheduled start time from POLB (used for chain order)

1'
'k
i
i
i
t
i
*
i
i
i
i
i
i
*
*
*
i
i
*
up time of storages as sampled by ADVANCE (rvexpo) block *
t
*
*
i
i
*
t
*
i
t
t
i
*
*
i
i
*
activity duration from beta distributed around POLB duration *
*

*

activity number (per problem data matrix)

remaining for activity start

**********************iti'i'ii'ii*iiiiiiri'kt*******i'ki*************************

&I,&J,&K,&L,&M,&SPD1,&DISl,&PREC,&NACT,&NRES
&D4,&R1,&R2,&R3,&NTR1,&NTR2,&NTR3
&DUR,&SPD,&MRK,&SFT,&D,&DS,&DIS,&TMR

&D2,&D3

RN(3).C8
0,0/0.02,0.03/0.14,0.11/0.67,0.41/0.85,0.56/0.94,0.68/0.99,0.81/l,1

271

 

 

*
iii***********i******i*******i**********

* technical/time feasibility
*

RELT BVARIABLE ((PBSFEZ)'E'(O))
*
**ittiiiiitii*ii******iii*****t***ii*tit
* resource (storage) feasibility
i
RELR BVARIABLE ((PBSRESl)'E'(0))*((PB$RESZ)'E'(0))*((PB$RES3)'E'(0))
*
i*itit*ittiiiii*iiiiiiitt*******tii*iit*itiit********iiiiittiiitiitttitiiitit
* Dynamic Program Code *
itiitttti*tiiittiiii*************i***tttittiittitii*ittt*iittiiiiitiiititiiti
*

GENERATE ,,,&NACT,,OPF,1PH,6PB,1PL
*
******************iiititiittiittiiiiiiii

* assign actnum, resource requirements,

* schedstart, and duration
*

BLET &K=&K-1
ASSIGN ANUM,&K,PB
*
ASSIGN RESI,MH$DAT1(PB$ANUM,9),PB
ASSIGN RE82,MH$DAT1(PB$ANUM,10),PB
ASSIGN RESB,MH$DAT1(PB$ANUM,11),PB
*
ASSIGN SST,MH$DAT1(PB$ANUM,2),PH
*
BLET &DUR=MH$DAT1(PB$ANUM,3)*(1-(&SPD/3)+&SPD*FN(BETA))
ASSIGN LGT,&DUR,PL
*
TEST G PB$ANUM,1,WRIT * start node skip to end (writ)
*
BLET &TMR=FLT(PH$SST)
TEST G &TMR,AC1,CKFZ * if SST<=AC1, skip next else
ADVANCE &TMR-AC1 * wait until SST=AC1 then

*
******iiii****************t********i**i*
********iiittiiii*ti******i******ii****i

* update technical feasibility

* sum undone prec activities for self
*

CKFZ ASSIGN TOT,&NACT,PB
BLET &PREC=0

CKPR BLET &PREC=&PREC+MB$DAT2(PB$TOT,PB$ANUM)
LOOP TOT$PB,CKPR
ASSIGN FEZ,&PREC,PB

*
‘******i*iiit******i******************iii
'*****Qiii*******i*iii*****i********i**ii

* update resource feasibility and start

* this activity if all feas satisfied
*

TEST GE R1,PB$RESl,ELSl
BLET &NTR1=PB$RESI
TRANSFER ,ELSZ

ELSl BLET &NTR1=R1

272

 

ELSZ

ELS3

ELS4

ELSS

EL86

LWAT
CKRS

RESUl
RESU2

*

TEST GE
BLET
TRANSFER
BLET

TEST GE
BLET
TRANSFER
BLET

ASSIGN
ASSIGN
ASSIGN

ENTER
ENTER
ENTER

TEST E
LINK
TEST E

MARK

TEST E
ADVANCE
TRANSFER

ADVANCE
LEAVE
LEAVE
LEAVE

R2,PB$RESZ,EL83
&NTR2=PB$RESZ
,ELS4

&NTR2=R2

R3,PB$RESB,ELSS
&NTR3=PB$RE33
,ELSG

&NTR3=R3

RESl-,&NTR1,PB
RESZ-,&NTR2,PB
RES3-,&NTR3,PB

1,&NTR1
2,&NTR2
3,&NTR3

BV$RELT,0,CKRS
WAIT,SST$PH
BV$RELR,1,LWAT

&SPD,&DIS,RESU1
PL$LGT-(AC1-(FIX(AC1)))
,RESU2

PL$LGT
l,MH$DATl(PB$ANUM,9)
2,MH$DAT1(PB$ANUM,10)
3,MH$DAT1(PB$ANUM,11)

**'kii'k*‘tiiiiit*i************************

*i'i’i'*ii‘tiiii‘fiii‘ki‘k‘kiii'k'ki'k'ki************

* write activity information to raw matrix

*
WRIT

*

BLET

BLET

MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE

&MRK=AC1—Ml
&SFT=MH$DAT1(PB$ANUM,2)+MH$DAT1(PB$ANUM,3)
DAT3,PB$ANUM,1,PB$ANUM,ML
DAT3,PB$ANUM,2,PH$SST,ML
DAT3,PB$ANUM,3,&MRK,ML
DAT3,PB$ANUM,4,&SFT,ML
DAT3,PB$ANUM,5,AC1,ML
DAT3,PB$ANUM,6,MH$DAT1(PB$ANUM,3),ML
DAT3,PB$ANUM,7,PL$LGT,ML
DAT3,PB$ANUM,8,MH$DAT1(PB$ANUM,9),ML
DAT3,PB$ANUM,9,MH$DAT1(PB$ANUM,10),ML
DAT3,PB$ANUM,10,MH$DAT1(PB$ANUM,11),ML

fink*********************i************tii

*********i’i************************it'h'kt

e update prec feas matrix for followers

*

 

.ASSIGN TOT,&NACT,PB
ZERO MSAVEVALUE DAT2,PB$ANUM,PB$TOT,O,MB
LOOP TOT$PB,ZERO

*
ti****i*i’**iii-************i*************

* kick all activities to tech/resource

273

 

(& start if qual)

UNLINK WAIT,CKFZ,ALL

ADVANCE 0.0001

*
*tiiiiiii*itiitiiit*********************
* act 1 goes to clone for disruptions
*

TEST G PB$ANUM,1,DRUP

DIE TERMINATE l

*
****************************************

*ttiii*titi*i******i*****i*i**ti*i******

* dummy start activity (and clones) now

* generate some disruptions
*

DRUP SPLIT &R1-1,NEXT1,ANUM$PB
SPLIT &R2,NEXT2,ANUM$PB
SPLIT &R3,NEXT3,ANUM$PB
TRANSFER ,NEXTl
*
NEXT3 ASSIGN ANUM,3,PB
TRANSFER ,NEXT
NEXTz ASSIGN ANUM,2,PB
TRANSFER ,NEXT
NEXTl ASSIGN ANUM,1,PB
*
NEXT PRIORITY 1
*
CYCL UNLINK WAIT,CKFZ,ALL
ADVANCE 0.0001
*
TEST E &DIS,0,CYCL2
TERMINATE o
*
CYCLZ ADVANCE RVEXPO(2,&D) * uptime (huge, 15, 5)
TEST GE R(PB$ANUM),1,CYCL2
ENTER PB$ANUM,1
MARK
ADVANCE RVEXPO(4,3/(&DIS+0.0001)) * downtime (huge, 3, 1)
LEAVE PB$ANUM,1
MSAVEVALUE DT+,1,PB$ANUM,M1,ML
TEST GE N$DIE,&NACT-1,CYCL
TRANSFER ,DIE

*

i*****i***********************i********t*i***i********ii*********************

*

i

*

Program Execution & Control
titiiii*iittiitti*************iti*tiittttit*******************************i**

DO

&L=1,18

*****ii*********************i********i**

* read input file,

*

DATl
DAT2
DAT3
DT

GETLIST
MATRIX
MATRIX
MATRIX
MATRIX

set feas & out matrix

FILE=POLB,&NACT,&NRES,&D2
MH,&NACT,11
MB,&NACT,&NACT
ML,&NACT,10

ML,1,3

274

i t O O

t

* number of problems read from POLB

input matrix

feasibility matrix

raw output matrix
resource downtime matrix

 

GETLIST FILE=POLB,&D3,&Rl,&R2,&R3,&D4,&D5

GETLIST FILE=POLB,(((MH$DAT1(&I,&J),&J=l,ll),&I=l,&NACT))
e
*eeeeeeeeteeeeeeeeeeee*teeeeeeeeeeeeeeee

* set multiple runs over the multiple

* values of variability and disruption
*

DO &SPD1=0,1,1 * set multiple values of spread
LET &SPD=&SPD1*O.6 * adjust to O, .6 (IO-2+4)
*
DO &DISl=O,2,1 * set multiple values of disruption
IF &DISl=2 * factor to be 0, 1, 3
LET &DISl=&DISl+l
ENDIF
LET &DIS=&DISl*l.0 * format &DISl to real &DIS
LET &D=15/(&DIS+0.0001) * dis factor (0, 1, 3)->(M, 15, 5)
*
DO &M=1,35 * number of reps for each problem

*
iti*iitiiitfirii*tiiirk*tiiiiiiitiiiri'kitti
* initialize feasibility matrix

*

DO &I=l,&NACT

DO &J=4,8

IF (MHSDATI(&I,&J))'G'(0l
INITIAL MBSDATZ(&I,MH$DAT1(&I,&J)),1
ELSE

ENDIF

ENDDO

ENDDO

*
*i'******iiiiiiitti’t‘kiitiitiii*iiitiitiii

* set initial run conditions
i

STORAGE Sl,&Rl/SZ,&R2/S3,&R3
*

LET &K=&NACT+1
*

START &NACT-l

*
iii”.'k***********iii'kiiii’i‘biiti*********t

* end of run file writing
*

PUTPIC FILE=SIMPOL1,&D2,&SPD,&DIS,ML$DT(1,1),MLSDT(1,2),MLSDT(1,3)
******** *.* ** ****.** **fi.** ****.*'k
*

Do &I=1,&NACT

PUTPIC FILE=SIMPOL1,ML$DAT3(&I,l),ML$DAT3(&I,2),MLSDAT3(&I,3),_

MLSDATB(&I,4),ML$DAT3(&I,5),ML$DAT3(&I,6),ML$DAT3(&I,7),ML$DAT3(&I,8),_
ML$DAT3 (&I , 9) , ML$DAT3 (&I , 10)

*ii’ iii ***.** *** ***.** ii **.** *‘t *i' if

ENDDO
PUTSTRING FILE=SIMPOL1,(")

RMULT &M*124,&M*124,&M*124,&M*124
CLEAR MHSDATI

*
******************i*********************

275

 

* boundaries of multiple runs
*

ENDDO * &M; number of reps of each problem
*
ENDDO * &DIS; disruption level
*
ENDDO * &SPD; variability (spread) level
*
ENDDO * &L; number of problems read
1'
END

**i***************************************************i*********************i

PR02.GPS - A Project Simulator

Planning: Per schedule from POL (priority based on SST)
Execution: Full Reservation (tech feas act's lock resources when avail)
No Waiting (act's advance when feas, even if SST not expired)

PROl: Full Reservation-Wait (lock partial resources/wait till schedule)
>PR02: Full Reservation-No Wait (lock partial resources/go when feasible)
PRO3: No Reservation-Wait (lock iff fully avail/wait till schedule)
PRO4: No Reservation-No Wait (lock iff fully avail/go when feasible)

POLB: file containing problem data sets
SIMPOLZ: file written to with simulation results

MHSDATI: matrix containing problem data from POL

MBSDATZ: sparse matrix representing activity feasibility

MLSDATB: matrix containing simulation output to write to SIMPOLZ

MLSDT: matrix accumulating downtime (total time) of resource 1, 2 or 3

RN(l): reserved

RN(2): up time of storages as sampled by ADVANCE (rvexpo) block
RN(3): duration of activities as sampled by BETA function
RN(4): downtime of storages as sampled by ADVANCE (rvexpo) block

&SPD: variability (spread) ratio of activity durations
&DIS: number of expected disruptions to each resource during project

&L: number of individual problems read from the POLB data file
&M: number of simulation repetitions of each individual problem

*1l‘l'ififiiifiiifiiiiflrfifilfitfifitfififi1'

TECH: chain holding technical/time infeasible activities (first stage)
RESO: chain holding resource infeasible activities (second stage)

i
i
i
i
t
i
*
i
i
*
t
i
t
i
i
*
*
i
'k
t
t
*
t
*
i
*
i
*
i
*
t
t
*
pgsamnnu: activity number (per problem data matrix) *
PBSRESx: number of resources (storage) remaining for activity start *
PB$FEZ: number of precedence activities remaining for activity start *
PB$TOT: "tote" counter for looping and xact management *
PH$SST: scheduled start time from POL (used for chain order) *
pLsDUR: activity duration from beta distributed around POLB duration *
*
fir

*****************drift-kit*******ii‘i‘k‘kiii‘kt'kiiiii‘kii*************************

*Irlrl'fil'irfil-l'l'il'

SIMULATE

276

 

REALLOCATE FMS,0
REALLOCATE FSV,0
REALLOCATE GRP,O
REALLOCATE HSV,O
REALLOCATE LOG,O
REALLOCATE QUE,O
REALLOCATE TAB,O
REALLOCATE COM,25008

INTEGER &I,&J,&K,&L,&M,&SPD1,&DISl,&PREC,&NACT,&NRES
INTEGER &D4,&R1,&R2,&R3,&NTR1,&NTRZ,&NTR3

REAL &DUR,&SPD,&MRK,&SFT,&D,&DS,&DIS

CHAR*8 &DZ,&D3

*

BETA FUNCTION RN(3),C8
0,0/0.02,0.03/0.14,0.11/0.67,0.41/0.85,0.56/0.94,0.68/0.99,0.81/1,1
*

*******ittiiiiiiaiitiittiii***i********i

* technical/time feasibility
*

RELT BVARIABLE ((PB$FEZ)'E'(O))

*

ii*iitii******iii**********************t

* resource (storage) feasibility

*

RELR BVARIABLE ((PB$RESl)'E'(0))*((PB$RESZ)'E'(0))*((PB$RESB)'E'(0))

*
*iiitititiiiiit*******t****ttii*tiiitttttit*iitiiii********i*i****iii***ii***

* Dynamic Program Code *
{itt*itiitittiitiitit************i****************************************i*i

*
GENERATE ,,,&NACT,,0PF,1PH,6PB,1PL
*
ittiiiti***ii******************tt*******
* assign actnum, resource requirements,
* schedstart, and duration
*

BLET &K=&K-1
ASSIGN ANUM,&K,PB
*
ASSIGN RESl,MH$DAT1(PB$ANUM,9),PB
ASSIGN RESZ,MH$DAT1(PB$ANUM,10),PB
ASSIGN RE83,MH$DAT1(PB$ANUM,11),PB
*
ASSIGN SST,MH$DAT1(PB$ANUM,2),PH
*
BLET &DUR=MH$DAT1(PB$ANUM,3)*(1-(&SPD/3)+&SPD*FN(BETA))
ASSIGN LGT,&DUR,PL
*
TEST G PB$ANUM,1,WRIT * start node skip to end (writ)
LINK WAIT,SST$PH

*
*itiOWHkt***tiiiiti*********************i

ti**tt*t****i**************i********t***
e update technical feasibility
«e sum undone prec activities for self

*

CKFZ .ASSIGN TOT,&NACT,PB
BLET‘ &PREC=O
CKPR BLET &PREC=&PREC+MB$DAT2 (PB$TOT, PBSANUM)

277

 

*

LOOP
ASSIGN

TOT$PB,CKPR

FEZ,&PREC,PB

i************ii*****i**iiitiiiiiiitiiiii

*iiiiit'k'kiiiitii*ttrkiiiiitiiiii’i'ti'ktiiii

* update resource feasibility and start
* this activity if all feas satisfied

*

ELSl

ELSZ

ELS3

ELS4

ELSS

ELSG

LWAT
CKRS

*

TEST GE
BLET
TRANSFER
BLET

TEST GE
BLET
TRANSFER
BLET

TEST GE
BLET
TRANSFER
BLET

ASSIGN
ASSIGN
ASSIGN

ENTER
ENTER
ENTER

TEST E
LINK
TEST E

MARK
ADVANCE
LEAVE
LEAVE
LEAVE

R1,PB$RESI,ELSI
&NTRl=PB$RESl
,ELSZ

&NTR1=R1

R2,PB$RESZ,ELS3
&NTR2=PB$RESZ
,ELS4

&NTR2=R2

R3,PB$RES3,ELSS
&NTR3=PB$RE83
,EL86

&NTR3=R3

RESl-,&NTR1,PB
RESZ-,&NTR2,PB
RESB-,&NTR3,PB

1,&NTR1
2,&NTR2
3,&NTR3

BV$RELT,0,CKRS
WAIT,SST$PH
BV$RELR,1,LWAT

PL$LGT
1,MH$DAT1(PB$ANUM,9)
2,MH$DAT1(PB$ANUM,10)
3,MH$DAT1(PB$ANUM,11)

t**************i’iiflkfiiiiifiiiifii'k'k'kiiiitii

it*i'**'k*i'iiiriii'kii*i'ii'kii'kiiii'kiiiiitiii

* write activity information to raw matrix

*
WRIT

*

BLET

BLET

MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE
MSAVEVALUE

&MRK=AC1-Ml
&SFT=MH$DAT1(PB$ANUM,2)+MH$DAT1(PB$ANUM,3)
DAT3,PB$ANUM,1,PB$ANUM,ML
DAT3,PB$ANUM,2,PH$SST,ML
DAT3,PB$ANUM,3,&MRK,ML
DAT3,PB$ANUM,4,&SFT,ML
DAT3,PB$ANUM,S,AC1,ML
DAT3,PB$ANUM,6,MH$DAT1(PB$ANUM,3),ML
DAT3,PB$ANUM,7,PL$LGT,ML
DAT3,PB$ANUM,8,MH$DAT1(PB$ANUM,9),ML
DAT3,PB$ANUM,9,MH$DAT1(PB$ANUM,10),ML
DAT3,PB$ANUM,10,MH$DAT1(PB$ANUM,11),ML

**g.*****************iiii‘tiiiti’ii’iiiii'kii

************************i********t******

278

 

* update prec feas matrix for followers

*

ZERO

*

ASSIGN
MSAVEVALUE

LOOP

TOT,&NACT,PB
DAT2,PB$ANUM,PB$TOT,O,MB
TOT$PB,ZERO

*‘ki'iiii'i'kii'iiiiii**************i********

* kick all activities to tech/resource

* (& start if qual)

*

*

UNLINK

ADVANCE

WAIT,CKFZ,ALL

0.0001

***********i‘t‘kii‘kiiii*ittiiit'ttii'kiiti‘it

* act 1 goes to Clone for disruptions

*

DIE

*

TEST G
TERMINATE

PB$ANUM,1,DRUP

l

************************************i***

*******************itirt'kifitti'kiiit'kti'iii

* dummy start activity (and clones) now
* generate some disruptions

*

DRUP

NEXT3

NEXTZ

NEXTl

NEXT

CYCL

CYCL2

*

SPLIT
SPLIT
SPLIT
TRANSFER

ASSIGN
TRANSFER
ASSIGN
TRANSFER
ASSIGN

PRIORITY

UNLINK
ADVANCE

TEST E
TERMINATE

ADVANCE
TEST GE
ENTER
MARK
ADVANCE
LEAVE

MSAVEVALUE

TEST GE
TRANSFER

&Rl-1,NEXT1,ANUM$PB

&R2,NEXT2,ANUM$PB
&R3,NEXT3,ANUM$PB

,NEXTl

ANUM,3,PB
,NEXT
ANUM,2,PB
,NEXT
ANUM,1,PB

WAIT,CKFZ,ALL

0.0001

&DIS,O,CYCL2

0

RVEXPO(2.&D)
R(PB$ANUM),1,CYCL2

PB$ANUM,1

RVEXPO(4,3/(&DIS+0.000I))

PB$ANUM,1

* uptime (huge, 15, S)

* downtime (huge, 3, 1)

DT+,1,PB$ANUM,M1,ML
N$DIE,&NACT—1,CYCL

,DIE

***********‘ii’ifiiiirkitfiii‘kiiii'i*ii’itifttiiiiiiiiti****************************

*

Program Execution & Control

*

********************tti**********‘I’fittfiitii****************‘I‘itii'iiiiiiii'iiiiii

*

DO

&L=1,18

* number of problems read from POL

279

 

****************************************

* read input file, set feas & out matrix
*

GETLIST FILE=POLB,&NACT,&NRES,&D2
DATl MATRIX MH,&NACT,11 * input matrix
DAT2 MATRIX MB,&NACT,&NACT * feasibility matrix
DAT3 MATRIX ML,&NACT,10 * raw output matrix
DT MATRIX ML,1,3 * resource downtime matrix
*
GETLIST FILE=POLB,&D3,&R1,&R2,&R3,&D4,&D5
GETLIST FILE=POLB,(((MHSDAT1(&I,&J).&J=1,11),&I=1,&NACT))
*
*i**************************************
* set multiple runs over the multiple
* values of variability and disruption
*
DO &SPD1=0,1,1 * set multiple values of spread
LET &SPD=&SPD1*0.6 * adjust to 0, .6
*
DO &DISl=0,2,1 * set multiple values of disruption
IF &DISl=2 * factor to be 0, 1, 3
LET &DISl=&DISl+1
ENDIF
LET &DIS:&DISl*1.0 * format &DISl to real &DIS
LET &D=15/(&DIS+0.0001) * dis factor (0, 1, 3)->(M, 15, S)
*
DO &M=1,35 * number of reps for each problem

*
****ii‘ii********************************
* initialize feasibility matrix

*

DO &I=1,&NACT

DO &J=4,8

IF (MHSDAT1(&I,&J)l'G'(O)
INITIAL MB$DAT2(&I,MH$DAT1(&I,&J)),1
ELSE

ENDIF

ENDDO

ENDDO

*
*i'i‘ki'kttiiiii***************************

* set initial run conditions
*

STORAGE Sl,&R1/SZ,&R2/S3,&R3
*

LET &K=&NACT+1
*

START &NACT-l

*
'k************************itiii'ki'it'ki'ktt'k

* end of run file writing
*

PUTPIC FILE=SIMPOL2,&D2,&SPD,&DIS,ML$DT(1,1),ML$DT(1,2),ML$DT(1,3)
******** e.* ** ****.** **e*.** *eee.**
*

DO &I=1,&NACT

PUTPIC FILE=SIMPOL2,ML$DAT3(&I,1),ML$DAT3(&I,2),ML$DAT3(&I,3),_

ML$DAT3 (&I . 4) , ML$DAT3 (&I , 5) , ML$DAT3 (&I , 6), ML$DAT3 (&I , 7) .MLsDATB (&I , 3) ,_
ML$DAT3(&I.9).ML$DAT3(&I,10)

*** *** ***.** *ii ***.** it **.** if *i' it

280

 

 

ENDDO
PUTSTRING FILE=SIMPOL2,(")

RMULT &M*124,&M*124,&M*124,&M*124
CLEAR MHSDATI

*
itifif*ittiit‘kii'kiiiiiitiii********iii”.i

* boundaries of multiple runs
*

ENDDO * &M; number of reps of each problem
*
ENDDO * &DIS; disruption level
i
ENDDO * &SPD; variability (spread) level
e
ENDDO * &L; number of problems read
t
END

i'ki'ii************************************************************************

PR03.GPS - A Project Simulator

Planning: Per schedule from POL (priority based on SST)
Execution: No Reservation (FCFS, by priority, of tech feasible act's)
Waiting (act's advance iff BOTH tech and SST conditions met)

PROI: Full Reservation-Wait (lock partial resources/wait till schedule)
PROZ: Full Reservation-No Wait (lock partial resources/go when feasible)
>PRO3: No Reservation-Wait (lock iff fully avail/wait till schedule)
PRO4: No Reservation-No Wait (lock iff fully avail/go when feasible)

POLB: file containing problem data sets
SIMPOL3: file written to with simulation results

MH$DAT1: matrix containing problem data from POLB

MBSDATZ: sparse matrix representing activity feasibility

ML$DAT3: matrix containing simulation output to write to SIMPOL3

MLSDT: matrix accumulating downtime (total time) of resource 1, 2 or 3

RN(l) : reserved

RN(2): up time of storages as sampled by ADVANCE (rvexpo) block
RN(3): duration of activities as sampled by BETA function

RN(4): down time of storages as sampled by ADVANCE (rvexpo) block

&SPD: variability (spread) ratio of activity durations
&DIS: number of expected disruptions to each resource during project

&L: number of individual problems read from the POLB data file
&M: number of simulation repetitions of each individual problem

TECH: chain holding technical/time infeasible activities (first stage)
RESO: chain holding resource infeasible activities (second stage)

PB$ANUM: activity number (per problem data matrix)
PB$RESx: number of resources (storage) remaining for activity start

QDI'I’I'*I'I'I'I’I'*‘Ofi’i‘fifi’fiifitiififittiififi
fitlrtl'I’ll'I'lrlrfl‘fiIfilrfiirtl'ii'I-tl'fifilriivlrl-tlrt

281

* PBSFEZ: number of precedence activities remaining for activity start *
* PB$TOT: "tote" counter for looping and xact management *
* PH$SST= scheduled start time from POL (used for chain order) *
* PL$DUR: activity duration from beta distributed around POLB duration *
i *
*tiiiiiiittiiiititiitfitttttiiii*iiittittttiiiittttiiitt*ttiitti'itiiiii’ittttii

SIMULATE

REALLOCATE FMS,O
REALLOCATE FSV,0
REALLOCATE GRP,0
REALLOCATE HSV,0
REALLOCATE LOG,0
REALLOCATE QUE,0
REALLOCATE TAB,O
REALLOCATE COM,25008

INTEGER &I,&J,&K,&L,&M,&SPD1,&DISl,&PREC,&NACT,&NRES
INTEGER &D4,&Rl,&R2,&R3
REAL &DUR,&SPD,&MRK,&SFT,&D,&D5,&DIS,&TMR
CHAR*8 &D2,&D3
*
BETA FUNCTION RN(3),C8

0,0/0.02,0.03/0.14,0.ll/0.67,0.41/0.BS,0.56/O.94,0.68/0.99,0.81/1,1

*
*****************iiiiiiiiii'fittiiiit‘iiiit

* technical feasibility
*

RELT BVARIABLE

*

((PB$FEZ)'E'(O))

*********************************i******

* resource (storage) feasibility
i

RELR BVARIABLE

*

((PB$RESll'E'(0))*((PB$RESZ)'E'(O))*((PB$RESB)'E'(0))

*ttiii*iiiiiitiiiiit*iitititiitittittttt'ktti*iiiti't'k'kttiid‘iiiitittti*iiiiitii
* Dynamic Program Code *
*ittt************itiiitfiitiiiii********iii*i'ii'iittirtiiittiiii'iitii*iiiitiii'ki

*

GENERATE ,,,&NACT,,OPF,IPH,6PB,1PL

*

i*‘ti'hi*ii'iiiti‘k‘kt*ir'k'tiitiiiiiii*********

* assign actnum, resource requirements,

* schedstart, and duration
*

BLET &K=&K-1
ASSIGN ANUM,&K,PB
*
ASSIGN RESl,MH$DAT1(PB$ANUM,9),PB

 

ASSIGN RESZ,MH$DAT1(PB$ANUM,10),PB
ASSIGN RES3,MH$DAT1(PB$ANUM,11),PB
*
ASSIGN SST,MH$DAT1(PB$ANUM,2),PH
*
BLET &DUR=MH$DAT1(PB$ANUM,3)*(1-(&SPD/3)+&SPD*FN(BETA))
ASSIGN LGT,&DUR,PL
*
TEST G PB$ANUM,1,WRIT * start node skip to end (writ)

*

***************************ii***********

282

 

*itiiii'iiiit'hiiiii*iiiflkiiiitiiiiiitiiiii

* sum undone prec activities for self
i

CKFZ ASSIGN TOT,&NACT,PB
BLET &PREC=0

CKPR BLET &PREC=&PREC+MB$DAT2(PB$TOT,PB$ANUM)
LOOP TOTSPB,CKPR
ASSIGN FEZ,&PREC,PB

*

i**************i**********************it

* if tech & time feas, wait on reso chain

* else go back to tech chain
i

TEST E BVSRELT,1,NYET * if not yet tech feas, back to TECH
BLET &TMR=FLT(PH$SST)
TEST G &TMR,AC1,CKRS * if SST > AC1, then
ADVANCE &TMR—ACl * wait here until SST = AC1, then
TRANSFER ,CKRS * go to check resources

LRES LINK RESO,SST$PH * tech/time feas go to reso

NYET LINK TECH,SST$PH * not yet tech/time feas back to TECH

*
*i****i***************i‘iiiiiii‘kiiiiiiiii

**********************iiii'iiiti'itiiii'tit

* update resource feasibility and start

* this activity if all resources avail
*

CKRS TEST GE R1,MH$DAT1(PB$ANUM,9),LRES
TEST GE R2,MH$DAT1(PB$ANUM,10),LRES
TEST GE R3,MH$DAT1(PB$ANUM,11),LRES
*
ASSIGN RESl,0,PB
ASSIGN RESZ,O,PB
ASSIGN RES3,0,PB
*
ENTER 1,MH$DAT1(PB$ANUM,9)
ENTER 2,MH$DAT1(PB$ANUM,10)
ENTER 3,MH$DAT1(PB$ANUM,11)
*
TEST E BVSRELR,1,LRES
e
MARK
ADVANCE PL$LGT
LEAVE 1,MH$DAT1(PB$ANUM,9)
LEAVE 2,MH$DAT1(PB$ANUM,10)
LEAVE 3,MH$DAT1(PB$ANUM,11)

*
*iiii‘ti********i******‘kiifi‘tiiiiiiititrki
****************************************

* write activity information to raw matrix
*

WRIT BLET &MRK=AC1-M1
BLET &SFT=MH$DAT1(PB$ANUM,2)+MH$DAT1(PB$ANUM,3)
MSAVEVALUE DAT3,PB$ANUM,l,PB$ANUM,ML
MSAVEVALUE DAT3,PB$ANUM,2,PH$SST,ML
MSAVEVALUE DAT3,PB$ANUM,3,&MRK,ML
MSAVEVALUE DAT3,PB$ANUM,4,&SFT,ML
MSAVEVALUE DAT3,PB$ANUM,S,AC1,ML
MSAVEVALUE DAT3,PB$ANUM,6,MH$DAT1(PB$ANUM,3),ML
MSAVEVALUE DAT3,PB$ANUM,7,PL$LGT,ML
MSAVEVALUE DAT3,PB$ANUM,8,MH$DAT1(PB$ANUM,9),ML

283

 

MSAVEVALUE DAT3,PB$ANUM,9,MH$DAT1(PB$ANUM,10),ML
MSAVEVALUE DAT3,PB$ANUM,10,MH$DAT1(PB$ANUM,11),ML

*
*tiiiit*titititttiiitiiitiiiii‘ititii‘tiii
***************‘k‘l‘itii‘ii‘itiiiiiiitii‘kiiit

* update prec feas matrix for followers
*

ZERO

ASSIGN

TOT,&NACT,PB

MSAVEVALUE DAT2,PB$ANUM,PB$TOT,0,MB

LOOP

TOT$PB,ZERO

*

itii'i'kiiiiiiiiitiiiiiiiir'kii'iiiiti'tt*****

* kick all tech/time feas activities to
* resource update (& start if qual)
*

UNLINK RESO,CKRS,ALL

ADVANCE 0.00001

t
**i*************************************
* trigger feas update of all waiting on
* tech chain (& send to reso if qual)

*

UNLINK TECH,CKFZ,ALL
e

ADVANCE 0.00001
*

TEST G PB$ANUM,1,DRUP

DIE

*

TERMINATE l

***********i***iiiiii'tiiiiiifiiit'AHti'kii'i

iii'fii‘kitiiiifiiiitiiii’i’*************i****

* dummy start activity (and clones) now

* generate some disruptions
*

DRUP SPLIT &Rl-1,NEXT1,ANUM$PB
SPLIT &R2,NEXT2,ANUM$PB
SPLIT &R3,NEXT3,ANUM$PB
TRANSFER ,NEXTl

*

NEXT3 ASSIGN ANUM,3,PB
TRANSFER ,NEXT

NEXT2 ASSIGN ANUM,2,PB
TRANSFER ,NEXT

NEXTl ASSIGN ANUM,1,PB

*

NEXT PRIORITY 1

*

CYCL UNLINK WAIT,CKFZ,ALL
ADVANCE 0.0001
UNLINK RESO,CKRS,ALL
ADVANCE 0.0001

*
TEST E &DIS,0,CYCL2
TERMINATE 0

*

CYCLZ ADVANCE RVEXPO(2,&D) * uptime (huge, 15, 5)
TEST GE R(PB$ANUM),1,CYCL2
ENTER PB$ANUM,1

284

 

MARK

ADVANCE RVEXPO(4,3/(&DIS+0.0001)) * downtime (huge, 3, 1)
LEAVE PB$ANUM,1

MSAVEVALUE DT+,1,PB$ANUM,M1,ML

TEST GE N$DIE,&NACT-1,CYCL

TRANSFER ,DIE

*
*t‘ki*iitit*i'k'kitif*******************************i*****************i****i**i*
* Program Execution & Control *
*i*iti*titiiiiiiiiiititiitrkiii*iit'k'kti'kiiiti*i'ki'kiiiriiitiiiiiiiii'*iiiitiiit'ki
*
DO &L=1,18 * number of problems read from POL
*
**i**********************ttiiiiiriitiiiii

* read input file, set feas & out matrix
*

 

GETLIST FILE=POLB,&NACT,&NRES,&DZ
DATl MATRIX MH,&NACT,11 * input matrix
DAT2 MATRIX MB,&NACT,&NACT * feasibility matrix
DAT3 MATRIX ML,&NACT,10 * raw output matrix
DT MATRIX ML,1,3 * resource downtime matrix
*
GETLIST FILE=POLB,&DB,&Rl,&R2,&R3,&D4,&DS
GETLIST FILE=POLB,(((MHSDAT1(&I,&J),&J=1,11),&I=l,&NACT))
*
***************************************i
* set multiple runs over the multiple
* values of variability and disruption
*
DO &SPD1=0,1,1 * set multiple values of spread
LET &SPD=&SPD1*0.6 * adjust to 0, .6
*
DO &DISl=0,2,1 * set multiple values of disruption
IF &DISl=2 * factor to be 0, 1, 3
LET &DISl=&DISl+l
ENDIF
LET &DIS=&DISI*1.0 * convert to real
LET &D=1S/(&DIS+0.0001) * dis factor (0, 1, 3)->(M, 15, S)
*
DO &M=1,35 * number of reps for each problem

*
i'k*irki*iiitiitititirrkitti****************
* initialize feasibility matrix

*

DO &I=1,&NACT

DO &J=4,8

IF (MHSDAT1(&I,&J))'G'(0)
INITIAL MB$DAT2(&I,MH$DAT1(&I,&J)l,1
ELSE

ENDIF

ENDDO

ENDDO

*
*i'********************i*****************

* set initial run conditions
*

STORAGE Sl,&R1/82,&R2/S3,&R3

 

LET &K=&NACT+1

285

START &NACT-l
e

*iiiiii*********i**i********i'kiiiiiii'kii

* end of run file writing
i

PUTPIC FILE=SIMPOL3,&D2,&SPD,&DIS,ML$DT(1,1),MLSDT(1,2),MLSDT(1,3)
***i**** e.* it ****_*t ****.** ****_**
*

DO &I=1,&NACT

PUTPIC FILE=SIMPOL3,ML$DAT3(&I,1),MLSDAT3(&I,2),MLSDAT3(&I,3),_

ML$DAT3(&I,4),MLSDAT3(&I,5),MLSDAT3(&I,6),MLSDAT3(&I,7),ML$DAT3(&I,8),_
ML$DAT3(&I,9),ML$DAT3(&I,10)

{it fit iii-it iii iii-fit ** **.** if it **

ENDDO
PUTSTRING FILE=SIMPOL3,(")

RMULT &M*124,&M*124,&M*124,&M*124

CLEAR MH$DAT1
*

************************i**************i

* boundaries of multiple runs
*

ENDDO * &M; number of reps of each problem
*
ENDDO * &DIS; disruption level
*
ENDDO * &SPD; variability (spread) level
a
ENDDO * &L; number of problems read
*
END

*tiiiiii*ii'k**ttii‘ktittit*tiii'tiitiiiiiii*****iii*i'i'ii*iii'rk‘kiiitiii'iiiii‘kii'ii

PRO4.GPS - A Project Simulator

Planning: Per schedule from POLB (priority based on SST)
Execution: No Reservation (FCFS, by priority, of tech feasible act's)
No Waiting (act's advance when feas, even if SST not expired)

PROl: Full Reservation-Wait (lock partial resources/wait till schedule)
PROZ: Full Reservation-No Wait (lock partial resources/go when feasible)
PRO3: No Reservation-Wait (lock iff fully avail/wait till schedule)
>PRO4: No Reservation-No Wait (lock iff fully avail/go when feasible)

POLB: file containing problem data sets
SIMPOL4: file written to with simulation results

MH$DAT1: matrix containing problem data from POLB

MB$DAT2= sparse matrix representing activity feasibility

ML$DAT3: matrix containing simulation output to write to SIMPOL4

ML$DT: matrix accumulating downtime (total time) of resource 1, 2 or 3

RN(l): reserved
RN(2): up time of storages as sampled by ADVANCE (rvexpo) block
RN(3): duration of activities as sampled by BETA function

tfi‘ifitfil‘titl’iilfiiifiififl-

##OOOOOOOOOOQI'l’itfiI-élri

286

 

RN(4): down time of storages as sampled by ADVANCE (rvexpo) block

&SPD: variability (spread) ratio of activity durations
&DIS: number of expected disruptions to each resource during project

&L: number of individual problems read from the POLB data file
&M; number of simulation repetitions of each individual problem

i i
t t
i *
i *
i i
i *
i i
* t
* TECH: chain holding technical/time infeasible activities (first stage) *
* RESO: chain holding resource infeasible activities (second stage) *
t *
i i
i t
i i
i t
i t
* i
* i
t *

PB$ANUM: activity number (per problem data matrix)

PB$RESx: number of resources (storage) remaining for activity start
PBSPEZ: number of precedence activities remaining for activity start
PB$TOT: "tote" counter for looping and xact management

PHSSST: scheduled start time from POLB (used for chain order)
PL$DUR: activity duration from beta distributed around POLB duration

************iii********it***ii****iiiititiifiiiitiitti*********************

SIMULATE

REALLOCATE FMS,0
REALLOCATE FSV,0
REALLOCATE GRP,0
REALLOCATE HSV,0
REALLOCATE LOG,0
REALLOCATE QUE,0
REALLOCATE TAB,0
REALLOCATE COM,25008

INTEGER &I,&J,&K,&L,&M,&SPD1,&DISI,&PREC,&NACT,&NRES
INTEGER &D4,&R1,&R2,&R3

REAL &DUR,&SPD,&MRK,&SFT,&D,&DS,&DIS

CHAR*8 &D2,&D3

*

BETA FUNCTION RN(3),C8
0,0/0.02,0.03/0.14,0.11/0.67,0.41/0.85,0.56/0.94,0.68/0.99,0.81/1,l

*
*************************************iii

* technical/time feasibility
*

RELT BVARIABLE ((PB$FEZ)'E'(0))
i
*************************t***********tit

* resource (storage) feasibility
*

RELR BVARIABLE ((PB$RESl)'E'(0))*((PB$RESZ)'E'(0))*((PB$RES3)'E'(0))

*
*************************itt*********************************************i***
* Dynamic Program Code *
*******************i*********************************************************
*

GENERATE ,,,&NACT,,0PF,1PH,6PB,1PL
*

******i******ii*************************

* assign actnum, resource requirements,

* schedstart, and duration
*

BLET &K=&K-1
ASSIGN ANUM,&K,PB

287

 

 

*

ASSIGN
ASSIGN
ASSIGN
ASSIGN

BLET
ASSIGN

TEST G

RESl,MH$DAT1(PB$ANUM,9),PB
RESZ,MH$DAT1(PB$ANUM,10),PB
RES3,MH$DAT1(PB$ANUM,11),PB
SST,MH$DAT1(PB$ANUM,2),PH

&DUR=MH$DAT1(PB$ANUM,3)*(1-(&SPD/3)+&SPD*FN(BETA))
LGT,&DUR,PL

PB$ANUM,1,WRIT * start node skip to end (writ)

i*iiiiiiiiiiiiiiiiti*iiii'kiiifli'iittiitii

*i*****i******i****§*i*iiiiiiiiitirii‘tt'kt

* sum undone prec activities for self

*

CKFZ

CKPR

*

ASSIGN
BLET
BLET
LOOP
ASSIGN

TOT,&NACT,PB

&PREC=0
&PREC=&PREC+MB$DAT2(PB$TOT,PB$ANUM)
TOT$PB,CKPR

FEZ,&PREC,PB

*******iti*iiiiiiiiiiiiiiiit'kiti*iiiiiit

* if tech/time feas, wait on reso chain
* else go back to tech chain

*

LRES
NYET

*

TEST E
LINK
LINK

BV$RELT,1,NYET
RESO,SST$PH
TECH,SST$PH

‘-

tech/time feas go to reso
not yet tech/time feas back to tech

*

*iitii'kitiiiiiiiii'iiiii'kitiiiiitiiiiii't'k

iiiiti'ki'kiiii*i't'k'k*iiiiifiiiiiiif'ktiiiii

* update resource feasibility and start
* this activity if all resources avail

*

CKRS

*

TEST GE
TEST GE
TEST GE

ASSIGN
ASSIGN
ASSIGN

ENTER
ENTER
ENTER

TEST E

MARK
ADVANCE
LEAVE
LEAVE
LEAVE

R1,MH$DAT1(PB$ANUM,9),LRES
R2,MH$DAT1(PB$ANUM,10),LRES
R3,MH$DAT1(PB$ANUM,11),LRES

RESl,0,PB
RESZ,0,PB
RES3,0,PB

1,MH$DAT1(PB$ANUM,9)
2,MH$DAT1(PB$ANUM,10)
3,MH$DAT1(PB$ANUM,11)

BV$RELR,1,LRES

PL$LGT
1,MH$DAT1(PB$ANUM,9)
2,MH$DAT1(PB$ANUM,10)
3,MH$DAT1(PB$ANUM,11)

*‘kiii'kii'i'i*************************tttii’

*itiitiii*i‘kiiitiiififi*iti’i’iiiiiitttiitit

* write activity information to raw matrix

*

WRIT

BLET

&MRK=ACl-Ml

288

 

 

*

BLET &SFT=MH$DAT1(PB$ANUM,2)+MH$DAT1(PB$ANUM,3)
MSAVEVALUE DAT3,PB$ANUM,1,PB$ANUM,ML

MSAVEVALUE DAT3,PB$ANUM,2,PH$SST,ML

MSAVEVALUE DAT3,PB$ANUM,3,&MRK,ML

MSAVEVALUE DAT3,PB$ANUM,4,&SFT,ML

MSAVEVALUE DAT3,PB$ANUM,S,AC1,ML

MSAVEVALUE DAT3,PB$ANUM,S,MH$DAT1(PB$ANUM,3),ML
MSAVEVALUE DAT3,PB$ANUM,7,PL$LGT,ML

MSAVEVALUE DAT3,PB$ANUM,8,MH$DAT1(PB$ANUM,9),ML
MSAVEVALUE DAT3,PB$ANUM,9,MH$DAT1(PB$ANUM,10),ML
MSAVEVALUE DAT3,PB$ANUM,10,MH$DAT1(PB$ANUM,11),ML

*i'iiiii'iiiiiiiii*itittiiiiiiiiitiiiiiiii

*tirtiiitiiiitii'i************************

* update prec feas matrix for followers

i

ASSIGN TOT,&NACT,PB
ZERO MSAVEVALUE DAT2,PB$ANUM,PB$TOT,0,MB
LOOP TOTSPB,ZERO

*

*iiitfiiiiiiiittiiiiiiiiiiiiitiiiiiiiiii

* trigger feas update of all waiting on
* tech chain (& send to reso if qual)

*

*

UNLINK
ADVANCE

TECH,CKFZ,ALL
0.00001

iiiiiiiii*i*******i‘iiiiiiittiiii’iiittiii

* kick all tech/time feas activities to
* resource update

i

(& start if qual)

UNLINK RESO,CKRS,ALL
*

ADVANCE 0.00001
*

TEST G PB$ANUM,1,DRUP
DIE TERMINATE 1

*

****************************************

***********it‘kiiiiiiiiifi****************

* dummy start activity (and clones) now

* generate some disruptions

*

DRUP SPLIT &Rl-1,NEXT1,ANUM$PB
SPLIT &R2,NEXT2,ANUM$PB
SPLIT &R3,NEXT3,ANUM$PB
TRANSFER ,NEXTI

*

NEXT3 ASSIGN ANUM,3,PB
TRANSFER ,NEXT

NEXTZ ASSIGN ANUM,2,PB
TRANSFER ,NEXT

NEXTl ASSIGN ANUM,1,PB

*

NEXT PRIORITY 1

*

CYCL UNLINK WAIT,CKFZ,ALL
ADVANCE 0.0001
UNLINK RESO,CKRS,ALL
ADVANCE 0.0001

289

 

TEST E &DIS,0,CYCL2
TERMINATE 0

CYCL2 ADVANCE RVEXPO(2,&D) * uptime (huge, 15, 5)
TEST GE R(PB$ANUM),1,CYCL2
ENTER PB$ANUM,1
MARK
ADVANCE RVEXPO(4,3/(&DIS+0.0001)) * downtime (huge, 3, 1)
LEAVE PB$ANUM,1
MSAVEVALUE DT+,1,PB$ANUM,M1,ML
TEST GE N$DIE,&NACT-1,CYCL
TRANSFER ,DIE

*
*iiir'k'hfl'kiiit*tart*******************************i***********i'iiitiiiititittti'i
* Program Execution & Control *
********itt-kitiiiiitirkiii'k'kiit*i'iiittiitttitt'ki-kit'k'k'k****************i*****i*
*

DO &L=1,18 * number of problems read from POLB
i
*i**************************************

* read input file, set feas & out matrix
*

GETLIST FILE=POLB,&NACT,&NRES,&D2
DATl MATRIX MH,&NACT,11 * input matrix
DAT2 MATRIX MB,&NACT,&NACT * feasibility matrix
DAT3 MATRIX ML,&NACT,10 * raw output matrix
DT MATRIX ML,1,3 * resource downtime matrix
*
GETLIST FILE=POLB,&D3,&R1,&R2,&R3,&D4,&DS
GETLIST FILE=POLB,(((MH$DAT1(&I,&J),&J=1,11),&I=1,&NACT))

*
it*ii’kii‘ti‘kii*********i*****************

* set multiple runs over the multiple

* values of variability and disruption
*

DO &SPD1=0,1,1 * set multiple values of spread
LET &SPD=&SPD1*O.6 * adjust to o, .6
1*
DO &DISl=0,2,1 * set multiple values of disruption
IF &DISl=2 * factor to be (0, 1, 3)
LET &DISl:&DISl+1
ENDIF
LET &DIS=&DISI*1.0 * convert to real
LET &D=lS/(&DIS+0.0001) * dis factor (0, l, 3)->(M, 15, 5)
*
DO &M=1,35 * number of reps for each problem

*
*i*iitii'ktii'i'kii*irkti’i’ttiii’iti'ttii******
* initialize feasibility matrix

*

DO &I=1,&NACT

DO &J=4,8

IF (MHSDAT1(&I,&J))'G'(0)
INITIAL MB$DAT2(&I,MH$DAT1(&I,&J)),l
ELSE

ENDIF

ENDDO

ENDDO

290

 

*iiiiiiii'k***i********i****ii'ktititiitti

* set initial run conditions
*

STORAGE Sl,&Rl/SZ,&R2/S3,&R3
*

LET &K=&NACT+1
*

START &NACT-l

t
it*‘t'k'titiiiiii'**************************

* end of run file writing
*

PUTPIC FILE=SIMPOL4,&D2,&SPD,&DIS,ML$DT(1,1),ML$DT(1,2),MLSDT(1,3)
*****e** e.* *e **e*_** *e**.** **t* it
*

DO &I=l,&NACT

PUTPIC FILE=SIMPOL4,ML$DAT3(&I,1),MLSDAT3(&I,2),ML$DAT3(&I,3),_

ML$DAT3(&I,4),ML$DAT3(&I,5),MLSDAT3(&I,6),ML$DAT3(&I,7),MLSDAT3(&I,8),_
ML$DAT3(&I,9),ML$DAT3(&I,10)

iii *** ***.** *** iii.** ** **.*i it ** it

ENDDO
PUTSTRING FILE=SIMPOL4,(")

RMULT &M*124,&M*l24,&M*124,&M*124
CLEAR MH$DAT1

*
it*tiiiiiiitii**********************t***

* boundaries of multiple runs
*

ENDDO * &M; number of reps of each problem
*
ENDDO * &DIS; disruption level
*
ENDDO * &SPD; variability (spread) level
*
ENDDO * &L; number of problems read
*
END

291

 

APPENDIX K

PASCAL LISTINGS

292

 

***************i'i't**********iiiriii'kitiiii'k‘k‘ki'kiitiii*i’i‘kt'kiri'iiititiriiiii'iii

CONTST.PAS

{ l
{ l
{ l
{ }
{ Filel: Input file; problem schedule data }
{ Pilez: Input file; simulation output data 30 reps x 6 factor combos }
{ File3: Input file; problem characteristics from Demographics file }
{ File4: Output file; the calculated results of this conversion program }
{ l
( l
{ }
{ }
{ }

}

}

ArInl: Array (60x11) problem schedule characteristics from Pilel
ArInZ: Array (60x10) simulation output data from File2 (reps x factors)

{

{*****i*********************************************************************

program Convert;

const
Costl = 25;
Cost2 = 25;
Cost3 = 25;
R = -0.1S/36S;
var

Done: Boolean;
Filel, Filez, File3, File4: Text;
NAct, NRes, Dis, Dum2, OCPL, I, J, K, L, M, N: Integer;

ArInl: array[1..51, 1..11] of Real;
ArIn2: array[1..51, 1..10] of Real;
Arl, Ar2: array[1..102, 1..4] of Real;

Resl, ResZ, Res3, DTl, DT2, DT3, Lodl, Lodz, Lod3, Capl, Cap2, Cap3: Real;
ADur, PDur, RDur, Spd, AARU, RARU, AMRU, RMRU, SNPV, ANPV, RNPV: Real;
Den, SlL, 81E, $1, $21, 820, 82, S3I, 830, ResLod, Tmpl, Tmp2: Real;

PMT, EPMT, APMT, ARU, MRU, Numl, Numz, Dum, TLast: Real;

Filename,Al,A2,A3,A4,Bl,BZ,B3,B4,BS,B6,B7,BB,B9,BlO: String;
C1,C2,C3,C4,C5,C6,C7,C8,C9: String;

Name: String[12];

NAC: String[4];

MDF, NDR, NCR, ARC, MRC: String[9l;
Naml, Nam2, Duml: String[12];
Sked, Exec: String[3];

{**********i***i****ti************i*****************************************}

begin

Write('Please enter schedule data input filename: ');
ReadLn(FileName);
Assign(File1, FileName);

Write('Please enter simulation data input filename: ');

ReadLn(FileName);
Assign(File2, FileName);

293

 

Write('Please enter problem demographic data input filename: ');
ReadLn(FileName);
Assign(File3, FileName);

Write('Please enter conversion data output filename: ');
ReadLn(Fi1ename);
Assign(File4, FileName);

Write('Please enter scheduling method used (3 char): ');
ReadLn<Sked);

Write('Please enter execution method used (3 char): ');
ReadLn<Exec);

Reset(File1);
Reset(File2);
Reset(File3);
ReWrite(File4);

{i*‘k*iifiiitititiiit******iiiiiiiiii*****ii**********i*************}

{* initialize ArInl & ArIn2 matrices containing problem data }
for I:=1 to 18 do {* number of problems }
begin

ReadLn(File1, NAct, NRes, Naml);
ReadLn(File1, Duml, Resl, ResZ, Res3, Dum2, OCPL);

for K:=1 to NAct do
begin
for L:=1 to 11 do
Read(File1, ArIn1[K, L]);
end;

ReadLn(File1); {* skip the blank line }

ReadLn(File3, Name, NAC, PDur, MDF, NDR, NCR, ARC, MRC, ARU, MRU);

{ii'k**************************************************************}

{* initialize ArIn2 matrix containing 35 reps x 6 factors sim data}

for J:=1 to 210 do {* number of reps in Filez}
{ for each problem }

begin
ReadLn(File2, Nam2, Spd, Dis, DTl, DT2, DT3);

for K:=1 to NAct do
begin
for L:=1 to 10 do
Read(File2, ArIn2[K, Ll);
end;

ReadLn(Fi1e2); {* skip the blank line }

294

 

{***********‘k'k‘kiiii'hiitiii'i’i'iti‘iii******i***************}

{* assign actual project duration ADur }

ADur:=ArIn2[NAct, 5];

{*************i*****************************************}

{* calculate percent project duration over sched PDur }

RDur:=ADur/PDur;

{*i'kir'kii'k'kii*iii‘i’iiiiiir'kii'kiiiiiii'ki********************}

{* calculate Actual Average Resource Utilization AARU }

LOdl:=0;
Lod2:=0;
Lod3:=0;

Cap1:=ADur*Resl;
Cap2:=ADur*ResZ;
Cap3:=ADur*ResB;

for K:=1 to NAct do

begin
Lod1:=Lod1+ArIn2[K,8]*ArIn2[K,7];
Lod2z=Lod2+ArIn2[K,9]*ArIn2[K,7];
Lod3z=Lod3+ArIn2[K,10]*ArIn2[K,7];

end;

AARU:=(Lod1+Lod2+Lod3)/(Cap1+Cap2+Cap3);

RARU:=AARU/ARU;

{*‘k*i’ti‘iii********************if*i**********************}

{* calculate Actual Maximum Resource Utilization AMRU }

if (Lodl/Capl) > (Lod2/Cap2)
then AMRU:=(Lod1/Cap1)
else AMRU:=(Lod2/Cap2);

if (Lod3/Cap3) > AMRU
then AMRU:=(Lod3/Cap3)
else;

RMRU:=AMRU/MRU;

{'k********************************************i*********}

{* calculate project Net Present Values A/S/RNPV }
SNPV:=0;
ANPV:=0;
PMT:=0;

for K:=1 to NAct do

begin
SNPV:=SNPV+((Cost1*ArIn2[K,8]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
SNPV:=SNPV+((Cost2*ArIn2[K,9]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
SNPV:=SNPV+((Cost3*ArIn2[K,lO]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
ANPV:=ANPV+((Cost1*ArIn2[K,8]*ArIn2[K,7])*(exp(R*ArIn2[K,5])));
ANPV:=ANPV+((Cost2*ArIn2[K,9]*ArIn2[K,7])*(exp(R*ArIn2[K,5])));
ANPV:=ANPV+((Cost3*ArIn2[K,10]*ArIn2[K,7])*(exp(R*ArIn2[K,5])));

295

end;
PMT:=1.S*(SNPV/(exp(R*ArIn2[NAct,4]))); {* what the firm will charge }

EPMT:=PMT*(exp(R*ArIn2[NAct,4])); {* Expected NPV of the payment }
APMT:=PMT*(exp(R*ArIn2[NAct,5])); {* Actual NPV of the payment )

SNPV:=EPMT-SNPV; {* Firm's expected total NPV }
ANPV:=APMT-ANPV; {* Firm's actual total NPV }
RNPV:=ANPV/SNPV; {* Ratio of actual/expected }

{*****i*************iiii************t****t***********tit}

{* calculate Stability Sl/L/E (Weighted Act Deviation) }

Numl:=0;
Num2:=0;
Den:=0;

for K:=1 to NAct do

begin
if ArIn2[K,3] > ArIn2[K,2] {* if late start }
then Numl:=Num1+ArIn2[K,3]—ArIn2[K,2] {* add lateness to N1 }
else;
if ArIn2[K,3] < ArIn2[K,2] {* if early start }
then Num2:=Num2+ArIn2[K,2]-ArIn2[K,3] {* add earliness to N2 }
else;
Den:=Den+ArIn2[K,6]; {* sum scheduled durations }
end;
Den:=Den/Nact; {* calc avg sched act dur }

SlL:=Num1/(NAct*Den);
SlE:=Num2/(NAct*Den);
Sl:=(Num1+Num2)/(NAct*Den);

{**tiiiitiiitiiiti’iiii‘kii****i’iit'ktiiit'kittiiiiitiit*i‘ki}

{* calculate Stability SZ/I/O (Res-Weighted Dis) }
Numl:=0;
Num2z=0;

Den:=ArIn2[NAct,S]*Resl;
Den:=Den+ArIn2[NAct,5]*Resz;
Den:=Den+ArIn2[NAct,S]*Res3;

for K:=1 to NAct do

begin

if ArIn2[K,3]-ArIn2[K,2]>0 {* AST>SST (idle) }
then Numl:=Num1+ArIn2[K,3]-ArIn2[K,2] {* add to Numl }
else;

if ArIn2[K,4]-ArIn2[K,5]>0 {* SFT>AFT (idle) }
then Num1:=Num1+ArIn2[K,4]-ArIn2[K,S] {* add to Numl }
else;

if ArIn2[K,2]-ArIn2[K,3]>0 {* SST>AST (over) }
then Num2:=Num2+ArIn2[K,2]-ArIn2[K,3] {* add to Num2 }
else;

if ArIn2[K,S]-ArIn2[K,4]>0 {* AFT>SFT (over) }
then Num2:=Num2+ArIn2[K,S]-ArIn2[K,4] {* add to Num2 }
else;

296

 

end;

SZI:=1-(Num1/Den);
SZO:=1-(Num2/Den);
SZ:=SZI+SZO-1;

{*i‘i‘ki'iiiii'tiitrki***************************************}

{* calculate Stability S3/I/O (res profile mismatch) }
{* initialize matrices Arl & Ar2 }

for K:=1 to 102 do
for L:=1 to 4 do
begin
Arl [K, L] :=0;
Ar2[K,L]:=0;
end;

 

for K:=1 to NAct do
for L:=1 to 2 do
begin
Ar1[K,L]:=ArIn2[K,L+1];
Ar1[K,L+2]:=ArIn2[K,8]+ArIn2[K,9]+ArIn2[K,10];
Ar1[K+NAct,L]:=ArIn2[K,L+3];
Ar1[K+NAct,L+2]:=-1*(ArIn2[K,8]+ArIn2[K,9]+ArIn2[K,lO]);
end;

{* chronologic sort matrix Arl scheduled (1,3) and actual (2,4) columns }

for K:=1 to 2 do
for L:=1 to 2*NAct do

begin
Tmp1:=Ar1[L,K];
Tmp2:=Ar1[L,K+Zl;

for M:=L+1 to 2*NAct do
begin
if Tmp1>Ar1[M,K] then
begin
ArllL,K]:=Arl[M,K];
Ar1[L,K+2]:=Ar1[M,K+2];
Arl[M,K]:=Tmp1;
Arl[M,K+2]:=Tmp2;
Tmp1:=Arl [L, K];
Tmp2:=Arl[L,K+2l
end;
end;
end;

{* compress Arl matrix into Ar2 matrix; eliminating duplicate times }

Tmp1:=0; {* Time }
Tmp2:=0; {* Resources }
for Kz= 1 to 2 do {* 2 passes through matrix }
begin
L:=1; {* initialize Arl index }

297

 

N:

wh

end;

:1;

ile (L<=2*NAct) do
begin
Tmp1:=Arl [L, K];
Tmp2:=0;
M:=L;

while
begin

Tmp2;=Tmp2+Arl[M,K+2];

M:=M+l;
L:=L+l;
end;

Ar2[N,K]:=Tmpl;
Ar2[N,K+2]:=Tmp2;
N:=N+l;

end;

(Tmp1=Arl IM, Kl)

do

{* initialize Ar2 index }

{* Run until Sched / Act done }

{* Time = current value in Arl }

{* initialize resource cumulator }
{* initialize cumulator pointer }

{* as long as current time=time ...}
{* add curr resources into cumulator }
{ increment cumulator pointer }

{* increment Arl pointer }

{* loop until time <> time ...}

{* put value of time into Ar2 }

{* put value of cum res into Ar2 }
{* increment Ar2 pointer }

{* loop through sched/act ...}

{* Both Sched and Act complete }

{* transfer Ar2 resource deltas into Arl resource levels }

Tmpl
Tmp2

:=0;
:=0;

for K:=1 to 102 do
for L:=1 to 4 do
ArllK,L]:=0;

for K:=1 to 102 do
begin

Arl [K, 1] :=Ar2 [K, 1];
Ar1[K,2] :=Ar2[K,2] ,'
'I‘mp1:=Tmp1+Ar2 [K, 3];
Tmp2:=Tmp2+Ar2[K,4l;
Arl[K,3]:=Tmpl;
Ar1[K,4l:=Tmp2;

end;

{* scheduled level cumulator }
{* actual level cumulator }

{* cumulate area under the scheduled resource profile }

Den:

for

=0;

k:=1 to 102 do

if Ar1[K+1,1]<>0 then
Den:=Den+((Ar1[K+1,1]-Ar1[K,l])*(Ar1[K,2]));

{* scheduled resource profile area }

{* cumulate areas between the actual/scheduled resource profiles }

K:=1;
L:=1;
Tmpl:=0;
Tmp2:=0;

298

{* Index for Schedule }

{* Index for Actual }

{* Current # resources Scheduled }
{* Current # resources Actual }

TLast:=0; {* Time of last event }

Num1:=0; {* cumulate SBI time Sched>Actual }
Num2:=0; {* cumulate S30 time Actual>Sched }
Dum:=0; {* dummy to carry current area calc }
Done:=False; {* exit criteria for cumulating loop }

while (Done=False) do {* Run until both Sched and Act done }
begin {* Go until done loop }
if ArllK,1] = Ar1[L,2] then {* Sched Time = Actual Time }
begin

Dum:=(Arl[K,1]-TLast)*(Tmp1—Tmp2);
if Dum>0 then Num1:=Num1+Dum else Num2:=Num2+(-1*Dum);

 

Tmpl:=Tmp1+Ar1[K,3]; {* Update resources in use Sched }
Tmp2:=Tmp2+Ar1[L,4]; {* Update resources in use Actual }
TLast::Arl[K,1]; {* Sched=Act Time was the last event }
K:=K+1; {* increment both counters and }
L:=L+l; {* start again }
end
else * Sched Time <> Actual Time }

{
begin {* Sched Time <> Actual Time loop }
if Ar1[K,1] < Ar1[L,2] then {* Sched Time < Actual Time }
begin

Dum:=(Ar1[K,1]-TLast)*(Tmp1-Tmp2);
if Dum>0 then Num1:=Num1+Dum else Num2:=Num2+(—1*Dum);

Tmpl:=Tmp1+Ar1[K,3]; {* Update resources in use Sched }
TLast:=Ar1[K,1]; {* Sched Time was the last event }
K:=K+l;
end
else {* Sched Time not <= Actual Time }
if Ar1[K,l] > Ar1[L,2] then {* Sched Time > Actual Time }
begin

Dum:=(Ar1iL,2]-TLast)*(Tmpl-Tmp2);
if Dum>0 then Numlz=Num1+Dum else Num2:=Num2+(—1*Dum);

Tmp2:=Tmp2+Ar1[L,4]; {* Update resources in use Actual }
TLast::Ar1[L,2]; {* Actual Time was the last event }
L:=L+l;
end
else {* Sched Time not <=> Actual Time?! }
end; {* Sched Time <> Actual Time Loop }
if ((Ar1[K+1,3]=0) and (Ar1[K+2,3]=0)) then {* Schedule has expired }

299

 

begin
Ar1[K+1,1]:=Ar1[L+1,2]; {* force another pass }
end
else

if ((Ar1[L+l,4]-O) and (Ar1[L+2,4l=0)) then {* Actuals have expired }

begin
Arl[L+1,2]:=Arl[K+1,1]; {* force another pass }
end
else;

if ((Arl[K,3]=O)and(Ar1[K+1,3]=0)and(Ar1[L,4]=0)and(Arl[L+1,4]=0))
then Done:=True else;

if ((L>=2*NAct) or (K>=2*NAct)) then Done:=True else;

end; {* Go until done loop }

{* Both Sched and Act have expired }

S3I:=Num1/Den;

S30:=Num2/Den;

{*iiii’iiiitii********************iiiiiiiiiiiiiiiitiiiiii}

{ convert spd & dis to factor names }

if spd = 0 then A1:='none'else
A1:='some';

if dis = 0 then A2:='none' else
if dis = 1 then A2:='infq' else
A2:='freq';

{*iiiiiiiiiiiitfiiitiii*i'kittitii*iiiittiiiiiiiiiiiiiiir'ki}

{* format all numerical values into strings for writing }

Str(ARU: 1:5, A3);
Str(MRU: 1:5, A4);
Str(AARU: 2:5, Bl);
Str(RARU: 2:5, BZ);
Str(AMRU: 2:5, B3);
Str(RMRU: 2:5, B4);
Str(PDur: 3:3, B5);
Str(ADur: 3:3, B6);
Str(RDur: 2:4, B7);
Str(SNPV: 8:2, B8);
Str(ANPV: 8:2, B9);
Str(RNPV: 2:4, BIO);
Str(SlL: 4:4, C1);
Str(SlE: 4:4, C2);
Str(Sl: 4:4, C3);
Str(SZI: 2:4, C4);
Str(SZO: 2:4, C5);
Str(SZ: 2:4, C6);
Str(S3I: 4:4, C7);
Str(SBO: 4:4, C8);

{iitii*****ttfiii‘k'ki'i'fiitti'kiiifi*************************}

300

{* Write converted data strings to File4 }

Write(File4,Name,' ',Sked,‘ ',Exec,' ',A1,' ',A2,NAc,MDF,NDR,NCR,ARC,MRC);
Write(File4,‘ ',A3,’ ',Bl,‘ ',BZ,‘ ',A4,’ ',BB,’ ',B4,’ ');
Write(File4,B5,' ',B6,‘ ',B7,‘ ',BB,‘ ',B9,‘ ',BlO,’ ');
WriteLn(File4,Cl,' ',C2,’ ',C3,' ',C4,’ ',C5,' ',C6,‘ ',C7,’ ',C8);

{*i************i*i******i********i*******iti'kii'kii'***********************}

ReadLn(File2); {* next line of simulation data }
end; {* Next J- # reps/prob in File 2 }
ReadLn(Pilel); {* next line of schedule data }
end; {* Next I- # probe in Files 1 & 3}

{*****************************************iit***********ii*i*****i*******}

Close(File1);
Close(File2);
Close(File3);
Close(File4);

end.

*************************iri*i'ki*iit******i****************************i****

{
{
{ CONVl . PAS
(

{ Filel: Input file; problem characteristics from schedule data file

{ File3: Input file; unconstrained CPM CPL from Patterson Set

{ File2: Output file; the calculated results of this conversion program
{

{ ArInl: Array (60x11) problem information from Filel (single problem)
{
{
{
{

ArIn2: Array (lloxl) unconstrained, CPM CPL for Patterson set
ArOut: Array (30x18) converted sim data (each factor set) to File3

{

1
}
}
}
}
}
l
1
}
}
}
}
}
}
{*iii'ki'iii'kiii'rkiiti’i*‘kiii'k'kit'k'k**************iii‘ki************i'i'k'ktiiiii'i'k'k‘t}

program Convert;

var
Filel, File2, File3: Text;

ArInl: array[1..60, 1..11] of Real;
ArIn2: array[1..110, 1..l] of Integer;

NAct, NRes, Dum2, CPL, UNC, I, J, K, NArc, PArc: Integer;

Resl, ResZ, ResB, MDF, NDR, NCR, ARC, MRC, ARU, MRU: Real;
Lodl, Lod2, Lod3, Capl, Cap2, Cap3: Real;

Naml, Duml, FileName: String[12];
Bl, BZ, B3, B4, BS, B6, B7, B8, B9: String;

301

{*iiitttiitii***********ittiii*i’iii‘kiii'ki*iiiitiiit‘ti'fiiii‘iiiii**************}

begin

Write('Please enter problem data input filename: ');
ReadLn(FileName);
Assign(File1, FileName);

Write('Please enter unconstrained CPL data input file name: ');
ReadLn(FileName);
Assign(File3, FileName);

Write('Please enter conversion data output filename: ');
ReadLn(Filename);
Assign(File2, FileName);

Reset(File1);
Reset(FileB);
ReWrite<File2);

{****i******t*****t*******titi*i'i'i*i'i'i'****************************}

{* initialize ArInl matrix containing Patterson problem data }
for I:=1 to 18 do {* number of problems in Filel }
begin

ReadLn(Filel, NAct, NRes, Naml);
ReadLn(File1, Duml, Resl, Resz, Res3, Dum2, CPL);
ReadLn(File3, UNC);

for J:=1 to NAct do
begin
for K:=1 to 11 do
Read(File1, ArInllJ, Kl);
end;

ReadLn(File1);

{*itittfii‘tiiit'kii************iiiiitit'k'kiii'*************i}

{* calculate Makespan Delay Factor MDF/B3 }

MDF:=CPL/UNC;

{*ii'iiiii'i'kiit'k'kt'ki'i'kii*************t*******************}

{* calculate Network Density Ratio NDR/B4 }
NArc:=0;

for J:=1 to NAct do

begin
for K:=4 to 8 do
begin
if ArIn1[J, K]<>O
then NArC:=NArc+1
else
end;
end;

NDR:=NArc/NAct;

302

{********************************************i**********}

{* calculate Network Complexity Ration NCR/BS }
PArC:=0;

for J:=1 to NAct-1 do
PArc:=PArc+J;

NCR:=NArc/PArc;

{iiii‘i’itiiiit‘ti‘iitiiiii********************i************}

{* calculate Average Resource Constrainedness ARC/BS }
Lodl:=0;
Lod2:=0;
Lod3:=0;

Cap1:=UNC*Resl;
Cap2:=UNC*ResZ;
Cap3::UNC*Res3;

for Jzzl to NAct do

begin
Lod1:=Lod1+ArIn1[J,9]*ArIn1[J,3];
Lod2:=Lod2+ArIn1[J,10]*ArInl[J,3];
Lod3:=Lod3+ArIn1[J,11]*ArIn1[J,3];

end;

ARC:=(Lod1+Lod2+Lod3)/(Capl+Cap2+Cap3);

{********************i".*i'i'ki'kiiiiiiiiiiiiii*************}

{* calculate Maximum Resource Constrainedness MRC/B7 }

if (Lodl/Capl) > (Lod2/Cap2)
then MRC:=(Lod1/Cap1)
else MRC:=(Lod2/Cap2);

if (Lod3/Cap3) > MRC
then MRC:=(Lod3/Cap3)
else;

{it*****************************************************}

{* calculate Average Resource Utilization ARU/B8 }

Cap1:=CPL*Resl;
Cap2:=CPL*Resz;
Cap3z=CPL*Res3;

ARU:=(Lod1+Lod2+Lod3)/(Cap1+Cap2+Cap3);

{e*eeeete**eeee**ee***e*eeeteeee****e****************t**}

{* calculate Maximum Resource Utilization MRU/B9 }
if (Lodl/Capl) > (Lod2/Cap2)
then MRU:=(Lod1/Cap1)
else MRU:=(Lod2/Cap2);

if (Lod3/Cap3) > MRU
then MRU:=(Lod3/Cap3)

303

 

 

else;

{************************i******************************}

{* format all real values into strings for writing )
Str(NAct: 2, Bl);
Str(CPL: 3, B2);
Str(MDF: 2:5, B3);
Str(NDR: 2:5, B4);
Str(NCR: 2:5, B5);
Str(ARC: 2:5, 86);
Str(MRC: 2:5, B7);
Str(ARU: 2:5, BB);
Str(MRU: 2:5, B9);

{tiiii'k******************ii'kiii*iiti************i*******}

 

{* Write converted data strings to Filez }
Write(File2,Nam1,' ',Bl,' ',BZ,‘ ',B3,’ ',B4,’ ');
WriteLn(File2,BS,' ',B6,' ',B7,' ',BB,‘ ',39);

{**********ii**********iiii*************iiitiiiiititii'kiiti*******}

ReadLn(File1); {* skip the blank line }

end; {* num of probs in Filel }

{itii*‘k**************it***iiiititii'k'kit'k'ki****************iii*****}

Close(File1);
Close(File2);
Close(File3);

end.

iii**i'*i‘iiiiiiititi'k'k'k'kii‘ki'i'k*ii’i’iiiii'ki'********************************i**

CONVERT.PAS

{ }
{ }
{ }
{ }
{ Filel: Input file; problem schedule data }
{ File2: Input file; simulation output data 30 reps x 6 factor combos }
{ File3: Input file; problem characteristics from Demographics file }
{ File4: Output file; the calculated results of this conversion program }
{ }
{ }
( }
{ }
{ }

}

}

ArInl: Array (60x11) problem schedule characteristics from Filel
ArIn2: Array (60x10) simulation output data from File2 (reps x factors)

{

{****'k**********************************ifi*********************************

program Convert;

 

const
Costl = 25;
Cost2 = 25;
Cost3 = 25;

304

R = -0.06;
var
Done: Boolean;
Filel, File2, File3, File4: Text;
NAct, NRes, Dis, Dum2, CPL, I, J, K, L, M, N: Integer;

ArInl: array[1..51, 1..11] of Real;
ArIn2: array[1..51, 1..10] of Real;
Arl, Ar2: array[1..102, 1..4] of Real;

Resl, Resz, Res3, DTl, DT2, DT3, Lodl, Lod2, Lod3, Capl, Cap2, Cap3: Real;
ADur, RDur, Spd, AARU, AMRU, SNPV, ANPV, PMT, EPMT, APMT, Numl, Num2: Real;
Den, SlL, 81E, $1, 321, $20, 32, S31, S30, 83, ResLod, Tmpl, Tmp2: Real;
Dum, TLast: Real;

Filename,A1,A2,B1,B2,B3,B4,B5,B6,C1,C2,C3,C4,C5,C6,C7,C8,C9: String;
Name: String[12];

NAC: String[4];

CP: String[S];

MDF, NDR, NCR, ARC, MRC, ARU, MRU: String[9l;

Naml, Nam2, Duml: String[12];

Sked, Exec: String[3];

{*tiiiiiiiiiiiiiiiiii’iiiii'iiiii*iiiiiitfli*titii*ifiiiiiii'k'ktiiiii‘ititit******}
begin

Write('Please enter schedule data input filename: ');
ReadLn(FileName);
Assign(File1, FileName);

Write('Please enter simulation data input filename: ');
ReadLn(FileName);
Assign(File2, FileName);

Write('Please enter problem demographic data input filename: ');
ReadLn(FileName);
Assign(File3, FileName);

Write('Please enter conversion data output filename: ');
ReadLn(Filename);
Assign(File4, FileName);

Write('Please enter scheduling method used (3 char): ');
ReadLn(Sked);

Write('Please enter execution method used (3 char): ');
ReadLn(Exec);

Reset(File1);
Reset(FileZ);
Reset(FileB);
ReWrite(File4);

{***************ii*iiiiitii‘tiiit‘ttii’i‘ti‘n‘tii***********************}

{* initialize ArInl & ArIn2 matrices containing problem data }

305

for I:=1 to 18 do {* number of problems

begin

ReadLn(Filel, NAct, NRes, Naml);
ReadLn(Filel, Duml, Resl, ResZ, Res3, Dum2, CPL);

for K:=1 to NAct do
begin
for L:=1 to 11 do
Read(File1, ArIn1[K, Ll);
end;

ReadLn(Filel); {* skip the blank line

ReadLn(File3, Name, NAC, CP, MDF, NDR, NCR, ARC, MRC, ARU, MRU);

}

{titi'k**i*****i*****i**i*ttiitiiiiiittiii*tfitiiiitit*t‘kii‘kiiiitiii’}

{* initialize ArIn2 matrix containing 30 reps x 6 factors sim data}

for J:=1 to 360 do {* number of reps in File2)

{ for each problem

begin
ReadLn(FileZ, Nam2, Spd, Dis, DT1, DT2, DT3);

for K:=1 to NAct do
begin
for L:=1 to 10 do
Read(File2, ArIn2[K, L1);
end;

ReadLn(FileZ); {* skip the blank line

{******************i************************************}

{* assign actual project duration ADur }

ADur:=ArIn2[NAct, 5];

{*i'*************itiitit‘ii‘itiii‘i‘*iiiititii*‘kttiiiii’iiti’ii}

{* calculate percent project duration over sched PDur }

RDur:=ADur/CPL;

{*ii’i‘ii'ii'kiitiiiit*ii'ki'ii*******************************}

{* calculate Actual Average Resource Utilization AARU }

Lod1:=0;
Lod2:=0;
Lod3:=0;

Cap1:=ADur*Resl;
Cap2:=ADur*Resz;
Cap3:=ADur*ResB;

for K:=1 to NAct do

306

}

}

begin

Lod1:=Lod1+ArIn2[K,8]*ArIn2[K,7l;
Lod2:=Lod2+ArIn2[K,9]*ArIn2[K,7];
Lod3z=Lod3+ArIn2[K,10]*ArIn2[K,7];

end;

AARU:=(Lod1+Lod2+Lod3)/(Cap1+Cap2+Cap3);

{*iittiifii‘iiii'i'ki'itiit*********iii'ki'*iiiitiiit'kti'kitifit'k}

{* calculate Actual Maximum Resource Utilization AMRU }

if (Lodl/Capl) > (Lod2/Cap2)
then AMRU:=(Lod1/Capl)
else AMRU:=(Lod2/Cap2);

if (Lod3/Cap3) > AMRU
then AMRU:=(Lod3/Cap3)

else;

{*iiiiiiii‘tittiiti'kittiiiiii'kiii'kiiitii'iiiitifiii********}

{* calculate project Net Present Values A/S/RNPV }

SNPV:=0;
ANPV:=0;

PMT:=0;

for K:=1 to NAct do

begin
SNPV:

SNPV:

SNPV:
ANPV:
ANPV:

ANPV:

end;

PMT:=1.

=SNPV+((Cost1*ArIn2[K,8]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
=SNPV+((Cost2*ArIn2[K,9]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
=SNPV+((Cost3*ArIn2[K,10]*ArIn2[K,6])*(exp(R*ArIn2[K,4])));
=ANPV+((Costl'ArInZ[K,8]*ArIn2[K,7])*(exp(R*ArIn2[K,5])));
=ANPV+((Cost2*ArIn2[K,9]*ArIn2[K,7])*(exp(R*ArIn2[K,5])));
=ANPV+((Cost3*ArIn2[K,10]*ArIn2[K,71)*(exp(R*ArIn2[K,S])));

5*(SNPV/(exp(R*ArIn2[NAct,4])1); {* what the firm will charge}

EPMT:=PMT*(exp(R*ArIn2[NAct,4ll); {* Expected NPV the payment}
APMT:=PMT*(exp(R*ArIn2[NAct,Sll); {* Actual NPV of the payment}

SNPV:=EPMT-SNPV; {* Firm's expected total NPV}
ANPV:=APMT-ANPV; {* Firm's actual total NPV}

{*iti********************************************i******}

{* calculate project Stability Sl/L/E (act deviation) }

Numl:=0;
Num2::0;
Den:=0;

for K:=1 to NAct do

begin

if ArIn2[K,3] > ArIn2[K,2]
then Num1:=Num1+ArIn2[K,3]-ArIn2[K,2]
else;

if ArIn2[K,3] < ArIn2[K,2]
then Num2:=Num2+ArIn2[K,2]-ArIn2[K,3]
else;

307

Den:=Den+ArIn2[K,7];
end;

Den:=NAct*ArIn2[Nact,5]—Den;

SlL:=1-(Num1/Den);
SlE:=1—(Num2/Den);
Sl:=(Num1+Num2)/NAct;

{i*i'i'kiiiiiiiiiiii’tiiiitiii*i'i'i'iiitiiiiiiiii'kiiiiitii'kti}

{* calculate project Stability SZ/I/O (res-weighted dis)}

Numl:=0;
Num2:=0;

Den:=ArIn2[NAct,5]*Resl-DTI;

Den:=Den+ArIn2[NAct,5]*ResZ-DT2;
Den:=Den+ArIn2[NAct,5]*Res3-DT3;

for K:=1 to NAct do

begin
if ArIn2[K,3]-ArIn2[K,2]>0 {* AST>SST (idle)
then Num1:=Num1+ArIn2[K,3]-ArIn2[K,2] {* add to Numl
else;
if ArIn2[K,4]-ArIn2[K,5]>0 {* SFT>AFT (idle)
then Numl:=Numl+ArIn2[K,4]-ArIn2[K,S] {* add to Numl
else;
if ArIn2[K,2]-ArIn2[K,3]>0 {* SST>AST (over)
then Num2:=Num2+ArIn2[K,2]-ArIn2[K,3] {* add to Num2
else;
if ArIn2[K,S]-ArIn2[K,4]>0 {* AFT>SFT (over)
then Num2:=Num2+ArIn2[K,S]-ArIn2[K,4] {* add to Num2
else;
end;

SZI:=1-(Num1/Den);
SZO:=1-(Num2/Den);
82:=SZI+SZO-1;

{***i***********i*****ititiii*it***************t***i**i*}

{* calculate Stability SB/I/O (res profile mismatch) }
{* initialize matrices Arl & Ar2 }

for K:=1 to 102 do
for L:=1 to 4 do
begin
Ar1[K,L]:=O;
Ar2[K,L]:=O;
end;

for K:=1 to NAct do
for L:=1 to 2 do
begin
Ar1[K,L]:=ArIn2[K,L+1];
Ar1[K,L+2]:=ArIn2[K,8]+ArIn2[K,9]+ArIn2[K,10];
Ar1[K+NACt,L]:=ArIn2[K,L+3];
Ar1[K+NAct,L+2]:=-1*(ArIn2[K,8]+ArIn2[K,9]+ArIn2[K,10]);
end;

308

{* chronologic sort matrix Arl scheduled (1,3) and actual (2,4) columns }

for K:=1 to 2 do
for L:=1 to 2*NAct do

begin
Tmp1:=Ar1[L.Kl;
Tmp2:=Ar1[L,K+2];

for M:=L+1 to 2*NAct do
begin
if Tmp1>Ar1[M,K] then
begin
Ar1[L,K]:=Ar1[M,K];
Ar1[L,K+2]:=Ar1[M,K+2];
Ar1[M,K]:=Tmpl;
Arl[M,K+2]:=Tmp2;
Tmp1:=Ar1[L,K] ,-
Tmp2 : =Ar1 [L, K+2l
end;
end;
end;

{* compress Arl matrix into Ar2 matrix; eliminating duplicate times }

Tmp1:=0; {* Time }
Tmp2:=0; {* Resources }
for K:= 1 to 2 do {* 2 passes through matrix } ‘
begin ,i
L:=1; {* initialize Arl index } @
N:=1; {* initialize Ar2 index } 5
while (L<=2*NAct) do {* Run until Sched / Act done } :3-
begin ‘fi
Tmp1:=Ar1[L,K]; {* Time = current value in Arl } TE
Tmp2:=0; {* initialize resource cumulator } E3
M:=L; {* initialize cumulator pointer } E
SE
while (Tmp1=Ar1[M,K]) do {* as long as current time=time ...} fig
begin 5%“
Tmp2:=Tmp2+Ar1[M,K+2]; {* add curr resources into cumulator } j;
M:=M+1; {* increment cumulator pointer } ‘fi,
L:=L+1; {* increment Arl pointer } s;
end; {* loop until time <> time ...} §§
Ar2[N,K]:=Tmp1; {* put value of time into Ar2 } 3i
Ar2[N,K+2]:=Tmp2; {* put value of cum res into Ar2 } ii
an
N:=N+1; {* increment Ar2 pointer } i1
31
; :5:
end; {* loop through sched/act ...} 3?.
3:3
end; {* Both Sched and Act complete } f~

{* cumulate areas under the resource profiles }

309

 

K:=1; { Index for Schedule }
L:=1; {* Index for Actual }
Tmp1:=0; {* Current # resources Scheduled }
Tmp2:=0; {* Current # resources Actual }
TLast:=0; {* Time of last event }
Num1:=0; {* cumulate SBI time Sched>Actual }
Num2:=0; {* cumulate 830 time Actual>Sched }
Dum:=0; {* dummy to carry current area calc }
Den:=0; {* total resource profile area }
Done:=False; {* exit criteria for cumulating loop }
while (Done=False) do {* Run until both Sched and Act done }

begin {* Go until done loop }

if Ar2[K,1] = Ar2[L,2] then {* Sched Time = Actual Time }
begin

Dum:=(Ar2[K,1]-TLast)*(Tmp1-Tmp2);
if Dum>0 then Num1:=Num1+Dum else Num2:=Num2+(-1*Dum);

Den:=Den+(Ar2[K,1]-TLast)*(Tmp1+Tmp2); {* Sched + Actual area }

Tmpl:=Tmp1+Ar2[K,3]; {* Update resources in use Sched }
Tmp2:=Tmp2+Ar2[L,4]; {* Update resources in use Actual }
TLast:=Ar2[K,1]; {* Sched=Act Time was the last event }
K:=K+1; {* increment both counters and }
L:=L+l; {* start again }

end

else {* Sched Time <> Actual Time }

begin {* Sched Time <> Actual Time loop }

if Ar2[K,1] < Ar2[L,2] then {* Sched Time < Actual Time }
begin

Dum:=(Ar2[K,1]-TLast)*(Tmp1-Tmp2);
if Dum>0 then Num1:=Num1+Dum else Num2:=Num2+(-1*Dum);

Den:=Den+(Ar2[K,1]-TLast)*(Tmp1+Tmp2); {* Sched + Actual area }

Tmpl:=Tmp1+Ar2[K,3]; {* Update resources in use Sched }
TLast::Ar2[K,1]; {* Sched Time was the last event }
K:=K+l;
end
else {* Sched Time not <= Actual Time }
if Ar2[K,1] > Ar2[L,2] then {* Sched Time > Actual Time }
begin

Dum:=(Ar2[L,2]—TLast)*(Tmp1-Tmp2);
if Dum>0 then Num1:=Num1+Dum else Num2:=Num2+(—1*Dum);

Den:=Den+(Ar2[L,2]-TLast)*(Tmp1+Tmp2); {* Sched + Actual area }

Tmp2::Tmp2+Ar2[L,4]; {* Update resources in use Actual }

310

TLast::Ar2[L,2]; {* Actual Time was the last event }

 

L:=L+1;
end
else {* Sched Time not <=> Actual Time?! }
end; {* Sched Time <> Actual Time Loop }
if ((Ar2[K+1,3]=0) and (Ar2[K+2,3]=O)) then {* Schedule has expired }
begin
Ar2[K+1,1]:=Ar2[L+l,2]; {* force another pass }
end
else
if ((Ar2[L+1,4]=0) and (Ar2[L+2,4]=0)) then {* Actuals have expired }
begin
Ar2[L+l,2]:=Ar2[K+l,1]; {* force another pass }
end
else;

if ((Ar2[K,3]=O)and(Ar2[K+1,3]=0)and(Ar2[L,4]=0)and(Ar2[L+1,4]=0))
then Done:=True else;

if ((L>=2*NAct) or (K>=2*NAct)) then Done:=True else;
end; {* Go until done loop }
{* Both Sched and Act have expired }
$3I2=1—Num1/Den;
SBO:=1-Num2/Den;

S3:=S3I+S30-l;

{i*i'**********iitif*i'rkiiiitii-i*iiiiiiiitttitt***********}

{* format all numerical values into strings for writing }

Str(Spd: 1:1, A1);
Str(Dis: 2, A2);
Str(AARU: 2:5, Bl);
Str(AMRU: 2:5, 82);
Str(ADur: 3:3, B3);
Str(RDur: 2:4, B4);
Str(SNPV: 6:2, BS);
Str(ANPV: 6:2, B6);
Str(SlL: 2:4, Cl);
Str(SlE: 2:4, C2);
Str(Sl: 4:4, C3);
Str(SZI: 2:4, C4);
Str(SZO: 2:4, C5);
Str(SZ: 2:4, C6);
Str(SBI: 2:4, C7);
Str(S30: 2:4, C8);
Str(S3: 2:4, C9);

{**************iiiitttiiiittiitii*i********************i}

{* Write converted data strings to File4 }

311

 

 

Write(File4,Name,' ',Sked,’ ',Exec,' ',A1,' ',A2,NAc,MDF,NDR,NCR,ARC,MRC);
Write(File4,ARU,' ',Bl,MRU,' ',BZ,CP,' ',B3,‘ ',B4,‘ ',BS,’ ',B6,' ');
WriteLn(File4,C1,' ',C2,‘ ',C3,' ',C4,‘ ',CS,‘ ',C6,' ',C7,' ',C8,‘ ',C9);

{*iitii*trkiiif'kii'iiit'kitiiiiii*iiiiti‘iit'fiiiiiitii’iii*iii*****ii***t******}

ReadLn(FileZ); {* next line of simulation data }
end; {* Next J~ # reps/prob in File 2 }
ReadLn(Filel); {* next line of schedule data }
end; {* Next I- # probs in Files 1 & 3}

{iiii*t't‘ktiifiiiiii'iif'kiiii'iiit*itiriiiiiittti**tit*************i**********}

Close(File1);
Close(File2);
Close(File3);
Close(Pile4);

end.

312

APPENDIX L

NPV VS. RT

313

Figure L-l:
NPV vs. rt: OPT

NPV vs. rt: OPT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60000

50000 . . ..i _ __ __ _

40000 1. -- _

30000 r 7 —

20000 . —

10000 » e

0 .— c
2
rt
Table L-l:
NPV vs. rt: OPT
rt Factor
1 2 4 Slope %elope

HEUR013A 5910 5882 5854 5827 -28 -0.47
HEUR013C 13285 13147 13011 12877 -136 -1.04
HEUR048A 6664 6628 6592 6557 -36 -0.54
HEUR048C 16624 16426 16232 16040 -195 -1.19
HEUROSGA 6660 6620 6580 6541 -40 -0.60
HEUROSSC 19677 19445 19217 18992 -228 -1.18
HEUR014A 3910 3870 3831 3793 -39 -1.02
HEURO14B 7746 7619 7496 7374 -124 -1.64
HEUR014C 9978 9786 9599 9417 -187 -1.93
HEURO1 5A 6450 6387 6326 6265 -61 -0.97
HEURO15B 12721 12521 12325 12133 -196 -1.58
HEURO1SC 16499 16170 15848 15535 -321 -2.01
HEUR105A 19591 19288 18991 18699 -297 -1.55
HEUR105C 48027 46473 44985 43561 -1489 -3.25
HEUR1 07A 20190 19862 19540 19226 -321 -1.63
HEUR107C 51635 49719 47899 46168 -1822 -3.73
HEUR110A 12646 12518 12393 12268 -126 -1.01
HEUR11OC 32619 31862 31129 30419 -733 -2.33

 

314

 

Figure L-2:
NPV vs. rt: SLK

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NPV vs. rt: SLK

60000

50000 -__,_ .. 4 77+ m - -— —-— - .- ..

40000 .____ - - ' L

30000 ,-_- - ———. 5

20000 . - -

10000 ,L._

o
1 2 3 4
rt
Table L-2:
N PV vs. rt: SLK
rt Factor
1 2 4 Slope %slope

HEURO1 3A 5909 5880 58952 5824 £8 -0.48
HEURO13C 13279 13134 12992 12851 -142 -1.09
HEUR048A 6661 6622 6583 6545 -39 -0.59
HEUR0480 16623 16424 16228 16035 -196 -1.20
HEUR056A 6660 6620 6580 6541 ~40 -0.60
HEUROSSC 19675 19441 19210 18983 -230 -1.19
HEUR014A 3910 3870 3831 3793 —39 -1.02
HEURO14B 7738 7605 7474 7346 -131 -1.74
HEUR014C 9952 9736 9525 9321 -21 1 -2.18
HEU R01 5A 6450 6388 6327 6266 -61 -0.96
HEURO1 58 12697 12474 12257 12044 -218 -1.76
HEURO15C 16493 16158 15832 15514 -327 -2.04
HEUR1 05A 19583 19273 18970 18672 -304 -1.59
HEU R1 050 48027 46474 44986 43562 -1488 -3.25
HEUR1 07A 20190 19862 19542 19227 -321 -1.63
HEUR1 07C 51614 49679 47840 46093 -1840 -3.77
HEUR110A 12642 12510 12381 12253 -130 -1.04
HEUR1 1 00 32625 31874 31146 30441 -728 -2.31

 

315

 

Figure L-3:
NPV vs. rt: LFT

NPV vs. rt: LFT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60000
50000 ) i.._ ~ _ e —
40000 .L_ A _ I: _ I ’ __ .E
30000 ~—— —— —— — 4
20000 «es — r I
10000 . — 1 '
O l
1 2 3 4
It
Table L-3:
N PV vs. rt: LFT
rt Factor
1 2 4 Slope %elope
__H_EUR01 3A 5909 5880 5851 5823 -29 -0.49
HEUR013C 13280 13138 12997 12858 -141 -1.08
HEUR048A 6661 6623 6585 6547 -38 —O.58
HEUR048C 16624 16427 16232 16041 -195 -1.19
HEUR056A 6660 6620 6580 6541 -40 -0.60
HEUR056C 19677 19444 19216 18990 -229 -1.18
HEUR014A 3910 3870 3831 3793 -39 -1.02
HEUR014B 7732 7592 7455 7321 -137 -1 .82
HEUR014C 9963 9757 9557 9361 -201 -2.08
HEURO15A 6450 6388 6327 6266 -61 -0.96
HEURO1SB 12715 12510 12309 12112 -201 -1.62
HEURO15C 16498 16167 15845 15531 -322 -2.01
HEUR105A 19584 19275 18973 18676 -303 -1.58
HEUR1 056 48028 46476 44989 43566 -1487 -3.25
HEUR1 07A 20184 19851 19525 19206 -326 -1.66
HEUR1 070 51619 49689 47855 461 12 -1836 -3.76
HEUR110A 12642 12511 12382 12255 -129 -1.04
HEUR11OC 32626 31875 31 148 30443 -727 -2.31

 

316

 

Figure L-4:
NPV vs. rt: RSO

NPV VS. rt: RSO

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60000

50000 1— —— —- -—~ — e ’ a

40000 e — i — s —— i — —

a 30000 «— s A—
20000 1% --
10000 ...__
0
rt
Table L-4:
NPV vs. rt: RSO
rt Factor
1 2 4 Slope %elope
figURM 3A 5910 5882 5854 5827 -28 -0.47

HEUR°13C 13285 13147 13011 12877 -136 -1.04
HEUR°48A 6663 6627 6591 6555 -36 -0.55
HEUR°48C 16624 16426 16232 16040 -195 -1.19
HEUR°56A 6657 6614 6572 6530 -42 -O.64
HEUR°56C 19677 19445 19217 18992 -228 -1.18
HEUR°14A 3907 3864 3822 3780 -42 -1 .10
HEUR°14B 7745 7618 7493 7371 -125 -1.65
HEUR°14C 9978 9786 9598 9416 -187 -1.93
HEUR°1 5A 6446 6380 6315 6251 -65 -1.03
HEURO1SB 12720 12518 12321 12128 -197 -1.59
HEURO15C 16498 16168 15846 15533 -322 -2.01
HEUR1°5A 19585 19277 18975 18679 -302 -1.58
HEUR1°5C 48027 46473 44985 43561 -1489 -3.25
HEUR107A 20181 19845 19516 19195 -329 -1.67
HEUR1°7C 51635 49719 47899 46168 -1822 -3.73
HEUR1 1 0A 12645 12516 12390 12265 -127 -1.02
HEUR1 1°C 32619 31862 31129 30419 -733 -2.33

 

317

 

Figure L-5:
NPV vs. rt: LSC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NPV ve. rt: LSC

60000

50000 ~~ ——.. — 7 e ——— —~

40000 .._ —— — h H

§ 30000 4e— A- - a: 4
20000 .. ——
10000 __
0
2
rt
Table L-5:
NPV vs. rt: LSC
rt Factor
1 2 4 Slope %slope
flUR01 3A 5908 5879 5849 5820 -29 -0.50

HEUR013C 13279 13134 12992 12851 -142 -1.09
HEURO48A 6661 6623 6584 6547 -38 -0.58
HEUR048C 16623 16424 16228 16035 -196 -1.20
HEUR056A 6657 6614 6571 6529 -43 -0.65
HEUR056C 19675 19441 19210 18983 -230 -1.19
HEUR014A 3908 3866 3825 3784 -41 -1.07
HEURO14B 7736 7600 7466 7336 -133 -1.77
HEURO14C 9953 9738 9528 9324 -210 -2.18
HEUR01 5A 6445 6378 6312 6246 -66 -1.04
HEUR01 58 12695 12471 12252 12037 -219 -1.77
HEURO1 SC 16492 16156 15829 15509 -328 -2.05
HEUR1 05A 19580 19267 18960 18659 -307 -1.61
HEUR105C 48027 46474 44986 43562 -1488 -3.25
HEUR107A 20181 19845 19516 19195 -329 -1.67
HEUR107C 51614 49679 47840 46093 -1840 -3.77
HEUR110A 12642 12511 12382 12255 -129 -1.04
HEUR11 DC 32625 31874 31146 30441 -728 -2.31

 

318

 

 

Figure L-6:
NPV vs. rt: DCF

NPV V8. rt: DCF

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60000

50000 1W- W:-.-_:- ~. -_ . +7.-. . ~_—~ —°~

40000 —— -—W W W — — —— W

E 30000 :W— : - W - ________ W ,
20000 A _._____,
10000 W
0
0.1 0.2 0.3 0.4
rt
Table L-6:
NPV vs. rt: DCF
rt Factor
1 2 4 Slope %slope
JEURM 3A 5916 5895 5874 5853 -21 -0.36

HEUR01 3C 13328 13232 13137 13043 -95 -0.72
HEUR048A 6671 6643 6615 6587 -28 -0.43
HEUR0480 16688 16553 16419 16286 ~134 -0.81
HEUROSSA 6673 6645 6618 6591 -27 -0.41
HEUR056C 19755 19600 19446 19293 -154 -0.79
HEUR014A 3921 3893 3865 3837 -28 -0.73
HEUR014B 7771 7670 7570 7471 -100 -1.31
HEUR014C 10016 9861 9709 9559 -152 -1.56
HEUR01 5A 6467 6423 6378 6334 -44 -0.69
HEUR01 53 12765 12607 12452 12299 —155 -1.24
HEURO15C 16594 16355 16120 15890 -235 -1.44
HEUR1 05A 19665 19433 19205 18980 -228 -1 . 18
HEUR1 05C 48560 47502 46474 45475 -1028 -2.19
HEUR107A 20282 20042 19806 19574 -236 -1.18
HEUR1 070 52291 50978 49709 48482 -1270 -2.52
HEUR1 1 GA 12679 12584 12490 12397 -94 -0.75
HEUR1 1 06 32874 32360 31856 31363 -504 -1.57

 

319

 

Figure L-7:
NPV vs. rt: BCP

NPV vs. rt: BCP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a 30000 — W

20000 — I

10000 W— ____, g

0 i

2 i

rt
Table L-7:
NPV vs. rt: BCP
rt Factor
1 2 4 Slope %slope

_H_EUR01 3A 5908 5878 5849 5820 -29 -0. 50
HEUR013C 13288 13152 13019 12887 -134 -1.02
HEUR048A 6659 6619 6579 6539 -40 -0.61
HEUR04BC 16624 16427 16232 16040 -195 -1.19
HEUROSGA 6660 6620 6580 6541 -40 -0.60
HEUROSGC 19676 19444 19215 18989 -229 -1.18
HEUR014A 3910 3870 3830 3792 -39 -1.02
HEUR014B 7741 7610 7482 7357 -128 -1.70
HEUR014C 9960 9751 9548 9350 -203 -2.1 1
HEURO15A 6450 6388 6327 6266 -61 -0.96
HEURO1SB 12705 12489 12279 12073 -211 -1.70
HEURO15C 16474 16121 15777 15443 ~344 -2.15
HEUR1 05A 19556 19221 18892 18571 -328 -1.72
HEUR1 05C 48027 46474 44987 43562 -1488 -3.25
HEU R1 07A 20190 19862 19542 19227 -321 -1.63
HEUR1 07C 51609 49670 47827 46075 -1845 -3.78
HEUR110A 12636 12499 12364 12231 -135 -1.09
HEUR110C 32617 31859 31124 30413 ~735 -2.33

 

320

 

 

APPENDIX M

DEGRADATION (PERCENT CHANGE)

321

 

Table M-l: Percent Change (variability none-some)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADE; av WADC av avg
OPT FRN -1.9 -2.2 -29.8 -28.3 6,} «4.9
FRW -2.9 -3l.2 -5.5
NRN -1.3 -23.5 -3.8
NRW -2.7 -28.5 -4.9
SLK FRN -1.6 -l.9 -29.8 -22.9 6,} 1-5.1
FRW -2.7 -31.7 -S.6
NRN -1.1 -27.5 -4.6 ,
NRW -2.2 -27.6 -5.0
LFT FRN -1.5 -3.8 -28.2 -27.8 ~5.l -4.9
FRW -2.6 -30.6 -5.4
NRN -9.0 -24.9 -4.2
NRW -2.2 -27.3 -4.9
RSO FRN -2.1 -3.8 -26.1 -25.8 -2.9 -3.4
FRW -3.2 -3 l .4 -5.1
NRN -1.3 -l7.2 -1.3
NRW -2.9 -28.4 -4.4
LSC FRN -1.6 -2.1 -24.0 -25.9 -2.5 -3.4
FRW -2.8 -30.0 -5.0
NRN -1.5 -23.8 -l.9
NRW -2.6 -25.6 -4.3
DCF FRN -1.1 -3.0 -28.0 -25.4 -. +5.3
FRW -2.2 -28.5 -5.9
NRN -7.2 -20.8 -4.4
NRW -l.5 -24.4 -5.0
BCP FRN -1.5 -2.9 -31.9 -30.2 -5.6 -5.3
FRW -2.6 -32.8 -5.8
NRN -5.2 -28.0 -4.6
NRW -2.1 -28.4 -5.1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

322

 

Table M-2: Percent Change (disruption none-frequent/short)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ADUR Avg WADC av R av

OPT FRN -2.0 -2.1 -22.7 -33.9 -3.2 -3.9
FRW -1.8 -25.7 -3.6
NRN -2.7 -53.4 -4.5
NRW -2.5 -33.8 -4.1

SLK FRN -1.9 -2.1 -23.6 -34.9 -3.3 -3.9
FRW -1.7 -26.6 -3.6
NRN -2.5 -56.0 -4.6
NRW -2.2 -33.5 -4.1

LFT FRN -1.8 -2.1 £9 -36.1 -;.2 -3.9
FRW -1.7 -26.1 -3.6
NRN -2.6 -61.8 —4.9
NRW -2.3 -33.4 -3.9

RSO FRN -1.9 -2.0 -21.1 -32.0 ii -3.4
FRW -1.8 -25.0 -3.4
NRN -2.4 -49.1 -3.5
NRW -2.5 -32.9 -3.9

LSC FRN 2.0 -2.1 -21.1 -32.7 -2.5 -3.4
FRW -1.8 -26.1 -3.5
NRN -2.2 -51.3 -3.4
NRW -2.4 -32.6 —4.0

DCF FRN -1.6 -1.7 -20.6 -32.5 -3.2 -3.8
FRW -l .4 -24.2 -3.8
NRN -1.8 -50.7 -4.0
NRW -1.9 -34.5 -4.3

BCP FRN -1.6 -1.7 20.4 -34.8 -;9 -3.7
FRW -1.5 -24.5 -3.5
NRN ~1.5 -61.5 -4.5
NRW -2.2 -32.9 -4.0

 

 

 

 

 

 

 

323

 

 

Table M-3: Percent Change (disruption none-infrequent/long)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AQUR av WADC v v

OPT FRN -6.2 ~5.4 -85.6 -80.0 -8.2 -7.6
FRW -5.4 -81.0 -8.0
NRN -4.9 -76.1 -6.4
NRW -5.8 -77.2 -7.8

SLK FRN -6.2 -5.3 -87.6 -80.4 -§.4 -7.6
FRW -5.3 -82.8 -8.1
NRN -4.4 -74.6 -6.4
NRW -S.2 -76.5 -7.6

LFT FRN -5.9 -5.0 -85.3 -78.9 -8.3 -7.5
FRW -5.2 -83.6 -8.1
NRN -4.1 -73.5 -6.3
NRW -4.9 -73.3 -7.4

RSO FRN -6.1 -5.5 -82.1 -76.9 -7.1 -6.8
FRW —5.5 -79.9 -7.8
NRN -4.5 -71.2 -4.9
NRW -5.7 -74.5 -7.4

LSC FRN -6.3 -5.5 -82.4 -77.4 -7.0 -7.0
FRW -5.6 -82.7 -8.1
NRN -4.1 -67.5 -5.0
NRW -5.8 -77.0 -7.7

DCF FRN -5.6 -4.9 -83.3 -82.6 -8.7 -8.2
FRW -4.8 -80.9 -8.8
NRN -4.4 -83.4 -6.8
NRW -4.7 -82.8 -8.4

BCP FRN -5.4 -4.7 -81.1 -78.6 -7.6 -7.3
FRW -4.8 -78.0 -7.6
NRN -3.5 -80.4 —6.4
NRW -4.9 -74.8 -7.4

 

 

 

324

 

Table M-4: Percent Change (disruption frequent/short-infiequent/long)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AD_I_J_R__ av WAD av mi
OPT FRN 4.1 -3.3 ;6_2.9 -46.1 -5.0 -3.8
FRW -3.6 -55.2 —4.4
NRN -2.2 -22.7 -l.9
NRW -3.3 -43.4 -3.7
SLK FRN -4.2 -3.2 -64.1 -45.5 -5.1 -3.7
FRW -3.5 -56.2 -4.5
NRN -2.0 -18.6 -1.8
NRW -2.9 -43.0 -3.5
LFT FRN -4.0 -3.0 -62.4 -42.9 -5.1 -3.6
FRW -3.5 -S7.4 -4.5
NRN -1.7 -11.7 -l.4 ,
NRW -2.6 -39.9 -3.4
RSO FRN -4.1 -3.3 -61.0 -44.9 -4.4 -3.4
FRW -3.7 -55.0 -4.4
NRN -2.1 -22.1 -1.5
NRW -3.2 -41.6 -3.4
LSC FRN -4.2 -3.3 -6l.3 -44.7 -4.6 -3.6
FRW -3.7 -56.6 -4.7
NRN -2.0 -16.3 -1.5
NRW -3.3 -44.4 -3.7
DCF FRN -3.9 -3.2 -62.7 -50.0 -5.5 -4.4
FRW -3.4 -56.6 -5.0
NRN -2.7 -32.7 -2.9
NRW -2.7 -48.2 -4.0
BCP FRN -3.8 -2.9 -60.6 -43.7 -4.7 -3.6
FRW -3.2 -53.4 -4.1
NRN -2.0 -18.9 -1.9
NRW -2.7 -41.9 -3.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

325

 

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