Constraint Theory (eBook)

​George Friedman is a Professor of Practice in the Astronautical Engineering Department of the Viterbi School of Engineering of the University of Southern California. He has developed and taught graduate courses in systems engineering with emphasis on the management of complexity and decision science. This book is the product of one of these courses. He has had over 45 years of experience in industry, retiring from the Northrop Corporation as their Corporate Vice President of Engineering and Technology. He worked on a wide variety of aerospace programs and served as a consultant to all branches of the Department of Defense, NASA, the National Science Foundation, and Department of Energy as well as to the NATO industrial advisory group. He was a founder of the International Council on Systems Engineering (INCOSE), served as its third president, was elected a fellow and is on the editorial board of INCOSE’s journal, Systems Engineering. He has also been a member of the Institute of Electrical and Electronic Engineers (IEEE) since its formation from the IRE and AIEE, was elected a fellow and was the vice president for publications of the IEEE Transactions on Aerospace and Electronics Systems.  He received the Baker Prize for the best paper published by all societies of the IEEE in 1970 -- the subject of the paper was Constraint Theory. Phan Phan is a Lecturer in the Astronautical Engineering Department of the Viterbi School of Engineering of the University of Southern California (USC).  He has assisted and taught graduate courses in systems engineering, systems management, lean operations and economic analysis. He has had over 36 years of technical and managerial experience in government, military and various industries, including oil & gas exploration, commercial and military aircraft, unmanned sensors, and major weapon systems. His industry assignments included Mobil Research & Development, General Dynamics, Lockheed Aeronautical Systems, McDonnell Douglas and Boeing Integrated Defense Systems. As a registered Professional Engineer in California, he currently works as a reliability analyst with the Naval Surface Warfare Center -- Corona Division. He has also served in the U.S. Navy Reserve as an Engineering Duty Officer, attaining the rank of Captain, and currently assigned to Naval Sea Systems Command. His previous Navy assignments included Office of Naval Research/Naval Research Laboratory, Program Executive Office Integrated Warfare Systems, Naval Space & Warfare Systems Command, Mobile Mine Assembly Group, Naval Weapons Station Seal Beach and Naval Shipyard Long Beach. He received his B.S. in Engineering from the University of Alabama in Huntsville, Master of Engineering from the University of Texas at Arlington, MBA from California State University - Fullerton, M.S. in Systems Architecture & Engineering from USC, Master of Engineering Acoustics from the Naval Postgraduate School, and Ph.D. in Industrial & Systems Engineering from USC. The topic of his doctoral dissertation was “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models," the main contribution to the second edition of this book.

Fronticepiece 6
Preface 8
Acknowledgments 9
Introduction 10
A Warmup Problem in Complexity 14
About the Authors 16
Contents 18
Chapter 1 MOTIVATIONS 21
1.1 TRENDS AND PROBLEMS IN SYSTEM TECHNOLOGIES 21
1.2 AN EXAMPLE OF LOW DIMENSION 24
1.3 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE 36
1.4 PRELIMINARY CONCLUSIONS 40
1.5 A LITTLE WINDOW INTO FUTURE CHAPTERS 42
1.6 PROBLEMS FOR THE CURIOUS READER 43
Chapter 2 THE FOUR-FOLD WAY 44
2.1 PROLOGUE: THE MANAGER AND ANALYST DISCUSS THE ORIGINS OF MULTIDIMENSIONAL MODELS AND WELLPOSEDNESS 44
2.2 THE FIRST VIEW: SET THEORETIC 47
2.3 THE SECOND VIEW: FAMILY OF SUBMODELS 54
2.4 THE THIRD VIEW: THE BIPARTITE GRAPH 57
2.5 THE FOURTH VIEW: THE CONSTRAINT MATRIX 58
2.6 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY 59
2.7 THE MANAGER AND ANALYST CONTINUE THEIR DIALOGUE 59
2.8 CHAPTER SUMMARY 65
2.9 PROBLEMS FOR THE INTERESTED STUDENT 67
Chapter 3 GENERAL RESULTS 68
3.1 LANGUAGE AND MATHEMATICS 68
3.2 MOST GENERAL TRUSTWORTHY RESULTS 70
3.3 CLASSES OF RELATIONS 75
3.4 MANAGER AND ANALYST REVISITED 78
3.5 CHAPTER SUMMARY 79
3.6 PROBLEMS FOR THE GENERAL STUDENT 79
Chapter 4 REGULAR RELATIONS 80
4.1 COGNITIVE BARRIERS TO CIRCUITS 80
4.2 NODE, KNOT AND BASIC NODAL SQUARE SANCTIFICATION 82
4.3 USEFUL PROPERTIES OF BIPARTITE GRAPHS 91
4.4 CORNERING THE CULPRIT KERNELS TEN EASY PIECES
4.5 CONTINUING THE PURSUIT INSIDE THE CIRCUIT CLUSTERS (cc) 107
4.6 LOCATING BNSs WITHIN A MODEL GRAPH 110
4.7 QUERIES FOR THE REGULAR STUDENT 118
Chapter 5 MODEL CONSISTENCY AND COMPUTATIONAL ALLOWABILITY 120
5.1 ZERO CONSTRAINT ALL ALONG THE COMPUTATIONAL PATH 120
5.2 RECAPITULATION OF COMPUTATIONAL FLOW 122
5.3 GENERAL PROCEDURE FOR DETERMINING CONSISTENCY AND ALLOWABILITY IN A MODEL OF REGULAR RELATIONS 124
5.4 DETECTION OF OVERLAPPING BNS 128
5.5 RELIEF OF OVER-CONSTRAINT 133
5.6 EXPANSION OF RESULTANT CONSTRAINT DOMAINS 134
5.7 PROCESSING OF COMPUTATIONAL REQUESTS 143
5.7.1 INITIAL SIMPLIFICATION OF MODEL GRAPH 143
5.7.2 SIMPLIFYING MODEL GRAPH DURING CONSTRAINT PROPAGATION 145
5.7.3 UNALLOWABLE COMPUTATIONAL REQUESTS 147
5.7.3.1 OVER-CONSTRAINT OF NODES 147
5.7.3.2 RELEVANCY OF DEPENDENT VARIABLES 148
5.8 SUMMARY OF CHAPTER AND CONSTRAINT THEORY TOOLKIT 150
5.9 QUERIES FOR THE REGULAR STUDENT 155
Chapter 6 DISCRETE AND INTERVAL RELATIONS 156
6.1 METAMODEL ISSUES AND PERSPECTIVES 156
6.2 THE GENERAL TAXONOMY AND PRIMARY PROPERTY OF DISCRETE RELATIONS 157
6.3 BOOLEAN RELATIONS 157
6.4 TOPOLOGICAL IMPLICATIONS 164
6.5 ALLOWABILITY OF DISCRETE COMPUTATIONS 166
6.6 INEQUALITY RELATIONS 168
6.7 SUMMARY 171
6.8 PROBLEMS FOR THE DISCRETE STUDENT 173
Chapter 7 THE LOGICAL STRUCTURE OF CONSTRAINT THEORY 174
7.1 OVERVIEW 174
7.2 POSTULATES AND PHILOSOPHICAL ASSUMPTIONS 174
7.3 DEFINITIONS 175
7.4 THEOREMS 175
7.5 GRAPHS OF THE LOGICAL STRUCTURE OF CONSTRAINT THEORY 176
7.6 COMPLETENESS 177
Chapter 8 EXAMPLES OF CONSTRAINT THEORY APPLIED TO REAL-WORLD PROBLEMS 182
8.1 APOLOGIES NOT REQUIRED 182
8.2 COST AS AN INDEPENDENT VARIABLE (CAIV) 182
8.3 THE KINEMATICS OF FREE-FALL WEAPONS 190
8.4 THE DEFLECTION OF AN EARTH-THREATENING ASTEROID EMPLOYING MASS DRIVERS 195
Chapter 9 MANAGER AND ANALYST MEET AGAIN 202
Appendix A COMPUTATIONAL REQUEST DISAPPOINTMENTS RESULTS OF THE USC ALLOW ABILITY PROJECT
Appendix B GRAPH THEORY OVERVIEW 215
Appendix C THE LOGIC OF “IF” AND “IF AND ONLY IF” 219
Appendix D ALGEBRAIC STRUCTURES 221
References 228
Index 231