Optimal Resource Allocation – With Practical Statistical Applications and Theory

IGOR USHAKOV, DrSci, was previously a professor at both The George Washington University and the University of California, San Diego; chair of the Department of Large Scale Systems at the Moscow Institute of Physics and Technology; and a principal engineer at Qualcomm. In addition, he is founder of the International Group on Reliability's Gnedenko Forum and has authored or edited dozens of books and published more than 300 journal papers on reliability engineering, logistics, and quality assurance.

Preface xi 1 BASIC MATHEMATICAL REDUNDANCY MODELS 1 1.1 Types of Models 2 1.2 Non-repairable Redundant Group with Active Redundant Units 3 1.3 Non-repairable Redundant Group with Standby Redundant Units 7 1.4 Repairable Redundant Group with Active Redundant Units 10 1.5 Repairable Redundant Group with Standby Redundant Units 13 1.6 Multi-level Systems and System Performance Estimation 15 1.7 Brief Review of Other Types of Redundancy 16 1.8 Time Redundancy 24 1.9 Some Additional Optimization Problems 27 Chronological Bibliography of Main Monographs on Reliability Theory (with topics on Optimization) 30 2 FORMULATION OF OPTIMAL REDUNDANCY PROBLEMS 33 2.1 Problem Description 33 2.2 Formulation of the Optimal Redundancy Problem with a Single Restriction 35 2.3 Formulation of Optimal Redundancy Problems with Multiple Constraints 39 2.4 Formulation of Multi-Criteria Optimal Redundancy Problems 43 Chronological Bibliography 45 3 METHOD OF LAGRANGE MULTIPLIERS 48 Chronological Bibliography 55 4 STEEPEST DESCENT METHOD 56 4.1 The Main Idea of SDM 56 4.2 Description of the Algorithm 57 4.3 The Stopping Rule 60 4.5 Approximate Solution 66 Chronological Bibliography 68 5 DYNAMIC PROGRAMMING 69 5.1 Bellman's Algorithm 69 5.2 Kettelle's Algorithm 73 Chronological Bibliography 84 6 UNIVERSAL GENERATING FUNCTIONS 85 6.1 Generating Function 85 6.2 Universal GF (U-function) 87 Chronological Bibliography 94 7 GENETIC ALGORITHMS 96 7.1 Introduction 96 7.2 Structure of Steady-State Genetic Algorithms 100 7.3 Related Techniques 102 Chronological Bibliography 104 8 MONTE CARLO SIMULATION 107 8.1 Introductory Remarks 107 8.2 Formulation of Optimal Redundancy Problems in Statistical Terms 108 8.3 Algorithm for Trajectory Generation 108 8.4 Description of the Idea of the Solution 111 8.5 Inverse Optimization Problem 114 8.6 Direct Optimization Problem 124 Chronological Bibliography 129 9 COMMENTS ON CALCULATION METHODS 130 9.1 Comparison of Methods 130 9.2 Sensitivity Analysis of Optimal Redundancy Solutions 135 10 OPTIMAL REDUNDANCY WITH SEVERAL LIMITING FACTORS 142 10.1 Method of "Weighing Costs" 142 10.2 Method of Generalized Generating Functions 146 Chronological Bibliography 149 11 OPTIMAL REDUNDANCY IN MULTISTATE SYSTEMS 150 Chronological Bibliography 170 12 CASE STUDIES 172 12.1 Spare Supply System for Worldwide Telecommunication System Globalstar 172 12.2 Optimal Capacity Distribution of Telecommunication Backbone Network Resources 179 12.3 Optimal Spare Allocation for Mobile Repair Station 183 Chronological Bibliography 190 13 COUNTER-TERRORISM: PROTECTION RESOURCES ALLOCATION 191 13.1 Introduction 191 13.2 Written Description of the Problem 192 13.3 Evaluation of Expected Loss 195 13.4 Algorithm of Resource Allocation 197 13.5 Branching System Protection 201 13.6 Fictional Case Study 210 13.7 Measures of Defense, Their Effectiveness, and Related Expenses 217 13.8 Antiterrorism Resource Allocation under Fuzzy Subjective Estimates 223 13.9 Conclusion 232 Chronological Bibliography 232 About the author 235