Optimal Resource Allocation With Practical Statistical Applications and Theory

by Ushakov, Igor A.

• ISBN13: 9781118389973
• ISBN10: 1118389972
• Edition: 1st
• Format: Hardcover
• Copyright: 2013-04-08
• Publisher: Wiley

Summary

With an overview of different approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology, this book details the applied methods of optimization, describes various methods of optimal redundancy problem solutions, and demonstrates how they can be solved with numerical examples and statistical methods. it is an ideal text for statistics and mathematics students as well as for students and practitioners in engineering and operations research.

Author Biography

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.

Table of Contents

1.  BASIC MATHEMATICAL REDUNDANCY MODELS 8

1.1. Types of Models 8

1.2. Non-repairable redundant group with active redundant units 9

1.3. Non-repairable redundant group with standby redundant units 11

1.4. Repairable redundant group with active redundant units 13

1.5. Repairable redundant group with standby redundant units 16

1.6. Multi-level  systems and system performance estimation 17

1.7. Brief review of other types of redundancy 18

1.8. Time redundancy 23

1.9. Some additional optimization problems 25

Chronological Bibliography of Main Monographs 26

2. FORMULATION OF THE OPTIMAL REDUNDANCY PROBLEMS 29

2.1. Problems description 29

2.2. Formulation of the optimal redundancy problem with a single restriction 29

2.3. FORMULATION OF OPTIMAL REDUNDANCY PROBLEM WITH MULTIPLE CONSTRAINS 33

2.4. Formulation of multi-criteria optimal redundancy problems 35

Bibliography to Chapter 2 36

3. METHOD OF LAGRANGE MULTIPLIERS 40

Bibliography to Chapter 3 44

4. STEEPEST DESCENT METHOD 45

4.1. The main idea of SDM 45

4.2. Description of the algorithm 46

4.3. The stopping rule 47

4.5. Approximate solution 50

Bibliography to Chapter 452

5. DYNAMIC PROGRAMMING 53

5.1. Bellman’s  Algorithm 53

5.2. Kettelle's Algorithm 57

Bibliography to Chapter 5 62

6. UNIVERSAL GENERATING FUNCTIONS 62

6.1. Generating function 62

6.2. Universal GF (U-function) 63

Bibliography to Chapter 6 69

7. GENETIC ALGORITHMS 69

7.1. Introductory 69

7.2. Structure of Steady-state Genetic Algorithms 71

7.3. Related techniques 72

Bibliography to Chapter 773

8. MONTE CARLO SIMULATION 75

8.1. Introductory remarks 75

8.2. Formulation of optimal redundancy problems in statistical terms 75

8.3. Algorithm for Trajectory Generation 75

8.4. Description of the Idea of the Solution 77

8.5. Inverse Optimization Problem 79

8.6. Direct Optimization Problem 86

Bibliography to Chapter 8 89

9. COMMENTS ON CALCULATION METHODS 89

9.1. Comparison of methods 89

9.2. Sensitivity analysis of optimal redundancy solutions 92

10. OPTIMAL REDUNDANCY WITH SEVERAL LIMITING FACTORS 97

10.1. Method of “weighing costs” 97

10.2. Method of Generalized Generating Functions 99

Bibliography to Chapter 10 100

11. Optimal Redundancy in Multistate Systems 101

Bibliography to Chapter 11 112

12. CASE STUDIES 113

A. Spare supply system for worldwide telecommunication system Globalstar 113

B. Optimal capacity distribution of telecommunication backbone network resources 120

C. Optimal Spare Allocation for Mobile Repair Station 123

Bibliography to Chapter 12 126

13. Counter-terrorism: Protection Resources Allocation 127

13.1. Introduction 127

13.2. Verbal description of the problem 127

13.3. Evaluation of expected loss 129

13.4. Algorithm of resources allocation 129

13.5. Branching System Protection 132

13.6. Fictional “Case Study” 138

13.7. Antiterrorism resources allocation under fuzzy subjective estimates 146

The problem of optimal resources allocation for antiterrorism preventive measures is naturally based on subjective estimates made by experts in this field. Relying on expert estimates is inevitable in this case: there is no other possibility to get input data for the system survivability analysis. There is no such phenomenon like “collecting real data”, moreover, there is no “homogenous samples” for consistent statistical analysis of observations, since any case is unique and non-reproducible. Nevertheless, quantitative analysis of necessary level of protection has to be performed 146

What are the subjects of such expertise? It seems to us that they are: 146

Bibliography to Chapter 13 152

About the author 155