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Optimal Resource Allocation: With Practical Statistical Applications and Theory

Book Description


Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems.

Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features:

  • An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology

  • Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection

  • The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems

  • Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithms

Optimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.

Table of Contents

  1. Cover
  2. Title page
  3. Copyright page
  4. Dedication
  5. Preface
  6. CHAPTER 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
    4. 1.4 Repairable Redundant Group with Active Redundant Units
    5. 1.5 Repairable Redundant Group with Standby Redundant Units
    6. 1.6 Multi-level Systems and System Performance Estimation
    7. 1.7 Brief Review of Other Types of Redundancy
    8. 1.8 Time Redundancy
    9. 1.9 Some Additional Optimization Problems
  7. CHAPTER 2: Formulation of Optimal Redundancy Problems
    1. 2.1 Problem Description
    2. 2.2 Formulation of the Optimal Redundancy Problem with a Single Restriction
    3. 2.3 Formulation of Optimal Redundancy Problems with Multiple Constraints
    4. 2.4 Formulation of Multi-Criteria Optimal Redundancy Problems
  8. CHAPTER 3: Method of Lagrange Multipliers
  9. CHAPTER 4: Steepest Descent Method
    1. 4.1 The Main Idea of SDM
    2. 4.2 Description of the Algorithm
    3. 4.3 The Stopping Rule
    4. 4.5 Approximate Solution
  10. CHAPTER 5: Dynamic Programming
    1. 5.1 Bellman's Algorithm
    2. 5.2 Kettelle's Algorithm
  11. CHAPTER 6: Universal Generating Functions
    1. 6.1 Generating Function
    2. 6.2 Universal GF (U-function)
  12. CHAPTER 7: Genetic Algorithms
    1. 7.1 Introduction
    2. 7.2 Structure of Steady-State Genetic Algorithms
    3. 7.3 Related Techniques
  13. CHAPTER 8: Monte Carlo Simulation
    1. 8.1 Introductory Remarks
    2. 8.2 Formulation of Optimal Redundancy Problems in Statistical Terms
    3. 8.3 Algorithm for Trajectory Generation
    4. 8.4 Description of the Idea of the Solution
    5. 8.5 Inverse Optimization Problem
    6. 8.6 Direct Optimization Problem
  14. CHAPTER 9: Comments on Calculation Methods
    1. 9.1 Comparison of Methods
    2. 9.2 Sensitivity Analysis of Optimal Redundancy Solutions
  15. CHAPTER 10: Optimal Redundancy with Several Limiting Factors
    1. 10.1 Method of “Weighing Costs”
    2. 10.2 Method of Generalized Generating Functions
  16. CHAPTER 11: Optimal Redundancy in Multistate Systems
  17. CHAPTER 12: Case Studies
    1. 12.1 Spare Supply System for Worldwide Telecommunication System Globalstar
    2. 12.2 Optimal Capacity Distribution of Telecommunication Backbone Network Resources
    3. 12.3 Optimal Spare Allocation for Mobile Repair Station
  18. CHAPTER 13: Counter-Terrorism: Protection Resources Allocation
    1. 13.1 Introduction
    2. 13.2 Written Description of the Problem
    3. 13.3 Evaluation of Expected Loss
    4. 13.4 Algorithm of Resource Allocation
    5. 13.5 Branching System Protection
    6. 13.6 Fictional Case Study
    7. 13.7 Measures of Defense, Their Effectiveness, and Related Expenses
    8. 13.8 Antiterrorism Resource Allocation under Fuzzy Subjective Estimates
    9. 13.9 Conclusion
  19. About the Author
  20. Index