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Optimal Resource Allocation: With Practical Statistical Applications and Theory PDF

251 Pages·2013·8.38 MB·English
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OPTIMAL RESOURCE ALLOCATION OPTIMAL RESOURCE ALLOCATION With Practical Statistical Applications and Theory Igor A. Ushakov Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http:// www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifi cally disclaim any implied warranties of merchantability or fi tness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profi t or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data Ushakov, I. A. (Igor Alekseevich) Optimal resource allocation : with practical statistical applications and theory / Igor A. Ushakov. pages cm Includes bibliographical references and index. ISBN 978-1-118-38997-3 (cloth) 1. Resource allocation–Statistical methods. I. Title. T57.77.U84 2013 658.4’033–dc23 2012040258 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 In memory of John D. Kettelle, Jr., my friend, colleague, and informal teacher CONTENTS 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 vii viii CONTENTS 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 CONTENTS ix 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 x CONTENTS 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 Index 237

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A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATIONOptimal 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
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