Military Operations Research: Quantitative Decision Making

388 Pages·1997·27.67 MB·english

by  N. K. Jaiswal (auth.)

MILITARY OPERATIONS
RESEARCH:
Quantitative
Decision Making
INTERNATIONAL SERIES IN
OPERATIONS RESEARCH & MANAGEMENT SCIENCE
FrederickS. Hillier, Series Editor
DepartmentofOperations Research
Stanford University
Stanford, California
Saigal, Romesh
The UniversityofMichigan
LINEARPROGRAMMING: A Modern IntegratedAnalysis
Nagurney, AnnalZhang, Ding
UniversityofMassachusetts@Amherst
PROJECTEDDYNAMICALSYSTEMSAND VARIATIONAL INEQUALITIES
WITHAPPLICATIONS
Padberg, ManfrediRijal, MinendraP.
NewYorkUniversity
LOCATION, SCHEDULING, DESIGNANDINTEGER
PROGRAMMING
Vanderbei, RobertJ.
PrincetonUniversity
LINEARPROGRAMMING: FoundationsandExtensions
MILITARY OPERATIONS
RESEARCH :
Quantitative
Decision Making
N. K. JAISWAL
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
Jaiswal, N. K.
Military operations research : quantitative decision making / N. K.
Jaiswal.
p. cm. --(International series in operations research &
management science ; 5)
Includes bibliographical references and index.
ISBN 978-1-4613-7880-8 ISBN 978-1-4615-6275-7 (eBook)
DOI 10.1007/978-1-4615-6275-7
1. Military art and science--Decision making--Mathematical models.
2. Operations research. 1. Title. II. Series.
VI 04.134 1997
355.4--dc21 96-53961
CIP
Copyright © 1997 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1997
Softcover reprint of the hardcover 1s t edition 1997
AII rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC
Printed an acid-free paper.
CONTENTS
Preface ix
Acknowledgments xi
1 OPERATIONS RESEARCH IN DEFENSE 1
1.1 The Need forOperations Research in Defense 1
1.2 The Birth of OR 2
1.3 MilitaryOR 5
1.4 MethodologyofOR Analysis 6
1.5 Success ofaMilitaryOR Study 10
2 SEARCH, DETECTION AND DAMAGE ASSESSMENT 13
2.1 TargetAcquisition, Engagementand Damage Assessment 13
2.2 DetectionTheory 15
Sensors 15
DetectionModels 16
DetectionModelsfor RadarandSonar 17
2.3 Search Models 19
TargetDistribution,Lateral Rangeand SweepWidth 20
Random and ExhaustiveSearch 21
OptimalSearchStrategy 24
Localization andTracking 25
Identification and Recognition 28
2.4 HitProbability 28
DistributionofErrors 29
Circular,Rectangularand EllipticTargets 30
2.5 Damage Assessment 38
PointTargets 39
AreaTargets 42
2.6 Salvo and Pattern Firing 47
2.7 SingleVs. MultipleAiming Point 52
2.9 Shooting Tactics Based on Damage Information 53
3 SIMULATION OF MILITARYSYSTEMS 59
3.1 System, Model and Simulation 59
VI
3.2 Monte Carlo Sampling Procedure 60
AreaDamaged by BombsorShells 61
3.3 Continuous System Simulation 65
3.4 Discrete System Simulation 66
HitProbabilityofaGunagainstaCircularTarget 68
SurvivabilityofaTank 69
AchievableHitProbability from aTankGun 74
AnAirDefenseNavalEngagement 77
3.5 Weapon System Simulation Vs. Combat Simulation 81
3.6 Simulation Packages 83
4 WAR GAMES 91
4.1 Combat Simulations, WarGames and Theoryof Games 91
4.2 HistoryofWarGames 92
4.3 Classification ofWarGames 93
4.4 Development ofWarGames 96
4.5 Land WarGames 102
4.6 Naval WarGames 105
4.7 AirWarGames 106
4.8 OtherWarGames 107
5 COSTEFFECTIVENESSANALYSIS 111
5.1 Effectiveness and System Cost 111
5.2 Cost Effectiveness Using Fixed EffectivenessApproach 112
5.3 Cost Effectiveness Using Figure of Merit 116
CostEffectivenessofAirDefenseGunsand Surface-to-AirMissiles 117
CostEffectivenessofAir-to-SurfaceMissilesandBombs 121
5.4 Fallacies of Cost Effectiveness Analysis 124
5.5 Cost and Operational Effectiveness Analysis (COEA) 125
6 OPTIMIZATION PROBLEMS 129
6.1 Resource Allocation Problems 129
6.2 Linear Programming 130
TheWeaponMixProblem 132
WeaponDeploymentProblem 134
Weapon TargetAllocation Problem 137
SortieAllocationProblem 137
AirliftProblem 139
6.3 The Transportation Problem 142
6.4 The Assignment Problem 144
6.5 IntegerProgramming 145
146
GomoryCuttingPlaneMethod
148
BranchandBound Method
vii
6.6 Multiobjective Programming 151
6.7 Dynamic Programming 152
6.8 NonlinearProgramming 158
6.9 Applications ofOptimization Techniques in Gulf War 165
7 HEURISTICOPTIMIZATION 169
7.1 HeuristicOptimization Algorithms 169
7.2 Weapon Target Allocation Problem in Multiple LayerDefense 169
7.3 Simulated Annealing 172
7.4 Genetic Algorithm 179
7.5 Artificial Neural Networks 184
Cohen-GrossbergTheorem 186
TheContinuous Hopfield Neural NetworkModel 187
OptimizationUsingNeural Networks 188
7.6 Salient Features ofthe Three HeuristicOptimizationTechniques 205
8 THE ANALYTIC HIERARCHYPROCESS 209
8.1 Multicriteria Decision Making 209
8.2 Delphi Method 209
8.3 Decision MatrixApproach 210
8.4 Forced Decision MatrixApproach 211
8.5 Analytic Hierarchy Process 213
Prioritization ofAirborneSurveillanceSystems 216
EvaluatingPerformanceofTanks 224
ProjectSelection 225
8.6 Problems and Modifications of AHP 227
9 HOMOGENEOUS COMBAT MODELS 233
9.1 Lanchester Equations ofWarfare 233
9.2 OtherAttrition Laws 238
9.3 CombatTermination Rules 243
9.4 Measure of Combat Success 246
9.5 Combat Modeling with Spatial Effects 260
9.6 Stochastic Duels 268
9.7 Stochastic Combat Models 270
9.8 Combat Models with NonlinearEffects 276
9.9 Airand Naval Combat Models 277
10 HETEROGENEOUS COMBAT MODELS 283
10.1 The (m,n) model 283
FireAllocationPolicies 284
Solutionofthe(m,n)Model 284
Vlll
10.2 Aggregation 287
10.3 Scaling Methods 290
10.4 An Alternative Approach to Aggregation 293
10.5 Variable Resolution Models 296
10.6 Optimization Models 298
ApplicationofOptimizationModels toStudy Weapon Dominance 305
ApplicationofOptimization Models toStudyWeaponIntroduction 306
11 THREAT ASSESSMENT: STATIC AND DYNAMIC ANALYSES 311
11.1 Threat Assessment 311
11.2 StaticAnalysis 312
BeanCountMethod 313
Weapon EffectivenessIndex(WEI)/WeaponUnitValue(WUV) 313
Potential Anti-PotentialMethod 315
ForcePotential UsingOperational LethalityIndices (OUs) 317
Situationally ModifiedForceStrength (SMFS)Method 322
11.3 Dynamic Analysis 328
QuantifiedJudgmentMethodofAnalysis(QJMA) 328
SituationalForceScoring(SFS) 333
Adaptive DynamicModel 342
Arms Race Models 351
12 ANALYSIS OFSTRATEGIC STABILITY ISSUES 355
12.1 Concept of Stability 355
12.2 Measureof MilitaryStability 357
12.3 Linear Defense Models of Stability 359
StationaryLinearDefenseModel 360
MobileLinearDefenseModel 363
12.4 Stable Regional Force Ratio Model 365
Analytical StabilityModel (ASAM) 366
GeneralizedForceRatioModel (GEFRAM) 369
12.5 Methods for Enhancing Stabilityinthe Region 371
Author Index 373
SUbject Index 379
PREFACE
Operations Research (OR) emerged in an effortto improve the effectiveness of
newly inducted weapons and equipment during World War II. While rapid
growthofORledto itsbecomingan importantaidto decision making in all sectors
including defense, its contribution in defense remained largely confined to
classified reports. Very few books dealing with applications of quantitative
decision making techniques in military have been published presumably due to
limitedavailabilityofrelevantinformation.
The situation changedrapidly during the last few years. The recognition ofthe
subject of Military Operations Research (MOR) gave tremendous boost to its
development. Books and journals on MOR started appearing. The number of
sessions on MOR at national and international conferences also registered an
increase. The volume of teaching, training and research activities in the field of
MORatmilitaryschoolsandnon-militaryschoolsenhancedconsiderably. Military
executives and commanders started taking increasing interest in getting scientific
answers to questions pertaining to weapon acquisition, threat perception and
quantification, assessment of damage or casualties, evaluation of chance of
winning a battle, force mix, deployment and targeting ofweapons against enemy
targets, war games and scenario evaluation. Most of these problems were being
tackled on the basis ofintuition, judgment and experience or analysis under very
simple assumptions. In an increasingly sophisticatedand complex defense scenario
resulting in advances in equipment and communications, the need for
supplementingthesepracticesbyscientificresearch inMORbecameimperative.
Due to the above reasons, the need of preparing a book on MOR, useful for
institutions and OR groups in the Ministry of Defense, service organizations,
defense consultancy and research organizations, military schools and universities
involved in teaching and research in MOR, was strongly felt. This book is
primarilywritten for those interested in learningthe applicationsofORtechniques
to solve military problems. It also discusses theoretical concepts needed for
analysis of military issues both at tactical and strategic levels. The research
scholars in the area ofMOR may also find it useful for their research work as it
contains a comprehensive bibliography. An elementary knowledge of OR and
ComputerScienceispresumed.
A brief preview ofthe book is as follows: Chapter I presents the origin and
methodology of OR, need for MOR and factors relevant in a MOR study.
x
Chapter 2 discusses search, detection and damage assessment. These topics,
generally discussed separately, have been merged in one chapter to provide the
reader with the basic concepts and formulae needed in subsequent chapters.
Chapter 3 discusses discrete and continuous system simulation and illustrates the
methodology through a number of examples relevant to military systems. A
number of packages useful for combat simulation have been briefly discussed.
Chapter 4 extends the idea ofsimulation to design and development ofwar games
and briefly discusses a number of software packages. Chapter 5 deals with the
methodology of Cost Effectiveness Analysis and also Cost and Operational
Effectiveness Analysis. Chapter 6 illustrates a number ofoptimization techniques
such as Linear Programming, Integer Programming, Multiobjective Programming,
Dynamic Programming and Nonlinear Programming. The examples considered in
this chapterrelateto mission planningand logisticsmanagement. Chapter7covers
heuristic optimization techniques such as Simulated Annealing, Genetic Algorithm
and Artificial Neural Networks. Chapter 8 deals with Analytic Hierarchy Process
for ranking and shortlisting ofalternatives orcourses ofaction in situations where
qualitativeevaluationofalternatives isonly possible. Chapters9and 10deal with
homogeneous and heterogeneous combat models. Chapter 11 discusses a number
ofstatic techniques for force potential evaluation such as Weapon Effectiveness
Index (WEI)/Weapon Unit Value (WUV), Potential Anti-Potential method and
Situationally Modified Force Strength. It also discusses dynamic models such as
Quantified Judgment Method of Analysis (QJMA), Situational Force Scoring
(SFS), Adaptive Dynamic Model (ADM) and Arms Race Model. Finally, Chapter
12 extends the methodology of threat analysis discussed in Chapter 11 to the
analysisofregionalstabilityand itsrelevancetothemultipolarworld.
A number of examples have been solved in each chapter to illustrate the
application ofthe techniques ofMOR to military systems. The data used in these
examples are hypothetical. These do not correspond to any existing weapon or
military situation since the purpose is to illustrate the application of MOR in
defense decisionmakingratherthan actual problem solving.
It is hopedthatthe bookwill promote further researchand applicationsof MOR
techniquesto defensedecisionmaking.
A-2/28, Janakpuri N. K. Jaiswal
New Delhi-I10058, India