Table Of ContentINTERNATIONAL SERIES IN OPERATIONS
RESEARCH AND MANAGEMENT SCIENCE
Combat Modeling
Alan Washburn
Moshe Kress
Combat Modeling
INT.SERIESINOPERATIONSRESEARCH&MANAGEMENTSCIENCE
SeriesEditor:FrederickS.Hillier,StanfordUniversity
SpecialEditorialConsultant:CamilleC.Price,StephenF.AustinStateUniversity
Titleswithanasterisk(*)wererecommendedbyDr.Price
Washburn & Kress/COMBAT MODELING
Netessine&Tang/CONSUMER-DRIVENDEMANDANDOPERATIONSMANAGEMENTMODELS:
ASystematicStudyofInformation-Technology-EnabledSalesMechanisms
Saaty&Vargas/DECISIONMAKINGWITHTHEANALYTICNETWORKPROCESS:Economic,
Political,Social&TechnologicalApplicationsw.Benefits,Opportunities,Costs&Risks
Yu/TECHNOLOGYPORTFOLIOPLANNINGANDMANAGEMENT:PracticalConceptsandTools
Kandiller/PRINCIPLESOFMATHEMATICSINOPERATIONSRESEARCH
Lee&Lee/BUILDINGSUPPLYCHAINEXCELLENCEINEMERGINGECONOMIES
Weintraub/MANAGEMENTOFNATURALRESOURCES:AHandbookofOperationsResearch
Models,Algorithms,andImplementations
Hooker/INTEGRATEDMETHODSFOROPTIMIZATION
Dawandeetal/THROUGHPUTOPTIMIZATIONINROBOTICCELLS
Friesz/NETWORKSCIENCE,NONLINEARSCIENCEandINFRASTRUCTURESYSTEMS
Cai,Sha&Wong/TIME-VARYINGNETWORKOPTIMIZATION
Mamon&Elliott/HIDDENMARKOVMODELSINFINANCE
delCastillo/PROCESSOPTIMIZATION:AStatisticalApproach
Jo´zefowska/JUST-IN-TIMESCHEDULING:Models&AlgorithmsforComputer&Manufacturing
Systems
Yu,Wang&Lai/FOREIGN-EXCHANGE-RATEFORECASTINGWITHARTIFICIALNEURAL
NETWORKS
Beyeretal/MARKOVIANDEMANDINVENTORYMODELS
Shi&Olafsson/NESTEDPARTITIONSOPTIMIZATION:MethodologyandApplications
Samaniego/SYSTEMSIGNATURESANDTHEIRAPPLICATIONSINENGINEERINGRELIABILITY
Kleijnen/DESIGNANDANALYSISOFSIMULATIONEXPERIMENTS
Førsund/HYDROPOWERECONOMICS
Kogan&Tapiero/SUPPLYCHAINGAMES:OperationsManagementandRiskValuation
Vanderbei/LINEARPROGRAMMING:Foundations&Extensions,3rdEdition
Chhajed&Lowe/BUILDINGINTUITION:InsightsfromBasicOperationsMgmt.Modelsand
Principles
Luenberger&Ye/LINEARANDNONLINEARPROGRAMMING,3rdEdition
Drewetal/COMPUTATIONALPROBABILITY:AlgorithmsandApplicationsintheMathematical
Sciences*
Chinneck/FEASIBILITYANDINFEASIBILITYINOPTIMIZATION:AlgorithmsandComputation
Methods
Tang,Teo&Wei/SUPPLYCHAINANALYSIS:AHandbookontheInteractionofInformation,System
andOptimization
Ozcan/HEALTHCAREBENCHMARKINGANDPERFORMANCEEVALUATION:AnAssessment
usingDataEnvelopmentAnalysis(DEA)
Wierenga/HANDBOOKOFMARKETINGDECISIONMODELS
Agrawal&Smith/RETAILSUPPLYCHAINMANAGEMENT:QuantitativeModelsandEmpirical
Studies
Brill/LEVELCROSSINGMETHODSINSTOCHASTICMODELS
Zsidisin&Ritchie/SUPPLYCHAINRISK:AHandbookofAssessment,Management&Performance
Matsui/MANUFACTURINGANDSERVICEENTERPRISEWITHRISKS:AStochasticManagement
Approach
Zhu/QUANTITATIVEMODELSFORPERFORMANCEEVALUATIONANDBENCHMARKING:Data
EnvelopmentAnalysiswithSpreadsheets
Kubiak/PROPORTIONALOPTIMIZATIONANDFAIRNESS*
Bier&Azaiez/GAMETHEORETICRISKANALYSISOFSECURITYTHREATS*
∼Alistoftheearlypublicationsintheseriesisfoundattheendofthebook∼
·
Alan Washburn Moshe Kress
Combat Modeling
123
AlanWashburn MosheKress
DepartmentofOperationsResearch DepartmentofOperationsResearch
NavalPostgraduateSchool NavalPostgraduateSchool
Monterey,CA93943 Monterey,CA93943
USA USA
awashburn@nps.edu mkress@nps.edu
ISSN0884-8289
ISBN978-1-4419-0789-9 e-ISBN978-1-4419-0790-5
DOI10.1007/978-1-4419-0790-5
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2009929309
(cid:2)c SpringerScience+BusinessMedia,LLC2009
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein
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software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if
they are not identified as such, is not to be taken as an expression of opinion as to whether or not
theyaresubjecttoproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
This book deals with the processes, methods, and concepts that lie behind modern
models of combat. It is intended for readers with at least a scientific bachelor’s
degree and some background in basic probability concepts. It includes three ap-
pendices that address general quantitative methods that are applied throughout the
book. Appendix A is a review of probability concepts, which are involved in al-
most every chapter. A reader who has never studied probability before should con-
sider reading this appendix, at least, before continuing. Appendices B and C are
minimal introductions to the topics of optimization and Monte Carlo simulation.
Use will be made throughout this book of Microsoft Excel™ workbooks de-
veloped by the authors. Some of these workbooks include VBA (Visual Basic for
Applications) code for certain functions or commands. The reader should obtain
the zipped folder CombatModeling1.zip from the “downloads” link at the url
http://faculty.nps.edu/awashburn/ . After obtaining the folder, unzip it and read
Readme.txt and Errata1.txt. As long as proper credit for authorship is given, the
workbooks may be freely distributed. An email link for author Washburn will also
be found at that url or substitute “mkress” for “awashburn” to reach author Kress.
Feedback will be appreciated. If you find an error, please point it out so we
can incorporate it in the errata. If there are subsequent editions of this book, we
will take advantage of your comments about organization and utility.
We hope you find our book useful.
Alan Washburn Moshe Kress
Operations Research Department Operations Research Department
Naval Postgraduate School Naval Postgraduate School
v
Contents
Chapter 1: Generalities and Terminology...........................................................1
1.1 Introduction..........................................................................................1
1.2 Classification of Combat Models.........................................................2
1.3 Modeling Shortcuts..............................................................................4
1.4 Notation and Conventions..................................................................10
1.5 Book Overview..................................................................................11
Chapter 2: Shooting Without Feedback............................................................15
2.1 Introduction........................................................................................15
2.2 Single-Shot Kill Probability...............................................................16
2.3 Multiple-Shot Kill Probability............................................................22
2.4 Multiple Shots, Multiple Targets, One Salvo.....................................35
2.5 Further Reading..................................................................................40
Chapter 3: Shooting with Feedback...................................................................47
3.1 Introduction........................................................................................47
3.2 Feedback on the Status of a Single Target.........................................48
3.3 Feedback on Miss Distances..............................................................49
3.4 Shoot Look Shoot with Multiple Targets...........................................52
3.5 Further Reading..................................................................................59
Chapter 4: Target defense..................................................................................65
4.1 Introduction........................................................................................65
4.2 Defense of One Target Against Several Identical Attackers..............66
4.3 Defense of Multiple Targets Against ICBM Attack...........................73
Chapter 5: Attrition Models...............................................................................79
5.1 Introduction........................................................................................79
5.2 Deterministic Lanchester Models.......................................................79
5.3 Stochastic Lanchester Models............................................................86
5.4 Data for Lanchester models................................................................92
5.5 Aggregation and Valuation.................................................................98
5.6 The FAst THeater Model (FATHM)................................................100
vii
viii Contents
Chapter 6: Game Theory and Wargames.......................................................111
6.1 Introduction......................................................................................111
6.2 Game Theory....................................................................................112
6.3 Wargames.........................................................................................128
Chapter 7: Search..............................................................................................133
7.1 Introduction......................................................................................133
7.2 Sweep Width....................................................................................135
7.3 Three “Laws” for Detection Probability...........................................137
7.4 Barrier Patrol....................................................................................143
7.5 Optimal Distribution of Effort for Stationary Targets......................145
7.6 Moving Targets................................................................................151
7.7 Further Reading................................................................................158
Chapter 8: Mine Warfare.................................................................................161
8.1 Introduction......................................................................................161
8.2 Simple Minefield Models.................................................................162
8.3 The Uncountered Minefield Planning Model (UMPM)...................163
8.4 Minefield Clearance.........................................................................168
8.5 Mine Games.....................................................................................174
Chapter 9: Unmanned Aerial Vehicles............................................................185
9.1 Introduction......................................................................................185
9.2 Routing a UAV................................................................................186
9.3 Unmanned Combat Aerial Vehicles.................................................198
9.4 Summary, Extensions and Further Reading.....................................208
Chapter 10: Terror and Insurgency................................................................211
10.1 Introduction......................................................................................211
10.2 The Effect of Suicide Bombing........................................................212
10.3 Response Policies for Bioterrorism – The Case of Smallpox...........221
10.4 Counterinsurgency...........................................................................228
Appendix A: Probability – the Mathematics of Uncertainty.........................237
Appendix B: Optimization................................................................................257
Appendix C: Monte Carlo Simulation.............................................................263
References..........................................................................................................267
Index...................................................................................................................275
Chapter 1
Generalities and Terminology
I’m no model lady. A
model’s just an imitation of
the real thing.
Mae West
1.1 Introduction
A model is an abstraction of reality. An abstraction can take many forms: an archi-
tect might construct a physical miniature model of the building he plans; a CEO of
a corporation might use a diagram to present a new business idea, and a physicist
might use a set of differential equations to represent some physical phenomenon.
The need for models stems from the fact that the real world is too complicated for
us to reason about and contains many details that are not necessarily relevant. Our
limited intellects permit us to deal only with abstractions that retain the essence of
the matter without the distracting details. The miniature model of the building, the
diagram, and the set of differential equations are manifestations of these abstrac-
tions and henceforth called simply models. Thus, models are entities of various
types – physical, notional, or mathematical – that share the fact that they represent
only an abstraction of a real object or situation. Models are used for reasoning,
insight, planning, and prediction. They need to capture the key factors of the
object or situation and faithfully represent them so that the models can be util-
ized effectively.
This book is about combat models, models that describe or represent weapon
systems and combat situations. As mentioned above, there are several types. In
order to organize our thinking on the matter, it is important to introduce terms by
which one type of model can be distinguished from another, as well as terms about
how such models are developed, used, and tested. The development of such a lexi-
con is one object of this chapter (Section 1.2). Another object (Section 1.3) is to
discuss certain modeling assumptions that are employed frequently enough to de-
serve names. It is the authors’ contention that these “shortcut” assumptions are
dangerous as well as useful and powerful and should therefore be discussed im-
mediately in a book such as this. Section 1.4 summarizes the notational conven-
tions that will be used throughout the book, and Section 1.5 is an overview of
subsequent chapters.
A. Washburn, M. Kress, Combat Modeling, International Series in Operations 1
Research & Management Science 134, DOI 10.1007/978-1-4419-0790-5_1,
© Springer Science+Business Media, LLC 2009
2 1 Generalities a nd Terminology
1.2 Classification of Combat Models
Unfortunately, the business of combat modeling has long suffered from a lexicon
that often obscures fundamental relationships and parallels. There have been sev-
eral attempts to remedy this by authorities who announce glossaries of what terms
should mean, but none of these have been completely successful. It is more or less
like trying to impose standards on (say) French – the people will speak as they
wish, despite the best efforts of the authorities. Terms such as “identity simula-
tion” and “agent-based simulation” are regularly used in spite of being missing
from such glossaries and seem to ease communication between those in the know.
Still, one ought to make an effort to use terms that are in some sense standard. Our
approach in this book will roughly follow the glossary defined by the United
States Department of Defense (DoD, 1998). Our first, definitive use of terms will
be italicized in the following.
The real combat situation will inevitably differ from its model, particularly be-
cause of the complexity and uncertainty associated with combat. Judging the ex-
tent to which the model agrees with the real world is called validation, to be dis-
tinguished from judging whether a particular implementation of a model (e.g., a
computer program) is correct in the sense of being faithful to the model. The latter
activity is called verification and has nothing to do with the real world, at least not
directly.
Models are either stochastic or deterministic. Intuitively, a stochastic model as-
sumes uncertain or probabilistic inputs regarding an experiment or a situation and
makes an indefinite prediction of the results. A deterministic model states exactly
what will happen, as if there were no uncertainty. More formally, a stochastic
model requires the terminology of the theory of probability (events, random vari-
ables and probabilities, see Appendix A) for its description, whereas a determinis-
tic model does not. The contrast is particularly important for Lanchester models
(Chapter 5), where the same data can be employed by both types of model. Most
combat models considered in this book are stochastic.
The DoD glossary points out that the terms “modeling” and “simulation” are
often used interchangeably, but nonetheless offers a separate definition of simula-
tion. Our habit in this book will be to use the word simulation only to refer to a
particular method for implementing stochastic models that generates a sequence of
replications of an abstract experiment, making inferences from the sequence. The
most important kind of simulation is Monte Carlo simulation, as described in Ap-
pendix C. This type of model is one of seven shown in Fig. 1. The three types to
the right of it are also simulations, by our definition, since all face the problem of
generating sufficient replications in an uncertain environment to enable reliable in-
ference. The models differ in the way in which replications are generated and
managed, whether computationally or manually. Contrary to simulations, analytic
models do not rely on multiple replications, instead developing formulas that de-
scribe results in a concise way. Analytic models may or may not be stochastic.
