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INTERNATIONAL 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 [email protected] [email protected] 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 connection with any form of information storage and retrieval, electronic adaptation, computer 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 appendices 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 developed 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 abstractions 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 lexicon 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 conventions 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 several 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 simulation” 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 distinguished 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 deterministic 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 simulation. 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 describe results in a concise way. Analytic models may or may not be stochastic.