Professor of Operations Research, Operations Research Department, Naval Postgraduate School, Monterey, California 93943

Robert M. Oliver

Professor Emeritus, Department of Industrial Engineering and Operations
Research, University of California at Berkeley

McGraw Hill Reference Page to "Decision Making and Forecasting"

- Hard Cover: 0-07-048027-3
- Soft Cover: 0-07-113970-2

- Model Building with Influence Diagrams
- Integration of Forecasting and Decision Making
- Graphical Presentation of Solutions and Policy Analysis
- Analysis of multi-attribute problems

Preface xv 1 BASIC CONCEPTS 1 1.1 Introduction 1 1.2 The Importance of Models in Decision Making 2 1.3 The Nature of a Decision Problem 3 1.4 Modeling Uncertainty with Probability 4 1.5 A Brief Review of Probability 6 Outcomes, Events, and Probabilities 7 Conditional Probability and Independence 10 Partitions and the Law of Total Probability 12 Bayes' Rule 13 Random Variables and Distributions 14 Expected Values 18 Marginal, Conditional, and Joint Probabilities 20 Probabilities and Odds 22 Conditional Independence 23 Coherence 24 1.6 The Role of Forecasting 24 1.7 Elements of Influence Diagrams and Decision Trees 26 Directed Arcs in Influence Diagrams 27 Branches in Decision Trees 27 1.8 The Decision Sapling 28 The Value of Perfect Information 32 1.9 Criteria for Comparing Results 33 1.10 Clarifying Terminology 35 1.11 Book Overview 36 1.12 Summary and Insights 39 Problems 40 2 USING BASELINE FORECASTS 43 2.1 Introduction 43 2.2 A Crop Protection Decision 46 2.3 A Decision in Football 48 The Coach's Decision 48 Betting on the Football Game 50 Analysis of the Football Betting Problem 52 An Alternate Modeling of Outcomes: Point Scores 55 2.4 A Limited Life Inventory Problem 56 Marginal Analysis 58 2.5 The Newsboy Problem 59 2.6 The Value of Perfect Information 63 2.7 Airline Seat Allocation Based on Price and Demand 65 Space Allocation for Two Passenger Classes 65 Two-Class Space Allocation with Perfect Information 69 Discount-Seat Allocations in One Passenger Class 71 A Dynamic Decision Model 73 2.8 Pricing and Marketing of Hotel Rooms 74 2.9 The Newsboy Problem with Additional Information 77 2.10 Summary and Insights 78 Problems 79 3 FORECASTS FOR DECISION MODELS 83 3.1 Introduction 83 3.2 The Role and Value of Forecasts 84 Some Examples of Forecasts 88 3.3 Several Types of Forecasts 88 Point Forecasts 89 Probability and Odds Forecasts 90 Categorical Forecasts 92 3.4 Decision Probabilities, Likelihoods, and Bayes' Rule 95 Decision Probabilities and Likelihoods 96 Bayes' Rule with Probability Forecasts 97 Bayes' Rule with Categorical Forecasts 99 Summary of Results in Matrix Notation 101 Sensitivity of Decision Probabilities 101 Node and Arc Reversal with Bayes' Rule 103 Using Bayes' Rule with Odds 105 3.5 Multiple Likelihoods and Dependent Forecasts 108 Two Forecasts for a Single Event 109 Likelihoods for Four Colon Cancer Tests 111 Forecasts for Sequential Tests 115 3.6 Optimal Crop Protection 116 3.7 Credit Scoring Decisions 121 Notation for Scores and Forecasts 121 Expected Profit and Risk of an Individual 124 Expected Profit for the Portfolio 126 3.8 Summary and Insights 128 Problems 130 4 MODEL BUILDING 133 4.1 Introduction 133 4.2 Constructing Influence Diagrams 135 The Procedure 136 Arc Reversal and Cycles 139 No-Forgetting Arcs 140 Perfect Information 141 4.3 Examples of Model Formulations 143 A Decision to Seed Clouds in Hurricanes 144 Keeping Good Credit Accounts at a Bank 148 A Navy Mobile Basing Decision Problem 152 Colon Cancer Diagnosis 156 4.4 Building and Solving Decision Trees 160 Node Outcome and Alternative Sets 161 Drawing Consistent Decision Trees 164 Perfect Information 166 Decision Tree Solutions 167 4.5 The Bank Credit Problem 169 The Economic Value of a Performance Forecast 171 Perfect Information about Performance 172 4.6 Colon Cancer Decision Problems 173 Sequential Decisions for Colon Cancer Detection 177 4.7 Irrelevant Decisions and a Game-Show Problem 179 4.8 A Budget Planning Problem 182 4.9 Summary and Insights 187 Problems 190 5 MODEL ANALYSIS 192 5.1 Introduction 192 5.2 Betting on the Football Game 193 5.3 An Expert Opinion Model 197 An Aircraft Part Decision Problem 199 A Crop Protection Problem 202 5.4 Sensitivity Analysis Using Decision Probabilities 204 The Economic Value of a Forecast 207 5.5 Sensitivity Analysis Using Forecast Likelihoods 210 5.6 Problems with One or More Forecasts 213 Optimal Policies and Expected Returns 215 A Numeric Example 217 A Single Decision with Two Forecasts 219 5.7 Sequential Decisions Using Sequential Forecasts 222 5.8 Summary and Insights 227 Problems 229 6 SUBJECTIVE MEASURES AND UTILITY 232 6.1 Introduction 232 6.2 Basics of Utility Theory 233 Indifference Probabilities and Certainty Equivalents 234 Assumptions of Utility Theory 235 6.3 Determination of Utility Functions 237 Utilities as Indifference Probabilities 238 Utilities from Certainty Equivalents 239 Cautionary Comments 240 6.4 Examples of Utility Functions 241 An Exponential Utility Function 242 A Logarithmic Utility Function 243 6.5 Measures of Risk 244 Risk Premium 245 A Risk Aversion Function 245 6.6 Some Properties of Utility Functions 248 6.7 Summary and Insights 249 Problems 250 7 MULTIATTRIBUTE PROBLEMS 252 7.1 Introduction 252 7.2 A Decision Sapling with Two Attributes 253 7.3 The Crop Protection Problem with Two Attributes 256 7.4 Car Ranking and Replacement 258 Ranking Cars by Preference 258 Car Replacement 261 7.5 The Added Cost of Conflict Resolution 263 Car Ranking Revisited 265 7.6 Assessment of Trade-Offs through Preferences 266 Two Attributes 267 Many Attributes and Alternatives 268 Ranking Cars Using Three Attributes 269 The Car Replacement Problem Revisited 270 7.7 A Hierarchical Multiattribute Model 271 A Hierarchical Cost-Benefit Model 272 * The Two-Hierarchy Multigroup Model 275 * Tradeoff Weights through Indifference Probabilities 276 7.8 The Analytic Hierarchy Process 278 Ranking Alternatives with AHP 280 Avoiding Rank Reversal in AHP 284 Finding the Weights in AHP 286 7.9 A Budget Planning Example with Three Attributes 288 7.10* Multiattribute Utility 291 An Example with Two Attributes 295 7.11 Summary and Insights 298 Problems 300 8 FORECAST PERFORMANCE 303 8.1 Introduction 303 8.2 Forecast Calibration 304 Calibration of Categorical Forecasts 304 Calibration of Probability Forecasts 305 Calibration in Expectation 307 8.3 Forecast Discrimination 308 Discrimination in Probability Forecasts 309 Discriminating Categorical Forecasts 312 8.4 Comparing Discrimination and Calibration 315 8.5 Forecast Correlation 317 8.6 Measuring Forecast Performance with Brier Scores 318 An Example 319 8.7 Calibration Effects in Decision Models 320 Effect of Calibration on Crop Protection Policies 320 Uncalibrated Forecasts in a Credit Portfolio 323 Stable Likelihoods 325 Numeric Example 328 8.8 Coherent Categorical and Probability Forecasts 328 The Protect Decision with a Categorical Forecast 330 8.9 Coherent Aggregation of Categorical Forecasts 331 8.10 Forecast Aggregation and Optimal Decisions 333 8.11 Summary and Insights 336 Problems 340 9 ADVANCED CONCEPTS 342 9.1 Introduction 342 9.2 Classifying Influence Diagrams 343 A Proper Influence Diagram 345 Influence Diagrams in Extensive Form 347 Irrelevant Decision and Chance Nodes 349 9.3 Chance Influence Diagrams 350 Directed Graphs, Predecessor and Successor Sets 351 Equivalent Chance Influence Diagrams 353 Bayes' Rule and Arc Reversal 354 Barren Nodes 356 Cancer Diagnosis 357 Arc Reversal and Barren Node Removal 360 9.4 Path History and Rollback Computations 362 A History Vector Algorithm 363 Engine Maintenance 364 Rollback Using Path History Vectors 365 A Nuclear Reactor Decision Example 366 9.5 Multiattribute Rollback with and without Trade-Offs 370 Calculating Noninferior Points with Two Attributes 370 Rollback with Linear Trade-Offs 371 Reactor Decision Revisited 372 Economic Value per Life Saved 375 History and Rollback with Nonlinear Utilities 376 Nonlinear Utilities in the Nuclear Reactor Problem 379 9.6 Reducing Influence Diagrams 381 Equivalent Influence Diagrams 381 An Example of EFID Reduction 384 Chance Node Removal through Expectation 385 Node Removal through Maximization 387 Revisiting the Aircraft Part Problem 388 9.7 Summary and Insights 390 Problems 393 References 394 Author INDEX 399 Subject Index 403