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This unique text provides a systematic review of decision-making under uncertainty and regards forecasting as an integral component to the decision-making process. The book covers both decision trees and influence diagrams and shows how they relate to each other and how emphasis is placed on the value of information and the assessment of probabilities. Targeted at both upper-level operations research courses and at practitioners. This text is packaged with an accessible, useful decision tree analysis program.

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CONTENTS
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
  1.5.1 Outcomes, Events, and Probabilities = 7
  1.5.2 Conditional Probability and Independence = 10
  1.5.3 Partitions and the Law of Total Probability = 12
  1.5.4 Bayes' Rule = 13
  1.5.5 Random Variables and Distributions = 14
  1.5.6 Expected Values = 18
  1.5.7 Marginal, Conditional, and Joint Probabilities = 20
  1.5.8 Probabilities and Odds = 22
  1.5.9 Conditional Independence = 23
  1.5.10 Coherence = 24
 1.6 The Role of Forecasting = 24
 1.7 Elements of Influence Diagrams and Decision Trees = 26
  1.7.1 Directed Arcs in Influence Diagrams = 27
  1.7.2 Branches in Decision Trees = 27
 1.8 The Decision Sapling = 28
  1.8.1 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
  2.3.1 The Coach's Decision = 48
  2.3.2 Betting on the Football Game = 50
  2.3.3 Analysis of the Football Betting Problem = 52
  2.3.4 An Alternate Modeling of Outcomes : Point Scores = 55
 2.4 A Limited Life Inventory Problem = 56
  2.4.1 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
  2.7.1 Space Allocation for Two Passenger Classes = 65
  2.7.2 Two - Class Space Allocation with Perfect Information = 69
  2.7.3 Discount - Seat Allocations in One Passenger Class = 71
  2.7.4 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
  3.2.1 Some Examples of Forecasts = 88
 3.3 Several Types of Forecasts = 88
  3.3.1 Point Forecasts = 89
  3.3.2 Probability and Odds Forecasts = 90
  3.3.3 Categorical Forecasts = 92
 3.4 Decision Probabilities, Likelihoods, and Bayes' Rule = 95
  3.4.1 Decision Probabilities and Likelihoods = 96
  3.4.2 Bayes' Rule with Probability Forecasts = 97
  3.4.3 Bayes' Rule with Categorical Forecasts = 99
  3.4.4 Summary of Results in Matrix Notation = 101
  3.4.5 Sensitivity of Decision Probabilities = 101
  3.4.6 Node and Arc Reversal with Bayes' Rule = 103
  3.4.7 Using Bayes' Rule with Odds = 105
 3.5 Multiple Likelihoods and Dependent Forecasts = 108
  3.5.1 Two Forecasts for a Single Event = 109
  3.5.2 Likelihoods for Four Colon Cancer Tests = 111
  3.5.3 Forecasts for Sequential Tests = 115
 3.6 Optimal Crop Protection = 116
 3.7 Credit Scoring Decisions = 121
  3.7.1 Notation for Scores and Forecasts = 121
  3.7.2 Expected Profit and Risk of an Individual = 124
  3.7.3 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
  4.2.1 The Procedure = 136
  4.2.2 Arc Reversal and Cycles = 139
  4.2.3 No - Forgetting Arcs = 140
  4.2.4 Perfect Information = 141
 4.3 Examples of Model Formulations = 143
  4.3.1 A Decision to Seed Clouds in Hurricanes = 144
  4.3.2 Keeping Good Credit Accounts at a Bank = 148
  4.3.3 A Navy Mobile Basing Decision Problem = 152
  4.3.4 Colon Cancer Diagnosis = 156
 4.4 Building and Solving Decision Trees = 160
  4.4.1 Node Outcome and Alternative Sets = 161
  4.4.2 Drawing Consistent Decision Trees = 164
  4.4.3 Perfect Information = 166
  4.4.4 Decision Tree Solutions = 167
 4.5 The Bank Credit Problem = 169
  4.5.1 The Economic Value of a Performance Forecast = 171
  4.5.2 Perfect Information about Performance = 172
 4.6 Colon Cancer Decision Problems = 173
  4.6.1 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
  5.3.1 An Aircraft Part Decision Problem = 199
  5.3.2 A Crop Protection Problem = 202
 5.4 Sensitivity Analysis Using Decision Probabilities = 204
  5.4.1 The Economic Value of a Forecast = 207
 5.5 Sensitivity Analysis Using Forecast Likelihoods = 210
 5.6 Problems with One or More Forecasts = 213
  5.6.1 Optimal Policies and Expected Returns = 215
  5.6.2 A Numeric Example = 217
  5.6.3 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
  6.2.1 Indifference Probabilities and Certainty Equivalents = 234
  6.2.2 Assumptions of Utility Theory = 235
 6.3 Determination of Utility Functions = 237
  6.3.1 Utilities as Indifference Probabilities = 238
  6.3.2 Utilities from Certainty Equivalents = 239
  6.3.3 Cautionary Comments = 240
 6.4 Examples of Utility Functions = 241
  6.4.1 An Exponential Utility Function = 242
  6.4.2 A Logarithmic Utility Function = 243
 6.5 Measures of Risk = 244
  6.5.1 Risk Premium = 245
  6.5.2 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
  7.4.1 Ranking Cars by Preference = 258
  7.4.2 Car Replacement = 261
 7.5 The Added Cost of Conflict Resolution = 263
  7.5.1 Car Ranking Revisited = 265
 7.6 Assessment of Trade - Offs through Preferences = 266
  7.6.1 Two Attributes = 267
  7.6.2 Many Attributes and Alternatives = 268
  7.6.3 Ranking Cars Using Three Attributes = 269
  7.6.4 The Car Replacement Problem Revisited = 270
 7.7 A Hierarchical Multiattributed Model = 271
  7.7.1 A Hierarchical Cost - Benefit Model = 272
  7.7.2* The Two - Hierarchy Multigroup Model = 275
  7.7.3* Tradeoff Weights through Indifference Probabilities = 276
 7.8 The Analytic Hierarchy Process = 278
  7.8.1 Ranking Alternatives with AHP = 280
  7.8.2 Avoiding Rank Reversal in AHP = 284
  7.8.3 Finding the Weights in AHP = 286
 7.9 A Budget Planning Example with Three Attributes = 288
 7.10* Multiattribute Utility = 291
  7.10.1 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
  8.2.1 Calibration of Categorical Forecasts = 304
  8.2.2 Calibration of Probability Forecasts = 305
  8.2.3 Calibration in Expectation = 307
 8.3 Forecast Discrimination = 308
  8.3.1 Discrimination in Probability Forecasts = 309
  8.3.2 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
  8.6.1 An Example = 319
 8.7 Calibration Effects in Decision Models = 320
  8.7.1 Effect of Calibration on Crop Protection Policies = 320
  8.7.2 Uncalibrated Forecasts in a Credit Portfolio = 323
  8.7.3 Stable Likelihoods = 325
  8.7.4 Numeric Example = 328
 8.8 Coherent Categorical and Probability Forecasts = 328
  8.8.1 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
  9.2.1 A Proper Influence Diagram = 345
  9.2.2 Influence Diagrams in Extensive Form = 347
  9.2.3 Irrelevant Decision and Chance Nodes = 349
 9.3 Chance Influence Diagrams = 350
  9.3.1 Directed Graphs, Predecessor and Successor Sets = 351
  9.3.2 Equivalent Chance Influence Diagrams = 353
  9.3.3 Bayes' Rule and Arc Reversal = 354
  9.3.4 Barren Nodes = 356
  9.3.5 Cancer Diagnosis = 357
  9.3.6 Arc Reversal and Barren Node Removal = 360
 9.4 Path History and Rollback Computations = 362
  9.4.1 A History Vector Algorithm = 363
  9.4.2 Engine Maintenance = 364
  9.4.3 Rollback Using Path History Vectors = 365
  9.4.4 A Nuclear Reactor Decision Example = 366
 9.5 Multiattribute Rollback with and without Trade - Offs = 370
  9.5.1 Calculating Noninferior Points with Two Attributes = 370
  9.5.2 Rollback with Linear Trade - Offs = 371
  9.5.3 Reactor Decision Revisited = 372
  9.5.4 Economic Value per Life Saved = 375
  9.5.5 History and Rollback with Nonlinear Utilities = 376
  9.5.6 Nonlinear Utilities in the Nuclear Reactor problem = 379
 9.6 Reducing Influence Diagrams = 381
  9.6.1 Equivalent Influence Diagrams = 381
  9.6.2 An Example of EFID Reduction = 384
  9.6.3 Chance Node Removal through Expectation = 385
  9.6.4 Node Removal through Maximization = 387
  9.6.5 Revisiting the Aircraft Part Problem = 388
 9.7 Summary and Insights = 390
 Problems = 393
References = 394
Author Index = 399
Subject Index = 403