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CHAPTER 1 DECISION ANALYSIS 1

CHAPTER 1 DECISION ANALYSIS 1

1.1 A Decision Tree Model and its Analysis 2

1.2 Summary of the General Method of Decision Analysis 16

1.3 Another Decision Tree Model and its Analysis 17

1.4 The Need for a Systematic Theory of Probability 30

1.5 Further Issues and Concluding Remarks on Decision Analysis 33

Kendall Crab and Lobster, Inc. 35

1.6 Case Modules 35

The Acquisition of DSOFT 38

Buying a House 38

National Realty Investment Corporation 39

1.7 Exercises 44

CHAPTER 2 FUNDAMENTALS OF DISCRETE PROBABILITY 49

CHAPTER 2 FUNDAMENTALS OF DISCRETE PROBABILITY 49

2.1 Outcomes, Probabilities and Events 50

2.2 The Laws of Probability 51

2.3 Working with Probabilities and Probability Tables 54

2.4 Random Variables 65

2.5 Discrete Probability Distributions 66

2.6 The Binomial Distribution 67

2.7 Summary Measures of Probability Distributions 72

2.8 Linear Functions of a Random Variable 79

2.9 Covariance and Correlation 82

2.10 Joint Probability Distributions and Independence 86

2.11 Sums of Two Random Variables 88

2.12 Some Advanced Methods in Probability* 91

2.13 Summary 96

Arizona Instrumentation, Inc and the Economic Development Board of Singapore 97

2.14 Case Modules 97

San Carlos Mud Slides 98

Graphic Corporation 99

2.15 Exercises 100

CHAPTER 3 CONTINUOUS PROBABILITY DISTRIBUTIONS AND THEIR APPLICATIONS 111

3.1 Continuous Random Variables 111

CHAPTER 3 CONTINUOUS PROBABILITY DISTRIBUTIONS AND THEIR APPLICATIONS 111

3.2 The Probability Density Function 112

3.3 The Cumulative Distribution Function 115

3.4 The Normal Distribution 120

3.5 Computing Probabilities for the Normal Distribution 127

3.6 Sums of Normally Distributed Random Variables 132

3.7 The Central Limit Theorem 135

3.8 Summary 139

3.9 Exercises 139

CHAPTER 4 STATISTICAL SAMPLING 147

CHAPTER 4 STATISTICAL SAMPLING 147

4.1 Random Samples 148

4.2 Statistics of a Random Sample 150

4.3 Confidence Intervals for the Mean, for Large Sample Size 161

4.4 The t-Distribution 165

4.5 Confidence Intervals for the Mean, for Small Sample Size 166

4.6 Estimation and Confidence Intervals for the Population Proportion 169

4.7 Experimental Design 174

4.8 Comparing Estimates of the Mean of Two Distributions 178

4.9 Comparing Estimates of the Population Proportion of Two Populations 180

4.10 Summary and Extensions 182

4.11 Case Modules 183

Consumer Convenience, Inc. 183

POSIDON, Inc. 184

Housing Prices in Lexington, Massachusetts 185

Scallop Sampling 185

4.12 Exercises 189

CHAPTER 5 SIMULATION MODELING： CONCEPTS AND PRACTICE 195

CHAPTER 5 SIMULATION MODELING: CONCEPTS AND PRACTICE 195

5.1 A Simple Problem: Operations at Conley Fisheries 196

5.2 Preliminary Analysis of Conley Fisheries 197

5.3 A Simulation Model of the Conley Fisheries Problem 199

5.4 Random Number Generators 201

5.5 Creating Numbers that Obey a Discrete Probability Distribution 203

5.6 Creating Numbers that Obey a Continuous Probability Distribution 205

5.7 Completing the Simulation Model of Conley Fisheries 211

5.8 Using the Sample Data for Analysis 213

5.10 Computer Software for Simulation Modeling 217

5.9 Summary of Simulation Modeling and Guidelines on the Use of Simulation 217

5.11 Typical Uses of Simulation Models 218

The Gentle Lentil Restaurant 219

5.12 Case Modules 219

To Hedge or not to Hedge? 223

Ontario Cateway 228

Casterbridge Bank 235

CHAPTER 6 REGRESSION MODELS: CONCEPTS AND PRACTICE 245

CHAPTER 6 REGRESSION MODELS: CONCEPTS AND PRACTICE 245

6.1 Prediction Based on Simple Linear Regression 246

6.2 Prediction Based on Multiple Linear Regression 253

6.3 Using Spreadsheet Software for Linear Regression 258

6.4 Interpretation of Computer Output of a Linear Regression Model 259

6.5 Sample Correlation and R2 in Simple Linear Regression 271

6.6 Validating the Regression Model 274

6.7 Warnings and Issues in Linear Regression Modeling 279

6.8 Regression Modeling Techniques 283

6.9 Illustration of the Regression Modeling Process 288

6.10 Summary and Conclusions 294

6.11 Case Modules 295

Predicting Heating Oil Consumption at OILPLUS 295

Executive Compensation 297

The Construction Department at Croq Pain 299

Sloan Investors, Part I 306

6.12 Exercises 313

CHAPTER 7 LINEAR OPTIMIZATION 323

CHAPTER 7 LINEAR OPTIMIZATION 323

7.1 Formulating a Management Problem as a Linear Optimization Model 324

7.2 Key Concepts and Definitions 332

7.3 Solution of a Linear Optimization Model 335

7.4 Creating and Solving a Linear Optimization Model in a Spreadsheet 347

7.5 Sensitivity Analysis and Shadow Prices on Constraints 354

7.6 Guidelines for Constructing and Using Linear Optimization Models 365

7.7 Linear Optimization Under Uncertainty* 367

7.8 A Brief Historical Sketch of the Development of Linear Optimization 374

7.9 Case Modules 375

Short-Run Manufacturing Problems at DEC 375

Sytech International 380

Filatoi Riuniti 389

7.10 Exercises 397

CHAPTER 8 NONLINEAR OPTIMIZATION 411

CHAPTER 8 NONLINEAR OPTIMIZATION 411

8.1 Formulating a Management Problems as a Nonlinear Optimization Model 412

8.2 Graphical Analysis of Nonlinear Optimization Models in Two Variables 420

8.3 Computer Solution of Nonlinear Optimization Problems 425

8.4 Shadow Prices Information in Nonlinear Optimization Models 428

8.5 A Closer Look at Portfolio Optimization 431

8.6 Taxonomy of the Solvability of Nonlinear Optimization Problems* 432

8.7 Case Modules 436

Endurance Investors 436

Capacity Investment, Marketing and Production at ILG, Inc. 442

8.8 Exercises 444

CHAPTER 9 DISCRETE OPTIMIZATION 451

CHAPTER 9 DISCRETE OPTIMIZATION 451

9.1 Formulating a Management Problem as a Discrete Optimization Model 452

9.2 Graphical Analysis of Discrete Optimization Models in Two Variables 461

9.3 Computer Solution of Discrete Optimization Problems 464

9.4 The Branch-and-Bound Method for Solving a Discrete Optimization Model* 468

9.5 Summary 471

9.6 Case Modules 471

International Industries, Inc. 471

The National Basketball Dream Team 476

9.7 Exercises 478

CHAPTER 10 INTEGRATION IN THE ART OF DECISION MODELING 485

CHAPTER 10 INTEGRATION IN THE ART OF DECISION MODELING 485

10.1 Management Science Models in the Airline Industry 486

10.2 Management Science Models in the Investment Management Industry 496

10.3 A Year in the Lift of a Manufacturing Company 498

10.4 Summary 501

10.5 Case Modules 502

Sloan Investors, PartⅡ 502

Revenue Management at Atlantic Air 503

A Strategic Alliance for the Lexington Laser Corporation 508

Yield of a Multi-step Manufacturing Process 510

Prediction of Yields in Manufacturing 512

Allocation of Production Personnel 513

APPENDIX 517

APPENDIX 517

REFERENCES 521

REFERENCES 521

INDEX 525

INDEX 525