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Internal Designer: Michael Stratton/ cmiller design Cover Designer: Craig Ramsdell Library of Congress Control Number: 2011936338 Cover Image: ©Tom Merton/Getty Images Package ISBN-13: 978-0-8400-6233-8 Rights Acquisitions Specialist: Package ISBN-10: 0-8400-6233-8 Amber Hosea Book only ISBN-13: 978-0-8400-6234-5 Book only ISBN-10: 0-8400-6234-6 South-Western 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd. For your course and learning solutions, visit www.com Purchase any of our products at your local college store or at our preferred online store www.com Printed in the United States of America 1 2 3 4 5 6 7 15 14 13 12 11 To My Children Krista, Justin, Mark, and Colleen DRA To My Children Mark, Linda, Brad, Tim, Scott, and Lisa DJS To My Children Cathy, David, and Kristin TAW To My Family Karen, Jennifer, Stephanie, and Allison JDC To My Wife Teresa JJC To My Family Nicole and Ian MJF To My Family Amie and Willa JWO This page intentionally left blank Brief Contents Preface xvii About the Authors xxiv Chapter 1 Introduction 1 Chapter 2 Introduction to Probability 27 Chapter 3 Probability Distributions 62 Chapter 4 Decision Analysis 101 Chapter 5 Utility and Game Theory 157 Chapter 6 Time Series Analysis and Forecasting 188 Chapter 7 Introduction to Linear Programming 245 Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution 304 Chapter 9 Linear Programming Applications in Marketing, Finance, and Operations Management 358 Chapter 10 Distribution and Network Models 419 Chapter 11 Integer Linear Programming 481 Chapter 12 Advanced Optimization Applications 530 Chapter 13 Project Scheduling: PERT/CPM 585 Chapter 14 Inventory Models 623 Chapter 15 Waiting Line Models 672 Chapter 16 Simulation 712 Chapter 17 Markov Processes 772 Appendix A Building Spreadsheet Models 798 Appendix B Binomial Probabilities 827 vi Brief Contents Appendix C Poisson Probabilities 834 Appendix D Areas for the Standard Normal Distribution 840 Appendix E Values of eⴚλ 842 Appendix F References and Bibliography 843 Appendix G Self-Test Solutions and Answers to Even-Numbered Problems 845 Index 902 Contents Preface xvii About the Authors xxiv Chapter 1 Introduction 1 1.1 Problem Solving and Decision Making 3 1.2 Quantitative Analysis and Decision Making 5 1.3 Quantitative Analysis 7 Model Development 7 Data Preparation 10 Model Solution 11 Report Generation 13 A Note Regarding Implementation 13 1.4 Models of Cost, Revenue, and Profit 14 Cost and Volume Models 14 Revenue and Volume Models 15 Profit and Volume Models 15 Breakeven Analysis 16 1.5 Quantitative Methods in Practice 17 Methods Used Most Frequently 17 Summary 19 Glossary 19 Problems 20 Case Problem Scheduling a Golf League 23 Appendix 1.1 Using Excel for Breakeven Analysis 23 Chapter 2 Introduction to Probability 27 2.1 Experiments and the Sample Space 29 2.2 Assigning Probabilities to Experimental Outcomes 31 Classical Method 31 Relative Frequency Method 32 Subjective Method 32 2.3 Events and Their Probabilities 33 2.4 Some Basic Relationships of Probability 34 Complement of an Event 34 Addition Law 35 Conditional Probability 38 Multiplication Law 42 2.5 Bayes’ Theorem 43 The Tabular Approach 46 2.6 Simpson’s Paradox 47 Summary 50 Glossary 50 viii Contents Problems 51 Case Problem Hamilton County Judges 59 Case Problem College Softball Recruiting 61 Chapter 3 Probability Distributions 62 3.2 Discrete Random Variables 65 Probability Distribution of a Discrete Random Variable 65 Expected Value 67 Variance 68 3.3 Binomial Probability Distribution 69 Nastke Clothing Store Problem 70 Expected Value and Variance for the Binomial Distribution 73 3.4 Poisson Probability Distribution 73 An Example Involving Time Intervals 74 An Example Involving Length or Distance Intervals 74 3.5 Continuous Random Variables 76 Applying the Uniform Distribution 76 Area as a Measure of Probability 77 3.6 Normal Probability Distribution 79 Standard Normal Distribution 80 Computing Probabilities for Any Normal Distribution 84 Grear Tire Company Problem 85 3.7 Exponential Probability Distribution 87 Computing Probabilities for the Exponential Distribution 87 Relationship Between the Poisson and Exponential Distributions 89 Summary 89 Glossary 90 Problems 91 Case Problem Specialty Toys 97 Appendix 3.1 Computing Discrete Probabilities with Excel 98 Appendix 3.2 Computing Probabilities for Continuous Distributions with Excel 99 Chapter 4 Decision Analysis 101 4.1 Problem Formulation 103 Influence Diagrams 104 Payoff Tables 104 Decision Trees 105 4.2 Decision Making Without Probabilities 106 Optimistic Approach 106 Conservative Approach 107 Minimax Regret Approach 107 4.3 Decision Making With Probabilities 109 Expected Value of Perfect Information 112 4.4 Risk Analysis and Sensitivity Analysis 113 Risk Analysis 113 Sensitivity Analysis 114 Contents ix 4.5 Decision Analysis with Sample Information 118 Influence Diagram 119 Decision Tree 120 Decision Strategy 123 Risk Profile 125 Expected Value of Sample Information 128 Efficiency of Sample Information 129 4.6 Computing Branch Probabilities 129 Summary 133 Glossary 133 Problems 135 Case Problem 1 Property Purchase Strategy 148 Case Problem 2 Lawsuit Defense Strategy 149 Appendix 4.1 Decision Analysis with TreePlan 150 Chapter 5 Utility and Game Theory 157 5.1 The Meaning of Utility 158 5.2 Utility and Decision Making 160 The Expected Utility Approach 162 Summary of Steps for Determining the Utility of Money 164 5.3 Utility: Other Considerations 165 Risk Avoiders Versus Risk Takers 165 5.4 Introduction to Game Theory 170 Competing for Market Share 171 Identifying a Pure Strategy 173 5.5 Mixed Strategy Games 174 A Larger Mixed Strategy Game 176 Summary of Steps for Solving Two-Person, Zero-Sum Games 178 Extensions 178 Summary 178 Glossary 179 Problems 179 Chapter 6 Time Series Analysis and Forecasting 188 6.1 Time Series Patterns 190 Horizontal Pattern 190 Trend Pattern 192 Seasonal Pattern 194 Trend and Seasonal Pattern 196 Cyclical Pattern 197 Selecting a Forecasting Method 197 6.3 Moving Averages and Exponential Smoothing 204 Moving Averages 204 Weighted Moving Averages 207 Exponential Smoothing 208 6.4 Linear Trend Projection 211 6.5 Seasonality 216 Seasonality Without Trend 216 x Contents Seasonality with Trend 219 Models Based on Monthly Data 221 Summary 222 Glossary 222 Problems 223 Case Problem 1 Forecasting Food and Beverage Sales 231 Case Problem 2 Forecasting Lost Sales 232 Appendix 6.1 Forecasting with Excel Data Analysis Tools 233 Appendix 6.2 Using CB Predictor for Forecasting 242 Chapter 7 Introduction to Linear Programming 245 7.1 A Simple Maximization Problem 247 Problem Formulation 248 Mathematical Model for the RMC Problem 250 7.2 Graphical Solution Procedure 251 A Note on Graphing Lines 260 Summary of the Graphical Solution Procedure for Maximization Problems 261 Slack Variables 262 7.3 Extreme Points and the Optimal Solution 264 7.4 Computer Solution of the RMC Problem 265 Interpretation of Answer Report 266 7.5 A Simple Minimization Problem 267 Summary of the Graphical Solution Procedure for Minimization Problems 269 Surplus Variables 270 Computer Solution of the M&D Chemicals Problem 271 7.6 Special Cases 272 Alternative Optimal Solutions 272 Infeasibility 272 Unbounded 274 7.7 General Linear Programming Notation 276 Summary 278 Glossary 279 Problems 280 Case Problem 1 Workload Balancing 295 Case Problem 2 Production Strategy 296 Case Problem 3 Hart Venture Capital 297 Appendix 7.1 Solving Linear Programs with Excel 2010 298 Appendix 7.2 Solving Linear Programs with LINGO 301 Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution 304 8.1 Introduction to Sensitivity Analysis 306 8.2 Objective Function Coefficients 307 8.3 Right-Hand Sides 310 Cautionary Note on the Interpretation of Shadow Prices 314 8.4 Limitations of Classical Sensitivity Analysis 315 Simultaneous Changes 315 Changes in Constraint Coefficients 316 Nonintuitive Shadow Prices 317 Contents xi 8.5 More Than Two Decision Variables 319 Modified RMC Problem 320 Bluegrass Farms Problem 322 8.6 Electronic Communications Problem 325 Problem Formulation 326 Solution and Interpretation 327 Summary 330 Glossary 331 Problems 332 Case Problem 1 Product Mix 351 Case Problem 2 Investment Strategy 352 Case Problem 3 Truck Leasing Strategy 352 Appendix 8.1 Sensitivity Analysis with Excel 353 Appendix 8.2 Sensitivity Analysis with LINGO 354 Chapter 9 Linear Programming Applications in Marketing, Finance, and Operations Management 358 9.1 Marketing Applications 360 Media Selection 360 Marketing Research 363 9.2 Financial Applications 366 Portfolio Selection 366 Financial Planning 369 9.3 Operations Management Applications 373 A Make-or-Buy Decision 373 Production Scheduling 377 Workforce Assignment 384 Blending Problems 389 Summary 393 Problems 394 Case Problem 1 Planning an Advertising Campaign 407 Case Problem 2 Phoenix Computer 408 Case Problem 3 Textile Mill Scheduling 409 Case Problem 4 Workforce Scheduling 410 Case Problem 5 Duke Energy Coal Allocation 412 Appendix 9.1 Excel Solution of Hewlitt Corporation Financial Planning Problem 414 Chapter 10 Distribution and Network Models 419 10.1 Supply Chain Models 420 Transportation Problem 420 Problem Variations 423 A General Linear Programming Model 426 Transshipment Problem 427 Problem Variations 433 A General Linear Programming Model 433 10.2 Assignment Problem 435 Problem Variations 438 A General Linear Programming Model 438 xii Contents 10.3 Shortest-Route Problem 440 A General Linear Programming Model 443 10.4 Maximal Flow Problem 444 10.5 A Production and Inventory Application 448 Summary 451 Glossary 452 Problems 453 Case Problem 1 Solutions Plus 470 Case Problem 2 Supply Chain Design 472 Appendix 10.1 Excel Solution of Transportation, Transshipment, and Assignment Problems 473 Chapter 11 Integer Linear Programming 481 11.1 Types of Integer Linear Programming Models 484 11.2 Graphical and Computer Solutions for an All-Integer Linear Program 485 Graphical Solution of the LP Relaxation 486 Rounding to Obtain an Integer Solution 487 Graphical Solution of the All-Integer Problem 487 Using the LP Relaxation to Establish Bounds 488 Computer Solution 489 11.3 Applications Involving 0-1 Variables 490 Capital Budgeting 490 Fixed Cost 491 Supply Chain Design 493 Bank Location 498 Product Design and Market Share Optimization 500 11.