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Quantitative Analysis For Management ELEVENTH EDITION

BARRY RENDER

Charles Harwood Professor of Management Science Graduate School of Business, Rollins College

RALPH M. STAIR, JR.

Professor of Information and Management Sciences, Florida State University

MICHAEL E. HANNA

Professor of Decision Sciences, University of Houston—Clear Lake

To my wife and sons – BR

To Lila and Leslie – RMS

To Susan, Mickey, and Katie – MEH

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iii

ABOUT THE AUTHORS

Barry Render Professor Emeritus, the Charles Harwood Distinguished Professor of management sci- ence at the Roy E. Crummer Graduate School of Business at Rollins College in Winter Park, Florida. He received his MS in Operations Research and his PhD in Quantitative Analysis at the University of Cincinnati. He previously taught at George Washington University, the University of New Orleans, Boston University, and George Mason University, where he held the Mason Foundation Professorship in Decision Sciences and was Chair of the Decision Science Department. Dr. Render has also worked in the aerospace industry for General Electric, McDonnell Douglas, and NASA.

Dr. Render has coauthored 10 textbooks published by Prentice Hall, including Managerial Decision Modeling with Spreadsheets, Operations Management, Principles of Operations Management, Service Management, Introduction to Management Science, and Cases and Readings in Management Science. Dr. Render’s more than 100 articles on a variety of management topics have appeared in Decision Sciences, Production and Operations Management, Interfaces, Information and Management, Journal of Management Information Systems, Socio-Economic Planning Sciences, IIE Solutions and Operations Management Review, among others.

Dr. Render has been honored as an AACSB Fellow, and he was named a Senior Fulbright Scholar in 1982 and again in 1993. He was twice vice president of the Decision Science Institute Southeast Region and served as software review editor for Decision Line from 1989 to 1995. He has also served as editor of the New York Times Operations Management special issues from 1996 to 2001. From 1984 to 1993, Dr. Render was president of Management Service Associates of Virginia, Inc., whose technology clients included the FBI; the U.S. Navy; Fairfax County, Virginia and C&P Telephone.

Dr. Render has taught operations management courses in Rollins College’s MBA and Executive MBA programs. He has received that school’s Welsh Award as leading professor and was selected by Roosevelt University as the 1996 recipient of the St. Claire Drake Award for Outstanding Scholarship. In 2005, Dr. Render received the Rollins College MBA Student Award for Best Overall Course, and in 2009 was named Professor of the Year by full-time MBA students.

Ralph Stair is Professor Emeritus at Florida State University. He earned a BS in chemical engineer- ing from Purdue University and an MBA from Tulane University. Under the guidance of Ken Ramsing and Alan Eliason, he received a PhD in operations management from the University of Oregon. He has taught at the University of Oregon, the University of Washington, the University of New Orleans, and Florida State University.

He has twice taught in Florida State University’s Study Abroad Program in London. Over the years, his teaching has been concentrated in the areas of information systems, operations research, and operations management.

Dr. Stair is a member of several academic organizations, including the Decision Sciences Institute and INFORMS, and he regularly participates at national meetings. He has published numerous articles and books, including Managerial Decision Modeling with Spreadsheets, Introduction to Management Science, Cases and Readings in Management Science, Production and Operations Management: A Self-Correction Approach, Fundamentals of Information Systems, Principles of Information Systems, Introduction to Information Systems, Computers in Today’s World, Principles of Data Processing, Learning to Live with Computers, Programming in BASIC, Essentials of BASIC Programming, Essentials of FORTRAN Programming, and Essentials of COBOL Programming. Dr. Stair divides his time between Florida and Colorado. He enjoys skiing, biking, kayaking, and other outdoor activities.

iv ABOUT THE AUTHORS

Michael E. Hanna is Professor of Decision Sciences at the University of Houston–Clear Lake (UHCL). He holds a BA in Economics, an MS in Mathematics, and a PhD in Operations Research from Texas Tech University. For more than 25 years, he has been teaching courses in statistics, man- agement science, forecasting, and other quantitative methods. His dedication to teaching has been recognized with the Beta Alpha Psi teaching award in 1995 and the Outstanding Educator Award in 2006 from the Southwest Decision Sciences Institute (SWDSI).

Dr. Hanna has authored textbooks in management science and quantitative methods, has pub- lished numerous articles and professional papers, and has served on the Editorial Advisory Board of Computers and Operations Research. In 1996, the UHCL Chapter of Beta Gamma Sigma presented him with the Outstanding Scholar Award.

Dr. Hanna is very active in the Decision Sciences Institute, having served on the Innovative Education Committee, the Regional Advisory Committee, and the Nominating Committee. He has served two terms on the board of directors of the Decision Sciences Institute (DSI) and as regionally elected vice president of DSI. For SWDSI, he has held several positions, including president, and he received the SWDSI Distinguished Service Award in 1997. For overall service to the profession and to the university, he received the UHCL President’s Distinguished Service Award in 2001.

CHAPTER 1 Introduction to Quantitative Analysis 1

CHAPTER 2 Probability Concepts and Applications 21

CHAPTER 3 Decision Analysis 69

CHAPTER 4 Regression Models 115

CHAPTER 5 Forecasting 153

CHAPTER 6 Inventory Control Models 195

CHAPTER 7 Linear Programming Models: Graphical and Computer Methods 249

CHAPTER 8 Linear Programming Applications 307

CHAPTER 9 Transportation and Assignment Models 341

CHAPTER 10 Integer Programming, Goal Programming, and Nonlinear Programming 395

CHAPTER 11 Network Models 429

CHAPTER 12 Project Management 459

CHAPTER 13 Waiting Lines and Queuing Theory Models 499

CHAPTER 14 Simulation Modeling 533

CHAPTER 15 Markov Analysis 573

CHAPTER 16 Statistical Quality Control 601

ONLINE MODULES

1 Analytic Hierarchy Process M1-1

2 Dynamic Programming M2-1

3 Decision Theory and the Normal Distribution M3-1

4 Game Theory M4-1

5 Mathematical Tools: Determinants and Matrices M5-1

6 Calculus-Based Optimization M6-1

7 Linear Programming: The Simplex Method M7-1

v

BRIEF CONTENTS

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PREFACE xv

CHAPTER 1 Introduction to Quantitative Analysis 1

1.1 Introduction 2 1.2 What Is Quantitative Analysis? 2 1.3 The Quantitative Analysis Approach 3

Defining the Problem 3

Developing a Model 3

Acquiring Input Data 4

Developing a Solution 5

Testing the Solution 5

Analyzing the Results and Sensitivity Analysis 5

Implementing the Results 5

The Quantitative Analysis Approach and Modeling in the Real World 7

1.4 How to Develop a Quantitative Analysis Model 7 The Advantages of Mathematical Modeling 8

Mathematical Models Categorized by Risk 8

1.5 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach 9

1.6 Possible Problems in the Quantitative Analysis Approach 12 Defining the Problem 12

Developing a Model 13

Acquiring Input Data 13

Developing a Solution 14

Testing the Solution 14

Analyzing the Results 14

1.7 Implementation—Not Just the Final Step 15 Lack of Commitment and Resistance to Change 15

Lack of Commitment by Quantitative Analysts 15

Summary 16 Glossary 16 Key Equations 16 Self-Test 17 Discussion Questions and Problems 17 Case Study: Food and Beverages at Southwestern University Football Games 19 Bibliography 19

CHAPTER 2 Probability Concepts and Applications 21 2.1 Introduction 22 2.2 Fundamental Concepts 22

Types of Probability 23

2.3 Mutually Exclusive and Collectively Exhaustive Events 24

Adding Mutually Exclusive Events 26

Law of Addition for Events That Are Not Mutually Exclusive 26

2.4 Statistically Independent Events 27 2.5 Statistically Dependent Events 28 2.6 Revising Probabilities with Bayes’ Theorem 29

General Form of Bayes’ Theorem 31

2.7 Further Probability Revisions 32 2.8 Random Variables 33 2.9 Probability Distributions 34

Probability Distribution of a Discrete Random Variable 34

Expected Value of a Discrete Probability Distribution 35

Variance of a Discrete Probability Distribution 36

Probability Distribution of a Continuous Random Variable 36

2.10 The Binomial Distribution 38 Solving Problems with the Binomial Formula 39

Solving Problems with Binomial Tables 40

2.11 The Normal Distribution 41 Area Under the Normal Curve 42

Using the Standard Normal Table 42

Haynes Construction Company Example 44

The Empirical Rule 48

2.12 The F Distribution 48 2.13 The Exponential Distribution 50

Arnold’s Muffler Example 51

2.14 The Poisson Distribution 52 Summary 54 Glossary 54 Key Equations 55 Solved Problems 56 Self-Test 59 Discussion Questions and Problems 60 Case Study: WTVX 65 Bibliography 66

Appendix 2.1 Derivation of Bayes’ Theorem 66 Appendix 2.2 Basic Statistics Using Excel 66

CHAPTER 3 Decision Analysis 69 3.1 Introduction 70 3.2 The Six Steps in Decision Making 70 3.3 Types of Decision-Making Environments 71 3.4 Decision Making Under Uncertainty 72

Optimistic 72

Pessimistic 73

Criterion of Realism (Hurwicz Criterion) 73

CONTENTS

vii

Equally Likely (Laplace) 74

Minimax Regret 74

3.5 Decision Making Under Risk 76 Expected Monetary Value 76

Expected Value of Perfect Information 77

Expected Opportunity Loss 78

Sensitivity Analysis 79

Using Excel QM to Solve Decision Theory Problems 80

3.6 Decision Trees 81 Efficiency of Sample Information 86

Sensitivity Analysis 86

3.7 How Probability Values are Estimated by Bayesian Analysis 87 Calculating Revised Probabilities 87

Potential Problem in Using Survey Results 89

3.8 Utility Theory 90 Measuring Utility and Constructing a Utility

Curve 91

Utility as a Decision-Making Criterion 93

Summary 95 Glossary 95 Key Equations 96 Solved Problems 97 Self-Test 102 Discussion Questions and Problems 103 Case Study: Starting Right Corporation 110 Case Study: Blake Electronics 111 Bibliography 113

Appendix 3.1 Decision Models with QM for Windows 113 Appendix 3.2 Decision Trees with QM for Windows 114

CHAPTER 4 Regression Models 115 4.1 Introduction 116 4.2 Scatter Diagrams 116 4.3 Simple Linear Regression 117 4.4 Measuring the Fit of the Regression Model 119

Coefficient of Determination 120

Correlation Coefficient 121

4.5 Using Computer Software for Regression 122 4.6 Assumptions of the Regression Model 123

Estimating the Variance 125

4.7 Testing the Model for Significance 125 Triple A Construction Example 127

The Analysis of Variance (ANOVA) Table 127

Triple A Construction ANOVA Example 128

4.8 Multiple Regression Analysis 128 Evaluating the Multiple Regression Model 129

Jenny Wilson Realty Example 130

4.9 Binary or Dummy Variables 131 4.10 Model Building 132 4.11 Nonlinear Regression 133 4.12 Cautions and Pitfalls in Regression

Analysis 136 Summary 136 Glossary 137 Key Equations 137 Solved Problems 138 Self-Test 140 Discussion Questions and Problems 140 Case Study: North–South Airline 145 Bibliography 146

Appendix 4.1 Formulas for Regression Calculations 146

Appendix 4.2 Regression Models Using QM for Windows 148

Appendix 4.3 Regression Analysis in Excel QM or Excel 2007 150

CHAPTER 5 Forecasting 153 5.1 Introduction 154 5.2 Types of Forecasts 154

Time-Series Models 154

Causal Models 154

Qualitative Models 155

5.3 Scatter Diagrams and Time Series 156 5.4 Measures of Forecast Accuracy 158 5.5 Time-Series Forecasting Models 160

Components of a Time Series 160

Moving Averages 161

Exponential Smoothing 164

Using Excel QM for Trend-Adjusted Exponential Smoothing 169

Trend Projections 169

Seasonal Variations 171

Seasonal Variations with Trend 173

The Decomposition Method of Forecasting with Trend and Seasonal Components 175

Using Regression with Trend and Seasonal Components 177

5.6 Monitoring and Controlling Forecasts 179 Adaptive Smoothing 181

Summary 181 Glossary 182 Key Equations 182 Solved Problems 183 Self-Test 184 Discussion Questions and Problems 185 Case Study: Forecasting Attendance at SWU Football Games 189

Case Study: Forecasting Monthly Sales 190

Bibliography 191

Appendix 5.1 Forecasting with QM for Windows 191

CHAPTER 6 Inventory Control Models 195 6.1 Introduction 196 6.2 Importance of Inventory Control 196

Decoupling Function 197

Storing Resources 197

Irregular Supply and Demand 197

Quantity Discounts 197

Avoiding Stockouts and Shortages 197

6.3 Inventory Decisions 197 6.4 Economic Order Quantity: Determining How

Much to Order 199 Inventory Costs in the EOQ Situation 200

Finding the EOQ 202

Sumco Pump Company Example 202

Purchase Cost of Inventory Items 203

Sensitivity Analysis with the EOQ Model 204

6.5 Reorder Point: Determining When to Order 205

VIII CONTENTS

CONTENTS IX

6.6 EOQ Without the Instantaneous Receipt Assumption 206 Annual Carrying Cost for Production Run

Model 207

Annual Setup Cost or Annual Ordering Cost 208

Determining the Optimal Production Quantity 208

Brown Manufacturing Example 208

6.7 Quantity Discount Models 210 Brass Department Store Example 212

6.8 Use of Safety Stock 213 6.9 Single-Period Inventory Models 220

Marginal Analysis with Discrete Distributions 221

Café du Donut Example 222

Marginal Analysis with the Normal Distribution 222

Newspaper Example 223

6.10 ABC Analysis 225 6.11 Dependent Demand: The Case for Material

Requirements Planning 226 Material Structure Tree 226

Gross and Net Material Requirements Plan 227

Two or More End Products 229

6.12 Just-in-Time Inventory Control 230 6.13 Enterprise Resource Planning 232

Summary 232 Glossary 232 Key Equations 233 Solved Problems 234 Self-Test 237 Discussion Questions and Problems 238 Case Study: Martin-Pullin Bicycle Corporation 245 Bibliography 246

Appendix 6.1 Inventory Control with QM for Windows 246

CHAPTER 7 Linear Programming Models: Graphical and Computer Methods 249

7.1 Introduction 250 7.2 Requirements of a Linear Programming

Problem 250 7.3 Formulating LP Problems 251

Flair Furniture Company 252

7.4 Graphical Solution to an LP Problem 253 Graphical Representation of Constraints 253

Isoprofit Line Solution Method 257

Corner Point Solution Method 260

Slack and Surplus 262

7.5 Solving Flair Furniture’s LP Problem Using QM For Windows and Excel 263 Using QM for Windows 263

Using Excel’s Solver Command to Solve LP Problems 264

7.6 Solving Minimization Problems 270 Holiday Meal Turkey Ranch 270

7.7 Four Special Cases in LP 274 No Feasible Solution 274

Unboundedness 275

Redundancy 275

Alternate Optimal Solutions 276

7.8 Sensitivity Analysis 276 High Note Sound Company 278

Changes in the Objective Function Coefficient 278

QM for Windows and Changes in Objective Function Coefficients 279

Excel Solver and Changes in Objective Function Coefficients 280

Changes in the Technological Coefficients 280

Changes in the Resources or Right-Hand-Side Values 282

QM for Windows and Changes in Right-Hand- Side Values 283

Excel Solver and Changes in Right-Hand-Side Values 285

Summary 285 Glossary 285 Solved Problems 286 Self-Test 291 Discussion Questions and Problems 292 Case Study: Mexicana Wire Works 300 Bibliography 302

Appendix 7.1 Excel QM 302

CHAPTER 8 Linear Programming Applications 307 8.1 Introduction 308 8.2 Marketing Applications 308

Media Selection 308

Marketing Research 309

8.3 Manufacturing Applications 312 Production Mix 312

Production Scheduling 313

8.4 Employee Scheduling Applications 317 Labor Planning 317

8.5 Financial Applications 319 Portfolio Selection 319

Truck Loading Problem 322

8.6 Ingredient Blending Applications 324 Diet Problems 324

Ingredient Mix and Blending Problems 325

8.7 Transportation Applications 327 Shipping Problem 327

Summary 330 Self-Test 330 Problems 331 Case Study: Chase Manhattan Bank 339 Bibliography 339

CHAPTER 9 Transportation and Assignment Models 341

9.1 Introduction 342 9.2 The Transportation Problem 342

Linear Program for the Transportation Example 342

A General LP Model for Transportation Problems 343

9.3 The Assignment Problem 344 Linear Program for Assignment Example 345

9.4 The Transshipment Problem 346 Linear Program for Transshipment Example 347

X CONTENTS

9.5 The Transportation Algorithm 348 Developing an Initial Solution: Northwest

Corner Rule 350

Stepping-Stone Method: Finding a Least-Cost Solution 352

9.6 Special Situations with the Transportation Algorithm 358 Unbalanced Transportation Problems 358

Degeneracy in Transportation Problems 359

More Than One Optimal Solution 362

Maximization Transportation Problems 362

Unacceptable or Prohibited Routes 362

Other Transportation Methods 362

9.7 Facility Location Analysis 363 Locating a New Factory for Hardgrave Machine

Company 363

9.8 The Assignment Algorithm 365 The Hungarian Method (Flood’s Technique) 366

Making the Final Assignment 369

9.9 Special Situations with the Assignment Algorithm 371 Unbalanced Assignment Problems 371

Maximization Assignment Problems 371

Summary 373 Glossary 373 Solved Problems 374 Self-Test 380 Discussion Questions and Problems 381 Case Study: Andrew–Carter, Inc. 391 Case Study: Old Oregon Wood Store 392 Bibliography 393

Appendix 9.1 Using QM for Windows 393

CHAPTER 10 Integer Programming, Goal Programming, and Nonlinear Programming 395

10.1 Introduction 396 10.2 Integer Programming 396

Harrison Electric Company Example of Integer Programming 396

Using Software to Solve the Harrison Integer Programming Problem 398

Mixed-Integer Programming Problem Example 400

10.3 Modeling with 0–1 (Binary) Variables 402 Capital Budgeting Example 402

Limiting the Number of Alternatives Selected 404

Dependent Selections 404

Fixed-Charge Problem Example 404

Financial Investment Example 405

10.4 Goal Programming 406 Example of Goal Programming: Harrison Electric

Company Revisited 408

Extension to Equally Important Multiple Goals 409

Ranking Goals with Priority Levels 409

Goal Programming with Weighted Goals 410

10.5 Nonlinear Programming 411 Nonlinear Objective Function and Linear

Constraints 412

Both Nonlinear Objective Function and Nonlinear Constraints 413

Linear Objective Function with Nonlinear Constraints 414

Summary 415 Glossary 415 Solved Problems 416 Self-Test 419 Discussion Questions and Problems 419 Case Study: Schank Marketing Research 425 Case Study: Oakton River Bridge 425 Bibliography 426

CHAPTER 11 Network Models 429 11.1 Introduction 430 11.2 Minimal-Spanning Tree Problem 430 11.3 Maximal-Flow Problem 433

Maximal-Flow Technique 433

Linear Program for Maximal Flow 438

11.4 Shortest-Route Problem 439 Shortest-Route Technique 439

Linear Program for Shortest-Route Problem 441

Summary 444 Glossary 444 Solved Problems 445 Self-Test 447 Discussion Questions and Problems 448 Case Study: Binder’s Beverage 455 Case Study: Southwestern University Traffic Problems 456 Bibliography 457

CHAPTER 12 Project Management 459 12.1 Introduction 460 12.2 PERT/CPM 460

General Foundry Example of PERT/CPM 461

Drawing the PERT/CPM Network 462

Activity Times 463

How to Find the Critical Path 464

Probability of Project Completion 469

What PERT Was Able to Provide 471

Using Excel QM for the General Foundry Example 471

Sensitivity Analysis and Project Management 471

12.3 PERT/Cost 473 Planning and Scheduling Project Costs:

Budgeting Process 473

Monitoring and Controlling Project Costs 477

12.4 Project Crashing 479 General Foundary Example 480

Project Crashing with Linear Programming 480

12.5 Other Topics in Project Management 484 Subprojects 484

Milestones 484

Resource Leveling 484

Software 484

Summary 484 Glossary 485 Key Equations 485 Solved Problems 486 Self-Test 487 Discussion Questions and Problems 488 Case Study: Southwestern University Stadium Construction 494 Case Study: Family Planning Research Center of Nigeria 494 Bibliography 496

Appendix 12.1 Project Management with QM for Windows 497

CONTENTS XI

CHAPTER 13 Waiting Lines and Queuing Theory Models 499

13.1 Introduction 500 13.2 Waiting Line Costs 500

Three Rivers Shipping Company Example 501

13.3 Characteristics of a Queuing System 501 Arrival Characteristics 501

Waiting Line Characteristics 502

Service Facility Characteristics 503

Identifying Models Using Kendall Notation 503

13.4 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/1) 506 Assumptions of the Model 506

Queuing Equations 506

Arnold’s Muffler Shop Case 507

Enhancing the Queuing Environment 511

13.5 Multichannel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/M) 511 Equations for the Multichannel Queuing

Model 512

Arnold’s Muffler Shop Revisited 512

13.6 Constant Service Time Model (M/D/1) 514 Equations for the Constant Service Time

Model 515

Garcia-Golding Recycling, Inc. 515

13.7 Finite Population Model (M/M/1 with Finite Source) 516 Equations for the Finite Population Model 517

Department of Commerce Example 517

13.8 Some General Operating Characteristic Relationships 519

13.9 More Complex Queuing Models and the Use of Simulation 519 Summary 520 Glossary 520 Key Equations 521 Solved Problems 522 Self-Test 524 Discussion Questions and Problems 525 Case Study: New England Foundry 530 Case Study: Winter Park Hotel 531 Bibliography 532

Appendix 13.1 Using QM for Windows 532

CHAPTER 14 Simulation Modeling 533 14.1 Introduction 534 14.2 Advantages and Disadvantages

of Simulation 535 14.3 Monte Carlo Simulation 536

Harry’s Auto Tire Example 536

Using QM for Windows for Simulation 541

Simulation with Excel Spreadsheets 541

14.4 Simulation and Inventory Analysis 545 Simkin’s Hardware Store 545

Analyzing Simkin’s Inventory Costs 548

14.5 Simulation of a Queuing Problem 550 Port of New Orleans 550

Using Excel to Simulate the Port of New Orleans Queuing Problem 551

14.6 Simulation Model for a Maintenance Policy 553 Three Hills Power Company 553

Cost Analysis of the Simulation 557

14.7 Other Simulation Issues 557 Two Other Types of Simulation Models 557

Verification and Validation 559

Role of Computers in Simulation 560

Summary 560 Glossary 560 Solved Problems 561 Self-Test 564 Discussion Questions and Problems 565 Case Study: Alabama Airlines 570 Case Study: Statewide Development Corporation 571 Bibliography 572

CHAPTER 15 Markov Analysis 573 15.1 Introduction 574 15.2 States and State Probabilities 574

The Vector of State Probabilities for Three Grocery Stores Example 575

15.3 Matrix of Transition Probabilities 576 Transition Probabilities for the Three Grocery

Stores 577

15.4 Predicting Future Market Shares 577 15.5 Markov Analysis of Machine Operations 578 15.6 Equilibrium Conditions 579 15.7 Absorbing States and the Fundamental

Matrix: Accounts Receivable Application 582 Summary 586 Glossary 587 Key Equations 587 Solved Problems 587 Self-Test 591 Discussion Questions and Problems 591 Case Study: Rentall Trucks 595 Bibliography 597

Appendix 15.1 Markov Analysis with QM for Windows 597 Appendix 15.2 Markov Analysis With Excel 599

CHAPTER 16 Statistical Quality Control 601 16.1 Introduction 602 16.2 Defining Quality and TQM 602 16.3 Statiscal Process Control 603

Variability in the Process 603

16.4 Control Charts for Variables 605 The Central Limit Theorem 605

Setting -Chart Limits 606

Setting Range Chart Limits 609

16.5 Control Charts for Attributes 610 p-Charts 610

c-Charts 613

Summary 614 Glossary 614 Key Equations 614 Solved Problems 615 Self-Test 616 Discussion Questions and Problems 617 Bibliography 619

Appendix 16.1 Using QM for Windows for SPC 619

x

APPENDICES 621 APPENDIX A Areas Under the Standard

Normal Curve 622

APPENDIX B Binomial Probabilities 624 APPENDIX C Values of e for use in the Poisson

Distribution 629

APPENDIX D F Distribution Values 630 APPENDIX E Using POM-QM for Windows 632 APPENDIX F Using Excel QM and Excel Add-Ins 635 APPENDIX G Solutions to Selected Problems 636 APPENDIX H Solutions to Self-Tests 639

INDEX 641

ONLINE MODULES MODULE 1 Analytic Hierarchy Process M1-1

M1.1 Introduction M1-2 M1.2 Multifactor Evaluation Process M1-2 M1.3 Analytic Hierarchy Process M1-4

Judy Grim’s Computer Decision M1-4

Using Pairwise Comparisons M1-5

Evaluations for Hardware M1-7

Determining the Consistency Ratio M1-7

Evaluations for the Other Factors M1-9

Determining Factor Weights M1-10

Overall Ranking M1-10

Using the Computer to Solve Analytic Hierarchy Process Problems M1-10

M1.4 Comparison of Multifactor Evaluation and Analytic Hierarchy Processes M1-11 Summary M1-12 Glossary M1-12 Key Equations M1-12 Solved Problems M1-12 Self- Test M1-14 Discussion Questions and Problems M1-14 Bibliography M1-16

Appendix M1.1 Using Excel for the Analytic Hierarchy Process M1-16

MODULE 2 Dynamic Programming M2-1 M2.1 Introduction M2-2 M2.2 Shortest-Route Problem Solved using Dynamic

Programming M2-2 M2.3 Dynamic Programming Terminology M2-6 M2.4 Dynamic Programming Notation M2-8 M2.5 Knapsack Problem M2-9

Types of Knapsack Problems M2-9

Roller’s Air Transport Service Problem M2-9

Summary M2-16 Glossary M2-16 Key Equations M2-16 Solved Problems M2-17 Self-Test M2-19 Discussion Questions and Problems M2-20 Case Study: United Trucking M2-22 Internet Case Study M2-22 Bibliography M2-23

�L

MODULE 3 Decision Theory and the Normal Distribution M3-1

M3.1 Introduction M3-2 M3.2 Break-Even Analysis and the Normal

Distribution M3-2 Barclay Brothers Company’s New Product

Decision M3-2

Probability Distribution of Demand M3-3

Using Expected Monetary Value to Make a Decision M3-5

M3.3 Expected Value of Perfect Information and the Normal Distribution M3-6 Opportunity Loss Function M3-6

Expected Opportunity Loss M3-6

Summary M3-8 Glossary M3-8 Key Equations M3-8 Solved Problems M3-9 Self-Test M3-10 Discussion Questions and Problems M3-10 Bibliography M3-12

Appendix M3.1 Derivation of the Break-Even Point M3-12

Appendix M3.2 Unit Normal Loss Integral M3-13

MODULE 4 Game Theory M4-1 M4.1 Introduction M4-2 M4.2 Language of Games M4-2 M4.3 The Minimax Criterion M4-3 M4.4 Pure Strategy Games M4-4 M4.5 Mixed Strategy Games M4-5 M4.6 Dominance M4-7

Summary M4-7 Glossary M4-8 Solved Problems M4-8 Self-Test M4-10 Discussion Questions and Problems M4-10 Bibliography M4-12

Appendix M4.1 Game Theory with QM for Windows M4-12

MODULE 5 Mathematical Tools: Determinants and Matrices M5-1

M5.1 Introduction M5-2 M5.2 Matrices and Matrix

Operations M5-2 Matrix Addition and Subtraction M5-2

Matrix Multiplication M5-3

Matrix Notation for Systems of Equations M5-6

Matrix Transpose M5-6

M5.3 Determinants, Cofactors, and Adjoints M5-7 Determinants M5-7

Matrix of Cofactors and Adjoint M5-9

M5.4 Finding the Inverse of a Matrix M5-10

XII CONTENTS

CONTENTS XIII

Summary M5-12 Glossary M5-12 Key Equations M5-12 Self-Test M5-13 Discussion Questions and Problems M5-13 Bibliography M5-14

Appendix M5.1 Using Excel for Matrix Calculations M5-15

MODULE 6 Calculus-Based Optimization M6-1 M6.1 Introduction M6-2 M6.2 Slope of a Straight Line M6-2 M6.3 Slope of a Nonlinear Function M6-3 M6.4 Some Common Derivatives M6-5

Second Derivatives M6-6

M6.5 Maximum and Minimum M6-6 M6.6 Applications M6-8

Economic Order Quantity M6-8

Total Revenue M6-9

Summary M6-10 Glossary M6-10 Key Equations M6-10 Solved Problem M6-11 Self-Test M6-11 Discussion Questions and Problems M6-12 Bibliography M6-12

MODULE 7 Linear Programming: The Simplex Method M7-1

M7.1 Introduction M7-2 M7.2 How to Set Up the Initial Simplex

Solution M7-2 Converting the Constraints to Equations M7-3

Finding an Initial Solution Algebraically M7-3

The First Simplex Tableau M7-4

M7.3 Simplex Solution Procedures M7-8 M7.4 The Second Simplex Tableau M7-9

Interpreting the Second Tableau M7-12

M7.5 Developing the Third Tableau M7-13 M7.6 Review of Procedures for Solving LP

Maximization Problems M7-16 M7.7 Surplus and Artificial Variables M7-16

Surplus Variables M7-17

Artificial Variables M7-17

Surplus and Artificial Variables in the Objective Function M7-18

M7.8 Solving Minimization Problems M7-18 The Muddy River Chemical Company

Example M7-18

Graphical Analysis M7-19

Converting the Constraints and Objective Function M7-20

Rules of the Simplex Method for Minimization Problems M7-21

First Simplex Tableau for the Muddy River Chemical Corporation Problem M7-21

Developing a Second Tableau M7-23

Developing a Third Tableau M7-24

Fourth Tableau for the Muddy River Chemical Corporation Problem M7-26

M7.9 Review of Procedures for Solving LP Minimization Problems M7-27

M7.10 Special Cases M7-28 Infeasibility M7-28

Unbounded Solutions M7-28

Degeneracy M7-29

More Than One Optimal Solution M7-30

M7.11 Sensitivity Analysis with the Simplex Tableau M7-30 High Note Sound Company Revisited M7-30

Changes in the Objective Function Coefficients M7-31

Changes in Resources or RHS Values M7-33

M7.12 The Dual M7-35 Dual Formulation Procedures M7-37

Solving the Dual of the High Note Sound Company Problem M7-37

M7.13 Karmarkar’s Algorithm M7-39 Summary M7-39 Glossary M7-39 Key Equation M7-40 Solved Problems M7-40 Self-Test M7-44 Discussion Questions and Problems M7-45 Bibliography M7-53

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xv

PREFACE

OVERVIEW

The eleventh edition of Quantitative Analysis for Management continues to provide both graduate and undergraduate students with a solid foundation in quantitative methods and management sci- ence. Thanks to the comments and suggestions from numerous users and reviewers of this textbook over the last thirty years, we are able to make this best-selling textbook even better.

We continue to place emphasis on model building and computer applications to help students understand how the techniques presented in this book are actually used in business today. In each chapter, managerial problems are presented to provide motivation for learning the techniques that can be used to address these problems. Next, the mathematical models, with all necessary assump- tions, are presented in a clear and concise fashion. The techniques are applied to the sample problems with complete details provided. We have found that this method of presentation is very effective, and students are very appreciative of this approach. If the mathematical computations for a technique are very detailed, the mathematical details are presented in such a way that the instruc- tor can easily omit these sections without interrupting the flow of the material. The use of computer software allows the instructor to focus on the managerial problem and spend less time on the math- ematical details of the algorithms. Computer output is provided for many examples.