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Regression Models

Quantitative Analysis for Management twelfth edition

Barry Render • Ralph M. Stair, Jr. • Michael E. Hanna • Trevor S. Hale

This is a special edition of an established title widely used by colleges and universities throughout the world. Pearson published this exclusive edition for the benefit of students outside the United States and Canada. If you purchased this book within the United States or Canada you should be aware that it has been imported without the approval of the Publisher or Author.

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Q uantitative A

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Quantitative Analysis for Management

Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto

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TwelfTh ediTion Global ediTion

Barry render

Charles Harwood Professor of Management Science Crummer 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

trevor S. hale

Associate Professor of Management Sciences, University of Houston–Downtown

A01_REND9327_12_SE_FM.indd 1 11/02/14 8:19 PM

Editor in Chief: Donna Battista Head of Learning Asset Acquisition, Global Edition:

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The rights of Barry Render, Ralph M. Stair, Jr., Michael E. Hanna, and Trevor S. Hale to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Authorized adaptation from the United States edition, entitled Quantitative Analysis for Management, 12th edition, ISBN 978-0-13-350733-1, by Barry Render, Ralph M. Stair, Jr., Michael E. Hanna, and Trevor S. Hale, published by Pearson Education © 2015.

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3

About the Authors

Barry Render is Professor Emeritus, the Charles Harwood Distinguished Professor of Operations Management, Crummer Graduate School of Business, Rollins College, Winter Park, Florida. He received his B.S. in Mathematics and Physics at Roosevelt University and his M.S. in Operations Research and his Ph.D. 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 Pearson, 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. More than 100 articles of Dr. Render 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 was named twice as a Senior Fulbright Scholar. He was Vice President of the Decision Science Institute Southeast Region and served as software review editor for Decision Line for six years and as Editor of the New York Times Operations Management special issues for five years. 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. He is currently Consulting Editor to Financial Times Press.

Dr. Render has taught operations management courses at Rollins College for 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 B.S. in chemical engi- neering from Purdue University and an M.B.A. from Tulane University. Under the guidance of Ken Ramsing and Alan Eliason, he received a Ph.D. 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 taught twice 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 in national meetings. He has published numer- ous 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

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4 About the Authors

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.

Michael E. Hanna is Professor of Decision Sciences at the University of Houston–Clear Lake (UHCL). He holds a B.A. in Economics, an M.S. in Mathematics, and a Ph.D. 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 on the board of directors of the Decision Sciences Institute (DSI) for two terms and also 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.

Trevor S. Hale is Associate Professor of Management Science at the University of Houston– Downtown (UHD). He received a B.S. in Industrial Engineering from Penn State University, an M.S. in Engineering Management from Northeastern University, and a Ph.D. in Operations Research from Texas A&M University. He was previously on the faculty of both Ohio University–Athens, and Colorado State University–Pueblo.

Dr. Hale was honored three times as an Office of Naval Research Senior Faculty Fellow. He spent the summers of 2009, 2011, and 2013 performing energy security/cyber security research for the U.S. Navy at Naval Base Ventura County in Port Hueneme, California.

Dr. Hale has published dozens of articles in the areas of operations research and quantitative analysis in journals such as the International Journal of Production Research, the European Journal of Operational Research, Annals of Operations Research, the Journal of the Operational Research Society, and the International Journal of Physical Distribution and Logistics Management among several others. He teaches quantitative analysis courses in the University of Houston–Downtown MBA program and Masters of Security Management for Executives program. He is a senior mem- ber of both the Decision Sciences Institute and INFORMS.

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5

Chapter 1 Introduction to Quantitative Analysis 19

Chapter 2 Probability Concepts and Applications 41

Chapter 3 Decision Analysis 83

Chapter 4 Regression Models 131

Chapter 5 Forecasting 167

Chapter 6 Inventory Control Models 205

Chapter 7 Linear Programming Models: Graphical and Computer Methods 257

Chapter 8 Linear Programming Applications 309

Chapter 9 Transportation, Assignment, and Network Models 341

Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming 381

Chapter 11 Project Management 413

Chapter 12 Waiting Lines and Queuing Theory Models 453

Chapter 13 Simulation Modeling 487

Chapter 14 Markov Analysis 527

Chapter 15 Statistical Quality Control 555

Appendices 575

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

8 Transportation, Assignment, and Network Algorithms M8-1

brief Contents

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6

Contents

Preface 13

chaPter 1 Introduction to Quantitative Analysis 19

1.1 Introduction 20 1.2 What Is Quantitative Analysis? 20 1.3 Business Analytics 21 1.4 The Quantitative Analysis Approach 22

Defining the Problem 22 Developing a Model 22 Acquiring Input Data 23 Developing a Solution 23 Testing the Solution 24 Analyzing the Results and Sensitivity Analysis 24 Implementing the Results 24 The Quantitative Analysis Approach

and Modeling in the Real World 26 1.5 How to Develop a Quantitative Analysis

Model 26 The Advantages of Mathematical Modeling 27 Mathematical Models Categorized by Risk 27

1.6 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach 28

1.7 Possible Problems in the Quantitative Analysis Approach 31 Defining the Problem 31 Developing a Model 32 Acquiring Input Data 33 Developing a Solution 33 Testing the Solution 34 Analyzing the Results 34

1.8 Implementation—Not Just the Final Step 35 Lack of Commitment and Resistance

to Change 35 Lack of Commitment by Quantitative Analysts 35 Summary 35 Glossary 36 Key Equations 36 Self-Test 36 Discussion Questions and Problems 37 Case Study: Food and Beverages at Southwestern University Football Games 39 Bibliography 39

chaPter 2 Probability Concepts and Applications 41 2.1 Introduction 42 2.2 Fundamental Concepts 42

Two Basic Rules of Probability 42 Types of Probability 43 Mutually Exclusive and Collectively

Exhaustive Events 44 Unions and Intersections of Events 45 Probability Rules for Unions, Intersections,

and Conditional Probabilities 46 2.3 Revising Probabilities with Bayes’ Theorem 47

General Form of Bayes’ Theorem 49 2.4 Further Probability Revisions 49 2.5 Random Variables 50 2.6 Probability Distributions 52

Probability Distribution of a Discrete Random Variable 52

Expected Value of a Discrete Probability Distribution 52

Variance of a Discrete Probability Distribution 53 Probability Distribution of a Continuous

Random Variable 54 2.7 The Binomial Distribution 55

Solving Problems with the Binomial Formula 56 Solving Problems with Binomial Tables 57

2.8 The Normal Distribution 58 Area Under the Normal Curve 60 Using the Standard Normal Table 60 Haynes Construction Company Example 61 The Empirical Rule 64

2.9 The F Distribution 64 2.10 The Exponential Distribution 66

Arnold’s Muffler Example 67 2.11 The Poisson Distribution 68

Summary 70 Glossary 70 Key Equations 71 Solved Problems 72 Self-Test 74 Discussion Questions and Problems 75 Case Study: WTVX 81 Bibliography 81

Appendix 2.1: Derivation of Bayes’ Theorem 81

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Contents 7

chaPter 3 Decision Analysis 83 3.1 Introduction 84 3.2 The Six Steps in Decision Making 84 3.3 Types of Decision-Making Environments 85 3.4 Decision Making Under Uncertainty 86

Optimistic 86 Pessimistic 87 Criterion of Realism (Hurwicz Criterion) 87 Equally Likely (Laplace) 88 Minimax Regret 88

3.5 Decision Making Under Risk 89 Expected Monetary Value 89 Expected Value of Perfect Information 90 Expected Opportunity Loss 92 Sensitivity Analysis 92

3.6 A Minimization Example 93 3.7 Using Software for Payoff Table Problems 95

QM for Windows 95 Excel QM 96

3.8 Decision Trees 97 Efficiency of Sample Information 102 Sensitivity Analysis 102

3.9 How Probability Values Are Estimated by Bayesian Analysis 103 Calculating Revised Probabilities 103 Potential Problem in Using Survey Results 105

3.10 Utility Theory 106 Measuring Utility and Constructing

a Utility Curve 107 Utility as a Decision-Making Criterion 110 Summary 112 Glossary 112 Key Equations 113 Solved Problems 113 Self-Test 118 Discussion Questions and Problems 119 Case Study: Starting Right Corporation 127 Case Study: Blake Electronics 128 Bibliography 130

chaPter 4 Regression Models 131 4.1 Introduction 132 4.2 Scatter Diagrams 132 4.3 Simple Linear Regression 133 4.4 Measuring the Fit of the Regression Model 135

Coefficient of Determination 136 Correlation Coefficient 136

4.5 Assumptions of the Regression Model 138 Estimating the Variance 139

4.6 Testing the Model for Significance 139 Triple A Construction Example 141 The Analysis of Variance (ANOVA) Table 141 Triple A Construction ANOVA Example 142

4.7 Using Computer Software for Regression 142 Excel 2013 142 Excel QM 143 QM for Windows 145

4.8 Multiple Regression Analysis 146 Evaluating the Multiple Regression Model 147 Jenny Wilson Realty Example 148

4.9 Binary or Dummy Variables 149 4.10 Model Building 150

Stepwise Regression 151 Multicollinearity 151

4.11 Nonlinear Regression 151 4.12 Cautions and Pitfalls in Regression

Analysis 154 Summary 155 Glossary 155 Key Equations 156 Solved Problems 157 Self-Test 159 Discussion Questions and Problems 159 Case Study: North–South Airline 164 Bibliography 165

Appendix 4.1: Formulas for Regression Calculations 165

chaPter 5 Forecasting 167 5.1 Introduction 168 5.2 Types of Forecasting Models 168

Qualitative Models 168 Causal Models 169 Time-Series Models 169

5.3 Components of a Time-Series 169 5.4 Measures of Forecast Accuracy 171 5.5 Forecasting Models—Random Variations

Only 174 Moving Averages 174 Weighted Moving Averages 174 Exponential Smoothing 176 Using Software for Forecasting Time Series 178

5.6 Forecasting Models—Trend and Random Variations 181 Exponential Smoothing with Trend 181 Trend Projections 183

5.7 Adjusting for Seasonal Variations 185 Seasonal Indices 186 Calculating Seasonal Indices with No

Trend 186 Calculating Seasonal Indices with Trend 187

5.8 Forecasting Models—Trend, Seasonal, and Random Variations 188 The Decomposition Method 188 Software for Decomposition 191 Using Regression with Trend and Seasonal

Components 192 5.9 Monitoring and Controlling Forecasts 193

Adaptive Smoothing 195 Summary 195 Glossary 196 Key Equations 196 Solved Problems 197 Self-Test 198 Discussion Questions and Problems 199 Case Study: Forecasting Attendance at SWU Football Games 202 Case Study: Forecasting Monthly Sales 203 Bibliography 204

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8 Contents

chaPter 6 Inventory Control Models 205 6.1 Introduction 206 6.2 Importance of Inventory Control 207

Decoupling Function 207 Storing Resources 207 Irregular Supply and Demand 207 Quantity Discounts 207 Avoiding Stockouts and Shortages 207

6.3 Inventory Decisions 208 6.4 Economic Order Quantity: Determining How

Much to Order 209 Inventory Costs in the EOQ Situation 210 Finding the EOQ 212 Sumco Pump Company Example 212 Purchase Cost of Inventory Items 213 Sensitivity Analysis with the EOQ Model 214

6.5 Reorder Point: Determining When to Order 215

6.6 EOQ Without the Instantaneous Receipt Assumption 216 Annual Carrying Cost for Production Run

Model 217 Annual Setup Cost or Annual Ordering

Cost 217 Determining the Optimal Production

Quantity 218 Brown Manufacturing Example 218

6.7 Quantity Discount Models 220 Brass Department Store Example 222

6.8 Use of Safety Stock 224 6.9 Single-Period Inventory Models 229

Marginal Analysis with Discrete Distributions 230

Café du Donut Example 231 Marginal Analysis with the Normal

Distribution 232 Newspaper Example 232

6.10 ABC Analysis 234 6.11 Dependent Demand: The Case for Material

Requirements Planning 234 Material Structure Tree 235 Gross and Net Material Requirements

Plan 236 Two or More End Products 237

6.12 Just-In-Time Inventory Control 239 6.13 Enterprise Resource Planning 240

Summary 241 Glossary 241 Key Equations 242 Solved Problems 243 Self-Test 245 Discussion Questions and Problems 246 Case Study: Martin-Pullin Bicycle Corporation 253 Bibliography 254

Appendix 6.1: Inventory Control with QM for Windows 255

chaPter 7 Linear Programming Models: Graphical and Computer Methods 257

7.1 Introduction 258 7.2 Requirements of a Linear Programming

Problem 258 7.3 Formulating LP Problems 259

Flair Furniture Company 259 7.4 Graphical Solution to an LP Problem 261

Graphical Representation of Constraints 261 Isoprofit Line Solution Method 265 Corner Point Solution Method 268 Slack and Surplus 270

7.5 Solving Flair Furniture’s LP Problem Using QM for Windows, Excel 2013, and Excel QM 271 Using QM for Windows 271 Using Excel’s Solver Command to Solve

LP Problems 272 Using Excel QM 275

7.6 Solving Minimization Problems 277 Holiday Meal Turkey Ranch 277

7.7 Four Special Cases in LP 281 No Feasible Solution 281 Unboundedness 281 Redundancy 282 Alternate Optimal Solutions 283

7.8 Sensitivity Analysis 284 High Note Sound Company 285 Changes in the Objective Function

Coefficient 286 QM for Windows and Changes in Objective

Function Coefficients 286 Excel Solver and Changes in Objective Function

Coefficients 287 Changes in the Technological Coefficients 288 Changes in the Resources or Right-Hand-Side

Values 289 QM for Windows and Changes in Right-Hand-

Side Values 290 Excel Solver and Changes in Right-Hand-Side

Values 290 Summary 292 Glossary 292 Solved Problems 293 Self-Test 297 Discussion Questions and Problems 298 Case Study: Mexicana Wire Works 306 Bibliography 308

chaPter 8 Linear Programming Applications 309 8.1 Introduction 310 8.2 Marketing Applications 310

Media Selection 310 Marketing Research 311

8.3 Manufacturing Applications 314 Production Mix 314 Production Scheduling 315

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Contents 9

8.4 Employee Scheduling Applications 319 Labor Planning 319

8.5 Financial Applications 321 Portfolio Selection 321 Truck Loading Problem 324

8.6 Ingredient Blending Applications 326 Diet Problems 326 Ingredient Mix and Blending Problems 327

8.7 Other Linear Programming Applications 329 Summary 331 Self-Test 331 Problems 332 Case Study: Cable & Moore 339 Bibliography 340

chaPter 9 Transportation, Assignment, and Network Models 341

9.1 Introduction 342 9.2 The Transportation Problem 343

Linear Program for the Transportation Example 343

Solving Transportation Problems Using Computer Software 343

A General LP Model for Transportation Problems 344

Facility Location Analysis 345 9.3 The Assignment Problem 348

Linear Program for Assignment Example 348 9.4 The Transshipment Problem 350

Linear Program for Transshipment Example 350 9.5 Maximal-Flow Problem 353

Example 353 9.6 Shortest-Route Problem 355 9.7 Minimal-Spanning Tree Problem 356

Summary 360 Glossary 361 Solved Problems 361 Self-Test 363 Discussion Questions and Problems 364 Case Study: Andrew–Carter, Inc. 375 Case Study: Northeastern Airlines 376 Case Study: Southwestern University Traffic Problems 377 Bibliography 378

Appendix 9.1: Using QM for Windows 378

chaPter 10 Integer Programming, Goal Programming, and Nonlinear Programming 381

10.1 Introduction 382 10.2 Integer Programming 382

Harrison Electric Company Example of Integer Programming 382

Using Software to Solve the Harrison Integer Programming Problem 384

Mixed-Integer Programming Problem Example 386

10.3 Modeling with 0–1 (Binary) Variables 388 Capital Budgeting Example 388

Limiting the Number of Alternatives Selected 390

Dependent Selections 390 Fixed-Charge Problem Example 390 Financial Investment Example 392

10.4 Goal Programming 392 Example of Goal Programming: Harrison Electric

Company Revisited 394 Extension to Equally Important Multiple

Goals 395 Ranking Goals with Priority Levels 395 Goal Programming with Weighted Goals 396

10.5 Nonlinear Programming 397 Nonlinear Objective Function and Linear

Constraints 398 Both Nonlinear Objective Function and

Nonlinear Constraints 398 Linear Objective Function with Nonlinear

Constraints 400 Summary 400 Glossary 401 Solved Problems 401 Self-Test 404 Discussion Questions and Problems 405 Case Study: Schank Marketing Research 410 Case Study: Oakton River Bridge 411 Bibliography 412

chaPter 11 Project Management 413 11.1 Introduction 414 11.2 PERT/CPM 415

General Foundry Example of PERT/CPM 415 Drawing the PERT/CPM Network 417 Activity Times 417 How to Find the Critical Path 418 Probability of Project Completion 423 What PERT Was Able to Provide 424 Using Excel QM for the General Foundry

Example 424 Sensitivity Analysis and Project Management 425

11.3 PERT/Cost 427 Planning and Scheduling Project Costs:

Budgeting Process 427 Monitoring and Controlling Project Costs 430

11.4 Project Crashing 432 General Foundary Example 433 Project Crashing with Linear Programming 434

11.5 Other Topics in Project Management 437 Subprojects 437 Milestones 437 Resource Leveling 437 Software 437 Summary 437 Glossary 438 Key Equations 438 Solved Problems 439

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10 Contents

Self-Test 441 Discussion Questions and Problems 442 Case Study: Southwestern University Stadium Construction 447 Case Study: Family Planning Research Center of Nigeria 448 Bibliography 450

Appendix 11.1: Project Management with QM for Windows 450

chaPter 12 Waiting Lines and Queuing Theory Models 453

12.1 Introduction 454 12.2 Waiting Line Costs 454

Three Rivers Shipping Company Example 455 12.3 Characteristics of a Queuing System 456

Arrival Characteristics 456 Waiting Line Characteristics 456 Service Facility Characteristics 457 Identifying Models Using Kendall Notation 457

12.4 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/1) 460 Assumptions of the Model 460 Queuing Equations 460 Arnold’s Muffler Shop Case 461 Enhancing the Queuing Environment 465

12.5 Multichannel Queuing Model with Poisson Arrivals and Exponential Service Times (M/M/m) 465 Equations for the Multichannel Queuing

Model 466 Arnold’s Muffler Shop Revisited 466

12.6 Constant Service Time Model (M/D/1) 468 Equations for the Constant Service Time

Model 468 Garcia-Golding Recycling, Inc. 469

12.7 Finite Population Model (M/M/1 with Finite Source) 470 Equations for the Finite Population Model 470 Department of Commerce Example 471

12.8 Some General Operating Characteristic Relationships 472

12.9 More Complex Queuing Models and the Use of Simulation 472 Summary 473 Glossary 473 Key Equations 474 Solved Problems 475 Self-Test 478 Discussion Questions and Problems 479 Case Study: New England Foundry 483 Case Study: Winter Park Hotel 485 Bibliography 485

Appendix 12.1: Using QM for Windows 486

chaPter 13 Simulation Modeling 487 13.1 Introduction 488 13.2 Advantages and Disadvantages

of Simulation 489

13.3 Monte Carlo Simulation 490 Harry’s Auto Tire Example 490 Using QM for Windows for Simulation 495 Simulation with Excel Spreadsheets 496

13.4 Simulation and Inventory Analysis 498 Simkin’s Hardware Store 498 Analyzing Simkin’s Inventory Costs 501

13.5 Simulation of a Queuing Problem 502 Port of New Orleans 502 Using Excel to Simulate the Port of New Orleans

Queuing Problem 504 13.6 Simulation Model for a Maintenance

Policy 505 Three Hills Power Company 505 Cost Analysis of the Simulation 507

13.7 Other Simulation Issues 510 Two Other Types of Simulation Models 510 Verification and Validation 511 Role of Computers in Simulation 512 Summary 512 Glossary 512 Solved Problems 513 Self-Test 516 Discussion Questions and Problems 517 Case Study: Alabama Airlines 522 Case Study: Statewide Development Corporation 523 Case Study: FB Badpoore Aerospace 524 Bibliography 526

chaPter 14 Markov Analysis 527 14.1 Introduction 528 14.2 States and State Probabilities 528

The Vector of State Probabilities for Three Grocery Stores Example 529

14.3 Matrix of Transition Probabilities 530 Transition Probabilities for the Three Grocery

Stores 531 14.4 Predicting Future Market Shares 531 14.5 Markov Analysis of Machine Operations 532 14.6 Equilibrium Conditions 533 14.7 Absorbing States and the Fundamental

Matrix: Accounts Receivable Application 536 Summary 540 Glossary 541 Key Equations 541 Solved Problems 541 Self-Test 545 Discussion Questions and Problems 545 Case Study: Rentall Trucks 550 Bibliography 551

Appendix 14.1: Markov Analysis with QM for Windows 551 Appendix 14.2: Markov Analysis With Excel 553

chaPter 15 Statistical Quality Control 555 15.1 Introduction 556 15.2 Defining Quality and TQM 556 15.3 Statiscal Process Control 557

Variability in the Process 557

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Contents 11

15.4 Control Charts for Variables 559 The Central Limit Theorem 559 Setting x-Chart Limits 560 Setting Range Chart Limits 563

15.5 Control Charts for Attributes 564 p-Charts 564 c-Charts 566 Summary 568 Glossary 568 Key Equations 568 Solved Problems 569 Self-Test 570 Discussion Questions and Problems 570 Bibliography 573

Appendix 15.1: Using QM for Windows for SPC 573

appendices 575 appendix a Areas Under the Standard

Normal Curve 576 appendix B Binomial Probabilities 578 appendix c Values of e-l for Use in the Poisson

Distribution 583 appendix d F Distribution Values 584 appendix e Using POM-QM for Windows 586 appendix F Using Excel QM and Excel Add-Ins 589 appendix G Solutions to Selected Problems 590 appendix H Solutions to Self-Tests 594

index 597

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 Problem M2-16 Self-Test M2-18 Discussion Questions and Problems M2-19 Case Study: United Trucking M2-22 Internet Case Study M2-22 Bibliography M2-22

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 M3-9 Discussion Questions and Problems M3-10 Bibliography M3-11

Appendix M3.1: Derivation of the Break-Even Point M3-11 Appendix M3.2: Unit Normal Loss Integral M3-12

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 M4-6

Summary M4-7 Glossary M4-7 Solved Problems M4-7 Self-Test M4-8 Discussion Questions and Problems M4-9 Bibliography M4-10

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 M5-6 Determinants M5-6 Matrix of Cofactors and Adjoint M5-8

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12 Contents

M5.4 Finding the Inverse of a Matrix M5-10 Summary M5-11 Glossary M5-11 Key Equations M5-11 Self-Test M5-12 Discussion Questions and Problems M5-12 Bibliography M5-13

Appendix M5.1: Using Excel for Matrix Calculations M5-13

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 M7-41 Self-Test M7-44 Discussion Questions and Problems M7-45 Bibliography M7-54

MOduLe 8 Transportation, Assignment, and Network Algorithms M8-1

M8.1 Introduction M8-2 M8.2 The Transportation Algorithm M8-2

Developing an Initial Solution: Northwest Corner Rule M8-2

Stepping-Stone Method: Finding a Least-Cost Solution M8-4

M8.3 Special Situations with the Transportation Algorithm M8-9 Unbalanced Transportation Problems M8-9 Degeneracy in Transportation Problems M8-10 More Than One Optimal Solution M8-13 Maximization Transportation Problems M8-13 Unacceptable or Prohibited Routes M8-13 Other Transportation Methods M8-13

M8.4 The Assignment Algorithm M8-13 The Hungarian Method (Flood’s

Technique) M8-14 Making the Final Assignment M8-18

M8.5 Special Situations with the Assignment Algorithm M8-18 Unbalanced Assignment Problems M8-18 Maximization Assignment Problems M8-19

M8.6 Maximal-Flow Problem M8-20 Maximal-Flow Technique M8-20

M8.7 Shortest-Route Problem M8-23 Shortest-Route Technique M8-23 Summary M8-25 Glossary M8-25 Solved Problems M8-26 Self-Test M8-32 Discussion Questions and Problems M8-33 Cases M8-42 Bibliography M8-42

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13

Overview

Welcome to the twelfth edition of Quantitative Analysis for Management. Our goal is to provide undergraduate and graduate students with a genuine foundation in business analytics, quantitative methods, and management science. In doing so, we owe thanks to the hundreds of users and scores of reviewers who have provided invaluable counsel and pedagogical insight for more than 30 years.

To help students connect how the techniques presented in this book apply in the real world, computer-based applications and examples are a major focus of this edition. Mathematical models, with all the necessary assumptions, are presented in a clear and “plain-English” manner. The ensuing solution procedures are then applied to example problems alongside step-by-step “how-to” instruc- tions. We have found this method of presentation to be very effective and students are very apprecia- tive of this approach. In places where the mathematical computations are intricate, the details are presented in such a manner that the instructor can omit these sections without interrupting the flow of material. The use of computer software enables the instructor to focus on the managerial problem and spend less time on the details of the algorithms. Computer output is provided for many examples throughout the book.

The only mathematical prerequisite for this textbook is algebra. One chapter on probability and another on regression analysis provide introductory coverage on these topics. We employ standard notation, terminology, and equations throughout the book. Careful explanation is provided for the mathematical notation and equations that are used.

new tO this editiOn

● An introduction to business analytics is provided.

● Excel 2013 is incorporated throughout the chapters.

● The transportation, assignment, and network models have been combined into one chapter focused on modeling with linear programming.

● Specialized algorithms for the transportation, assignment, and network methods have been combined into Online Module 8.

● New examples, over 25 problems, 8 QA in Action applications, 4 Modeling in the Real World features, and 3 new Case Studies have been added throughout the textbook. Other problems and Case Studies have been updated.

PrefACe

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14 PrefACe

speCial Features

Many features have been popular in previous editions of this textbook, and they have been updated and expanded in this edition. They include the following:

● Modeling in the Real World boxes demonstrate the application of the quantitative analysis approach to every technique discussed in the book. Four new ones have been added.

● Procedure boxes summarize the more complex quantitative techniques, presenting them as a series of easily understandable steps.

● Margin notes highlight the important topics in the text.

● History boxes provide interesting asides related to the development of techniques and the people who originated them.

● QA in Action boxes illustrate how real organizations have used quantitative analysis to solve problems. Several new QA in Action boxes have been added.

● Solved Problems, included at the end of each chapter, serve as models for students in solving their own homework problems.

● Discussion Questions are presented at the end of each chapter to test the student’s understand- ing of the concepts covered and definitions provided in the chapter.

● Problems included in every chapter are applications oriented and test the student’s ability to solve exam-type problems. They are graded by level of difficulty: introductory (one bullet), moderate (two bullets), and challenging (three bullets). More than 40 new problems have been added.

● Internet Homework Problems provide additional problems for students to work. They are available on the Companion Website.

● Self-Tests allow students to test their knowledge of important terms and concepts in prepara- tion for quizzes and examinations.

● Case Studies, at the end of each chapter, provide additional challenging managerial applications.

● Glossaries, at the end of each chapter, define important terms.

● Key Equations, provided at the end of each chapter, list the equations presented in that chapter.

● End-of-chapter bibliographies provide a current selection of more advanced books and articles.

● The software POM-QM for Windows uses the full capabilities of Windows to solve quantita- tive analysis problems.

● Excel QM and Excel 2013 are used to solve problems throughout the book.

● Data files with Excel spreadsheets and POM-QM for Windows files containing all the examples in the textbook are available for students to download from the Companion Website. Instructors can download these plus additional files containing computer solutions to the rel- evant end-of-chapter problems from the Instructor Resource Center Web site.

● Online modules provide additional coverage of topics in quantitative analysis.

● The Companion Website, at www.pearsonglobaleditions.com/render, provides the online modules, additional problems, cases, and other material for almost every chapter.

signiFiCant Changes tO the twelFth editiOn

In the twelfth edition, we have introduced Excel 2013 in all of the chapters. Screenshots are integrated in the appropriate sections so that students can easily learn how to use Excel for the calculations. The Excel QM add-in is used with Excel 2013 allowing students with limited Excel experience to easily perform the necessary calculations. This also allows students to improve their Excel skills as they see the formulas automatically written in Excel QM.

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PrefACe 15

From the Companion Website, students can access files for all of the examples used in the textbook in Excel 2013, QM for Windows, and Excel QM. Other files with all of the end-of-chapter problems involving these software tools are available to the instructors.

Business analytics, one of the hottest topics in the business world, makes extensive use of the models in this book. A discussion of the business analytics categories is provided, and the relevant management science techniques are placed into the appropriate category.

The transportation, transshipment, assignment, and network models have been combined into one chapter focused on modeling with linear programming. The specialized algorithms for these models have been combined into a new online module.

Examples and problems have been updated, and many new ones have been added. New screen- shots are provided for almost all of the examples in the book. A brief summary of the other changes in each chapter are presented here.

Chapter 1 Introduction to Quantitative Analysis. A section on business analytics has been added, the self-test has been modified, and two new problems were added.

Chapter 2 Probability Concepts and Applications. The presentation of the fundamental concepts of probability has been significantly modified and reorganized. Two new problems have been added.

Chapter 3 Decision Analysis. A more thorough discussion of minimization problems with payoff tables has been provided in a new section. The presentation of software usage with payoff tables was expanded. Two new problems were added.

Chapter 4 Regression Models. The use of different software packages for regression analysis has been moved to the body of the textbook instead of the appendix. Five new problems and one new QA in Action item have been added.

Chapter 5 Forecasting. The presentation of time-series forecasting models was significantly revised to bring the focus on identifying the appropriate technique to use based on which time- series components are present in the data. Five new problems were added, and the cases have been updated.

Chapter 6 Inventory Control Models. The four steps of the Kanban production process have been updated and clarified. Two new QA in Action boxes, four new problems, and one new Modeling in the Real World have been added.

Chapter 7 Linear Programming Models: Graphical and Computer Methods. More discussion of Solver is presented. A new Modeling in the Real World item was added, and the solved problems have been revised.

Chapter 8 Linear Programming Applications. The transportation model was moved to Chapter 9, and a new section describing other models has been added. The self-test questions were modified; one new problem, one new QA in Action summary, and a new case study have been added.

Chapter 9 Transportation, Assignment, and Network Models. This new chapter presents all of the distribution, assignment, and network models that were previously in two separate chapters. The modeling approach is emphasized, while the special-purpose algorithms were moved to a new online module. A new case study, Northeastern Airlines, has also been added.

Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming. The use of Excel 2013 and the new screen shots were the only changes to this chapter.

Chapter 11 Project Management. Two new end-of-chapter problems and three new QA in Action boxes have been added.

Chapter 12 Waiting Lines and Queuing Theory Models. Two new end-of-chapter problems were added.

Chapter 13 Simulation Modeling. One new Modeling in the Real World vignette, one new QA in Action box, and a new case study have been added.

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16 PrefACe

Chapter 14 Markov Analysis. One new QA in Action box and two new end-of-chapter problems have been added.

Chapter 15 Statistical Quality Control. One new Modeling in the Real World vignette, one new QA in Action box, and two new end-of-chapter problems have been added.

Modules 1–8 The only significant change to the modules is the addition of Module 8: Transportation, Assignment, and Network Algorithms. This includes the special-purpose algorithms for the transportation, assignment, and network models.

Online MOdules

To streamline the book, eight topics are contained in modules available on the Companion Website for the book, located at www.pearsonglobaleditions.com/render.

1. Analytic Hierarchy Process

2. Dynamic Programming

3. Decision Theory and the Normal Distribution

4. Game Theory

5. Mathematical Tools: Determinants and Matrices

6. Calculus-Based Optimization

7. Linear Programming: The Simplex Method

8. Transportation, Assignment, and Network Algorithms

sOFtware

excel 2013 Instructions and screen captures are provided for, using Excel 2013, throughout the book. Instructions for activating the Solver and Analysis ToolPak add-ins in Excel 2013 are pro- vided in an appendix. The use of Excel is more prevalent in this edition of the book than in previous editions.

excel QM Using the Excel QM add-in that is available on the Companion Website makes the use of Excel even easier. Students with limited Excel experience can use this and learn from the formu- las that are automatically provided by Excel QM. This is used in many of the chapters.

pOM-QM for windows This software, developed by Professor Howard Weiss, is available to students at the Companion Website. This is very user-friendly and has proven to be a very popular software tool for users of this textbook. Modules are available for every major problem type pre- sented in the textbook.

COMpaniOn website

The Companion Website, located at www.pearsonglobaleditions.com/render, contains a variety of materials to help students master the material in this course. These include the following:

Modules There are eight modules containing additional material that the instructor may choose to include in the course. Students can download these from the Companion Website.

Files for examples in excel, excel QM, and pOM-QM for windows Students can down- load the files that were used for examples throughout the book. This helps them become familiar with the software, and it helps them understand the input and formulas necessary for working the examples.

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PrefACe 17

internet homework problems In addition to the end-of-chapter problems in the textbook, there are additional problems that instructors may assign. These are available for download at the Companion Website, located at www.pearsonglobaleditions.com/render.

internet Case studies Additional case studies are available for most chapters.

pOM-QM for windows Developed by Howard Weiss, this very user-friendly software can be used to solve most of the homework problems in the text.

excel QM This Excel add-in will automatically create worksheets for solving problems. This is very helpful for instructors who choose to use Excel in their classes but who may have students with limited Excel experience. Students can learn by examining the formulas that have been cre- ated, and by seeing the inputs that are automatically generated for using the Solver add-in for linear programming.