Old oregon wood store case study

Old Oregon Wood Store

1. Review the "Old Oregon Wood Store" case study in Quantitative Analysis.
2. Make notes of any questions you have on the case.
3. Complete the model in an Excel spreadsheet.

you will find it in chapter 9 from the book attached

Week 11 chapter 12

Action Items
Review the “Southwestern University Stadium Construction” case study at the end of Chapter 12 in Quantitative Analysis.
Complete the model in an Excel spreadsheet.
Answer each of the questions that follow the case.

The book is attached
check the cases from the book

separate each week alone in a different worksheet the one that needs excel use excel, the one that needs word use the word

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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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Copyright © 2012, 2009, 2006, 2003, 2000 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, New Jersey 07458. All rights reserved. Manufactured in the United States of America. This publi- cation is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited repro- duction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopy- ing, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458.

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ISBN-13: 978-0-13-214911-2 ISBN-10: 0-13-214911-7

10 9 8 7 6 5 4 3 2 1

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.

The only mathematical prerequisite for this textbook is algebra. One chapter on probability and another chapter on regression analysis provide introductory coverage of these topics. We use stan- dard notation, terminology, and equations throughout the book. Careful verbal explanation is pro- vided for the mathematical notation and equations used.

NEW TO THIS EDITION

� Excel 2010 is incorporated throughout the chapters.

� The Poisson and exponential distribution discussions were moved to Chapter 2 with the other statistical background material used in the textbook.

� The simplex algorithm content has been moved from the textbook to Module 7 on the Companion Website.

� There are 11 new QA in Action boxes, 4 new Model in the Real World boxes, and more than 40 new problems.

� Less emphasis was placed on the algorithmic approach to solving transportation and assign- ment model problems.

� More emphasis was placed on modeling and less emphasis was placed on manual solution methods.

xvi 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. 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 peo- ple who originated them.

� QA in Action boxes illustrate how real organizations have used quantitative analysis to solve problems. Eleven 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 2010 are used to solve problems throughout the book.

� Data files with Excel spreadsheets and POM-QM for Windows files containing all the exam- ples 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 rele- vant end-of-chapter problems from the Instructor Resource Center website.

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

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

SIGNIFICANT CHANGES TO THE ELEVENTH EDITION

In the eleventh edition, we have incorporated the use of Excel 2010 throughout the chapters. Whereas information about Excel 2007 is also included in appropriate appendices, screen captures and formulas from Excel 2010 are used extensively. Most of the examples have spreadsheet solu- tions provided. The Excel QM add-in is used with Excel 2010 to provide students with the most up-to-date methods available.

An even greater emphasis on modeling is provided as the simplex algorithm has been moved from the textbook to a module on the Companion Website. Linear programming models are pre- sented with the transportation, transshipment, and assignment problems. These are presented from a network approach, providing a consistent and coherent discussion of these important types of problems. Linear programming models are provided for some other network models as well. While a few of the special purpose algorithms are still available in the textbook, they may be easily omit- ted without loss of continuity should the instructor choose that option.

PREFACE xvii

In addition to the use of Excel 2010, the use of new screen captures, and the discussion of soft- ware changes throughout the book, other modifications have been made to almost every chapter. We briefly summarize the major changes here.

Chapter 1 Introduction to Quantitative Analysis. New QA in Action boxes and Managing in the Real World applications have been added. One new problem has been added.

Chapter 2 Probability Concepts and Applications. The presentation of discrete random variables has been modified. The empirical rule has been added, and the discussion of the normal distribution has been modified. The presentations of the Poisson and exponential distributions, which are impor- tant in the waiting line chapter, have been expanded. Three new problems have been added.

Chapter 3 Decision Analysis. The presentation of the expected value criterion has been modified. A discussion is provided of using the decision criteria for both maximization and minimization prob- lems. An Excel 2010 spreadsheet for the calculations with Bayes theorem is provided. A new QA in Action box and six new problems have been added.

Chapter 4 Regression Models. Stepwise regression is mentioned when discussing model building. Two new problems have been added. Other end-of-chapter problems have been modified.

Chapter 5 Forecasting. The presentation of exponential smoothing with trend has been modified. Three new end-of-chapter problems and one new case have been added.

Chapter 6 Inventory Control Models. The use of safety stock has been significantly modified, with the presentation of three distinct situations that would require the use of safety stock. Discussion of inventory position has been added. One new QA in Action, five new problems, and two new solved problems have been added.

Chapter 7 Linear Programming Models: Graphical and Computer Methods. Discussion has been expanded on interpretation of computer output, the use of slack and surplus variables, and the pres- entation of binding constraints. The use of Solver in Excel 2010 is significantly changed from Excel 2007, and the use of the new Solver is clearly presented. Two new problems have been added, and others have been modified.

Chapter 8 Linear Programming Modeling Applications with Computer Analysis. The production mix example was modified. To enhance the emphasis on model building, discussion of developing the model was expanded for many examples. One new QA in Action box and two new end-of-chapter problems were added.

Chapter 9 Transportation and Assignment Models. Major changes were made in this chapter, as less emphasis was placed on the algorithmic approach to solving these problems. A network repre- sentation, as well as the linear programming model for each type of problem, were presented. The transshipment model is presented as an extension of the transportation problem. The basic trans- portation and assignment algorithms are included, but they are at the end of the chapter and may be omitted without loss of flow. Two QA in Action boxes, one Managing in the Real World situation, and 11 new end-of-chapter problems were added.

Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming. More emphasis was placed on modeling and less emphasis was placed on manual solution methods. One new Managing in the Real World application, one new solved problem, and three new problems were added.

Chapter 11 Network Models. Linear programming formulations for the max-flow and shortest route problems were added. The algorithms for solving these network problems were retained, but these can easily be omitted without loss of continuity. Six new end-of-chapter problems were added.

Chapter 12 Project Management. Screen captures for the Excel QM software application were added. One new problem was added.

Chapter 13 Waiting Lines and Queuing Models. The discussion of the Poisson and exponential dis- tribution were moved to Chapter 2 with the other statistical background material used in the text- book. Two new QA in Action boxes and two new end-of-chapter problems were added.

Chapter 14 Simulation Modeling. The use of Excel 2010 is the major change to this chapter.

Chapter 15 Markov Analysis. One Managing in the Real World application was added.

Chapter 16 Statistical Quality Control. One new QA in Action box was added. The chapter on the simplex algorithm was converted to a module that is now available on the Companion Website with the other modules. Instructors who choose to cover this can tell students to download the complete discussion.

xviii PREFACE

ONLINE MODULES

To streamline the book, seven topics are contained in modules available on the Companion Website for the book.

1. Analytic Hierarchy Process

2. Dynamic Programming

3. Decision Theory and the Normal Distribution

4. Game Theory

5. Mathematical Tools: Matrices and Determinants

6. Calculus-Based Optimization

7. Linear Programming: The Simplex Method

SOFTWARE

Excel 2010 Instructions and screen captures are provided for, using Excel 2010, throughout the book. Discussion of differences between Excel 2010 and Excel 2007 is provided where relevant. Instructions for activating the Solver and Analysis ToolPak add-ins for both Excel 2010 and Excel 2007 are provided 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.pearsonhighered.com/render, contains a variety of mate- rials to help students master the material in this course. These include:

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

Self-Study Quizzes Some multiple choice, true-false, fill-in-the-blank, and discussion questions are available for each chapter to help students test themselves over the material covered in that chapter.

Files for Examples in Excel, Excel QM, and POM-QM for Windows Students can download 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.

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.

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.

PREFACE xix

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 lin- ear programming.

INSTRUCTOR RESOURCES

� Instructor Resource Center: The Instructor Resource Center contains the electronic files for the test bank, PowerPoint slides, the Solutions Manual, and data files for both Excel and POM-QM for Windows for all relevant examples and end-of-chapter problems. (www.pear- sonhighered.com/render).

� Register, Redeem, Login: At www.pearsonhighered.com/irc, instructors can access a variety of print, media, and presentation resources that are available with this text in downloadable, digital format. For most texts, resources are also available for course management platforms such as Blackboard, WebCT, and Course Compass.

� Need help? Our dedicated technical support team is ready to assist instructors with questions about the media supplements that accompany this text. Visit http://247.prenhall.com/ for answers to frequently asked questions and toll-free user support phone numbers. The supple- ments are available to adopting instructors. Detailed descriptions are provided on the Instructor Resource Center.

Instructor’s Solutions Manual The Instructor’s Solutions Manual, updated by the authors, is available to adopters in print form and as a download from the Instructor Resource Center. Solutions to all Internet Homework Problems and Internet Case Studies are also included in the manual.

Test Item File The updated test item file is available to adopters as a downloaded from the Instructor Resource Center.

TestGen The computerized TestGen package allows instructors to customize, save, and generate classroom tests. The test program permits instructors to edit, add, or delete questions from the test bank; edit existing graphics and create new graphics; analyze test results; and organize a database of test and student results. This software allows for extensive flexibility and ease of use. It provides many options for organizing and displaying tests, along with search and sort features. The software and the test banks can be downloaded at www.pearsonhighered.com/render.

ACKNOWLEDGMENTS

We gratefully thank the users of previous editions and the reviewers who provided valuable sugges- tions and ideas for this edition. Your feedback is valuable in our efforts for continuous improvement. The continued success of Quantitative Analysis for Management is a direct result of instructor and student feedback, which is truly appreciated.

The authors are indebted to many people who have made important contributions to this proj- ect. Special thanks go to Professors F. Bruce Simmons III, Khala Chand Seal, Victor E. Sower, Michael Ballot, Curtis P. McLaughlin, and Zbigniew H. Przanyski for their contributions to the excellent cases included in this edition. Special thanks also goes out to Trevor Hale for his extensive help with the Modeling in the Real World vignettes and the QA in Action applications, and for his serving as a sounding board for many of the ideas that resulted in significant improvements for this edition.

xx PREFACE

We thank Howard Weiss for providing Excel QM and POM-QM for Windows, two of the most outstanding packages in the field of quantitative methods. We would also like to thank the reviewers who have helped to make this one of the most widely used textbooks in the field of quantitative analysis:

Stephen Achtenhagen, San Jose University M. Jill Austin, Middle Tennessee State University Raju Balakrishnan, Clemson University Hooshang Beheshti, Radford University Bruce K. Blaylock, Radford University Rodney L. Carlson, Tennessee Technological University Edward Chu, California State University, Dominguez Hills John Cozzolino, Pace University–Pleasantville Shad Dowlatshahi, University of Wisconsin, Platteville Ike Ehie, Southeast Missouri State University Sean Eom, Southeast Missouri State University Ephrem Eyob, Virginia State University Mira Ezvan, Lindenwood University Wade Ferguson, Western Kentucky University Robert Fiore, Springfield College Frank G. Forst, Loyola University of Chicago Ed Gillenwater, University of Mississippi Stephen H. Goodman, University of Central Florida Irwin Greenberg, George Mason University Trevor S. Hale, University of Houston–Downtown Nicholas G. Hall, Ohio State University Robert R. Hill, University of Houston–Clear Lake Gordon Jacox, Weber State University Bharat Jain, Towson State University Vassilios Karavas, University of Massachusetts–Amherst Darlene R. Lanier, Louisiana State University Kenneth D. Lawrence, New Jersey Institute of Technology Jooh Lee, Rowan College Richard D. Legault, University of Massachusetts–Dartmouth Douglas Lonnstrom, Siena College Daniel McNamara, University of St. Thomas Robert C. Meyers, University of Louisiana Peter Miller, University of Windsor Ralph Miller, California State Polytechnic University

Shahriar Mostashari, Campbell University David Murphy, Boston College Robert Myers, University of Louisville Barin Nag, Towson State University Nizam S. Najd, Oklahoma State University Harvey Nye, Central State University Alan D. Olinsky, Bryant College Savas Ozatalay, Widener University Young Park, California University of Pennsylvania Cy Peebles, Eastern Kentucky University Yusheng Peng, Brooklyn College Dane K. Peterson, Southwest Missouri State University Sanjeev Phukan, Bemidji State University Ranga Ramasesh, Texas Christian University William Rife, West Virginia University Bonnie Robeson, Johns Hopkins University Grover Rodich, Portland State University L. Wayne Shell, Nicholls State University Richard Slovacek, North Central College John Swearingen, Bryant College F. S. Tanaka, Slippery Rock State University Jack Taylor, Portland State University Madeline Thimmes, Utah State University M. Keith Thomas, Olivet College Andrew Tiger, Southeastern Oklahoma State University Chris Vertullo, Marist College James Vigen, California State University, Bakersfield William Webster, The University of Texas at San Antonio Larry Weinstein, Eastern Kentucky University Fred E. Williams, University of Michigan-Flint Mela Wyeth, Charleston Southern University

We are very grateful to all the people at Prentice Hall who worked so hard to make this book a success. These include Chuck Synovec, our editor; Judy Leale, senior managing editor; Mary Kate Murray, project manager; and Jason Calcano, editorial assistant. We are also grateful to Jen Carley, our project manager at PreMediaGlobal Book Services. We are very appreciative of the work of Annie Puciloski in error checking the textbook and Solutions Manual. Thank you all!

Barry Render brender@rollins.edu

Ralph Stair

Michael Hanna 281-283-3201 (phone) 281-226-7304 (fax) hanna@uhcl.edu

1

After completing this chapter, students will be able to:

CHAPTER OUTLINE

LEARNING OBJECTIVES

1

Introduction to Quantitative Analysis

1. Describe the quantitative analysis approach.

2. Understand the application of quantitative analysis in a real situation.

3. Describe the use of modeling in quantitative analysis.

1.1 Introduction

1.2 What Is Quantitative Analysis?

1.3 The Quantitative Analysis Approach

1.4 How to Develop a Quantitative Analysis Model

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

1.6 Possible Problems in the Quantitative Analysis Approach

1.7 Implementation—Not Just the Final Step

4. Use computers and spreadsheet models to perform quantitative analysis.

5. Discuss possible problems in using quantitative analysis.

6. Perform a break-even analysis.

CHAPTER

Summary • Glossary • Key Equations • Self-Test • Discussion Questions and Problems • Case Study: Food and

Beverages at Southwestern University Football Games • Bibliography

2 CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS

1.1 Introduction

People have been using mathematical tools to help solve problems for thousands of years; how- ever, the formal study and application of quantitative techniques to practical decision making is largely a product of the twentieth century. The techniques we study in this book have been applied successfully to an increasingly wide variety of complex problems in business, govern- ment, health care, education, and many other areas. Many such successful uses are discussed throughout this book.

It isn’t enough, though, just to know the mathematics of how a particular quantitative technique works; you must also be familiar with the limitations, assumptions, and specific applicability of the technique. The successful use of quantitative techniques usually results in a solution that is timely, accurate, flexible, economical, reliable, and easy to understand and use.

In this and other chapters, there are QA (Quantitative Analysis) in Action boxes that provide success stories on the applications of management science. They show how organi- zations have used quantitative techniques to make better decisions, operate more efficiently, and generate more profits. Taco Bell has reported saving over $150 million with better forecast- ing of demand and better scheduling of employees. NBC television increased advertising revenue by over $200 million between 1996 and 2000 by using a model to help develop sales plans for advertisers. Continental Airlines saves over $40 million per year by using mathe- matical models to quickly recover from disruptions caused by weather delays and other factors. These are but a few of the many companies discussed in QA in Action boxes throughout this book.

To see other examples of how companies use quantitative analysis or operations research methods to operate better and more efficiently, go to the website www.scienceofbetter.org. The success stories presented there are categorized by industry, functional area, and benefit. These success stories illustrate how operations research is truly the “science of better.”

1.2 What Is Quantitative Analysis?

Quantitative analysis is the scientific approach to managerial decision making. Whim, emo- tions, and guesswork are not part of the quantitative analysis approach. The approach starts with data. Like raw material for a factory, these data are manipulated or processed into information that is valuable to people making decisions. This processing and manipulating of raw data into meaningful information is the heart of quantitative analysis. Computers have been instrumental in the increasing use of quantitative analysis.

In solving a problem, managers must consider both qualitative and quantitative factors. For example, we might consider several different investment alternatives, including certificates of deposit at a bank, investments in the stock market, and an investment in real estate. We can use quantitative analysis to determine how much our investment will be worth in the future when deposited at a bank at a given interest rate for a certain number of years. Quantitative analysis can also be used in computing financial ratios from the balance sheets for several companies whose stock we are considering. Some real estate companies have developed computer pro- grams that use quantitative analysis to analyze cash flows and rates of return for investment property.

In addition to quantitative analysis, qualitative factors should also be considered. The weather, state and federal legislation, new technological breakthroughs, the outcome of an elec- tion, and so on may all be factors that are difficult to quantify.

Because of the importance of qualitative factors, the role of quantitative analysis in the decision-making process can vary. When there is a lack of qualitative factors and when the problem, model, and input data remain the same, the results of quantitative analysis can automate the decision-making process. For example, some companies use quantitative inventory models to determine automatically when to order additional new materials. In most cases, however, quantitative analysis will be an aid to the decision-making process. The results of quantitative analysis will be combined with other (qualitative) information in making decisions.

Quantitative analysis uses a scientific approach to decision making.

Both qualitative and quantitative factors must be considered.

Defining the Problem

Developing a Model

Acquiring Input Data

Developing a Solution

Testing the Solution

Analyzing the Results

Implementing the Results

FIGURE 1.1 The Quantitative Analysis Approach

1.3 THE QUANTITATIVE ANALYSIS APPROACH 3

Quantitative analysis has been in existence since the beginning of recorded history, but it was Frederick W. Taylor who in the early 1900s pioneered the principles of the scientific approach to man- agement. During World War II, many new scientific and quantita- tive techniques were developed to assist the military. These new developments were so successful that after World War II many companies started using similar techniques in managerial decision making and planning. Today, many organizations employ a staff

of operations research or management science personnel or consultants to apply the principles of scientific management to problems and opportunities. In this book, we use the terms management science, operations research, and quantitative analysis interchangeably.

The origin of many of the techniques discussed in this book can be traced to individuals and organizations that have applied the principles of scientific management first developed by Taylor; they are discussed in History boxes scattered throughout the book.

HISTORY The Origin of Quantitative Analysis

1.3 The Quantitative Analysis Approach

The quantitative analysis approach consists of defining a problem, developing a model, acquir- ing input data, developing a solution, testing the solution, analyzing the results, and implement- ing the results (see Figure 1.1). One step does not have to be finished completely before the next is started; in most cases one or more of these steps will be modified to some extent before the fi- nal results are implemented. This would cause all of the subsequent steps to be changed. In some cases, testing the solution might reveal that the model or the input data are not correct. This would mean that all steps that follow defining the problem would need to be modified.

Defining the Problem The first step in the quantitative approach is to develop a clear, concise statement of the problem. This statement will give direction and meaning to the following steps.

In many cases, defining the problem is the most important and the most difficult step. It is essential to go beyond the symptoms of the problem and identify the true causes. One problem may be related to other problems; solving one problem without regard to other related problems can make the entire situation worse. Thus, it is important to analyze how the solution to one problem affects other problems or the situation in general.

It is likely that an organization will have several problems. However, a quantitative analysis group usually cannot deal with all of an organization’s problems at one time. Thus, it is usually necessary to concentrate on only a few problems. For most companies, this means selecting those problems whose solutions will result in the greatest increase in profits or reduction in costs to the company. The importance of selecting the right problems to solve cannot be overempha- sized. Experience has shown that bad problem definition is a major reason for failure of man- agement science or operations research groups to serve their organizations well.

When the problem is difficult to quantify, it may be necessary to develop specific, measurable objectives. A problem might be inadequate health care delivery in a hospital. The objectives might be to increase the number of beds, reduce the average number of days a patient spends in the hospital, increase the physician-to-patient ratio, and so on. When objectives are used, however, the real problem should be kept in mind. It is important to avoid obtaining spe- cific and measurable objectives that may not solve the real problem.

Developing a Model Once we select the problem to be analyzed, the next step is to develop a model. Simply stated, a model is a representation (usually mathematical) of a situation.

Even though you might not have been aware of it, you have been using models most of your life. You may have developed models about people’s behavior. Your model might be that friend- ship is based on reciprocity, an exchange of favors. If you need a favor such as a small loan, your model would suggest that you ask a good friend.

Of course, there are many other types of models. Architects sometimes make a physical model of a building that they will construct. Engineers develop scale models of chemical plants,

Defining the problem can be the most important step.

Concentrate on only a few problems.

The types of models include physical, scale, schematic, and mathematical models.

4 CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS

Operations Research and Oil Spills

Operations researchers and decision scientists have been investi- gating oil spill response and alleviation strategies since long before the BP oil spill disaster of 2010 in the Gulf of Mexico. A four-phase classification system has emerged for disaster response research: mit- igation, preparedness, response, and recovery. Mitigation means re- ducing the probability that a disaster will occur and implementing robust, forward-thinking strategies to reduce the effects of a disaster that does occur. Preparedness is any and all organization efforts that happen a priori to a disaster. Response is the location, allocation, and overall coordination of resources and procedures during the disaster that are aimed at preserving life and property. Recovery is the set of actions taken to minimize the long-term impacts of a particular dis- aster after the immediate situation has stabilized.

Many quantitative tools have helped in areas of risk analysis, insurance, logistical preparation and supply management, evacu- ation planning, and development of communication systems. Re- cent research has shown that while many strides and discoveries have been made, much research is still needed. Certainly each of the four disaster response areas could benefit from additional re- search, but recovery seems to be of particular concern and per- haps the most promising for future research.

Source: Based on N. Altay and W. Green. “OR/MS Research in Disaster Oper- ations Management,” European Journal of Operational Research 175, 1 (2006): 475–493.

called pilot plants. A schematic model is a picture, drawing, or chart of reality. Automobiles, lawn mowers, gears, fans, typewriters, and numerous other devices have schematic models (drawings and pictures) that reveal how these devices work. What sets quantitative analysis apart from other techniques is that the models that are used are mathematical. A mathematical model is a set of mathematical relationships. In most cases, these relationships are expressed in equa- tions and inequalities, as they are in a spreadsheet model that computes sums, averages, or stan- dard deviations.

Although there is considerable flexibility in the development of models, most of the models presented in this book contain one or more variables and parameters. A variable, as the name implies, is a measurable quantity that may vary or is subject to change. Variables can be controllable or uncontrollable. A controllable variable is also called a decision variable. An example would be how many inventory items to order. A parameter is a measurable quantity that is inherent in the problem. The cost of placing an order for more inventory items is an example of a parameter. In most cases, variables are unknown quantities, while parameters are known quantities. All models should be developed carefully. They should be solvable, real- istic, and easy to understand and modify, and the required input data should be obtainable. The model developer has to be careful to include the appropriate amount of detail to be solvable yet realistic.

Acquiring Input Data Once we have developed a model, we must obtain the data that are used in the model (input data). Obtaining accurate data for the model is essential; even if the model is a perfect represen- tation of reality, improper data will result in misleading results. This situation is called garbage in, garbage out. For a larger problem, collecting accurate data can be one of the most difficult steps in performing quantitative analysis.

There are a number of sources that can be used in collecting data. In some cases, company reports and documents can be used to obtain the necessary data. Another source is interviews with employees or other persons related to the firm. These individuals can sometimes provide excellent information, and their experience and judgment can be invaluable. A production su- pervisor, for example, might be able to tell you with a great degree of accuracy the amount of time it takes to produce a particular product. Sampling and direct measurement provide other sources of data for the model. You may need to know how many pounds of raw material are used in producing a new photochemical product. This information can be obtained by going to the plant and actually measuring with scales the amount of raw material that is being used. In other cases, statistical sampling procedures can be used to obtain data.

Garbage in, garbage out means that improper data will result in misleading results.

IN ACTION

1.3 THE QUANTITATIVE ANALYSIS APPROACH 5

Developing a Solution Developing a solution involves manipulating the model to arrive at the best (optimal) solution to the problem. In some cases, this requires that an equation be solved for the best decision. In other cases, you can use a trial and error method, trying various approaches and picking the one that results in the best decision. For some problems, you may wish to try all possible values for the variables in the model to arrive at the best decision. This is called complete enumeration. This book also shows you how to solve very difficult and complex problems by repeating a few simple steps until you find the best solution. A series of steps or procedures that are repeated is called an algorithm, named after Algorismus, an Arabic mathematician of the ninth century.

The accuracy of a solution depends on the accuracy of the input data and the model. If the in- put data are accurate to only two significant digits, then the results can be accurate to only two sig- nificant digits. For example, the results of dividing 2.6 by 1.4 should be 1.9, not 1.857142857.

Testing the Solution Before a solution can be analyzed and implemented, it needs to be tested completely. Because the solution depends on the input data and the model, both require testing.

Testing the input data and the model includes determining the accuracy and completeness of the data used by the model. Inaccurate data will lead to an inaccurate solution. There are sev- eral ways to test input data. One method of testing the data is to collect additional data from a different source. If the original data were collected using interviews, perhaps some additional data can be collected by direct measurement or sampling. These additional data can then be compared with the original data, and statistical tests can be employed to determine whether there are differences between the original data and the additional data. If there are significant differ- ences, more effort is required to obtain accurate input data. If the data are accurate but the results are inconsistent with the problem, the model may not be appropriate. The model can be checked to make sure that it is logical and represents the real situation.

Although most of the quantitative techniques discussed in this book have been computer- ized, you will probably be required to solve a number of problems by hand. To help detect both logical and computational mistakes, you should check the results to make sure that they are con- sistent with the structure of the problem. For example, (1.96)(301.7) is close to (2)(300), which is equal to 600. If your computations are significantly different from 600, you know you have made a mistake.

Analyzing the Results and Sensitivity Analysis Analyzing the results starts with determining the implications of the solution. In most cases, a solution to a problem will result in some kind of action or change in the way an organization is operating. The implications of these actions or changes must be determined and analyzed before the results are implemented.

Because a model is only an approximation of reality, the sensitivity of the solution to changes in the model and input data is a very important part of analyzing the results. This type of analysis is called sensitivity analysis or postoptimality analysis. It determines how much the solution will change if there were changes in the model or the input data. When the solution is sensitive to changes in the input data and the model specification, additional testing should be performed to make sure that the model and input data are accurate and valid. If the model or data are wrong, the solution could be wrong, resulting in financial losses or reduced profits.

The importance of sensitivity analysis cannot be overemphasized. Because input data may not always be accurate or model assumptions may not be completely appropriate, sensitivity analysis can become an important part of the quantitative analysis approach. Most of the chap- ters in the book cover the use of sensitivity analysis as part of the decision-making and problem- solving process.

Implementing the Results The final step is to implement the results. This is the process of incorporating the solution into the company. This can be much more difficult than you would imagine. Even if the solution is optimal and will result in millions of dollars in additional profits, if managers resist the new solution, all of the efforts of the analysis are of no value. Experience has shown that a large

The input data and model determine the accuracy of the solution.

Testing the data and model is done before the results are analyzed.

Sensitivity analysis determines how the solutions will change with a different model or input data.

6 CHAPTER 1 • INTRODUCTION TO QUANTITATIVE ANALYSIS

Defining the Problem CSX Transportation, Inc., has 35,000 employees and annual revenue of $11 billion. It provides rail freight services to 23 states east of the Mississippi River, as well as parts of Canada. CSX receives orders for rail deliv- ery service and must send empty railcars to customer locations. Moving these empty railcars results in hun- dreds of thousands of empty-car miles every day. If allocations of railcars to customers is not done properly, problems arise from excess costs, wear and tear on the system, and congestion on the tracks and at rail yards.

Developing a Model In order to provide a more efficient scheduling system, CSX spent 2 years and $5 million developing its Dynamic Car-Planning (DCP) system. This model will minimize costs, including car travel distance, car han- dling costs at the rail yards, car travel time, and costs for being early or late. It does this while at the same time filling all orders, making sure the right type of car is assigned to the job, and getting the car to the destination in the allowable time.

Acquiring Input Data In developing the model, the company used historical data for testing. In running the model, the DCP uses three external sources to obtain information on the customer car orders, the available cars of the type needed, and the transit-time standards. In addition to these, two internal input sources provide informa- tion on customer priorities and preferences and on cost parameters.

Developing a Solution This model takes about 1 minute to load but only 10 seconds to solve. Because supply and demand are con- stantly changing, the model is run about every 15 minutes. This allows final decisions to be delayed until ab- solutely necessary.

Testing the Solution The model was validated and verified using existing data. The solutions found using the DCP were found to be very good compared to assignments made without DCP.

Analyzing the Results Since the implementation of DCP in 1997, more than $51 million has been saved annually. Due to the im- proved efficiency, it is estimated that CSX avoided spending another $1.4 billion to purchase an additional 18,000 railcars that would have been needed without DCP. Other benefits include reduced congestion in the rail yards and reduced congestion on the tracks, which are major concerns. This greater efficiency means that more freight can ship by rail rather than by truck, resulting in significant public benefits. These benefits include reduced pollution and greenhouse gases, improved highway safety, and reduced road maintenance costs.

Implementing the Results Both senior-level management who championed DCP as well as key car-distribution experts who sup- ported the new approach were instrumental in gaining acceptance of the new system and overcoming problems during the implementation. The job description of the car distributors was changed from car al- locators to cost technicians. They are responsible for seeing that accurate cost information is entered into DCP, and they also manage any exceptions that must be made. They were given extensive training on how DCP works so they could understand and better accept the new system. Due to the success of DCP, other railroads have implemented similar systems and achieved similar benefits. CSX continues to enhance DCP to make DCP even more customer friendly and to improve car-order forecasts.

Source: Based on M. F. Gorman, et al. “CSX Railway Uses OR to Cash in on Optimized Equipment Distribution,” Interfaces 40, 1 (January–February 2010): 5–16.

MODELING IN THE REAL WORLD Railroad Uses Optimization Models to Save Millions

Defining the Problem

Developing a Model

Acquiring Input Data

Developing a Solution

Testing the Solution

Analyzing the Results

Implementing the Results

number of quantitative analysis teams have failed in their efforts because they have failed to im- plement a good, workable solution properly.

After the solution has been implemented, it should be closely monitored. Over time, there may be numerous changes that call for modifications of the original solution. A changing economy, fluctuating demand, and model enhancements requested by managers and decision makers are only a few examples of changes that might require the analysis to be modified.

1.4 HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL 7

The Quantitative Analysis Approach and Modeling in the Real World The quantitative analysis approach is used extensively in the real world. These steps, first seen in Figure 1.1 and described in this section, are the building blocks of any successful use of quan- titative analysis. As seen in our first Modeling in the Real World box, the steps of the quantita- tive analysis approach can be used to help a large company such as CSX plan for critical scheduling needs now and for decades into the future. Throughout this book, you will see how the steps of the quantitative analysis approach are used to help countries and companies of all sizes save millions of dollars, plan for the future, increase revenues, and provide higher-quality products and services. The Modeling in the Real World boxes in every chapter will demonstrate to you the power and importance of quantitative analysis in solving real problems for real or- ganizations. Using the steps of quantitative analysis, however, does not guarantee success. These steps must be applied carefully.