Table Of ContentT H I R T E E N T H E D I T I O N
QUANTITATIVE ANALYSIS
for MANAGEMENT
BARRY RENDER • RALPH M. STAIR, JR. • MICHAEL E. HANNA • TREVOR S. HALE
T H I R T E E N T H E D I T I O N
QUANTITATIVE ANALYSIS
for MANAGEMENT
BARRY RENDER
Charles Harwood Professor Emeritus of Management Science
Crummer Graduate School of Business, Rollins College
RALPH M. STAIR, JR.
Professor Emeritus 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
New York, NY
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To my wife and sons—BR
To Lila and Leslie—RMS
To Zoe and Gigi—MEH
To Valerie and Lauren—TSH
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Library of Congress Cataloging-in-Publication Data
Names: Render, Barry, author. | Stair, Ralph M., author. | Hanna, Michael E.,
author. | Hale, Trevor S., author.
Title: Quantitative analysis for management / 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.
Description: Thirteenth edition. | Boston : Pearson, 2016. | Includes
bibliographical references and index.
Identifiers: LCCN 2016037461| ISBN 9780134543161 (hardcover) | ISBN
0134543165 (hardcover)
Subjects: LCSH: Management science—Case studies. | Operations research—Case
studies.
Classification: LCC T56 .R543 2016 | DDC 658.4/03—dc23
LC record available at https://lccn.loc.gov/ 2016037461
10 9 8 7 6 5 4 3 2 1
ISBN 10: 0-13-454316-5
ISBN 13: 978-0-13-454316-1
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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 by Dr. Render on a variety of man-
agement 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
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
iii
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iv ABOUT THE AUTHORS
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.
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 sta-
tistics, management science, forecasting, and other quantitative methods. His dedication to teach-
ing 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
published 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 (DSI), having served on the
Innovative Education Committee, the Regional Advisory Committee, and the Nominating
Committee. He has served on the board of directors of 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 quantita-
tive 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 at the University
of Houston–Downtown. He is a senior member of both the Decision Sciences Institute and
INFORMS.
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Brief Contents
CHAPTER 1 Introduction to Quantitative Analysis 1
CHAPTER 2 Probability Concepts and Applications 21
CHAPTER 3 Decision Analysis 63
CHAPTER 4 Regression Models 111
CHAPTER 5 Forecasting 147
CHAPTER 6 Inventory Control Models 185
CHAPTER 7 Linear Programming Models: Graphical and Computer Methods 237
CHAPTER 8 Linear Programming Applications 289
CHAPTER 9 Transportation, Assignment, and Network Models 319
CHAPTER 10 Integer Programming, Goal Programming, and Nonlinear
Programming 357
CHAPTER 11 Project Management 387
CHAPTER 12 Waiting Lines and Queuing Theory Models 427
CHAPTER 13 Simulation Modeling 461
CHAPTER 14 Markov Analysis 501
CHAPTER 15 Statistical Quality Control 529
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
v
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Contents
PREFACE xiii CHAPTER 2 Probability Concepts and
Applications 21
CHAPTER 1 Introduction to Quantitative Analysis 1
2.1 Fundamental Concepts 22
1.1 What Is Quantitative Analysis? 2
Two Basic Rules of Probability 22
1.2 Business Analytics 2
Types of Probability 22
1.3 The Quantitative Analysis Approach 3
Mutually Exclusive and Collectively Exhaustive
Defining the Problem 4 Events 23
Developing a Model 4 Unions and Intersections of Events 25
Acquiring Input Data 4 Probability Rules for Unions, Intersections,
Developing a Solution 5 and Conditional Probabilities 25
Testing the Solution 5 2.2 Revising Probabilities with Bayes’
Theorem 27
Analyzing the Results and Sensitivity
Analysis 6 General Form of Bayes’ Theorem 28
Implementing the Results 6 2.3 Further Probability Revisions 29
The Quantitative Analysis Approach and Modeling 2.4 Random Variables 30
in the Real World 6 2.5 Probability Distributions 32
1.4 How to Develop a Quantitative Analysis
Probability Distribution of a Discrete Random
Model 6
Variable 32
The Advantages of Mathematical Modeling 9 Expected Value of a Discrete Probability
Mathematical Models Categorized Distribution 32
by Risk 9 Variance of a Discrete Probability
1.5 The Role of Computers and Spreadsheet Distribution 33
Models in the Quantitative Analysis
Probability Distribution of a Continuous
Approach 9
Random Variable 34
1.6 Possible Problems in the Quantitative 2.6 The Binomial Distribution 35
Analysis Approach 12
Solving Problems with the Binomial
Defining the Problem 12 Formula 36
Developing a Model 13 Solving Problems with Binomial
Acquiring Input Data 14 Tables 37
Developing a Solution 14 2.7 The Normal Distribution 38
Testing the Solution 14 Area Under the Normal Curve 40
Analyzing the Results 15 Using the Standard Normal Table 40
1.7 Implementation—Not Just the Final Haynes Construction Company Example 41
Step 15
The Empirical Rule 44
Lack of Commitment and Resistance to 2.8 The F Distribution 44
Change 16
2.9 The Exponential Distribution 46
Lack of Commitment by Quantitative
Arnold’s Muffler Example 47
Analysts 16
2.10 The Poisson Distribution 48
Summary 16 Glossary 16 Key Equations 17
Summary 50 Glossary 50 Key Equations 51
Self-Test 17 Discussion Questions and
Solved Problems 52 Self-Test 54 Discussion
Problems 18 Case Study: Food and
Questions and Problems 55 Case Study:
Beverages at Southwestern University Football
WTVX 61 Bibliography 61
Games 19 Bibliography 20
Appendix 2.1: Derivation of Bayes’ Theorem 61
vi
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CONTENTS vii
4.7 Multiple Regression Analysis 126
CHAPTER 3 Decision Analysis 63
Evaluating the Multiple Regression
3.1 The Six Steps in Decision Making 63
Model 127
3.2 Types of Decision-Making
Jenny Wilson Realty Example 128
Environments 65
4.8 Binary or Dummy Variables 129
3.3 Decision Making Under Uncertainty 65
4.9 Model Building 130
Optimistic 66
Stepwise Regression 131
Pessimistic 66
Multicollinearity 131
Criterion of Realism (Hurwicz Criterion) 67
4.10 Nonlinear Regression 131
Equally Likely (Laplace) 67
4.11 Cautions and Pitfalls in Regression
Minimax Regret 67
Analysis 134
3.4 Decision Making Under Risk 69
Summary 135 Glossary 135 Key
Expected Monetary Value 69 Equations 136 Solved Problems 137
Expected Value of Perfect Information 70 Self-Test 139 Discussion Questions and
Problems 139 Case Study: North–South
Expected Opportunity Loss 71
Airline 144 Bibliography 145
Sensitivity Analysis 72
Appendix 4.1: Formulas for Regression Calculations 145
A Minimization Example 73
3.5 Using Software for Payoff Table
Problems 75 CHAPTER 5 Forecasting 147
QM for Windows 75 5.1 Types of Forecasting Models 147
Excel QM 75 Qualitative Models 147
3.6 Decision Trees 77 Causal Models 148
Efficiency of Sample Information 82 Time-Series Models 149
Sensitivity Analysis 82 5.2 Components of a Time-Series 149
3.7 How Probability Values Are Estimated by 5.3 Measures of Forecast Accuracy 151
Bayesian Analysis 83 5.4 Forecasting Models—Random Variations
Calculating Revised Probabilities 83 Only 154
Potential Problem in Using Survey Results 85 Moving Averages 154
3.8 Utility Theory 86 Weighted Moving Averages 154
Measuring Utility and Constructing a Utility Exponential Smoothing 156
Curve 86 Using Software for Forecasting Time
Utility as a Decision-Making Criterion 88 Series 158
Summary 91 Glossary 91 Key Equations 92 5.5 Forecasting Models—Trend and Random
Solved Problems 92 Self-Test 97 Discussion Variations 160
Questions and Problems 98 Case Study: Starting Exponential Smoothing with Trend 160
Right Corporation 107 Case Study: Toledo
Trend Projections 163
Leather Company 107 Case Study: Blake
5.6 Adjusting for Seasonal Variations 164
Electronics 108 Bibliography 110
Seasonal Indices 165
CHAPTER 4 Regression Models 111 Calculating Seasonal Indices with
4.1 Scatter Diagrams 112 No Trend 165
4.2 Simple Linear Regression 113 Calculating Seasonal Indices with
Trend 166
4.3 Measuring the Fit of the Regression
Model 114 5.7 Forecasting Models—Trend, Seasonal,
and Random Variations 167
Coefficient of Determination 116
The Decomposition Method 167
Correlation Coefficient 116
Software for Decomposition 170
4.4 Assumptions of the Regression Model 117
Using Regression with Trend and Seasonal
Estimating the Variance 119
Components 170
4.5 Testing the Model for Significance 119
5.8 Monitoring and Controlling
Triple A Construction Example 121 Forecasts 172
The Analysis of Variance (ANOVA) Table 122 Adaptive Smoothing 174
Triple A Construction ANOVA Example 122 Summary 174 Glossary 174 Key
4.6 Using Computer Software for Equations 175 Solved Problems 176
Regression 122 Self-Test 177 Discussion Questions
and Problems 178 Case Study:
Excel 2016 122
Forecasting Attendance at SWU Football
Excel QM 123 Games 182 Case Study: Forecasting Monthly
QM for Windows 125 Sales 183 Bibliography 184
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viii CONTENTS
7.2 Formulating LP Problems 239
CHAPTER 6 Inventory Control Models 185
Flair Furniture Company 240
6.1 Importance of Inventory Control 186
7.3 Graphical Solution to an LP
Decoupling Function 186
Problem 241
Storing Resources 187
Graphical Representation of Constraints 241
Irregular Supply and Demand 187
Isoprofit Line Solution Method 245
Quantity Discounts 187
Corner Point Solution Method 248
Avoiding Stockouts and Shortages 187
Slack and Surplus 250
6.2 Inventory Decisions 187
7.4 Solving Flair Furniture’s LP Problem
6.3 Economic Order Quantity: Determining Using QM for Windows, Excel 2016, and
How Much to Order 189 Excel QM 251
Inventory Costs in the EOQ Situation 189 Using QM for Windows 251
Finding the EOQ 191 Using Excel’s Solver Command to Solve LP
Sumco Pump Company Example 192 Problems 252
Purchase Cost of Inventory Items 193 Using Excel QM 255
Sensitivity Analysis with the EOQ Model 194 7.5 Solving Minimization Problems 257
6.4 Reorder Point: Determining When to Holiday Meal Turkey Ranch 257
Order 194 7.6 Four Special Cases in LP 261
6.5 EOQ Without the Instantaneous Receipt No Feasible Solution 261
Assumption 196
Unboundedness 261
Annual Carrying Cost for Production Run
Redundancy 262
Model 196
Alternate Optimal Solutions 263
Annual Setup Cost or Annual Ordering
7.7 Sensitivity Analysis 264
Cost 197
Determining the Optimal Production High Note Sound Company 265
Quantity 197 Changes in the Objective Function
Brown Manufacturing Example 198 Coefficient 266
6.6 Quantity Discount Models 200 QM for Windows and Changes in Objective
Function Coefficients 266
Brass Department Store Example 202
Excel Solver and Changes in Objective Function
6.7 Use of Safety Stock 203
Coefficients 267
6.8 Single-Period Inventory Models 209
Changes in the Technological Coefficients 268
Marginal Analysis with Discrete
Changes in the Resources or Right-Hand-Side
Distributions 210
Values 269
Café du Donut Example 210
QM for Windows and Changes in Right-Hand-
Marginal Analysis with the Normal Side Values 270
Distribution 212
Excel Solver and Changes in Right-Hand-Side
Newspaper Example 212 Values 270
6.9 ABC Analysis 214 Summary 272 Glossary 272 Solved
6.10 Dependent Demand: The Case for Problems 273 Self-Test 277 Discussion
Material Requirements Planning 214 Questions and Problems 278 Case Study:
Mexicana Wire Winding, Inc. 286
Material Structure Tree 215
Bibliography 288
Gross and Net Material Requirements Plans 216
Two or More End Products 218
6.11 Just-In-Time Inventory Control 219 CHAPTER 8 Linear Programming Applications 289
6.12 Enterprise Resource Planning 220 8.1 Marketing Applications 289
Summary 221 Glossary 221 Key Media Selection 289
Equations 222 Solved Problems 223
Marketing Research 291
Self-Test 225 Discussion Questions and
8.2 Manufacturing Applications 293
Problems 226 Case Study: Martin-Pullin
Bicycle Corporation 234 Bibliography 235 Production Mix 293
Appendix 6.1: Inventory Control with QM for Production Scheduling 295
Windows 235 8.3 Employee Scheduling Applications 299
Labor Planning 299
8.4 Financial Applications 300
CHAPTER 7 Linear Programming Models:
Graphical and Computer Methods 237 Portfolio Selection 300
Truck Loading Problem 303
7.1 Requirements of a Linear Programming
Problem 238 8.5 Ingredient Blending Applications 305
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CONTENTS ix
Diet Problems 305 Ranking Goals with Priority Levels 371
Ingredient Mix and Blending Problems 306 Goal Programming with Weighted Goals 371
8.6 Other Linear Programming 10.4 Nonlinear Programming 372
Applications 308
Nonlinear Objective Function and Linear
Summary 310 Self-Test 310 Constraints 373
Problems 311 Case Study: Cable & Both Nonlinear Objective Function and Nonlinear
Moore 318 Bibliography 318 Constraints 373
Linear Objective Function with Nonlinear
CHAPTER 9 Transportation, Assignment,
Constraints 374
and Network Models 319
Summary 375 Glossary 375 Solved
9.1 The Transportation Problem 320 Problems 376 Self-Test 378 Discussion
Linear Program for the Transportation Questions and Problems 379 Case Study:
Example 320 Schank Marketing Research 384 Case Study:
Oakton River Bridge 385 Bibliography 385
Solving Transportation Problems Using
Computer Software 321
A General LP Model for Transportation CHAPTER 11 Project Management 387
Problems 322
11.1 PERT/CPM 389
Facility Location Analysis 323
General Foundry Example of PERT/CPM 389
9.2 The Assignment Problem 325
Drawing the PERT/CPM Network 390
Linear Program for Assignment Example 325
Activity Times 391
9.3 The Transshipment Problem 327
How to Find the Critical Path 392
Linear Program for Transshipment
Probability of Project Completion 395
Example 327
What PERT Was Able to Provide 398
9.4 Maximal-Flow Problem 330
Using Excel QM for the General Foundry
Example 330
Example 398
9.5 Shortest-Route Problem 332
Sensitivity Analysis and Project
9.6 Minimal-Spanning Tree Problem 334 Management 399
Summary 337 Glossary 338 Solved 11.2 PERT/Cost 400
Problems 338 Self-Test 340 Discussion
Planning and Scheduling Project Costs:
Questions and Problems 341 Case Study:
Budgeting Process 400
Andrew–Carter, Inc. 352 Case Study:
Northeastern Airlines 353 Case Study: Monitoring and Controlling Project
Southwestern University Traffic Problems 354 Costs 403
Bibliography 355 11.3 Project Crashing 405
Appendix 9.1: Using QM for Windows 355 General Foundry Example 406
Project Crashing with Linear Programming 407
CHAPTER 10 Integer Programming, Goal 11.4 Other Topics in Project Management 410
Programming, and Nonlinear Subprojects 410
Programming 357 Milestones 410
10.1 Integer Programming 358 Resource Leveling 410
Harrison Electric Company Example of Integer Software 410
Programming 358 Summary 410 Glossary 410 Key
Using Software to Solve the Harrison Integer Equations 411 Solved Problems 412
Programming Problem 360 Self-Test 414 Discussion Questions and
Problems 415 Case Study: Southwestern
Mixed-Integer Programming Problem
University Stadium Construction 422
Example 360
Case Study: Family Planning Research Center of
10.2 Modeling with 0–1 (Binary) Variables 363
Nigeria 423 Bibliography 424
Capital Budgeting Example 364
Appendix 11.1: Project Management with QM for
Limiting the Number of Alternatives Windows 424
Selected 365
Dependent Selections 365
CHAPTER 12 Waiting Lines and Queuing Theory
Fixed-Charge Problem Example 366
Models 427
Financial Investment Example 367
12.1 Waiting Line Costs 428
10.3 Goal Programming 368
Three Rivers Shipping Company Example 428
Example of Goal Programming: Harrison Electric
12.2 Characteristics of a Queuing System 429
Company Revisited 369
Arrival Characteristics 429
Extension to Equally Important Multiple
Goals 370 Waiting Line Characteristics 430
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