Isbn 978 0 13 214911 2

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

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iii

ABOUT THE AUTHORS

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

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

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

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

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

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

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

iv ABOUT THE AUTHORS

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

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

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

CHAPTER 1 Introduction to Quantitative Analysis 1

CHAPTER 2 Probability Concepts and Applications 21

CHAPTER 3 Decision Analysis 69

CHAPTER 4 Regression Models 115

CHAPTER 5 Forecasting 153

CHAPTER 6 Inventory Control Models 195

CHAPTER 7 Linear Programming Models: Graphical and Computer Methods 249

CHAPTER 8 Linear Programming Applications 307

CHAPTER 9 Transportation and Assignment Models 341

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

CHAPTER 11 Network Models 429

CHAPTER 12 Project Management 459

CHAPTER 13 Waiting Lines and Queuing Theory Models 499

CHAPTER 14 Simulation Modeling 533

CHAPTER 15 Markov Analysis 573

CHAPTER 16 Statistical Quality Control 601

ONLINE MODULES

1 Analytic Hierarchy Process M1-1

2 Dynamic Programming M2-1

3 Decision Theory and the Normal Distribution M3-1

4 Game Theory M4-1

5 Mathematical Tools: Determinants and Matrices M5-1

6 Calculus-Based Optimization M6-1

7 Linear Programming: The Simplex Method M7-1

v

BRIEF CONTENTS

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PREFACE xv

CHAPTER 1 Introduction to Quantitative Analysis 1

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

Defining the Problem 3

Developing a Model 3

Acquiring Input Data 4

Developing a Solution 5

Testing the Solution 5

Analyzing the Results and Sensitivity Analysis 5

Implementing the Results 5

The Quantitative Analysis Approach and Modeling in the Real World 7

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

Mathematical Models Categorized by Risk 8

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

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

Developing a Model 13

Acquiring Input Data 13

Developing a Solution 14

Testing the Solution 14

Analyzing the Results 14

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

Lack of Commitment by Quantitative Analysts 15

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

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

Types of Probability 23

2.3 Mutually Exclusive and Collectively Exhaustive Events 24

Adding Mutually Exclusive Events 26

Law of Addition for Events That Are Not Mutually Exclusive 26

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

General Form of Bayes’ Theorem 31

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

Probability Distribution of a Discrete Random Variable 34

Expected Value of a Discrete Probability Distribution 35

Variance of a Discrete Probability Distribution 36

Probability Distribution of a Continuous Random Variable 36

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

Solving Problems with Binomial Tables 40

2.11 The Normal Distribution 41 Area Under the Normal Curve 42

Using the Standard Normal Table 42

Haynes Construction Company Example 44

The Empirical Rule 48

2.12 The F Distribution 48 2.13 The Exponential Distribution 50

Arnold’s Muffler Example 51

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

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

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