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David R. Anderson
University of Cincinnati
Dennis J. Sweeney
University of Cincinnati
Thomas A. Williams
Rochester Institute of Technology
Jeffrey D. Camm
University of Cincinnati
James J. Cochran
Louisianna Tech University
Michael J. Fry
University of Cincinnati
Jeffrey W. Ohlmann
University of Iowa
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Quantitative Methods for Business, © 2013, 2010South-Western, Cengage Learning
Twelfth Edition
ALL RIGHTS RESERVED. No part of this work covered by the copyright
David R. Anderson, Dennis J. Sweeney,
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Thomas A. Williams, Jeffrey D. Camm,
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James J. Cochran, Michael J. Fry,
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Jeffrey W. Ohlmann
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To My Children
Krista, Justin, Mark, and Colleen
DRA
To My Children
Mark, Linda, Brad, Tim, Scott, and Lisa
DJS
To My Children
Cathy, David, and Kristin
TAW
To My Family
Karen, Jennifer, Stephanie, and Allison
JDC
To My Wife
Teresa
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To My Family
Nicole and Ian
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To My Family
Amie and Willa
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Brief Contents
Preface xvii
About the Authors xxiv
Chapter 1 Introduction 1
Chapter 2 Introduction to Probability 27
Chapter 3 Probability Distributions 62
Chapter 4 Decision Analysis 101
Chapter 5 Utility and Game Theory 157
Chapter 6 Time Series Analysis and Forecasting 188
Chapter 7 Introduction to Linear Programming 245
Chapter 8 Linear Programming: Sensitivity Analysis and
Interpretation of Solution 304
Chapter 9 Linear Programming Applications in Marketing,Finance,
and Operations Management 358
Chapter 10 Distribution and Network Models 419
Chapter 11 Integer Linear Programming 481
Chapter 12 Advanced Optimization Applications 530
Chapter 13 Project Scheduling: PERT/CPM 585
Chapter 14 Inventory Models 623
Chapter 15 Waiting Line Models 672
Chapter 16 Simulation 712
Chapter 17 Markov Processes 772
Appendix A Building Spreadsheet Models 798
Appendix B Binomial Probabilities 827
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vi Brief Contents
Appendix C Poisson Probabilities 834
Appendix D Areas for the Standard Normal Distribution 840
Appendix E Values of e(cid:2)λ 842
Appendix F References and Bibliography 843
Appendix G Self-Test Solutions and Answers to Even-Numbered
Problems 845
Index 902
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Contents
Preface xvii
About the Authors xxiv
Chapter 1 Introduction 1
1.1 Problem Solving and Decision Making 3
1.2 Quantitative Analysis and Decision Making 5
1.3 Quantitative Analysis 7
Model Development 7
Data Preparation 10
Model Solution 11
Report Generation 13
A Note Regarding Implementation 13
1.4 Models of Cost, Revenue, and Profit 14
Cost and Volume Models 14
Revenue and Volume Models 15
Profit and Volume Models 15
Breakeven Analysis 16
1.5 Quantitative Methods in Practice 17
Methods Used Most Frequently 17
Summary 19
Glossary 19
Problems 20
Case Problem Scheduling a Golf League 23
Appendix 1.1 Using Excel for Breakeven Analysis 23
Chapter 2 Introduction to Probability 27
2.1 Experiments and the Sample Space 29
2.2 Assigning Probabilities to Experimental Outcomes 31
Classical Method 31
Relative Frequency Method 32
Subjective Method 32
2.3 Events and Their Probabilities 33
2.4 Some Basic Relationships of Probability 34
Complement of an Event 34
Addition Law 35
Conditional Probability 38
Multiplication Law 42
2.5 Bayes’ Theorem 43
The Tabular Approach 46
2.6 Simpson’s Paradox 47
Summary 50
Glossary 50
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viii Contents
Problems 51
Case Problem Hamilton County Judges 59
Case Problem College Softball Recruiting 61
Chapter 3 Probability Distributions 62
3.1 Random Variables 64
3.2 Discrete Random Variables 65
Probability Distribution of a Discrete Random Variable 65
Expected Value 67
Variance 68
3.3 Binomial Probability Distribution 69
Nastke Clothing Store Problem 70
Expected Value and Variance for the Binomial Distribution 73
3.4 Poisson Probability Distribution 73
An Example Involving Time Intervals 74
An Example Involving Length or Distance Intervals 74
3.5 Continuous Random Variables 76
Applying the Uniform Distribution 76
Area as a Measure of Probability 77
3.6 Normal Probability Distribution 79
Standard Normal Distribution 80
Computing Probabilities for Any Normal Distribution 84
Grear Tire Company Problem 85
3.7 Exponential Probability Distribution 87
Computing Probabilities for the Exponential Distribution 87
Relationship Between the Poisson and Exponential Distributions 89
Summary 89
Glossary 90
Problems 91
Case Problem Specialty Toys 97
Appendix 3.1 Computing Discrete Probabilities with Excel 98
Appendix 3.2 Computing Probabilities for Continuous Distributions
with Excel 99
Chapter 4 Decision Analysis 101
4.1 Problem Formulation 103
Influence Diagrams 104
Payoff Tables 104
Decision Trees 105
4.2 Decision Making Without Probabilities 106
Optimistic Approach 106
Conservative Approach 107
Minimax Regret Approach 107
4.3 Decision Making With Probabilities 109
Expected Value of Perfect Information 112
4.4 Risk Analysis and Sensitivity Analysis 113
Risk Analysis 113
Sensitivity Analysis 114
