Contents

Cover

Half Title page

Title page

Copyright page

Preface

Part I: Motivations and Foundations

Chapter 1: Quantitative Methods: Should We Bother?

1.1 A Decision Problem Without Uncertainty: Product Mix

1.2 The Role of Uncertainty

1.3 Endogenous vs. Exogenous Uncertainty: Are We Alone?

1.4 Quantitative Models and Methods

1.5 Quantitative Analysis and Problem Solving

References

Chapter 2: Calculus

2.1 A Motivating Example: Economic Order Quantity

2.2 A Little Background

2.3 Functions

2.4 Continuous Functions

2.5 Composite Functions

2.6 Inverse Functions

2.7 Derivatives

2.8 Rules for Calculating Derivatives

2.9 Using Derivatives for Graphing Functions

2.10 Higher-Order Derivatives and Taylor Expansions

2.11 Convexity and Optimization

2.12 Sequences and Series

2.13 Definite Integrals

References

Chapter 3: Linear Algebra

3.1 A Motivating Example: Binomial Option Pricing

3.2 Solving Systems of Linear Equations

3.3 Vector Algebra

3.4 Matrix Algebra

3.5 Linear Spaces

3.6 Determinant

3.7 Eigenvalues and Eigenvectors

3.8 Quadratic Forms

3.9 Calculus in Multiple Dimensions

References

Part II: Elementary Probability and Statistics

Chapter 4: Descriptive Statistics: On the Way to Elementary Probability

4.1 What Is Statistics?

4.2 Organizing and Representing Raw Data

4.3 Summary Measures

4.4 Cumulative Frequencies and Percentiles

4.5 Multidimensional Data

References

Chapter 5: Probability Theories

5.1 Different Concepts of Probability

5.2 The Axiomatic Approach

5.3 Conditional Probability and Independence

5.4 Total Probability and Bayes’ Theorems

References

Chapter 6: Discrete Random Variables

6.1 Random Variables

6.2 Characterizing Discrete Distributions

6.3 Expected Value

6.4 Variance and Standard Deviation

6.5 A Few Useful Discrete Distributions

References

Chapter 7: Continuous Random Variables

7.1 Building Intuition: From Discrete to Continuous Random Variables

7.2 Cumulative Distribution and Probability Density Functions

7.3 Expected Value and Variance

7.4 Mode, Median, and Quantiles

7.5 Higher-Order Moments, Skewness, and Kurtosis

7.6 A Few Useful Continuous Probability Distributions

7.7 Sums of Independent Random Variables

7.8 Miscellaneous Applications

7.9 Stochastic Processes

7.10 Probability Spaces, Measurability, and Information

References

Chapter 8: Dependence, Correlation, and Conditional Expectation

8.1 Joint and Marginal Distributions

8.2 Independent Random Variables

8.3 Covariance and Correlation

8.4 Jointly Normal Variables

8.5 Conditional Expectation

References

Chapter 9: Inferential Statistics

9.1 Random Samples and Sample Statistics

9.2 Confidence Intervals

9.3 Hypothesis Testing

9.4 Beyond The Mean of One Population

9.5 Checking The Fit of Hypothetical Distributions: The Chi-Square Test

9.6 Analysis of Variance

9.7 Monte Carlo Simulation

9.8 Stochastic Convergence and The Law of Large Numbers

9.9 Parameter Estimation

9.10 Some More Hypothesis Testing Theory

References

Chapter 10: Simple Linear Regression

10.1 Least-Squares Method

10.2 The Need for A Statistical Framework

10.3 The Case of A Nonstochastic Regressor

10.4 Using Regression Models

10.5 A Glimpse of Stochastic Regressors and Heteroskedastic Errors

10.6 A Vector Space Look at Linear Regression

References

Chapter 11: Inferential Statistics

11.1 Before We Start: Framing The Forecasting Process

11.2 Measuring Forecast Errors

11.3 Time Series Decomposition

11.4 Moving Average

11.5 Heuristic Exponential Smoothing

11.6 A Glance At Advanced Time Series Modeling

References

Part III: Models for Decision Making

Chapter 12: Deterministic Decision Models

12.1 A Taxonomy of Optimization Models

12.2 Building Linear Programming Models

12.3 A Repertoire of Model Formulation Tricks

12.4 Building Integer Programming Models

12.5 Nonlinear Programming Concepts

12.6 A Glance At Solution Methods

References

Chapter 13: Decision Making Under Risk

13.1 Decision Trees

13.2 Risk Aversion and Risk Measures

13.3 Two-Stage Stochastic Programming Models

13.4 Multistage Stochastic Linear Programming With Recourse

13.5 Robustness, Regret, and Disappointment

References

Chapter 14: Multiple Decision Makers, Subjective Probability, and Other Wild Beasts

14.1 What Is Uncertainty?

14.2 Decision Problems with Multiple Decision Makers

14.3 Incentive Misalignment in Supply Chain Management

14.4 Game Theory

14.5 Braess’ Paradox for Traffic Networks

14.6 Dynamic Feedback Effects and Herding Behavior

14.7 Subjective Probability: The Bayesian View

References

Part IV: Advanced Statistical Modeling

Chapter 15: Introduction to Multivariate Analysis

15.1 Issues in Multivariate Analysis

15.2 An Overview of Multivariate Methods

15.3 Matrix Algebra and Multivariate Analysis

References

Chapter 16: Advanced Regression Models

16.1 Multiple Linear Regression by Least Squares

16.2 Building, Testing, and Using Multiple Linear Regression Models

16.3 Logistic Regression

16.4 A Glance At Nonlinear Regression

References

Chapter 17: Dealing with Complexity: Data Reduction and Clustering

17.1 The Need for Data Reduction

17.2 Principal Component Analysis (PCA)

17.3 Factor Analysis

17.4 Cluster Analysis

References

Index