Mathematical Modeling for Business Analytics 1st edition by William 1032476400 9781032476407

1. Introduction to Mathematical Modeling for Business Analytics

1.1 Introduction

1.2 Background

1.2.1 Overview and Process of Mathematical Modeling

1.2.2 The Modeling Process

1.2.3 Mathematical Modeling for Business Analytics as a Process

1.2.4 Steps in Model Construction

1.2.5 Illustrative Examples: Starting the Modeling Process

1.3 Technology

1.4 Conclusion

References and Suggested Readings

2. Introduction to Stochastic Decision-Making Models for Business Analytics

2.1 Introduction

2.2 Probability and Expected Value

2.2.1 Expected Value

2.3 Decision Theory and Simple Decision Trees

2.4 Sequential Decisions and Conditional Probability

2.5 Decision Criteria under Risk and under Uncertainty

2.6 EXCEL Add-Ins

References and Suggested Further Readings

3. Mathematical Programming Models: Linear, Integer, and Nonlinear Optimization

3.1 Introduction

3.2 Formulating Mathematical Programming Problems

3.3 Graphical Linear Programming

3.4 Mathematical Programming with Technology

3.4.1 Linear Programming

3.4.1.1 Using LINDO

3.4.1.2 Using LINGO

3.4.1.3 MAPLE

3.4.1.4 Integer and Nonlinear Programming

3.5 Case Studies in Mathematical Programming

3.6 Examples for Integer, Mixed-Integer, and Nonlinear Optimization

3.7 Simplex Method in Excel

3.7.1 Steps of the Simplex Method

References and Suggested Further Reading

4. Introduction to Multi-Attribute Decision-Making in Business Analytics

4.1 Introduction

4.2 Data Envelopment Analysis

4.2.1 Description and Uses

4.2.2 Methodology

4.2.3 Strengths and Limitations to Data Envelopment Analysis

4.2.4 Sensitivity Analysis

4.2.5 Illustrative Examples

4.3 Weighting Methods

4.3.1 Modified Delphi Method

4.3.2 Rank Order Centroid Method

4.3.3 Ratio Method

4.3.4 Pairwise Comparison (Analytical Hierarchy Process)

4.3.5 Entropy Method

4.4 Simple Additive Weighting Method

4.4.1 Description and Uses

4.4.2 Methodology

4.4.3 Strengths and Limitations

4.4.4 Sensitivity Analysis

4.4.5 Illustrative Examples: Simple Additive Weighting

4.5 Analytical Hierarchy Process

4.5.1 Description and Uses

4.5.2 Methodology of the Analytic Hierarchy Process

4.5.3 Strengths and Limitations of Analytic Hierarchy Process

4.5.4 Sensitivity Analysis

4.5.5 Illustrative Examples with Analytic Hierarchy Process

4.6 Technique of Order Preference by Similarity to the Ideal Solution

4.6.1 Description and Uses

4.6.2 Methodology

4.6.2.1 Normalization

4.6.3 Strengths and Limitations

4.6.4 Sensitivity Analysis

4.6.5 Illustrate Examples with Technique of Order Preference by Similarity to the Ideal Solution

References and Suggested Additional Readings

5. Modeling with Game Theory

5.1 Introduction

5.2 Background of Game Theory

5.2.1 Two-Person Total Conflict Games

5.2.2 Games Are Simultaneous and Repetitive

5.3 Illustrative Modeling Examples of Zero-Sum Games

5.4 Partial Conflict Games Illustrative Examples

5.5 Summary and Conclusions

References and Suggested Readings

6. Regression and Advanced Regression Models

6.1 Introduction to Regression

6.2 Modeling, Correlation, and Regression

6.2.1 Linear, Multiple, and Nonlinear Regression

6.2.2 Multiple Linear Regression

6.2.3 Nonlinear Regression (Exponential Decay)

6.3 Advanced Regression Techniques with Examples

6.3.1 Data

6.4 Conclusion and Summary

References and Suggested Reading

7. Discrete Dynamical System Models

7.1 Introduction to Modeling with Dynamical Systems and Difference Equations

7.2 Modeling Discrete Change

7.3 Equilibrium Values and Long-Term Behavior

7.3.1 Equilibrium Values

7.3.2 A Graphical Approach to Equilibrium Values

7.3.3 Stability and Long-Term Behavior

7.4 Modeling Nonlinear Discrete Dynamical Systems

7.4.1 Introduction and Nonlinear Models

7.5 Modeling Systems of Discrete Dynamical Systems

7.6 Summary

References and Suggested Further Readings

8. Simulation Modeling

8.1 Introduction

8.2 Random Number and Monte Carlo Simulation

8.2.1 Random-Number Generators in Excel

8.2.2 Examples in Excel

8.3 Probability and Monte Carlo Simulation Using Deterministic Behavior

8.3.1 Deterministic Simulation Examples

8.4 Probability and Monte Carlo Simulation Using Probabilistic Behavior

8.5 Applied Simulations and Queuing Models

Further Reading and References

9. Mathematics of Finance with Discrete Dynamical System

9.1 Developing a Mathematical Financial Model Formula

9.1.1 Simple Interest and Compound Interest

9.2 Rates of Interest, Discounting, and Depreciation

9.2.1 Annual Percentage Rate

9.2.2 APR for Continuous Compounding

9.2.3 Discounts

9.2.4 Depreciation

9.3 Present Value

9.3.1 Net Present Value and Internal Rate of Return

9.3.2 Internal Rate of Return

9.4 Bonds, Annuities, and Shrinking Funds

9.4.1 Government Bonds

9.4.2 Annuities and Sinking Funds

9.4.2.1 Ordinary Annuities

9.4.3 Present Value of an Annuity

9.5 Mortgages and Amortization

9.6 Financial Models Using Previous Techniques