Introduction to Business Analytics Using Simulation

450 Pages·2016·28.5 MB·English

by  Jonathan P. Pinder

Introduction to Business
Analytics Using Simulation
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Introduction to Business
Analytics Using Simulation
Jonathan P. Pinder
School of Business
Wake Forest University
Winston-Salem, NC, United States
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Contents
Preface ....................................................................................................................................................xi
Acknowledgments ...............................................................................................................................xiii
CHAPTER 1 Business Analytics is Making Decisions .......................................................1
Introduction .........................................................................................................................2
1.1 Business Analytics is Making Decisions Subject to Uncertainty ................................2
1.2 Components of Business Analytics .............................................................................2
1.3 Uncertainty = Probability = Stochastic ........................................................................3
1.4 What is Simulation? .....................................................................................................4
1.4.1 Why Use Simulation? ........................................................................................4
1.4.2 Simulation Applications .....................................................................................5
1.5 Monte Carlo Simulation and Random Variables .........................................................5
1.6 Simulation Terminology ............................................................................................10
1.7 Probability as Relative Frequency .............................................................................12
1.8 Overview of Simulation Process ................................................................................18
1.9 Random Number Generation in Excel .......................................................................18
Exercise Set 1: Introduction to Decision-Making and Simulation ...................................19
1.10 Extra Practice .............................................................................................................20
CHAPTER 2 Decision-Making and Simulation ...................................................................23
Introduction .......................................................................................................................23
2.1 Introduction to Decision-Making ..............................................................................23
2.1.1 Define the Problem ..........................................................................................24
2.1.2 Identify and Weight the Criteria ......................................................................24
2.1.3 Generate Alternatives .......................................................................................24
2.1.4 Evaluate Each Alternative ................................................................................25
2.1.5 Compute the Optimal Decision ........................................................................25
2.2 Probability: The Measure of Uncertainty ..................................................................28
2.3 Where do the Probabilities Come From? ...................................................................29
2.4 Elements of Probability .............................................................................................35
2.5 Probability Notation ...................................................................................................35
2.6 Examples of Simulation and Decision-Making .........................................................36
Exercise Set 2: Simulation and Decisions ........................................................................44
CHAPTER 3 Decision Trees ......................................................................................................47
Introduction .......................................................................................................................47
3.1 Decision Trees and Expected Value ...........................................................................47
3.2 Properties of Decision Trees. .....................................................................................49
3.2.1 Linear Transforms ............................................................................................49
v
vi Contents
3.3 Overview of the Decision Making Process ................................................................52
3.4 Sensitivity Analysis ....................................................................................................58
3.5 Expected Value of Perfect Information ......................................................................61
3.6 Summary of the Decision Analysis Process ..............................................................65
Exercise Set 3: Decision Trees ..........................................................................................65
CHAPTER 4 Probability: Measuring Uncertainty...............................................................71
Introduction .......................................................................................................................71
4.1 Probability: Measuring Likelihood ............................................................................71
4.2 Probability Distributions ............................................................................................72
4.3 General Probability Rules ..........................................................................................73
4.4 Conditional Probability and Bayes’ Theorem ............................................................77
Exercise Set 4: General Probability Rules ........................................................................82
Further Exercises: Common Interview Questions Regarding Probability ........................85
CHAPTER 5 Subjective Probability Distributions ..............................................................87
Introduction .......................................................................................................................87
5.1 Subjective Probability Distributions—Probability From Experience ........................88
5.2 Two-Point Estimation: Uniform Distribution ............................................................88
5.2.1 Discrete Uniform Distribution .........................................................................89
5.3 Three-Point Estimation: Triangular Distribution .......................................................96
5.3.1 Simulating a Symmetric Triangular Distribution.............................................98
5.3.2 Simulating an Asymmetric Triangular Distribution.......................................100
5.4 Five-Point Estimates for Subjective Probability Distributions ................................101
5.4.1 Simulating a Five-Point Distribution .............................................................104
5.4.2 Other Estimates for Subjective Probability Distributions ..............................106
Exercise Set 5: Subjective Probability Distributions ......................................................111
Exercise Set 6: Decision Models Using Subjective Probability .....................................112
CHAPTER 6 Empirical Probability Distributions ..............................................................117
Introduction .....................................................................................................................117
6.1 Empirical Probability Distributions—Probability From Data .................................118
6.2 Discrete Empirical Probability Distributions ...........................................................118
6.3 Continuous Empirical Probability Distributions......................................................127
Exercise Set 7: Empirical Probability Distributions .......................................................133
Exercise Set 8: Decision Models Using Empirical Probability ......................................137
CHAPTER 7 Theoretical Probability Distributions ..........................................................151
Introduction .....................................................................................................................151
7.1 Theoretical/Classical Probability .............................................................................152
7.2 Review of Notation for Probability Distributions ....................................................152
7.3 Discrete Theoretical Distributions ...........................................................................153
7.3.1 Uniform Distribution ......................................................................................153
7.3.2 Discrete Uniform Distribution .......................................................................153
Contents vii
7.3.3 Continuous Uniform Distribution ..................................................................154
7.3.4 Bernoulli Distribution ....................................................................................155
7.3.5 Binomial Distribution ....................................................................................155
7.3.6 Poisson Distribution .......................................................................................162
7.4 Continuous Probability Distributions ......................................................................169
7.4.1 Normal Distribution .......................................................................................169
7.5 Normal Approximation of the Binomial and Poisson Distributions ........................174
7.6 Using Distributions in Decision Analysis ................................................................179
7.7 Overview of Probability Distributions .....................................................................186
Exercise Set 9: Discrete Theoretical Probability Distributions.......................................187
Exercise Set 10: Continuous Theoretical Probability Distributions ...............................188
Exercise Set 11: Decision Models Using Theoretical Probability Distributions ............190
CHAPTER 8 Simulation Accuracy: Central Limit Theorem and Sampling ..............197
Introduction .....................................................................................................................197
8.1 Introduction to Sampling and the Margin of Error ..................................................198
8.2 Adding Distributions................................................................................................198
8.3 Samples ....................................................................................................................211
8.4 Central Limit Theorem ............................................................................................211
8.4.1 The Central Limit Theorem ...........................................................................212
8.5 Confidence Intervals and Hypothesis Testing for Proportions ................................219
8.5.1 Hypothesis Testing .........................................................................................226
8.6 Confidence Intervals and Hypothesis Testing for Means ........................................234
8.6.1 Small (n ≤ 30) Samples: Use Student’s t-Distribution .................................238
Exercise Set 12: Adding Independent Random Variables ...............................................248
Exercise Set 13: Sampling—Estimating and Testing Proportions ..................................252
Exercise Set 14: Sampling—Estimating and Testing Means ..........................................253
CHAPTER 9 Simulation Fit and Significance: Chi-Square and ANOVA ....................259
Introduction .....................................................................................................................260
9.1 Conditional Probabilities—Again ............................................................................260
9.1.1 Examples of Conditional Probability Estimation Procedures .......................261
9.2 Conditional Probability for Groups .........................................................................262
9.2.1 Examples of ANOVA and Chi-Square Situations ..........................................262
9.3 Chi-Square (χ2): Are the Probability Distributions the Same? ................................264
9.3.1 Chi-Square: Actual Frequencies Versus Expected Frequencies ....................266
9.4 Analysis of Variance: Are the Groups’ Averages the Same? ....................................276
9.4.1 Conducting an ANOVA: p-Value Again ........................................................278
9.4.2 Why is it Called Analysis of VARIANCE if Compares Averages? ...............283
9.4.3 An Approximate Comparison of More Than Two Groups ............................285
9.4.4 What if Groups Are, or Are Not, Significantly Different? ............................287
9.5 ANOVA Versus Chi-Square: Likert Scale ...............................................................295
Exercise Set 15: Statistical Tools: Chi-Square and ANOVA...........................................300
viii Contents
CHAPTER 10 Regression ...........................................................................................................313
Introduction .....................................................................................................................315
10.1 Overview of Regression ...........................................................................................315
10.1.1 Basic Linear Model .....................................................................................316
10.2 Measures of Fit and Significance .............................................................................319
10.2.1 Standard Error of the Slope: SE .................................................................319
β1
10.2.2 t -stat .............................................................................................................319
10.2.3 Standard Error of the Estimate ....................................................................320
10.2.4 Coefficient of Determination: r2 ..................................................................321
10.3 Multiple Regression .................................................................................................327
10.4 Nonlinear Regression: Polynomials.........................................................................329
10.4.1 Nonlinear Models: Polynomials ..................................................................330
10.4.2 Nonlinear Models: Nonlinear (Logarithmic) Transformations ...................332
10.5 Indicator Variables ...................................................................................................334
10.6 Interaction Terms .....................................................................................................347
10.7 Regression Pitfalls ...................................................................................................351
10.7.1 Nonlinearity .................................................................................................351
10.7.2 Extrapolation Beyond the Relevant Range ..................................................353
10.7.3 Correlation ≠ Causality ................................................................................354
10.7.4 Reverse Causality ........................................................................................354
10.7.5 Omitted-Variable Bias .................................................................................354
10.7.6 Serial Correlation .........................................................................................354
10.7.7 Multicollinearity ..........................................................................................355
10.7.8 Data Mining .................................................................................................355
10.7.9 Heteroscedasticity ........................................................................................355
10.8 Review of Regression ..............................................................................................356
Exercise Set 16: Regression ............................................................................................357
CHAPTER 11 Forecasting ..........................................................................................................371
Introduction .....................................................................................................................373
11.1 Overview of Forecasting ..........................................................................................373
11.2 Measures of Accuracy ..............................................................................................373
11.3 Components of Time Series Data ............................................................................377
11.4 Forecasting Trend ....................................................................................................382
11.4.1 Linear Trend ................................................................................................382
11.4.2 Exponential Trend ........................................................................................382
11.4.3 Autoregression .............................................................................................386
11.5 Forecasting Seasonality ...........................................................................................392
11.5.1 Ratio-to-Moving-Average Method (X-11 X-12) .........................................396
11.5.2 Summary of the Ratio-to-Moving-Average Method ...................................402
11.6 Aggregating Sales ....................................................................................................402
11.7 Review of Forecasting With Regression ..................................................................405
Exercise Set 17: Forecasting ...........................................................................................405
Contents ix
APPENDIX 1 Summary of Simulation ....................................................................................419
A1.1 Overview of the Simulation Process ........................................................................419
A1.2 Review of Probability Distributions ........................................................................419
A1.3 Methods to Simulate Probability Distributions .......................................................420
A1.3.1 Random Numbers by Single Formula Method ...........................................421
A1.3.2 Random Numbers by VLOOKUP Method .................................................422
APPENDIX 2 Statistical Tables ...............................................................................................425
A2.1 Normal Distribution .................................................................................................425
A2.2 Student’s t-Distribution ............................................................................................427
Index ...................................................................................................................................................429