Business Decisions. Spreadsheet Modeling. John F. Kros. Vfor\ B Third Edition Revised for Excel 2010

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1 1 Spreadsheet Modeling Vfor\ Business Decisions Third Edition Revised for Excel 2010 Featuring Risk Solver Platform for Decision Analysis, Simulation, and Optimization B John F. Kros

2 OffllEHS Preface xi Acknowledgements xv About the Author xvii Optimal Information Area 26 References 26 Problems 27 CHAPTER 1 The Art and Science of Becoming a More Effective and Efficient Problem Solver 2 Business Decision Modeling in Action Algorithm? What the Heck Is an Algorithm? 5 The Art and Science of Using Business Decision Modeling to Become a More Effective and Efficient Problem Solver 6 Definition of Quantitative Business Decision Making 6 Areas of Business Decision Modeling Application 7 Companies Using Business Decision Modeling Concepts 8 The Business Decision Modeling Process 8 The Business Decision Modeling Process 9 A Brief History 10 Step 1: Problem Identification 11 Step 2: Problem Definition 11 Step 3: Problem Modeling 11 Step 4: Initial Model Results 12 ' Step 5: Review and Iteration 12 Step 6: Implementation 13 Basic Financial Models 13 The RAND Corporation 14 Three Parts of the General Profit Equation 15 Cost and Volume Models 15 Revenue and Volume Models 15 Profit and Volume Models Putting It All Together 16 Break-Even Analysis 16 Crossover Analysis 18 Computer-Generated Solutions Using Spreadsheets 20 Solving Complex Problems Using Spreadsheets 20 Spreadsheet Solution for Break-Even Analysis Problem 21 Writing Business Decision Modeling Reports for Business 22 General Rules of Thumb 22 Creating a Structure 23 Executive Summary Example for Surfboard Inc. 24 CHAPTER 2 Introduction to Spreadsheet Modeling 30 Business Modeling in Action Using Spreadsheet Models 34 Introduction 36 Background 36 Categories of Models 37 Models versus Modeling 38 Process for Modeling 38 Why a Process for Modeling? 38 The Problem-Solving Process 39 Goals in Spreadsheet Design 41 Basic Spreadsheet Modeling Concepts 42 Layout of a Spreadsheet 42 Reference Cells and Ranges 43 Relative References 43 Copying Formulas 44 Absolute References 44 Mixed References 44 A Brief History of Spreadsheet Modeling 45 Applied Spreadsheet Modeling Goal Seek 46 Example 1 46 Applying Number Format to Cell 47 Naming Cells 48 Creating Data Tables in Excel 50 Using Excel to Generate PivotTables with One Variable 52 Using Excel to Generate PivotTables with Two Variables 55 Creating Charts Using Excel 56 Sensitivity Analysis 58 Using Goal Seek in Excel 59 Basic Excel Functions 61 Mathematical Operators 61 Built-in Functions 61 Statistical Functions 64 Logical Functions 65 Using Lookup Functions 67 Sorting Data in Excel 68 Applied Spreadsheet Modeling Using Basic Functions 71 III

3 iv CONTENTS Example 2 71 Using MIN Function 72 Using IF Function 73 Using VLOOKUP Function 74 Sensitivity Analysis Using Data Table 74 Expected Profit with Demand Probabilities 74 Using SUMPRODUCT 75 Applied Spreadsheet Modeling Using Solver 76 Example 3 76 Building the Spreadsheet Model 77 Using Excel Solver 80 Analysis of Results 83 Modification of Constraints and Rerun of Solver 83 Applied Spreadsheet Modeling Curve Fitting 84 Example 4 85 Spreadsheets in Real Business Situations 86 Linear Function 88 Power Function 89 Exponential Function 89 Mean Absolute Percentage Error (MAPE) 90 Adding in Solver in Excel 93 Summary 95 Executive Summary Example for Teez's Profit Problem 95 Case Study John Woo's Cellular Connections 97 Interactive Case Break-Even Analysis at SportsExchange 98 Summary of Key Excel Terms 99 Optimal Information Area 100 References 100 Problems 101 CHAPTER 3 Probability and Statistics A Foundation for Becoming a More Effective and Efficient Problem Solver 104 Business Decision Modeling in Action A Probabilistic Medical Testing Problem 108 Descriptive Statistics: Graphical and Numerical Methods for Describing Data Sets 110 Graphical Methods of Data Description 110 Histograms 110 Relative Frequency Diagrams 110 Numerical Methods of Data Description 112 Measures of Central Tendency 113 Simple Mean 113 Median 114 Comparison of Mean and Median 115 The Most Common Measure of Central Tendency 115 Measures of Dispersion 116 Range 116 Definition of Interquartile Range (IQR) 116 Definition of Variance 117 Definition of Standard Deviation 118 Painting the Full Picture A Classroom Example 119 Using Central Tendency and Dispersion 120 Excel Tutorial on Using Histogram Tool Function 120 Frequency Distributions 120 Installing Excel's Data Analysis Add-In within Excel 121 Example: Using Excel's Data Analysis Add-In 123 Steps for Determining Classes/Bins and Class Width 124 Excel's Histogram Tool 125 Probability Concepts 127 Subjective Probability 128 Intuition, Luck, and Subjective Probability Assessment 129 Guessing and Subjective Probability Assessment 129 Objective Probabilities 130 Cards, Coins, and Dice: Examples of Objective Probabilities 130 Objective Probabilities Defined as Relative Frequencies 130 Gambling and Probability 131 Rules of Probability 132 Analyzing an Event Space 133 The Language of Probability: Understanding the Terminology 134 Marginal Probability 135 Mutual Exclusivity 135 Venn Diagram of Mutual Exclusivity 136 Joint Probability 136 Venn Diagram of Non-Mutually Exclusive Events 137 Putting It All Together Using the Business Decision Modeling Process 137 Putting It All Together Using a Deck of Cards 138 Independence 139 Statistically Independent Events 140 Dependent Events 140 Conditional Probabilities 141 General Rule of Multiplication 141 Independent versus Dependent Events 141 Bayes'Rule 142 Law of Total Probability 142 The Story ofbayes 143

4 CONTENTS Probability Distributions 144 Discrete Probability Distributions 144 Expected Values 145 Probability Distributions and Standard Deviation 147 Standard Deviation Calculation for a Probability Distribution 147 Continuous Probability Distributions 148 Alternative Distributions Used by Managers 148 Lack of Symmetry 149 Sampling Outside of the High and Low Value Ranges 149 Triangular Distribution 149 Summary 150 Case Study: Slicky Lube Oil Products 152 Optimal Information Area 154 References 154 Problems 155 Appendix 3A: Probability and Statistics Review 162 CHAPTER 4 Decision Analysis: Building the Structure for Solving the Problem 196 Business Decision Modeling in Action How Legal Decision " Makers Use Decision Models 200 Decision Analysis: Building the Structure for Solving the Problem 201 Importance and Relevance of Decision Analysis and Theory 201 Linking Probability and Statistics to Decision Making 201 Framing the Decision Problem 201 Components of a Decision-Making Problem 202 States of Nature 202 Decision Alternatives 203 Outcomes 203 Outcomes versus Payoffs 203 Payoff Tables 203 A Brief History of Decision Making 205 Decision-Making Criteria without Probability Assessments 206 Spreadsheet Solution for Payoff Table Decision Problem 206 Steve's Mutual Fund Decision Problem 206 Maximax Criterion 207 Maximin Criterion 207 Minimax Regret 209 Management Science Definition of Regret 209 Economics Definition of Regret Opportunity Cost 209 Marketing Definition of Regret Buyer's Remorse 209 Psychological Definition of Regret Cognitive Dissonance 210 Minimax Regret Criterion Process 210 Regret as a Measure of Risk 211 Equal Likelihood Criterion LaPlace and Simple Weighted Averages 211 Hurwicz Criterion 212 Summary of Decision Criteria Results 213 Decision-Making Criteria with Probability Assessments 214 Expected Value of Perfect Information 214 Confusion over Multiple "Good" Choices 215 Three Areas of Sensitivity Analysis 216 Sensitivity Analysis 216 Step 1: Establish a Dominant Decision 216 Step 2: Examine the Trade-offs between Dominant Decisions 216 Step 3: Define and Quantify the Risk 217 Importance of Sensitivity Analysis 217 Sensitivity Analysis: Steve's Mutual Fund Example 218 "What If" Analysis 218 How to Construct a Sensitivity Graph in Excel 219 Analyzing the Sensitivity Graph 224 Establish Dominance 224 Risk Defined and Quantified by Regret 226 The Risk-Return Trade-off 227 Modeling, Decision Trees, and Influence Diagrams 227 Definition of Modeling 227 Why Model? 227 Five Main Reasons for Modeling 228 Structuring Decision Problems 229 Identifying and Defining Variables and Outcomes of Interest 229 Organizing Variables and Outcomes into a Logical Framework 230 Verification and Refinement of the Framework 230 Decision Trees 230 Decision Nodes, Chance Nodes, and Decision Trees Building Decision Trees 231 Folding Back the Tree: Calculating Expected Values 232 Example of Folding Back a Decision Tree 233 Multistage Decision Trees 234 Inadequacies of Decision Tree Structures 235 Influence Diagrams 235 Influence Diagram Symbols 236 Influence Diagrams and Depicting Influence 236

5 VI CONTENTS Random Variables Order, Precedence, and/or Influence Diagram Structure 238 Two-Way and Loop Influence 238 Influence Diagrams to Measure Time 239 Building the Influence Diagram Structure 240 Putting It All Together: A Real Estate Influence Diagram 240 Converting a Decision Tree to an Influence Diagram 241 Influence Diagrams and Decision Trees: A Comparison 242 Advantages of Influence Diagrams and Areas of Consideration 242 The Completed Real Estate Influence Diagram 243 Using TreePlan to Develop Decision Trees in Excel 244 Loading and Accessing TreePlan in Excel 244 Creating an Initial Decision Tree in TreePlan 247 Adding, Changing, and/or Modifying a Decision Tree in TreePlan 247 Creating Decision Trees with Risk Solver Platform 250 Summary 254 The Story of John von Neumann 255 Case Study: Ibanez Produce 258 References 259 Problems 261 CHAPTER 5 Simulation Modeling 270 Business Decision Modeling in Action The Super Flush Simulation 275 Simulation Modeling 276 Background 276 Computer Spreadsheet Simulation 276 What Is Simulation? And Why Are We Using It? 276 Real-World Simulation Examples 277 Simulation Affecting Managers 277 Types of Data 277 Numerical Data Discrete versus Continuous 277 Simulation and the Link to Earlier Chapters 278 Simulation, Spreadsheet Modeling, and Model Verification and Validity 278 Simulation Verification 278 Model Validity 278 Random Number Generation 279 Random Number Generation Techniques 279 Monte Carlo Simulation 280 Developing Random Number Generation Techniques 281 Generating Random Numbers by Spreadsheets 281 Simulation and Currency Exchange Rates 281 Cumulative Probability Distributions and Random Number Intervals 282 Generating Random Numbers and Simulating Currency Values 282 Excel Spreadsheet Simulation of Currency Value Example 283 Simulation of a Queuing System 284 Single Server Waiting Line System 284 The Major Players and the Story Behind the Development of Monte Carlo Simulation 285 Where Customers Come From The Calling Population 286 The Order in Which Customers Are Served The Queue Discipline 286 How Often Customers Arrive at the Queue The Arrival Rate 286 How Fast Customers Are Served The Service Time 287 Lunch Wagon Simulation Example: Arrivals and Profit Determination 287 Customer Spending Habits 288 Origination of Probability Distributions 288 Random Number and Normal Probability Generation 289 Computing Relevant Simulation Statistics and Distributions 289 Lunch Wagon Waiting Line Simulation 289 Interarrival Times 290 Customer Service Times 290 Simulation's Real Payoff The Sensitivity/What-If Analysis Tutorial 293 in Excel 293 : Will Do for the Modeler 293 User Responsibilities 293 Getting Started 294 Input Cells 295 The Triangular Distribution 296 The Normal Distribution 296 Output Cells 297 Summary of Inputs and Outputs Window 298 Running a Risk Analysis 298 Simulation Data Button 302 Simulation Sensitivities Button 303 Simulation Scenarios Button 304

6 CONTENTS vii Graphing the Results 305 Graphing: Understanding the Data More Clearly 306 to Create a Histogram of NPV 306 to Create a Smooth Bell-Shaped Curve of NPV 307 to Create a Cumulative Distribution Graph of NPV 307 Cumulative Distribution Outline Graph 309 Summary Output Graphs 309 Interpretation of the Summary Graph 310 Sensitivity Analysis and the Tornado Diagram 311 Graphing in Excel Example with Multiple Decision Alternatives 312 Structure of Project Input Cells for Project Output Cells 314 Running the Simulation 315 Interpreting the Results 315 Dominance 315 Trade-offs 316 Risk Analysis 316 Risk Solver Platform Tutorial 317 Getting Started with RSP and the XYZ Corporation Model 317 Input Cells 317 Simulation Modeling 318 The Normal Distribution 318 Output Cells 319 Summary of Inputs and Outputs 320 Solver Options and Model Specifications Window 320 Running a Risk Analysis 320 Options Menu in RSP 320 Simulation Tab 321 General Area 321 Sampling Method Area 322 Value to Display Area 322 Correlations Area 322 Running the Simulation 322 Analyzing the Results in RSP 322 Cumulative Distribution Outline Graph 324 Sensitivity Analysis and Tornado Diagrams 324 Summary 326 Conclusions 326 Summary 326 Case Study: Steve's Solar System 330 Interactive Case: Serving the Customers at Schenck's 331 Optimal Information Area 333 References 333 Problems 335 CHAPTER 6 Linear Regression Modeling 340 Business Decision Modeling in Action Linear Regression Analysis at General Motors 344 Linear Regression Modeling 345 Forecasting Technique 345 Areas of Statistics 345 Data Sources 346 Statistical Software 348 Population versus Sample 348 Sample Size 348 History of Regression 349 Scatter Plots 350 Hypothesis Testing 351 Simple Linear Regression Equation 353 The Scientists of Regression 355 Multiple Regression Model 356. Performance Measures 358 f Statistic 359 F Statistic 360 p Value 360 Confidence Level 361 Multicollinearity 363 Autocorrelation 365 Alternative Method for Computing the Durbin- Watson Statistic 367 Heteroscedasticity 368 Measuring Accuracy 369 Lagged Variables 371 MS Excel Tutorial: Using Add-lns 373 MS Excel Tutorial: Using Add-Ins 373 Excel Tutorial: Regression 373 Excel Tutorial: Correlation 380 The Leading Causes of Job Creation in Information Technology: A Regression Analysis 382 Background 382 Determining the Relationship: Dependent and Independent Variables 382 Data 382 Model Selection 384 Relative Effectiveness of Models 385 The Regression Line Equation 385 Dependent Variable versus Independent Variable 386 Type of Data 386 Regression Results 387 Regression Line Equation 387 Multiples 388

7 VIII CONTENTS R Square 388 Adjusted R Square 388 Standard Error of Estimates 388 rtest 388 F Statistic 389 p Value 389 Multicollinearity 389 Autocorrelation 390 Heteroscedasticity 390 Residual Plots 391 Line Fit Plots 392 Normal Probability Plot 392 Measuring Forecasting Errors 394 Forecasting 394 Conclusion 395 Case Study: Kealoha's Labor Lobby Regression 397 Interactive Case: Plotting Linear Trend for Ellis' DVD Service Demand 398 Optimal Information Area 399 References 399 Problems 401 CHAPTER 7 Introduction to Forecasting 406 Business Decision Modeling in Action Using Forecasting and Time Series in Stock Market Technical Analysis 409 Analyzing Time Series Data 412 Two Goals: Identify and Forecast 412 Identifying Patterns in Time Series Data 412 Linear Time Series 412 Nonlinear Time Series 413 Seasonal Time Series 413 Cyclical Time Series 415 Irregular Time Series 415 General Forms of Time Series Models 415 Analyzing Patterns in Time Series Data 415 Latest Period or Naive Method 416 Trend Analysis 416 Smoothing 416 Moving Average Example Using Excel 417 Exponential Smoothing 420 Exponential Smoothing Example Using Excel 421 Choosing a Smoothing Constant 422 Autocorrelation 423 Identifying Autocorrelation 423 Autocorrelation and Seasonality 424 Seasonal Adjustments 424 Seasonal Adjustment Example 425 Linear Regression Forecast and Seasonal Adjustment 426 Seasonal Regression Using Excel 427 The Seasonal Model 431 Import Beer Sales Example 432 Interpretation and Analysis of Regression Outputs 436 Construction of the Seasonal Regression Equation and Error Calculation 440 Business Forecasting More Art Than Science? 443 Summary 444 Case Study: Jaqui's Import Beers' Sales Seasonality 447 Interactive Case: Forecasting Using Exponential Smoothing for Bill's Brew Threw 448 Optimal Information Area 449 References 449 Problems 451 CHAPTER 8 Introduction to Optimization Models 456 Business Decision Modeling in Action Spreadsheet Optimization Models in Use, or Why Use Spreadsheets to Optimize? 460 Introduction to Optimization Models 461 How Does an Optimization Model Find an Optimal Solution? 461 Descriptive Models: The Foundation for Optimization Models 462 Transforming a Descriptive Model into an Optimization Model 462 Classic Descriptive Economic Order Quantity Model 462 EOQ Spreadsheet Optimization Model 464 Finding the Optimal EOQ 465 Excel's Solver 465 Solver as an Add-In to Excel 466 Mathematical Programming 472 Linear Programming Models 473 Properties of LP Models 473 Activity Scaling and LP Models 474 Modeling a Real Problem and the LP Assumptions 474 Three Parts of an LP Model 475 Definition of LP Terminology 475 The Objective Function 475 The Constraints 476 The Non-Negativity Assumptions 477 Putting It All Together Steps in Formulating an LP Model 477 Putting It All Together Modified Standard Form 477 Mark's Bats LP Example The Story 478 LP Example The Formulation Process 479 Identifying Decision Variables 479

8 CONTENTS IX Objective Function Formulation 479 Business Decision Modeling throughout the Ages- The History of Mathematical Programming 480 Constraint Formulation 482 Non-Negativity Assumptions 483 Modified Standard Form Mark's Bat Production Problem 483 Methods of Solving LP Problems 484 The Graphical Method 484 Steps in Implementing the Graphical Method 485 Using Spreadsheets to Model LP Problems 485 Creating the LP Spreadsheet Model 485 Using Solver to Find Solutions to a Spreadsheet Optimization Model 487 Comparison of Constraints and Sensitivity Analysis 490 Binding and Nonbinding Constraints 490 Results and Sensitivity Analysis in Excel 490 Answer Report in Excel 491 Sensitivity Report in Excel 493 Using Risk Solver Platform in Excel 496 Defining Optimization Model in RSP 497 Defining the Objective Cell in RSP 497 Defining the Variable Cells in RSP 498 Defining the Constraint Cell in RSP 500 Defining the Non-Negativity Conditions in RSP 502 Reviewing the Models in RSP 502 Solving the Model in RSP 503 Summary of Optimization Using RSP 504 A Brief Discussion of the Simplex Method 504 Simplex and Slack Variables 505 How the Simplex Method Finds the Optimal Solution 505 Summary 505 Classical Linear Optimization Problems 506 Network Flow/Transportation Problems 506 The Transportation Problem: Pirate Logistics 506 Characteristics of the Transportation LP 506 The General LP Formulation for the Transportation Problem 507 Setting Up the Transportation LP in a Spreadsheet 508 Description of the Spreadsheet 508 Decision Variables 508 Supply and Demand Constraints 508 The Objective Function 509 Non-Negativity Assumptions 509 Setting Up Solver to Find Solutions to the Pirate Logistics LP Problem 510 Answer Report in Excel 512 Sensitivity Report in Excel 515 Constraints Section 516 Summary of Pirate Logistics LP Problem 518 Integer Linear Programming 518 Stating Integer Properties and Solving ILPs 518 Basics of Binary ILP Problems 518 The Capital Budgeting Problem 518 Summary of Integer Programming 522 Summary of Linear Programming 523 The Development of Spreadsheet Optimization Programs 524 Case Study: Chris's Capital Budgeting Ballyhoo 528 Optimal Information Area 529 Problems 531 Appendix 8A: Review of Graphical Solutions to Optimization Problems 539 CHAPTER 9 Project Management: PERT/CPM 552 Business Decision Modeling in Action CPM, Project Scheduling, and Claims Litigation 555 Project Management: PERT/CPM 558 Introduction 558 Definition of a Project 558 Use of Spreadsheets for Project Management The History of PERT/CPM 559 Planning, Scheduling, and Control 560 Project Management Questions and PERT/CPM 560 A Framework for PERT and CPM 560 A PERT/CPM Example 561 Defining the Network and Developing Precedence Relationships 562 Finding the Critical Path 563 The Forward Pass 563 Earliest Start and Earliest Finish Times 563 The Backward Pass 565 Latest Start and Latest Finish Times 565 The Critical Path and Slack 566 Gantt Charts and Excel 568 Drawbacks to Gantt Charts in Excel 569 Creating Gantt Charts in Excel 569 Developing a Probabilistic PERT Network 571 Estimating Activity Completion Times and Distributions 572 PERT and the Beta Distribution 572 Critical Assumptions about PERT 574 Statistical Questions about Expected Completion Times 574

9 CONTENTS Trade-offs within CPM: Project Crashing 575 Project Crashing within CPM 575 Summary 577 PERT, Production Scheduling, and Filmmaking (No Pun Intended) 578 Case Study: Jennifer's Prototype Palpitations 582 Interactive Case: Critical Path Scheduling for Samantha's Custom Ceramics 584 Problems 585 CHAPTER 10 Introduction to Visual Basic Programming 592 Business Decision Modeling in Action Real-World VBA Project 595 Introduction: What Is Visual Basic Programming? 596 Why Visual Basic? Why Excel? 596 What Is a Macro? 597 Excel's Macro Recorder 597 Excel Macro Recorder Example 597 How to Record a Macro for Formatting Cells 597 Use the Macro You Created 599 Creating a Toolbar or Assigning a Keystroke for a Macro 599 Recording a Macro by Using Relative References 600 Managing Macros with the visual Basic Editor 600 What Is the Visual Basic Editor? 600 Viewing and Editing Excel Visual Basic Macros 600 Creating a Simple Macro in Visual Basic Editor 602 Working with VB Code: An Introduction to Procedures 605 What Is a Subroutine? 605 What Does the Code Mean? 606 How Does the Code Work? 606 The Chronology of Visual Basic 610 Managing Modules and Projects 612 Sharing Macros with Others 612 Technical Writing for the VB Programmer 612 The History and Origin of VB 613 Summary 614 Optimal Information Area 616 References 616 Problems 617 APPENDIX A Useful Information 619 Standard Normal Distribution Table 620 Student's ftable 621 The F Distribution (Upper 5 Percent Points) 622 Durbin-Watson Test Statistic Table 623 Writing Guide for Business Decision Modeling 624 INDEX 629

Chapter 1 INTRODUCTION TO SIMULATION

Chapter 1 INTRODUCTION TO SIMULATION Many problems addressed by current analysts have such a broad scope or are so complicated that they resist a purely analytical model and solution. One technique for