The Design Phase

1. The Design Phase

2. What Is A Model? • A model is a representation or abstraction of a real-world object, process, concept or “problem” which is reduced in scope or complexity relative to the problem itself but yet retains the certain “essential” aspects which we believe define or characterize the particular real-world problem. • A good model should have a good balance between accuracy and simplicity.

3. What Is A Model? • A models may be used to: • describe • predict, or • optimize • Three types of general models • Physical/iconic: model car, model house • Analog/graphic: road map, speedometer • Symbolic: algebraic or spreadsheet model

4. Why Use Models? • In support of Decision Making and help management make sound decisions • A model is valuable if you make better decisions when you use it (modeling approach) than when you don’t (intuition approach) • Models + Managerial Judgement = The best way to run business

5. Advantages of Using Models • Models are generally less expensive and disruptive than experimenting with real systems • Models allow managers to ask “what-if” questions • Models force a consistent and systematic approach to the analysis of problems

6. Advantages of Using Models “By modeling various alternatives for future system design, Federal Express has, in effect, made its mistakes on paper. Computer modeling works; it allows us to examine many different alternatives and it forces the examination of the entire problem” Fred Smith Chairman and CEO of FedEx

7. Disadvantages of Models • They may be expensive and time-consuming to develop and test • They are often misused and misunderstood because of their mathematical complexity • They may have assumptions that oversimplify the real-world system

8. Model Components Model - Relationships Inputs Outputs

9. Relationships Performance Measures or Objective Functions Decision Variables & Parameters Consequence Variables Decision Model Components Model Outputs Inputs

10. Model and Data • Useful (quantitative) models are developed based on relevant data (numbers); models without data are at best theoretical abstractions • Data are often collected according to the requirements of models • time series vs. cross-sectional • aggregated vs. disaggregated

11. Numbers in Models • Data • Count • Measure • Rank • Results • Constant • Variable • Coefficient • Precision

12. Model Classification • Deterministic Models • All model components and relevant data are known with certainty • Examples include: Ad hoc models, Forecasting, Decision analysis, Constrained optimization • Probabilistic (Stochastic) Models • Some components or data are not known with certainty • Examples of include: Monte Carlo simulation, Scheduling and queueing

13. Diagnose problem Organize facts Select methodology Formulate model Solve model Interpret results Validate Face validity Causal validity Computational validity Sensitivity analysis Implement solution Monitor results General Modeling Process

14. Is the model valid? Basic Modeling Process Study model behavior Real World Problem No Yes Make decisions Abstract aspect of real problem Monitor results Model solution Model

15. Fundamental Relationships • Accounting • Microeconomics • Logic

16. Terminology and Relationships • Sunk Costs • Overhead, Fixed & Period Costs • Depreciation and Amortization • Variable or incremental Costs • Capacity • Market Share • Price • Sales & Production Volume • Supply & Demand • Revenue • Market Share • Contribution • Historical & Replacement Costs • Marking to Market • Allocated Costs

17. Model Building: Influence Diagram • A graphical representation (flow chart) of the influencing relationship among variables in a particular problem • Constructing an influence diagram using Top-Down approach • start with output: performance measure • work downward to locate variables that affect the output as well as other variables

18. Profit TotalCost Revenue TVC Price Demand TFC Unit VC Advertising

19. Spreadsheet Modeling • Inputs should be logically grouped • Primary outputs should be easy to read • Input and output data should be labeled • Don’t embed parameters in a formula: using cell reference • Use range name • Use fonts and color but don’t overuse them

21. Validation • A Process of Establishing Confidence that an Inference from Model is Correct. • There is No Single Test for Validity. • Series of Hurdles to Increase Model Builder and User’s Confidence in the Model.

22. Face Validity • Is Model’s Output Reasonable? • When Changes Made in Input Variables, Is Value of Output Variable Reasonable? • Be Aware of Counter-Intuitive Model Output! • Enhanced by Using Well-Defined Financial (or Business) Relationships within Model. • Absolute Minimum for Validation.

23. Flowchart for Face Validity: Outputs Are Consistent with Expectations Establish Face Validity Change Inputs Model’s Logic Correct Counterintuitive Inconsistent with Expectations Make Changes to Model Model’s Logic Incorrect

24. Historical & Relational Validity • Compare Model’s Output to Historical Data. • Assess Assumptions About the Relations of the Model Components to Each Other • Builders Must State Assumptions. • Users Must Assess Assumptions. • Must Examine Included and Excluded Assumptions Within the Model. • Review List of Controllable and Uncontrollable Variables and Relevant Ranges.

26. Optimization • We wish to choose the “best” controllable input based upon the relations and constrains which we can’t control. • We may find this optimum: • Mathematically - using calculus & algebra • Arithmetically - using tables or spreadsheets • Iteratively -using optimization software (I.e.Solver)

27. Mathematical Optimization • If we have a model which lends itself to a continuous equation, we can use calculus to find a global minimum or maximum. I.e.: • Total Cost = Fixed + Variable Costs • TC = 2000 + 10 * Demand • Demand = 100 – 2 * Price • Profit = TR – TC = P * D – TC • Find the Profit Maximizing Price

28. Arithmetical Optimization • If we don’t have a differentiable equation or a continuous relation but do have a simple equation, we may find an optimum arithmetically using one way or two way tables or spreadsheets.

29. One-Way What-If Table

30. Two-Way What-If Table Order Cost Low Level, $20 High Level, $30 Order Size 1500 1400 1300

31. Iterative Optimization • If we have several controllable variables and/or the variables can take on many different values, we may find an optimum using software which iteratively applies numerical methods such as Excel’s Solver. • Since this is numerical (and not mathematical), we cannot be assured that we have found a truly global optimum but instead may have found a local one.

32. Hill Climbing

33. Using Excel’s Solver for Optimization • Answers Questions Such As: • What Order Size Will Minimize Total Annual Cost? • How Much Should I Invest in Stock 1 to Maximize Portfolio Return? • Output (AKA Target) Cell is Cell Whose Value You Wish to Maximize or Minimize.

34. Using Excel’s Solver • Input Variables or Changing Cells Are Those Cells Whose Values Are Adjusted Until a Solution is Found. • Constraint – The Range of Permissible Values for the Controllable Variables. • Uses an Iterative Procedure to Found the Peak or Valley for the Target Variable.

35. Optimization Using Solver

36. Problem Using Excel’s Solver • Problem: Solver Sometimes Find a Local Maximum (Hill Top) and Not the Global Maximum (Mountain Top). • Solution: Try Running Solver Several Times with Different Starting Values in the Changing Cells (Base Camps).

37. The Design Phase

39. Overview of Bivariate Data: Looking For Relationships Analyzing Specific Data

40. Data Base 1: Cross-Sectional Data Base (for One Period) Potential Predictor Variables Dependent Variable

41. Does Market Share Data Exhibit Much Variation (Data Base 1)? • Compute Coefficient of Variation (CV). • If CV Greater Than 25-30%, Generate Possible Predictor Variables That Might Affect the Dependent Variable, Market Share.

42. Types of Variables • Dependent Variable is the Variable You Wish to Understand or Predict. • Predictor, or Independent, Variables Are the Variables You Believe Affect the Dependent Variable.

43. Correlation • If two variables are related to each other, then changes in one can be related to changes in the other. In other words, they rise and/or fall together. • Measured by a coefficient -1 £ r £ 1. • One variable may be caused by the other OR they both may be caused by other causes (intervening variables).

44. Causal Models • Causal Models - where we have one numerical dependent variable and one or more independent variables which we say “cause” the dependent variable • Salary is “caused by” gender and months on the job. • Wrecks are “caused by” alcohol, cell phones, speed, etc. • Advertising “causes” sales.

45. Establishing Causality • Necessary (but not sufficient) determinates of Causality: • Correlation - variables rise and/or fall together. • Temporal precedence - cause precedes effect in time. • Logical mechanism - must have reasonable explanation of how independent variable causes the dependent variable to vary.

46. Organize Bivariate Data

47. Slide 2

48. Scatter Plot of Advertising Versus Share of Market, CS Data

49. Scatter Plot of Mean Sales Exp. Versus Share of Market, CS Data

50. Scatter Plot of Degree of Competitiveness Versus Market Share, CS Data