1. MIS 546 – Business Analysis and Modeling Simple Mathematical Models "All models are wrong; some are useful." - George Box (eminent statistician)

2. Heuristic 8 - Focus on model structure, not on data collection  Don't get too enamored with data. It's retrospective. Collection biases (IS and/or human) Data available not necessarily data needed  Don't let lack of data stop your modeling. Often useful insights can come from good models and limited data. Building a model will help focus your data collection. Model building can proceed while working on data collection. Just the process of building a model may obviate the need for data collection or even for more modeling.

3. Adapted from [from “The Art of Modeling with Spreadsheets”, Powell. S.G. and Baker, K.R., John Wiley and Sons, Inc., USA, 2004] Heuristic 9 – Hypothesize some mathematical form for an important input- output relationship between x (input) and y (output). Advantages of using simple functions instead of the data?

4. Simple mathematical models  Underlying “physics” of the process may lead to an appropriate mathematical model Constant multiplicative growth rate  Exponential growth  Easy to explore simple models with a small number of parameters to gain insights regarding the impact of changes in those parameters  May be able to embed simple mathematical model inside larger, more complex model Example: Price vs Demand model inside pricing optimization model

5. Linear response (one variable)  The linear function is easy to understand. Its graph is a straight line. When x changes by 1 unit, y change by b units. The constant a is called the intercept, and b is called the slope  Often applicable within a limited range of x even if not globally applicable

6. Power Function  The power function is a curve except in the special case where the exponent b is 1. Then it is a straight line. The shape of the curve depends primarily on the exponent b. If b >1, y increases at an increasing rate as x increases. If 0 < b < 1, y increases, but at a decreasing rate, as x increases. If b < 0, y decreases as x increases.  An important property of the power curve is that when x changes by 1%, y changes by a constant percentage, a constant percentage, and this percentage is approximately equal to b%.  An Excel tool for exploring the Power Functions

7. Exponential function  The exponential function also represents a curve whose shape depends primarily on the constant b in the exponent. If b > 0, y increases as x increases. If b < 0, y decreases as x increases.  An important property of the exponential function is that if x changes by 1 unit, y changes by a constant percentage, and this percentage is approximately equal to 100 x b%.  Another important note about the equation is that it contains e, the special number 2.7182…. In Excel, e to any power can be calculated by the EXP function.  Paper folding example Paper folding example

8. Example 2.5: The Golf Clubs Pricing Problem  This example is divided into three parts: estimating the relationship between price & demand creating the profit model Optimize price to maximize profit  Visualizing and modeling demand versus price Let’s build this in class together. Online: see Golf Clubs Pricing Problem video series Let’s build this in class together. Online: see Golf Clubs Pricing Problem video series

9. Uncertainty: The Gorilla in the Room  We’ve ignored uncertainty so far Fun with Uncertainty later in term  Probability and statistics are the language of uncertainty We’ll review this as needed  Sensitivity Analysis = “What matters in this decision?” which variables might I want to explicit model as uncertain and which ones might I just as well fix to my best guess of their value? On which variables should we focus our attention on either changing their value or predicting their value? We’ll use data tables, graphs, TopRank add-in  Monte-carlo simulation Explicit modeling of uncertainty @Risk makes this “easy” within spreadsheets Serious Play: How the World's Best Companies Simulate to Innovate Serious Play: How the World's Best Companies Simulate to Innovate by Michael Schrage, Tom PetersMichael SchrageTom Peters

10. The 7-11 Problem (Chapter 1 of PMS)  One cash register  Worried about customer wait times  Considering new cash register technology that could speed up checkout times  Considering additional cash register stations

11. 7-11 Influence Diagram  Major output variable or performance measure?  Input variables?  Which inputs are likely decision variables?  Which inputs influence outputs or other inputs?  Model? Where do we need a model? Which relationship is the most complex? Let’s build this in class together. Online: see 7-11 Problem video series Let’s build this in class together. Online: see 7-11 Problem video series

12. 7-11 Staffing Using a Descriptive Queueing Model Mathematical equations (2) Queueing Model(s) (1) Inputs (3) Outputs Given these Predict these Example_7-11.xls A real model used for managing call centers

13. Numeracy and logical skills  Make quick rough numerical estimates 7-11: about how long are times at cash register?  Use special cases to test limits of calculation 7-11: arrival rate=service rate  Check consistency of units 7-11:  “smell test” 7-11: Does A  resulting in W  “smell” right http://xkcd.com/687/

14. Many dimensions of model quality  Modularity  Reusability  Automation  Clarity  Flexibility  Power  Maintainability  Elegance  Usability  Aesthetics  Scope  Validity  Correctness  Acceptability

15. Reality Checks Neither building nor consuming models is easy  Model formulation and data collection are intertwined  Entire process filled with feedback loops and iteration  Modeling is a craft and is far from straightforward  Building models can be complex and time consuming  Presenting results from modeling/analysis efforts can be very challenging  Models can be given unjust credibility – VaR and Cupolas?  Massive amounts of time can be spent on collecting, extracting, cleaning and massaging data  Many people do not understand nor trust mathematical models  Many factors beyond model results affect real decision making and implementation of change  Often key data simply does not exist  Paralysis by analysis