Transcript BAM-Modeling-2x

MIS 546 – Business Analysis and
Modeling
Simple Mathematical
Models
"All models are wrong; some are
useful."
- George Box (eminent statistician)
Heuristic 8 - Focus on model
structure, not on data collection
 Don't get too enamored with data.
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It's retrospective.
Collection biases (IS and/or human)
Data available not necessarily data needed
 Don't let lack of data stop your modeling.
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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.
Heuristic 9 – Hypothesize some mathematical form for an important inputoutput relationship between x (input) and y (output).
y  a  bx
y  ax
b
y  ae
bx
Advantages
of using
simple
functions
instead of the
data?
𝑎𝐾
𝑦=
𝑎 + (𝐾 − 𝑎)𝑒 −𝑏𝑥
Adapted from [from “The Art of Modeling with Spreadsheets”, Powell. S.G. and Baker, K.R., John Wiley and Sons, Inc., USA, 2004]
Simple mathematical models
 Underlying “physics” of the process may lead to an
appropriate mathematical model
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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
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Example: Price vs Demand model inside pricing
optimization model
Linear response (one variable)
y  a  bx
 The linear function is easy to understand.
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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
Power Function
y  ax
b
 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.
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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
Exponential function
y  ae
bx
 The exponential function also represents a curve whose
shape depends primarily on the constant b in the exponent.
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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
Example 2.5: The Golf Clubs Pricing Problem
 This example is divided into three parts:
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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
Uncertainty: The Gorilla in the Room
 We’ve ignored uncertainty so far
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Fun with Uncertainty later in term
 Probability and statistics are the language of uncertainty
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We’ll review this as needed
 Sensitivity Analysis = “What matters in this decision?”
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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
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Explicit modeling of uncertainty
@Risk makes this “easy” within spreadsheets
Serious Play: How the World's Best Companies Simulate to Innovate
by Michael Schrage, Tom Peters
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
7-11 Influence Diagram
 Major output variable or
performance measure?
 Input variables?
Let’s build this in class together.
 Which inputs are likely
Online: see 7-11 Problem video series
decision variables?
 Which inputs influence
outputs or other inputs?
 Model? Where do we need
a model? Which
relationship is the most
complex?
7-11 Staffing
Using a Descriptive Queueing Model
(1) Inputs
Parameter
Units Symbol
Arrival Rate of Customers cust/minute a
Average Service Time
minutes/cust b
Given these
Predict these
(2) Queueing Model(s)
Mathematical
equations
(3) Outputs
Performance Measure
Example_7-11.xls
Expected Wait Time in Line
Probability of Waiting in Line
Probability of Waiting in Queue
less than t seconds
Units
Symbol
minutes
#N/A
W
P[W >0]
#N/A
P[W  t]
A real model used for managing call centers
Numeracy and logical skills
 Make quick rough numerical estimates
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7-11: about how long are times at cash register?
 Use special cases to test limits of calculation
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7-11: arrival rate=service rate
 Check consistency of units
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7-11:
W
A
S ( S  A)
minutes/cust 
http://xkcd.com/687/
(cust / minute)
(cust / minute)*(cust / minute - cust / minute)
 “smell test”
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7-11: Does A resulting in W “smell” right
Many dimensions of model quality
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Modularity
Reusability
Automation
Clarity
Flexibility
Power
Maintainability
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Elegance
Usability
Aesthetics
Scope
Validity
Correctness
Acceptability
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