Chapter 1
Introduction to
Quantitative
Qua
t tat e Analysis
a ys s
Quantitative Analysis for Management, Tenth Edition,
by Render, Stair, and Hanna
© 2008 Prentice-Hall, Inc.
Learning Objectives
After completing this chapter, students will be able to:
1. Describe the quantitative analysis approach
2 Understand the application of quantitative
2.
analysis in a real situation
3. Describe the use of modeling in quantitative
analysis
l i
4. Use computers and spreadsheet models to
perform quantitative
p
q
analysis
y
5. Discuss possible problems in using
quantitative analysis
6 Perform a break
6.
break-even
even analysis
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1–2
Chapter Outline
1.1
1.2
1.3
1.4
Introduction
What Is Quantitative Analysis?
The Quantitative Analysis Approach
How to Develop a Quantitative Analysis
Model
1.5 The Role of Computers and Spreadsheet
Models in the Quantitative Analysis
Approach
1 6 Possible Problems in the Quantitative
1.6
Analysis Approach
1.7 Implementation — Not Just the Final Step
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Introduction
„ Mathematical tools have been used for
thousands of years
„ Quantitative
Q
i i analysis
l i can be
b applied
li d to
a wide variety of problems
„ It
It’s
s not enough to just know the
mathematics of a technique
„ One must understand the specific
applicability of the technique, its
limitations, and its assumptions
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Examples of Quantitative Analyses
„ Taco Bell saved over $150 million using
forecasting and scheduling quantitative
analysis models
„ NBC television increased revenues by
over $200 million by
y using
gq
quantitative
analysis to develop better sales plans
„ Continental Airlines saved over $40
million
illi using
i quantitative
tit ti analysis
l i
models to quickly recover from weather
delays
y and other disruptions
p
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What is Quantitative Analysis?
Q
Quantitative
tit ti analysis
l i is
i a scientific
i tifi approach
h
to managerial decision making whereby raw
data are processed and manipulated
resulting in meaningful information
Raw Data
Quantitative
Analysis
Meaningful
Information
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What is Quantitative Analysis?
Quantitative factors might be different
investment alternatives, interest rates,
inventory levels
levels, demand
demand, or labor cost
Qualitative factors such as the weather,
state and federal legislation,
g
, and
technology breakthroughs should also be
considered
„ Information may
ma be diffic
difficult
lt to quantify
q antif but
b t
can affect the decision-making process
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The
e Qua
Quantitative
t tat e Analysis
a ys s Approach
pp oac
Defining the Problem
Developing a Model
Acquiring Input Data
D
Developing
l i
a Solution
S l ti
Testing
g the Solution
Analyzing the Results
Figure 1.1
Implementing the Results
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Defining the Problem
Need to develop a clear and concise
statement that gives direction and meaning
to the following steps
„ This may be the most important and difficult
step
„ It is essential to g
go beyond
y
symptoms
y p
and
identify true causes
„ May be necessary to concentrate on only a few
of the problems – selecting the right problems
is very important
„ Specific and measurable objectives may have
to be developed
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Developing a Model
$ Sales
Quantitative analysis
y
models are realistic,
solvable, and understandable mathematical
representations of a situation
$ Advertising
There are different types of models
Scale
models
Schematic
models
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Developing a Model
„ Models generally contain variables
(controllable and uncontrollable) and
parameters
„ Controllable variables are generally the
decision variables and are generally
unknown
„ Parameters are known quantities that
are a part of the problem
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Acquiring Input Data
Input data must be accurate – GIGO rule
Garbage
In
Process
Garbage
Out
Data may come from a variety of sources such as
p y reports,
p
company
p y documents, interviews,
company
on-site direct measurement, or statistical sampling
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Developing a Solution
„ The best (optimal) solution to a problem
is found by manipulating the model
variables until a solution is found that is
practical and can be implemented
„ Common techniques are
„ Solving
g equations
q
„ Trial and error – trying various approaches
and picking the best result
„ Complete enumeration – trying all possible
values
„ Using an algorithm – a series of repeating
p to reach a solution
steps
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Testing the Solution
Both input data and the model should be
tested for accuracy before analysis and
implementation
p
„ New data can be collected to test the model
„ Results should be logical, consistent, and
represent the real situation
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Analyzing the Results
Determine the implications of the solution
„ Implementing results often requires change
in an organization
„ The
Th impact
i
t off actions
ti
or changes
h
needs
d to
t
be studied and understood before
implementation
Sensitivity analysis determines how much
the results of the analysis will change if
the model or input data changes
„ Sensitive models should be very thoroughly
t t d
tested
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Implementing the Results
Implementation incorporates the solution
into the company
„ Implementation can be very difficult
„ People can resist changes
„ Many quantitative analysis efforts have failed
because a good, workable solution was not
properly implemented
Changes occur over time, so even
successful
f l implementations
i l
t ti
mustt be
b
monitored to determine if modifications are
necessary
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Modeling in the Real World
Quantitative analysis models are used
extensively by real organizations to solve
real problems
p
„ In the real world, quantitative analysis
models can be complex, expensive, and
difficult to sell
„ Following the steps in the process is an
important component of success
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How To Develop a Quantitative
A l i Model
Analysis
M d l
„ An important part of the quantitative
analysis approach
„ Let
Let’s
s look at a simple mathematical
model of profit
Profit = Revenue – Expenses
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How To Develop a Quantitative
A l i Model
Analysis
M d l
Expenses can be represented as the sum of fixed and
variable
i bl costs
t and
d variable
i bl costs
t are the
th product
d t off
unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units
sold) – [Fixed cost + (Variable costs per
unit)(Number
i )(N
b off units
i sold)]
ld)]
Profit = sX – [f + vX]
Profit = sX – f – vX
where
s = selling price per unit
f = fixed cost
v = variable cost per unit
X = number of units sold
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How To Develop a Quantitative
A l i Model
Analysis
M d l
Expenses can be represented as the sum of fixed and
variable
i bl costs
t and
d variable
i bl parameters
costs
t are the
th
product
dmodel
t off
The
of this
unit costs times the number
units
are f, v,of
and
s as these are the
inputs
p cost
inherent
in the cost)
model
Profit = Revenue – (Fixed
+ Variable
The
decision
variable
Profit = (Selling price
per
unit)(number
of of
units
interest
X
sold) – [Fixed
cost +is(Variable
costs per
unit)(Number
i )(N
b off units
i sold)]
ld)]
Profit = sX – [f + vX]
Profit = sX – f – vX
where
s = selling price per unit
f = fixed cost
v = variable cost per unit
X = number of units sold
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Pritchett’s
Pritchett
s Precious Time Pieces
The company buys, sells, and repairs old clocks.
R b ilt springs
Rebuilt
i
sell
ll for
f $10 per unit.
it Fixed
Fi d costt off
equipment to build springs is $1,000. Variable cost
for spring material is $5 per unit.
s = 10
f = 1,000
v=5
Number of spring sets sold = X
Profits = sX – f – vX
If sales
l = 0,
0 profits
fit = –$1,000
$1 000
If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)]
= $4,000
$4 000
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Pritchett’s
Pritchett
s Precious Time Pieces
Companies are often interested in their break
break--even
point
i t (BEP).
(BEP) Th
The BEP iis th
the number
b off units
it sold
ld
that will result in $0 profit.
0 = sX – f – vX,
or
0 = ((s – v)X
) –f
Solving for X, we have
f = (s
( – v)X
)
f
X= s–v
BEP =
Fixed cost
(Selling price per unit) – (Variable cost per unit)
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Pritchett’s
Pritchett
s Precious Time Pieces
Companies are often interested in their break
break--even
point
i t (BEP).
(BEP) Th
The BEP iis th
the number
b off units
it sold
ld
BEP for Pritchett’s Precious Time Pieces
that will result in $0 profit.
$1,000/($10
000/($10
= –200
0 BEP
= sX –= f$1
– vX,
or – 0$5)
= ((s
v)X
) units
–f
Salesfor
of less
200 units of rebuilt springs
Solving
X, wethan
have
will result in a loss
f = (s
( – v)X
)
Sales of over 200 unitsfof rebuilt springs will
result in a profit X =
s–v
BEP =
Fixed cost
(Selling price per unit) – (Variable cost per unit)
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Advantages
g of Mathematical Modeling
g
1. Models can accurately represent reality
1
2. Models can help a decision maker
formulate problems
3. Models can give us insight and information
y in
4. Models can save time and money
decision making and problem solving
5. A model may be the only way to solve large
or complex
l problems
bl
in
i a timely
ti l fashion
f hi
6. A model can be used to communicate
problems and solutions to others
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Models Categorized by Risk
„ Mathematical models that do not involve
risk are called deterministic models
„ We know all the values used in the model
with complete certainty
„ Mathematical models that involve risk,
chance, or uncertainty are called
probabilistic models
„ Values used in the model are estimates
based on probabilities
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Computers and Spreadsheet Models
QM for Windows
„ An easy to use
decision support
system for use in
POM and QM
courses
„ This is the main
menu of
quantitative
models
Program 1.1
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Computers and Spreadsheet Models
Excel QM’s Main Menu (2003)
„ Works automatically within Excel spreadsheets
Program 1.2A
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Computers and Spreadsheet Models
Excel QM’s
QM s
Main Menu
(2007)
Program 1.2B
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Computers and Spreadsheet Models
Excel QM
for the
BreakEven
Problem
Program 1.3A
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Computers and Spreadsheet Models
Excel QM
Solution
to the
Break
BreakEven
Problem
Program 1.3B
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Computers and Spreadsheet Models
Using
Goal Seek
in the
Break
BreakEven
Problem
Program 1.4
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Possible Problems in the
Q
Quantitative
tit ti Analysis
A l i Approach
A
h
Defining the problem
„ Problems are not easily identified
„ Conflicting viewpoints
„ Impact on other departments
„ Beginning assumptions
„ Solution outdated
Developing a model
„ Fitting the textbook models
„ Understanding the model
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Possible Problems in the
Q
Quantitative
tit ti Analysis
A l i Approach
A
h
Acquiring input data
„ Using accounting data
„ Validity of data
Developing a solution
„ Hard-to-understand mathematics
„ Only one answer is limiting
Testing the solution
Analyzing the results
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Implementation –
N tJ
Not
Justt th
the Fi
Finall Step
St
Lack of commitment and resistance
to change
„ Management may fear the use of
formal analysis processes will
reduce their decision-making power
„ Action-oriented managers may want
“quick and dirty” techniques
„ Management
M
t supportt and
d user
involvement are important
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Implementation –
N tJ
Not
Justt th
the Fi
Finall Step
St
Lack of commitment by quantitative
analysts
„ An analysts should be involved with
the problem and care about the
solution
„ Analysts should work with users and
take their feelings into account
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Summary
„ Quantitative analysis is a scientific
approach to decision making
„ The approach includes
„ Defining the problem
„ Acquiring input data
„ Developing a solution
„ Testing the solution
„ Analyzing the results
„ Implementing the results
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Summary
„ Potential p
problems include
„ Conflicting viewpoints
„ The impact on other departments
„ Beginning
B i i assumptions
ti
„ Outdated solutions
„ Fitting textbook models
„ Understanding the model
„ Acquiring good input data
„ Hard-to-understand mathematics
„ Obtaining only one answer
„ Testing the solution
„ Analyzing the results
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Summary
„ Implementation is not the final step
„ Problems can occur because of
„ Lack
L k off commitment
i
to the
h approach
h
„ Resistance to change
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