Introduction
Chapter 1
Introduction to
Quantitative Analysis
Quantitative Analysis for Management, Tenth Edition,
by Render, Stair, and Hanna
© 2008 Prentice-Hall, Inc.
Traditionally business decisions have been
based on subjective factors
Though mathematical tools have been
used for thousands of years, the formal
study of it to make management decisions
began in twentieth century
Quantitative analysis is based on numeric
data analysis, modeling and mathematical
calculations
Quantitative analysis can be used to solve
a wide variety of problems in business,
government, health care, education, …
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Introduction
What is Operations Management ?
It’s not enough to just know how the
mathematics of a technique (model) works
One must understand the specific
applicability of the technique (model), its
limitations, and its assumptions
The terms management science,
operations management or research, and
quantitative analysis are often
interchangeable
A set of activities that creates value in the
form of goods and services by carefully
managing the business operations to
produce and distribute products and
services efficiently and effectively
Increase profit …
Reduce cost …
One of three major functions (marketing,
finance, and operations) of any
organization and is integrally related to all
the other business functions
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What is Operations Management ?
What is Operations Management ?
Operations Management (OM) is
such a costly part of an organization
Operations management involves
using quantitative analysis methods
to help people analyze complicated
business processes and make good
decisions
A large percentage of the revenue of
most firms is spent in the OM function
OM provides a major opportunity for an
organization to improve its profitability
and enhance its service to society
These techniques are especially
useful for helping understand and
deal with business complexity and
uncertainty
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What is Quantitative Analysis?
Examples of Quantitative Analyses
Quantitative analysis (QA) is a scientific
approach to managerial decision making – no
whim, emotions and guesswork. The heart of
QA is the processing and manipulating of raw
data into meaningful information
Taco Bell saved over $150 million using
demand forecasting and employee
scheduling quantitative analysis models
NBC television increased revenues by over
$200 million by using quantitative analysis to
develop better sales plans for advertisers
Continental Airlines saved over $40 million
using quantitative analysis models to quickly
recover from weather delays and other
disruptions
Raw Data
Quantitative
Analysis
Meaningful
Information
Qualitative analysis involves the investigation
of factors in a decision-making problem that
cannot be quantified
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What is Quantitative Analysis?
What is Quantitative Analysis?
In most cases quantitative analysis
will be an aid to the decision-making
process.
The results of quantitative analysis
will be combined with other
(qualitative) information in making
the final decisions.
In solving real problems, both quantitative
and qualitative factors must be considered
Quantitative factors might be different
investment alternatives, interest rates,
inventory levels, demand, or labor cost
Qualitative factors such as the weather
condition, state and federal legislation, the
outcome of an election, technology
breakthroughs, etc.
may be difficult to quantify but can affect the
decision-making process
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The Quantitative Analysis Approach
1. Defining the Problem
Defining the Problem
The first step is to develop a clear and concise
statement of the problem that gives direction
and meaning to the subsequent steps
Developing a Model
This may be the most important and difficult step
It is essential to go beyond the symptoms of the
problem and identify true causes
Several problems may exist. It is necessary to
concentrate on only a few of the problems –
selecting the right problems is very important
If the problem is difficult to quantify, specific and
measurable objectives may have to be developed
(e.g. inadequate hospital health care delivery
raise # of beds, doctors, reduce waiting time …)
Acquiring Input Data
Developing a Solution
Testing the Solution
Analyzing the Results
Figure 1.1
Implementing the Results
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2. Developing a Model
2. Developing a Model
Quantitative analysis models are realistic,
solvable, and understandable mathematical
representations of a situation
QA Models generally contain variables
(controllable and uncontrollable) and
parameters
Variables are measurable quantities that
are subject to change and are generally
unknown (e.g. $ sales, $ advertising)
Controllable variables are generally the
decision variables (e.g. $ advertising)
Parameters are known quantities that are a
part of the problem (e.g. cost per second
rate for the ads)
$ Sales
Mathematic
models
$ Advertising
There are other types of models
Scale
models
Schematic
models
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3. Acquiring Input Data
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4. Developing a Solution
The best (optimal) solution to a problem
is found by manipulating the model until
a solution is found that is practical and
can be implemented
Common techniques are
Input data must be obtained for the model to make it
useful and they must be accurate – GIGO rule
Garbage
In
Solving equations
Trial and error – trying various approaches
and picking the best result
Complete enumeration – trying all possible
values
Using an algorithm – a series of repeating
steps to reach a solution
Process
Garbage
Out
Data may come from a variety of sources such as
company reports, company documents, interviews,
on-site direct measurement, or statistical sampling
The input data and model determine the
accuracy of the solution
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6. Analyzing the Results
5. Testing the Solution
Determine the implications of the solution
Both input data and the model should
be tested for accuracy before the
solution can be analyzed and
implemented
Implementing results often requires actions
and changes in an organization
The impact of actions or changes needs to
be studied and understood before
implementation
Collect additional data from a different
source to validate the accuracy of both
the model and model input data
Results should be logical, consistent,
and represent the real situation
Sensitivity analysis determines how much
the results of the analysis will change if
the model or input data changes
A model is only an approximation of reality
Sensitive models should be very thoroughly
tested to ensure their accuracy and validity
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Modeling in the Real World
7. Implementing the Results
Implementation incorporates the solution
into the company
Quantitative analysis models are used
extensively by real organizations to solve
real problems
Implementation can be very difficult
People can resist changes
Many quantitative analysis efforts have failed
because a good, workable solution was not
properly implemented
In the real world, quantitative analysis
models can be complex, expensive, and
difficult to sell
Following the steps of quantitative analysis
is an important component of success, but
not a guarantee
Changes occur over time, so even
successful implementations must be
monitored to determine if modifications are
necessary
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How To Develop a Quantitative
Analysis Model
How To Develop a Quantitative
Analysis Model
Expenses can be represented as the sum of fixed and
variable costs and variable costs are the product of
unit costs times the number of units
Developing a model is an important part
of the quantitative analysis approach
Let’s look at a simple mathematical
model of profit
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units
sold) – [Fixed cost + (Variable costs per
unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
Profit = Revenue – Expenses
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
Analysis Model
Pritchett’s Precious Time Pieces
The company buys, sells, and repairs old clocks and
clock parts. Rebuilt springs sell for $10 per unit.
Fixed cost of equipment to build springs is $1,000.
Variable cost for spring material is $5 per unit.
Expenses can be represented as the sum of fixed and
The parameters
of this
model
variable costs and variable
costs are the
product
of
are
f,
v,
and
s
as
these
are
the
unit costs times the number of units
inputs inherent in the model
Profit = Revenue – (Fixed
costX+are
Variable
cost)
Profit and
variables
Profit = (Selling price per unit)(number of units
The decision variable of
sold) – [Fixed cost + (Variable costs per
interest is X
unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
where
s = selling price per unit
f = fixed cost
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s = 10
f = 1,000
v=5
Number of spring sets sold = X
Profits = sX – f – vX = 10X – 1000 – 5X
If sales = 0, profits = –$1,000
If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)]
v = variable cost per unit
X = number of units sold
= $4,000
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Pritchett’s Precious Time Pieces
Pritchett’s Precious Time Pieces
break--even
Companies are often interested in their break
point (BEP). The BEP is the number of units sold
that will result in $0 profit.
break--even
Companies are often interested in their break
point (BEP). The BEP is the number of units sold
BEP for Pritchett’s Precious Time Pieces
that will result in $0 profit.
0 = sX – f – vX,
or
BEP
= –200
0=
sX –= f$1,000/($10
– vX, or – 0$5)
= (s
v)Xunits
–f
0 = (s – v)X – 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
Solving for X, we have
f = (s – v)X
f
X= s–v
Fixed cost
Fixed cost
BEP = (Selling price per unit) – (Variable cost per unit)
BEP = (Selling price per unit) – (Variable cost per unit)
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Bagels ‘R Us
Bagels ‘R Us
Assume you are the new owner of Bagels R Us and you want to
develop a mathematical model for your daily profits and
breakeven point. Your fixed overhead is $100 per day and your
variable costs are 0.50 per bagel (these are GREAT bagels). You
charge $1 per bagel.
f = $100, s = $1, v = $.50
BEP = f / (s – v)
BEP = $100 / ($1 – $.50)
Profits = Revenue – Expenses
(Price per Unit) ×
(Number Sold)
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BEP = 200 units
– Fixed Cost
– (Variable Cost/Unit) ×
(Number Sold)
When the number of units sold is equal to 200,
the profit is 0.
Profits = $1*Number Sold – $100 – $.50*Number Sold
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Advantages of Mathematical Modeling
Models Categorized by Risk
1. Models can accurately represent reality
2. Models can help a decision maker
formulate problems
3. Models can give us insight and information
4. Models can save time and money in
decision making and problem solving
5. A model may be the only way to solve large
or complex problems in a timely fashion
6. A model can be used to communicate
problems and solutions to others
Mathematical models that do not involve
risk are called deterministic models
We know all the values used in the model with
complete certainty (the outcome is also certain)
E.g. – profit and break-even models
Mathematical models that involve risk,
chance, or uncertainty are called
probabilistic models
Values used in the model are estimates based
on probabilities (the outcome is not certain)
E.g. – market for a new product:
good (60%), not good (40%)
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Computers and Spreadsheet Models
Computers and Spreadsheet Models
QM for Windows
Developing a solution, testing the solution,
and analyzing the results are important
steps in quantitative analysis approach
Since mathematical models are used,
these steps require mathematical
calculations.
Two computer programs can be used to
make these steps easier:
An easy to use
decision support
system for use in
POM and QM
courses
This is the main
menu of
quantitative
models
1) QM for Windows
2) Excel QM
Program 1.1
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Computers and Spreadsheet Models
Computers and Spreadsheet Models
Excel QM’s Main Menu (2003)
Excel QM’s
Main Menu
(2007)
Works automatically within Excel spreadsheets
Program 1.2A
Program 1.2B
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Computers and Spreadsheet Models
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Computers and Spreadsheet Models
Excel QM
for the
BreakEven
Problem
Excel QM
Solution
to the
BreakEven
Problem
Program 1.3A
Program 1.3B
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Possible Problems in the
Quantitative Analysis Approach
Computers and Spreadsheet Models
(Inventory
Inventory analysis example will be used)
used
Defining the problem – problems are not
easily identified
Using
Goal Seek
in the
BreakEven
Problem
Conflicting viewpoints – financial and
sales people have different view about the
inventory
Impact on other departments – inventory
is tied with cash flows and production
Beginning assumptions – problem implies
solution, e.g. inventory is too low ?
Solution outdated (the problem changed)
Program 1.4
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Possible Problems in the
Quantitative Analysis Approach
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Possible Problems in the
Quantitative Analysis Approach
Developing a model
Acquiring input data – not a simple task
Fitting the textbook models – they may
not fit a manager’s perception of a
problem (e.g. reducing holding &
ordering cost vs. cash flow & customer
satisfaction)
Understanding the model – trade-off
between the complexity and ease of
understanding (e.g. assume the demand
is known and constant, o.w. probability
need to be used)
Using accounting data – it may not
include holding & ordering costs
Validity of data – lack of “good & clean”
data
Developing a solution
Hard-to-understand mathematics –
managers tend to remain silent instead
of being critical
Only one answer is limiting – no options
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Implementation –
Not Just the Final Step
Possible Problems in the
Quantitative Analysis Approach
Testing the solution
Lack of commitment and resistance to
change from management
Complex models tend to give solutions
not so obvious to managers and tend to
be rejected
A review process is necessary to
convince the managers and correct any
errors in the models
Management may fear the use of formal
analysis processes will reduce their
decision-making power or just feel
uncomfortable about using them
Action-oriented managers may want
“quick and dirty” techniques
Management support and user
involvement are critical to the success
(manager: 98%, user: 70%, QA: 40%)
Analyzing the results
Even small changes in organization are
difficult to bring about
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Implementation –
Not Just the Final Step
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Summary
Lack of commitment by quantitative
analysts
Quantitative analysis is a scientific
approach to decision making
The approach includes
Analysts should be involved with the
problem and care about the solution
– be an integral part of the
department facing the problem
Analysts should work with users and
take their feelings into account (e.g.
not insisting on the users to follow
computer-calculated order
quantities)
Defining the problem
Developing a model
Acquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
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Summary
Summary
Potential problems include
Implementation is not the final step
Problems can occur because of
Conflicting viewpoints
The impact on other departments
Beginning assumptions
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
Lack of commitment to the approach
Resistance to change
(Homework #1: see the course website)
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