Chapter 1
Introduction to
Quantitative Analysis
To accompany
Quantitative Analysis for Management, Tenth Edition,
by Render, Stair, and Hanna
Power Point slides created by Jeff Heyl
© 2008 Prentice-Hall, Inc.
© 2009 Prentice-Hall, Inc.
Introduction
 Mathematical tools have been used for
thousands of years
 Quantitative analysis can be applied to
a wide variety of problems
 It’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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Need for Operations
Management
 The increased complexity of running a successful
business.
 Many large companies with complex business
processes have used OM for years to help executives
and managers make good strategic and operational
decisions.
 American Airlines and IBM have incredibly complex
operations in logistics, customer service and resource
allocation that are built on OM technologies.
 As the trend of increased business complexity moves to
smaller enterprises, OM will play vital operational and
strategic roles.
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Need for OM
 Lots of information, but no decisions.
 Enterprise resource planning (ERP) systems and the
Web have contributed to a pervasive information
environment; decision-makers have total access to
every piece of data in the organization.
 The problem is that most people need a way to
transform this wealth of data into actionable information
that helps them make good tactical and strategic
decisions.
 The role of OM decision methods is to help leverage a
company’s investment in information technology
infrastructure by providing a way to convert data into
actions.
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Need for OM
 A large nationwide bank is using OM
techniques to configure complicated
financial instruments for their customers.
 A process that previously required a human
agent and took minutes or hours to perform
is now executed automatically in seconds on
the bank’s Intranet.
 The resulting financial products are far
superior to those produced by the manual
process.
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Need for OM
 A major retail enterprise is using OM
methodology for making decisions about
customer relationship management
(CRM).
 They are using mathematical optimization to
achieve the most profitable match between a
large number of customer segments, a huge
variety of products and services, and an
expanding number of marketing and sales
channels such
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Need for OM
 Sears, Roebuck and Company
 Manages a U.S. fleet of more than 1,000 delivery
vehicles, some company owned and some not.
 The company makes more than 4 million deliveries
a year of 21,000 uniquely different items.
 It has 46 routing offices and provides the largest
home delivery service of furniture and appliances in
the United States.
 The company also operates a U.S. fleet of 12,500
service vehicles, together with an associated staff
of service technicians.
 Service demand is on the order of 15 million calls
per year and revenue generated is approximately $3
billion.
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Need for OM
 OM researchers designed a system to deal with such
variables as customer schedules and requested
performance times, time estimates for the required service,
vehicles and personnel available, skills needed, parts and
product availability and so on.
 The system was designed to automatically schedule all
facets of performance in such a way as to
 Provide accurate and convenient time windows for the
Sears customer
 Minimize costs
 Maximize certain objective measures of task
performance, including customer satisfaction.
 This effort generated a one time cost reduction of $9
million as well as ongoing savings of $42 million per year.
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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 using quantitative
analysis to develop better sales plans
 Continental Airlines saved over $40
million using quantitative analysis
models to quickly recover from weather
delays and other disruptions
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What is Quantitative Analysis?
Quantitative analysis is a scientific approach
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, demand, or labor cost
Qualitative factors such as the weather,
state and federal legislation, and
technology breakthroughs should also be
considered
 Information may be difficult to quantify but
can affect the decision-making process
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The Quantitative Analysis Approach
Defining the Problem
Developing a Model
Acquiring Input Data
Developing a Solution
Testing 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 go beyond symptoms 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 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
company reports, company documents, interviews,
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 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
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Testing the Solution
Both input data and the model should be
tested for accuracy before analysis and
implementation
 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 impact of actions or changes needs to
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
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 implementations must be
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
 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
Analysis Model
 An important part of the quantitative
analysis approach
 Let’s look at a simple mathematical
model of profit
Profit = Revenue – Expenses
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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
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
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
Expenses can be represented as the sum of fixed and
variable costs and variable
costs are the
product
of
The parameters
of this
model
unit costs times the number
units
are f, v,of
and
s as these are the
inputscost
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 of units sold)]
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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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.
Profits = Revenue - Expenses
(Price per Unit) 
(Number Sold)
- Fixed Cost
- (Variable Cost/Unit) 
(Number Sold)
Profits = $1*Number Sold - $100 - $.50*Number Sold
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Breakeven Example
f=$100, s=$1, v=$.50
X=f/(s-v)
X=100/(1-.5)
X=200
At this point, Profits are 0
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Pritchett’s Precious Time Pieces
The company buys, sells, and repairs old clocks.
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.
s = 10
f = 1,000
v=5
Number of spring sets sold = X
Profits = sX – f – vX
If sales = 0, profits = –$1,000
If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)]
= $4,000
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Pritchett’s Precious Time Pieces
Companies are often interested in their break-even
point (BEP). The BEP is the number of units sold
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
Fixed cost
BEP = (Selling price per unit) – (Variable cost per unit)
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Pritchett’s Precious Time Pieces
Companies are often interested in their break-even
point (BEP). The BEP is the number of units sold
BEP for Pritchett’s Precious Time Pieces
that will result in $0 profit.
= –200
0 BEP
= sX –= f$1,000/($10
– vX, or – 0$5)
= (s
v)Xunits
–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
Fixed cost
BEP = (Selling price per unit) – (Variable cost per unit)
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Examples
1. Selling price $1.50, cost/bagel $.80,
fixed cost $250 Breakeven point?
2. Seeking a profit of $1,000, selling
price $1.25, cost/bagel $.50, 100
sold/day. What is fixed cost?
3. What selling price is needed to
achieve a profit of $750 with a fixed
cost of $75 and variable cost of $.50
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Examples
Seeing a need for childcare in her community, Sue decided
to launch her own daycare service. Her service needed to be
affordable, so she decided to watch each child for $12 a day.
After doing her homework, Sue came up with the following
financial information:
Selling Price (per child per day) $12
Operating Expenses (per month)
Insurance 400 + Rent 200 = Total OE $600
Costs of goods sold $4.00 per unit
Meals 2 @ $1.50 (breakfast & lunch)
Snacks 2 @ $0.50
How many children will she need to watch on a monthly
basis to breakeven?
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Examples
Applying the formula, we have:
$600/($12-$4) = 75
She has to have a total of 75 children in her program over
the month to breakeven.
If she is open only 20 days per month then she needs
75/20=3.75 children per day on the average.
Expenses per month $600 + 75*$4.00 = $900
Revenue per month 75*$12 = $900
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Advantages of Mathematical Modeling
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
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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
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
BreakEven
Problem
Program 1.3B
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Computers and Spreadsheet Models
Using
Goal Seek
in the
BreakEven
Problem
Program 1.4
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Computers and Spreadsheet Models
Using
Goal Seek
in the
BreakEven
Problem
Program 1.4
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Possible Problems in the
Quantitative Analysis Approach
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
Quantitative Analysis Approach
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 –
Not Just the Final Step
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 support and user
involvement are important
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Implementation –
Not Just the Final Step
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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