:To assess your ability to
apply the terminology of decision making to describe business problems
compare and contrast deterministic and probabilistic models
Action Items
A situation in which you could use post optimality analysis (also known as sensitivity analysis).
Chapter 1
Introduction to
Quantitative Analysis
To accompany
Quantitative Analysis for Management, Eleventh Edition,
by Render, Stair, and Hanna
Power Point slides created by Brian Peterson
Learning Objectives
After completing this chapter, students will be able to:
1. Describe the quantitative analysis approach
2. Understand the application of quantitative
analysis in a real situation
3. Describe the use of modeling in quantitative
analysis
4. Use computers and spreadsheet models to
perform quantitative analysis
5. Discuss possible problems in using
quantitative analysis
6. Perform a break-even analysis
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Chapter Outline
1.1 Introduction
1.2 What Is Quantitative Analysis?
1.3 The Quantitative Analysis Approach
1.4 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
Analysis Approach
1.7 Implementation — Not Just the Final Step
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1-4
1.1 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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Examples of Quantitative Analyses
◼ In the mid 1990s, Taco Bell saved over $150
million using forecasting and scheduling
quantitative analysis models.
◼ NBC television increased revenues by over
$200 million between 1996 and 2000 by using
quantitative analysis to develop better sales
plans.
◼ Continental Airlines saved over $40 million in
2001 using quantitative analysis models to
quickly recover from weather delays and other
disruptions.
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1.2 What is Quantitative Analysis?
Quantitative analysis is a scientific approach
to managerial decision making in which raw
data are processed and manipulated to
produce meaningful information.
Raw Data
Quantitative
Analysis
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Meaningful
Information
1-7
1.2 What is Quantitative Analysis?
◼ Quantitative factors are data that can be
accurately calculated. Examples include:
◼ Different investment alternatives
◼ Interest rates
◼ Inventory levels
◼ Demand
◼ Labor cost
◼ Qualitative factors are more difficult to
quantify but affect the decision process.
Examples include:
◼ The weather
◼ State and federal legislation
◼ Technological breakthroughs.
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1.3 The Quantitative Analysis Approach
Defining the Problem
Figure 1.1
Developing a Model
Acquiring Input Data
Developing a Solution
Testing the Solution
Analyzing the Results
Implementing the Results
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Defining the Problem
Develop a clear and concise statement that
gives direction and meaning to subsequent
steps.
◼ This may be the most important and difficult
step.
◼ It is essential to go beyond symptoms and
identify true causes.
◼ It 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
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Schematic
models
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Developing a Model
Models generally contain variables
(controllable and uncontrollable) and
parameters.
◼ Controllable variables are the decision
variables and are generally unknown.
◼
How many items should be ordered for inventory?
◼ Parameters are known quantities that are a
part of the model.
◼
What is the holding cost of the inventory?
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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 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 may be resistant to 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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1.4 How To Develop a Quantitative
Analysis Model
A mathematical model of profit:
Profit = Revenue – Expenses
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1.4 How To Develop a Quantitative
Analysis Model
Expenses can be represented as the sum of fixed and
variable costs. 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
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v = variable cost per unit
X = number of units sold
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1.4 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
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v = variable cost per unit
X = number of units sold
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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 = -f = –$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 the 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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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.
◼ All of the values used in the model are
known 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 (2010)
◼ Works automatically within Excel spreadsheets
Program 1.2
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Computers and Spreadsheet Models
Selecting
Break-Even
Analysis in
Excel QM
Program 1.3A
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Computers and Spreadsheet Models
BreakEven
Analysis
in Excel
QM
Program 1.3B
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1.5 Use computers and spreadsheet
models to perform quantitative analysis
Using Goal
Seek in the
BreakEven
Problem
Program 1.4
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1.6 Possible Problems in the
Quantitative Analysis Approach
Defining the problem
◼ Problems may not be easily identified.
◼ There may be conflicting viewpoints
◼ There may be an impact on other
departments.
◼ Beginning assumptions may lead to a
particular conclusion.
◼ The solution may be outdated.
Developing a model
◼ Manager’s perception may not fit a textbook
model.
◼ There is a trade-off between complexity and
ease of understanding.
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1.6 Possible Problems in the
Quantitative Analysis Approach
Acquiring accurate input data
◼ Accounting data may not be collected for
quantitative problems.
◼ The validity of the data may be suspect.
Developing an appropriate solution
◼ The mathematics may be hard to understand.
◼ Having only one answer may be limiting.
Testing the solution for validity
Analyzing the results in terms of the whole
organization
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1.7 Implementation –
Not Just the Final Step
There may be an institutional 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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1.7 Implementation –
Not Just the Final Step
There may be a lack of commitment
by quantitative analysts.
◼ 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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Copyright
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in
any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise, without the prior
written permission of the publisher. Printed in the United
States of America.
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