Materi 2
(Chapter 2)
I ntroduction to
Quantitative
Analysis
Learning Objectives
Students will be able to:
1.
2.
3.
4.
5.
6.
Describe the quantitative
analysis (QA) approach.
Understand the application of
QA in a real situation.
Describe the use of modeling in
QA.
Use computers and spreadsheet
models to perform QA.
Discuss possible problems in
using quantitative analysis.
Perform a break-even analysis.
Chapter Outline
2.1 Introduction
2.2 What Is Quantitative Analysis
(QA)?
2.3 The QA Approach
2.4 How to Develop a QA Model
2.5 The Role of Computers and
Spreadsheet Models in the
QA Approach
2.6 Possible Problems in the QA
Approach
2.7 Implementation - Not Just the
Final Step
Introduction
 Mathematical tools have been
used for thousands of years.
 QA can be applied to a wide
variety of problems.
 One must understand the
specific applicability of the
technique, its limitations, and its
assumptions.
Examples of
Quantitative Analyses
 Taco Bell saved over $150
million using forecasting and
scheduling QA models.
 NBC increased revenues by over
$200 million by using QA to
develop better sales plans.
 Continental Airlines saved over
$40 million using QA models to
quickly recover from weather
and other disruptions.
Overview of
Quantitative Analysis
Quantitative Analysis:
A scientific approach to managerial decision
making whereby raw data are processed and
manipulated resulting in meaningful
information.
Raw Data
Quantitative
Analysis
Meaningful
Information
Qualitative Factors:
Information that may be difficult to quantify
but can affect the decision-making process
such as the weather, state, and federal
legislation.
The QA Approach:
Fig 1.1
Define
the problem
Develop
a model
Acquire
input data
Develop
a solution
Test
the solution
Analyze
the results
Implement
the results
Define the Problem
Problem Definition:
A clear and concise statement that
gives direction and meaning to the
subsequent QA steps and requires
specific, measurable objectives.
THIS MAY BE THE MOST DIFFICULT STEP!
…because true problem causes must be
identified and the relationship of the
problem to other organizational processes
must be considered.
Develop the Model
Quantitative Analysis Model:
A realistic, solvable, and understandable
mathematical statement showing the relationship
revenues
between variables.
sales
Models contain both controllable (decision variables)
and uncontrollable variables and parameters. Typically,
parameters are known quantities (salary of sales force)
while variables are unknown (sales quantity).
Acquire Data
Model Data:
Accurate input data that may come from a
variety of sources such as company reports,
company documents, interviews, on-site
direct measurement, or statistical sampling.
Garbage In
=
Garbage Out
Develop a Solution
Model Solution:
 The best model solution is found by
manipulating the model variables until a
practical and implemental solution is
obtained.
 Manipulation can be done by solving
the equation(s), trying various
approaches (trial and error), trying all
possible variables (complete
enumeration), and/or implementing an
algorithm (repeating a series of steps).
Test the Solution
Model Testing:
The collection of data
from a different source
to validate the accuracy
and completeness and
sensibility of both the
model and model input
data ~ consistency of
results is key!
Analyze the Results
Results Analysis:
Understanding actions implied by the
solution and their implications, as well
as conducting a sensitivity analysis (a
change to input values or the model) to
evaluate the impact of a change in
model parameters.
Sensitivity analyses allow the “whatifs” to be answered.
Implement the Results
Results Implementation:
The incorporation of the solution
into the company and the monitoring of
the results.
Modeling in the Real
World
Real World Models can be:
 Complex,
 expensive, and
 difficult to sell.
BUT…
Real world models are used in the real
world by real organizations to solve
real problems!
Possible Pitfalls in
Using Models
Prior to developing and implementing
models, managers should be aware of the
potential pitfalls.
Define the Problem
 Conflicting viewpoints
 Departmental impacts
 Assumptions
Develop a Model
 Fitting the model
 Understanding the model
Acquire Input Data
 Availability of data
 Validity of data
Possible Pitfalls
(Continued)
Develop a Solution
 Complex mathematics
 Solutions become quickly
outdated
Test the Solution
 Identifying appropriate test
procedures
Analyze the Results
 Holding all other conditions
constant
 Identifying cause and effect
Implement the Solution
 Selling the solution to others
Bagels R Us QA Model
Example
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 = $1Q - $100 - $.5Q
Bagels R Us QA Model
Breakeven Example
Breakeven point occurs when
Revenue = Expenses
So,
$1Q = $100 + $.5Q
Solve for Q
$1Q - .5Q = 100 => Q = 200
Where, Q = quantity of bagels sold
F = fixed cost per day of operation
V = variable cost/bagel
Breakeven Quantity = F/(P-V)
Conclusions
Models can help managers:
 Gain deeper insight into the nature of
business relationships.
 Find better ways to assess values in
such relationships; and
 See a way of reducing, or at least
understanding, uncertainty that
surrounds business plans and actions.
Conclusions
(continued)
Models:
 Are less expensive and disruptive than
experimenting with real world systems, but
may be expensive to develop and test.
 Allow “What if” questions to be asked.
 Are built for management problems and
encourage input, but may be
misunderstood due to the mathematical
complexity.
 Enforce consistency in approach.
 Require specific constraints and goals, but
tend to downplay qualitative information.
 Help communicate problem solutions to
others, but may oversimplify assumptions
and variables.
Models: The Up Side
Models:
 accurately represent reality.
 help a decision maker
understand the problem.
 save time and money in problem
solving and decision making.
 help communicate problems and
solutions to others.
 provide the only way to solve
large or complex problems in a
timely fashion.
Models: The Down Side
Models:
 may be expensive and timeconsuming to develop and test.
 are often misused and
misunderstood (and feared)
because of their mathematical
complexity.
 tend to downplay the role and
value of nonquantifiable
information.
 often have assumptions that
oversimplify the variables of the
real world.
QM for Windows
QM for Windows
Excel QM
Excel QM’s Main
Menu of Models
Excel QM’s Main Menu of
Models continued
The highlighted area shows forecasting models
The End