Using the definitions found in Chapter 1 of Quantitative Analysis, the Internet, and your own personal experiences, make notes on and post one example of each of the following to the class Discussion Board topic “Deterministic and Probabilistic Models”.A deterministic model;A probabilistic model; andA 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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1.1 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

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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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