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Introduction to Quantitative Analysis

To accompany Quantitative Analysis for Management, Twelfth Edition,

by Render, Stair, Hanna and Hale

Power Point slides created by Jeff Heyl

Describe the quantitative analysis approach

Understand the application of quantitative analysis in a real situation

Describe the three categories of business analytics

Describe the use of modeling in quantitative analysis

Use computers and spreadsheet models to perform quantitative analysis

Discuss possible problems in using quantitative analysis

Perform a break-even analysis

After completing this chapter, students will be able to:

LEARNING OBJECTIVES

1 – 2

1.1 Introduction

1.2 What Is Quantitative Analysis?

1.3 Business Analytics

1.4 The Quantitative Analysis Approach

1.5 How to Develop a Quantitative Analysis Model

1.6 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach

1.7 Possible Problems in the Quantitative Analysis Approach

1.8 Implementation — Not Just the Final Step

CHAPTER OUTLINE

1 – 3

Introduction

Mathematical tools have been used for thousands of years

Quantitative analysis can be applied to a wide variety of problems

Not enough to just know the mathematics of a technique

Must understand the specific applicability of the technique, its limitations, and assumptions

Successful use of quantitative techniques usually results in a solution that is timely, accurate, flexible, economical, reliable, and easy to understand and use

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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 between 1996 and 2000 by using quantitative analysis to develop better sales plans

Continental Airlines saves over $40 million every year using quantitative analysis models to quickly recover from weather delays and other disruptions

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Meaningful

Information

Quantitative

Analysis

Quantitative analysis is a scientific approach to managerial decision making in which raw data are processed and manipulated to produce meaningful information

What is Quantitative Analysis?

Raw Data

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Quantitative factors are data that can be accurately calculated

Different investment alternatives

Interest rates

Inventory levels

Demand

Labor cost

Qualitative factors are more difficult to quantify but affect the decision process

The weather

State and federal legislation

Technological breakthroughs

What is Quantitative Analysis?

1 – 7

Quantitative and qualitative factors may have different roles

Decisions based on quantitative data can be automated

Generally quantitative analysis will aid the decision-making process

Important in many areas of management

Production/Operations Management

Supply Chain Management

Business Analytics

What is Quantitative Analysis?

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Business Analytics

A data-driven approach to decision making

Large amounts of data

Information technology is very important

Statistical and quantitative analysis are used to analyze the data and provide useful information

Descriptive analytics – the study and consolidation of historical data

Predictive analytics – forecasting future outcomes based on patterns in the past data

Prescriptive analytics – the use of optimization methods

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Business Analytics

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BUSINESS ANALYTICS CATEGORY	QUANTITATIVE ANALYSIS TECHNIQUE (CHAPTER)
Descriptive analytics	Statistical measures such as means and standard deviations (Chapter 2) Statistical quality control (Chapter 15)
Predictive analytics	Decision analysis and decision trees (Chapter 3) Regression models (Chapter 4) Forecasting (Chapter 5) Project scheduling (Chapter 11) Waiting line models (Chapter 12) Simulation (Chapter 13) Markov analysis (Chapter 14)
Prescriptive analytics	Inventory models such as the economic order quantity (Chapter 6) Linear programming (Chapters 7, 8) Transportation and assignment models (Chapter 9) Integer programming, goal programming, and nonlinear programming (Chapter 10) Network models (Chapter 9)

Implementing the Results

Analyzing the Results

Testing the Solution

Developing a Solution

Acquiring Input Data

Developing a Model

The Quantitative Analysis Approach

Defining the Problem

FIGURE 1.1

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Defining the Problem

Develop a clear and concise statement of the problem to provide direction and meaning

This may be the most important and difficult step

Go beyond symptoms and identify true causes

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

Models are realistic, solvable, and understandable mathematical representations of a situation

Different types of models

$ Advertising

$ Sales

Y = b0 + b1X

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Scale models

Schematic models

Physical models

Developing a Model

Mathematical model – a set of mathematical relationships

Models generally contain variables and parameters

Controllable variables, decision variables, 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 cost of placing an order?

Required input data must be available

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Acquiring Input Data

Input data must be accurate – GIGO rule

Data may come from a variety of sources – company reports, documents, employee interviews, direct measurement, or statistical sampling

Garbage In

Process

Garbage Out

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Developing a Solution

Manipulating the model to arrive at the best (optimal) solution

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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How To Develop a Quantitative Analysis Model

A mathematical model of profit:

Profit = Revenue – Expenses

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Revenue and expenses can be expressed in different ways

How To Develop a Quantitative Analysis Model

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 v = variable cost per unit

f = fixed cost X = number of units sold

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How To Develop a Quantitative Analysis Model

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 v = variable cost per unit

f = fixed cost X = number of units sold

1 – 23

The parameters of this model are f, v, and s as these are the inputs inherent in the model

The decision variable of interest is X

Pritchett’s Precious Time Pieces

Profits = $8X – $1,000 – $3X

The company buys, sells, and repairs old clocks

Rebuilt springs sell for $8 per unit

Fixed cost of equipment to build springs is $1,000

Variable cost for spring material is $3 per unit

s = 8 f = 1,000 v = 3

Number of spring sets sold = X

If sales = 0, profits = –f = –$1,000

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If sales = 1,000, profits = [($8)(1,000) – $1,000 – ($3)(1,000)]

= $4,000

Pritchett’s Precious Time Pieces

0 = sX – f – vX, or 0 = (s – v)X – f

Companies are often interested in the break-even point (BEP), the BEP is the number of units sold that will result in $0 profit

Solving for X, we have

f = (s – v)X

X =

s – v

BEP =

Fixed cost

(Selling price per unit) – (Variable cost per unit)

1 – 25

Pritchett’s Precious Time Pieces

0 = sX – f – vX, or 0 = (s – v)X – f

Companies are often interested in the break-even point (BEP), the BEP is the number of units sold that will result in $0 profit

Solving for X, we have

f = (s – v)X

X =

s – v

BEP =

Fixed cost

(Selling price per unit) – (Variable cost per unit)

1 – 26

BEP for Pritchett’s Precious Time Pieces

BEP = $1,000/($8 – $3) = 200 units

Sales of less than 200 units of rebuilt springs will result in a loss

Sales of over 200 units of rebuilt springs will result in a profit

Advantages of Mathematical Modeling

Models can accurately represent reality

Models can help a decision maker formulate problems

Models can give us insight and information

Models can save time and money in decision making and problem solving

A model may be the only way to solve large or complex problems in a timely fashion

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 or chance are called deterministic models

All of the values used in the model are known with complete certainty

Mathematical models that involve risk or chance are called probabilistic models

Values used in the model are estimates based on probabilities

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Computers and Spreadsheet Models

POM-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

An Excel add-in

PROGRAM 1.1 – Main Menu

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Computers and Spreadsheet Models

PROGRAM 1.2A – Entering Data

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Computers and Spreadsheet Models

PROGRAM 1.2B – Solution Screen

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Computers and Spreadsheet Models

PROGRAM 1.3 – Excel Ribbon and Menu

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Computers and Spreadsheet Models

PROGRAM 1.4 – Entering Data

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Computers and Spreadsheet Models

PROGRAM 1.5 – Using Goal Seek

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Possible Problems in the Quantitative Analysis Approach

Defining the problem

Problems may not be easily identified

Conflicting viewpoints

Impact on other departments

Beginning assumptions

Solution outdated

Developing a model

Fitting the textbook models

Understanding the model

1 – 35

Possible Problems in the Quantitative Analysis Approach

Acquiring accurate input data

Using accounting data

Validity of the data

Developing a solution

Hard-to-understand mathematics

Only one answer is limiting

Testing the solution

Solutions not always intuitively obvious

Analyzing the results

How will it affect the total organization

1 – 36

Implementation – Not Just the Final Step

Lack of commitment and resistance to change

Fear formal analysis processes will reduce management’s decision-making power

Fear previous intuitive decisions exposed as inadequate

Uncomfortable with new thinking patterns

Action-oriented managers may want “quick and dirty” techniques

Management support and user involvement are important

1 – 37

Implementation – Not Just the Final Step

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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1-39

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.

1.6 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach

1.7 Possible Problems in the Quantitative Analysis Approach

1.8 Implementation—Not Just the Final Step

1.1 Introduction 1.2 What Is Quantitative Analysis? 1.3 Business Analytics 1.4 The Quantitative Analysis Approach 1.5 How to Develop a Quantitative Analysis Model

CHAPTER OUTLINE

5. Use computers and spreadsheet models to perform quantitative analysis.

6. Discuss possible problems in using quantitative analysis.

7. Perform a break-even analysis.

1. Describe the quantitative analysis approach. 2. Understand the application of quantitative analysis

in a real situation. 3. Describe the three categories of business analytics. 4. Describe the use of modeling in quantitative

analysis.

After completing this chapter, students will be able to:

Introduction to Quantitative Analysis

1CHAPTER

LEARNING OBJECTIVES

M01_REND7331_12_SE_C01_pp2.indd 1 01/10/13 9:50 AM

1.6 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach

1.7 Possible Problems in the Quantitative Analysis Approach

1.8 Implementation—Not Just the Final Step

1.1 Introduction 1.2 What Is Quantitative Analysis? 1.3 Business Analytics 1.4 The Quantitative Analysis Approach 1.5 How to Develop a Quantitative Analysis Model

CHAPTER OUTLINE

5. Use computers and spreadsheet models to perform quantitative analysis.

6. Discuss possible problems in using quantitative analysis.

7. Perform a break-even analysis.

1. Describe the quantitative analysis approach. 2. Understand the application of quantitative analysis

in a real situation. 3. Describe the three categories of business analytics. 4. Describe the use of modeling in quantitative

analysis.

After completing this chapter, students will be able to:

Introduction to Quantitative Analysis

1CHAPTER

LEARNING OBJECTIVES

M01_REND7331_12_SE_C01_pp2.indd 1 01/10/13 9:50 AM