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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                © 2009 Prentice-Hall, Inc.
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 Possible Problems in the Quantitative Analysis
    Approach
1.6 Implementation — Not Just the Final Step
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
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
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


                                     Meaningful
   Raw Data                          Information
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
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
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
Developing a Model
Quantitative analysis models are realistic, solvable,
and understandable mathematical representations
of a situation
                               X
                        b0 + b1
           $ Sales



                     Y=


                       $ Advertising

There are different types of models

  Scale                            Schematic
  models                           models
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
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
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
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
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
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
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
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
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   v = variable cost per unit
     f = fixed cost               X = number of units sold
How To Develop a Quantitative Analysis Model

Expenses can be represented as the sum of fixed and
variable costs and variable costs are the this model
                         The parameters of product of
unit costs times the number of units these are the
                         are f, v, and s as
                         inputs inherent in the model
  Profit = Revenue – (Fixed cost + Variable cost)
  Profit = (Selling price per unit)(number of of
                         The decision variable units
                         interest is X
           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
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
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)
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.
           BEP = $1,000/($10 – $5) = 200 units
           0 = sX – f – vX, or 0 = (s – v)X – f
 Solving for less than 200 units of rebuilt springs
   Sales of X, we have
   will result in a loss (s – v)X
                      f=
   Sales of over 200 units of rebuilt springs will
   result in a profit X = f
                            s–v

                            Fixed cost
  BEP =
        (Selling price per unit) – (Variable cost per unit)
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
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
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
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
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
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
Summary

• Quantitative analysis is a scientific
  approach to decision making
• The approach includes
    – Defining the problem
    – Acquiring input data
    – Developing a solution
    – Testing the solution
    – Analyzing the results
    – Implementing the results
Summary
• Potential problems include
    –   Conflicting viewpoints
    –   The impact on other departments
    –   Beginning assumptions
    –   Outdated solutions
    –   Fitting textbook models
    –   Understanding the model
    –   Acquiring good input data
    –   Hard-to-understand mathematics
    –   Obtaining only one answer
    –   Testing the solution
    –   Analyzing the results

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Chapter I-Intro to Quantitative Analysis

  • 1. 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 © 2009 Prentice-Hall, Inc.
  • 2. 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 Possible Problems in the Quantitative Analysis Approach 1.6 Implementation — Not Just the Final Step
  • 3. 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
  • 4. 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
  • 5. 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 Meaningful Raw Data Information
  • 6. 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
  • 7. 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
  • 8. 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
  • 9. Developing a Model Quantitative analysis models are realistic, solvable, and understandable mathematical representations of a situation X b0 + b1 $ Sales Y= $ Advertising There are different types of models Scale Schematic models models
  • 10. 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
  • 11. 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
  • 12. 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
  • 13. 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
  • 14. 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
  • 15. 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
  • 16. 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
  • 17. 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
  • 18. 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 v = variable cost per unit f = fixed cost X = number of units sold
  • 19. How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the this model The parameters of product of unit costs times the number of units these are the are f, v, and s as inputs inherent in the model Profit = Revenue – (Fixed cost + Variable cost) Profit = (Selling price per unit)(number of of The decision variable units interest is X 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
  • 20. 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
  • 21. 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)
  • 22. 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. BEP = $1,000/($10 – $5) = 200 units 0 = sX – f – vX, or 0 = (s – v)X – f Solving for less than 200 units of rebuilt springs Sales of X, we have will result in a loss (s – v)X f= Sales of over 200 units of rebuilt springs will result in a profit X = f s–v Fixed cost BEP = (Selling price per unit) – (Variable cost per unit)
  • 23. 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
  • 24. 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
  • 25. 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
  • 26. 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
  • 27. 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
  • 28. 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
  • 29. Summary • Quantitative analysis is a scientific approach to decision making • The approach includes – Defining the problem – Acquiring input data – Developing a solution – Testing the solution – Analyzing the results – Implementing the results
  • 30. Summary • Potential problems include – Conflicting viewpoints – The impact on other departments – Beginning assumptions – Outdated solutions – Fitting textbook models – Understanding the model – Acquiring good input data – Hard-to-understand mathematics – Obtaining only one answer – Testing the solution – Analyzing the results