Modelling, Break Even analysis

1. Introduction toIntroduction to
Quantitative MethodsQuantitative Methods
Introduction toIntroduction to
Quantitative MethodsQuantitative Methods
BBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESSBBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESS
by
Stephen Ong
Visiting Fellow, Birmingham City
University Business School, UK
Visiting Professor, Shenzhen

2. Today’s OverviewToday’s Overview

3. Learning ObjectivesLearning Objectives
1.1. Describe the quantitative analysis approachDescribe the quantitative analysis approach
2.2. Understand the application of quantitativeUnderstand the application of quantitative
analysis in a real situationanalysis in a real situation
3.3. Describe the use of modeling in quantitativeDescribe the use of modeling in quantitative
analysisanalysis
4.4. Use computers and spreadsheet models toUse computers and spreadsheet models to
perform quantitative analysisperform quantitative analysis
5.5. Discuss possible problems in using quantitativeDiscuss possible problems in using quantitative
analysisanalysis
6.6. Perform a break-even analysisPerform a break-even analysis
After this lecture, you will be able to:After this lecture, you will be able to:

4. OutlineOutline
1.11.1 IntroductionIntroduction
1.21.2 What Is Quantitative Analysis?What Is Quantitative Analysis?
1.31.3 The Quantitative Analysis ApproachThe Quantitative Analysis Approach
1.41.4 How to Develop a Quantitative AnalysisHow to Develop a Quantitative Analysis
ModelModel
1.51.5 The Role of Computers and SpreadsheetThe Role of Computers and Spreadsheet
Models in the Quantitative AnalysisModels in the Quantitative Analysis
ApproachApproach
1.61.6 Possible Problems in the QuantitativePossible Problems in the Quantitative
Analysis ApproachAnalysis Approach
1.71.7 ImplementationImplementation —— Not Just the Final StepNot Just the Final Step

5. IntroductionIntroduction
 Mathematical tools have been usedMathematical tools have been used
for thousands of years.for thousands of years.
 Quantitative analysis can be appliedQuantitative analysis can be applied
to a wide variety of problems.to a wide variety of problems.
 It’s not enough to just know theIt’s not enough to just know the
mathematics of a technique.mathematics of a technique.
 One must understand the specificOne must understand the specific
applicability of the technique, itsapplicability of the technique, its
limitations, and its assumptions.limitations, and its assumptions.

6. The Management Science ApproachThe Management Science Approach
 Management science is a scientific approachManagement science is a scientific approach
to solving management problems.to solving management problems.
 It is used in a variety of organizations toIt is used in a variety of organizations to
solve many different types of problems.solve many different types of problems.
 It encompasses a logical mathematicalIt encompasses a logical mathematical
approach to problem solving.approach to problem solving.
 Management science, also known asManagement science, also known as
operations research, quantitative methods,operations research, quantitative methods,
etc., involves a philosophy of problemetc., involves a philosophy of problem
solving in a logical manner.solving in a logical manner.

7. The Management Science ProcessThe Management Science Process
Figure 1.1 The management science process

8. Steps in the Management Science
Process
 ObservationObservation - Identification of a problem that exists (or
may occur soon) in a system or organization.
 Definition of the ProblemDefinition of the Problem - problem must be clearly and
consistently defined, showing its boundaries and
interactions with the objectives of the organization.
 Model ConstructionModel Construction - Development of the functional
mathematical relationships that describe the decision
variables, objective function and constraints of the
problem.
 Model SolutionModel Solution - Models solved using management
science techniques.
 Model ImplementationModel Implementation - Actual use of the model or its
solution.

9. Type of ModelsType of Models
• DeterministicDeterministic
• All relevant data known with certaintyAll relevant data known with certainty
• Mathematical modelsMathematical models
• ProbabilisticProbabilistic
• Some data uncertainSome data uncertain
• Use of probability and statisticsUse of probability and statistics

10. Type of ModelsType of Models
 QuantitativeQuantitative
 Numerical valuesNumerical values
 QualitativeQualitative
 Factors can’t be quantifiedFactors can’t be quantified
 Can be importantCan be important
 May be combined in decisionMay be combined in decision
makingmaking

11. Type of ModelsType of Models
 Spreadsheets in DecisionSpreadsheets in Decision
ModelingModeling
 Computers an integral partComputers an integral part
of decision modelingof decision modeling
 Spreadsheets often replaceSpreadsheets often replace
specialized softwarespecialized software
 Excel built-in functions andExcel built-in functions and
add-insadd-ins

12. Examples of Quantitative AnalysesExamples of Quantitative Analyses
 In the mid 1990s, Taco Bell saved over $150In the mid 1990s, Taco Bell saved over $150
million using forecasting and schedulingmillion using forecasting and scheduling
quantitative analysis models.quantitative analysis models.
 NBC television increased revenues by overNBC television increased revenues by over
$200 million between 1996 and 2000 by using$200 million between 1996 and 2000 by using
quantitative analysis to develop better salesquantitative analysis to develop better sales
plans.plans.
 Continental Airlines saved over $40 million inContinental Airlines saved over $40 million in
2001 using quantitative analysis models to2001 using quantitative analysis models to
quickly recover from weather delays and otherquickly recover from weather delays and other
disruptions.disruptions.

13. 1-13
MeaningfulMeaningful
InformationInformation
QuantitativeQuantitative
AnalysisAnalysis
Quantitative analysisQuantitative analysis is a scientific approachis a scientific approach
to managerial decision making in which rawto managerial decision making in which raw
data are processed and manipulated todata are processed and manipulated to
produce meaningful information.produce meaningful information.
What is Quantitative Analysis?What is Quantitative Analysis?
Raw DataRaw Data

14. 1-14
 Quantitative factorsQuantitative factors are data that can beare data that can be
accurately calculated. Examples include:accurately calculated. Examples include:
 Different investment alternativesDifferent investment alternatives
 Interest ratesInterest rates
 Inventory levelsInventory levels
 DemandDemand
 Labor costLabor cost
 Qualitative factorsQualitative factors are more difficult toare more difficult to
quantify but affect the decision process.quantify but affect the decision process.
Examples include:Examples include:
 The weatherThe weather
 State and federal legislationState and federal legislation
 Technological breakthroughs.Technological breakthroughs.
What is Quantitative Analysis?What is Quantitative Analysis?

15. 1-15
Implementing the ResultsImplementing the Results
Analyzing the ResultsAnalyzing the Results
TestingTesting thethe SolutionSolution
Developing a SolutionDeveloping a Solution
Acquiring Input DataAcquiring Input Data
Developing a ModelDeveloping a Model
The Quantitative Analysis ApproachThe Quantitative Analysis Approach
Defining the ProblemDefining the Problem
Figure 1.1

16. 1-16
Defining the ProblemDefining the Problem
Develop a clear and concise statement thatDevelop a clear and concise statement that
gives direction and meaning to subsequentgives direction and meaning to subsequent
steps.steps.
 This may be the most important and difficultThis may be the most important and difficult
step.step.
 It is essential to go beyond symptoms andIt is essential to go beyond symptoms and
identify true causes.identify true causes.
 It may be necessary to concentrate on only aIt may be necessary to concentrate on only a
few of the problems – selecting the rightfew of the problems – selecting the right
problems is very importantproblems is very important
 Specific and measurable objectives may haveSpecific and measurable objectives may have
to be developed.to be developed.

17. 1-17
Developing a ModelDeveloping a Model
Quantitative analysis models are realistic,Quantitative analysis models are realistic,
solvable, and understandable mathematicalsolvable, and understandable mathematical
representations of a situation.representations of a situation.
There are different types of models:
$ Advertising
$Sales
Y = b0
+ b1
X
Schematic
models
Scale
models

18. 1-18
Developing a ModelDeveloping a Model
Models generally contain variablesModels generally contain variables
(controllable and uncontrollable) and(controllable and uncontrollable) and
parameters.parameters.
 Controllable variables are theControllable variables are the
decision variables and are generallydecision variables and are generally
unknown.unknown.
 How many items should be ordered forHow many items should be ordered for
inventory?inventory?
 Parameters are known quantities thatParameters are known quantities that
are a part of the model.are a part of the model.
 What is the holding cost of theWhat is the holding cost of the
inventory?inventory?

19. Acquiring Input DataAcquiring Input Data
Input data must be accurate – GIGO rule:Input data must be accurate – GIGO rule:
Data may come from a variety of sources such as
company reports, company documents, interviews,
on-site direct measurement, or statistical sampling.
GarbageGarbage
InIn
ProcessProcess
GarbageGarbage
OutOut

20. 1-20
Developing a SolutionDeveloping a Solution
The best (optimal) solution to a problem isThe best (optimal) solution to a problem is
found by manipulating the model variablesfound by manipulating the model variables
until a solution is found that is practicaluntil a solution is found that is practical
and can be implemented.and can be implemented.
Common techniques areCommon techniques are
 SolvingSolving equations.equations.
 Trial and errorTrial and error – trying various approaches– trying various approaches
and picking the best result.and picking the best result.
 Complete enumerationComplete enumeration – trying all possible– trying all possible
values.values.
 Using anUsing an algorithmalgorithm – a series of repeating– a series of repeating
steps to reach a solution.steps to reach a solution.

21. 1-21
Testing the SolutionTesting the Solution
Both input data and the modelBoth input data and the model
should be tested for accuracyshould be tested for accuracy
before analysis andbefore analysis and
implementation.implementation.
 New data can be collected to testNew data can be collected to test
the model.the model.
 Results should be logical,Results should be logical,
consistent, and represent the realconsistent, and represent the real
situation.situation.

22. 1-22
Analyzing the ResultsAnalyzing the Results
Determine the implications of the solution:Determine the implications of the solution:
 Implementing results often requires change inImplementing results often requires change in
an organization.an organization.
 The impact of actions or changes needs to beThe impact of actions or changes needs to be
studied and understood beforestudied and understood before
implementation.implementation.
Sensitivity analysisSensitivity analysis determines
how much the results will change if
the model or input data changes.
 Sensitive models should be very thoroughly
tested.

23. 1-23
Implementing the ResultsImplementing the Results
Implementation incorporates the solution intoImplementation incorporates the solution into
the company.the company.
 Implementation can be very difficult.Implementation can be very difficult.
 People may be resistant to changes.People may be resistant to changes.
 Many quantitative analysis efforts have failedMany quantitative analysis efforts have failed
because a good, workable solution was notbecause a good, workable solution was not
properly implemented.properly implemented.
Changes occur over time, so even successfulChanges occur over time, so even successful
implementations must be monitored toimplementations must be monitored to
determine if modifications are necessary.determine if modifications are necessary.

24. 1-24
Modeling in the Real WorldModeling in the Real World
Quantitative analysis models areQuantitative analysis models are
used extensively by realused extensively by real
organizations to solve real problems.organizations to solve real problems.
 In the real world, quantitative analysisIn the real world, quantitative analysis
models can be complex, expensive,models can be complex, expensive,
and difficult to sell.and difficult to sell.
 Following the steps in the process isFollowing the steps in the process is
an important component of success.an important component of success.

25. Figure 1.6 Classification of management science techniques
Classification of Management Science
Techniques

26. 1.1. Linear Mathematical ProgrammingLinear Mathematical Programming - clear- clear
objective; restrictions on resources andobjective; restrictions on resources and
requirements; parameters known with certainty.requirements; parameters known with certainty.
2.2. Probabilistic TechniquesProbabilistic Techniques - results contain- results contain
uncertainty.uncertainty.
3.3. Network TechniquesNetwork Techniques - model often formulated- model often formulated
as diagram; deterministic or probabilistic.as diagram; deterministic or probabilistic.
4.4. Other TechniquesOther Techniques - variety of deterministic and- variety of deterministic and
probabilistic methods for specific types of problemsprobabilistic methods for specific types of problems
including forecasting, inventory, simulation,including forecasting, inventory, simulation,
multicriteria, AHP (analytic hierarchy process), etc.multicriteria, AHP (analytic hierarchy process), etc.
Characteristics of Modeling
Techniques

27.  Some application areas:Some application areas:
- Project Planning- Project Planning
- Capital Budgeting- Capital Budgeting
- Inventory Analysis- Inventory Analysis
- Production Planning- Production Planning
- Scheduling- Scheduling
 Interfaces -Interfaces - Applications journal published byApplications journal published by
Institute for Operations Research andInstitute for Operations Research and
Management Sciences (INFORMS)Management Sciences (INFORMS)
Business Usage of Management
Science

28. AA decision support systemdecision support system is a computer-basedis a computer-based
system that helps decision makers address complexsystem that helps decision makers address complex
problems that cut across different parts of anproblems that cut across different parts of an
organization and operations.organization and operations.
Features of Decision Support SystemsFeatures of Decision Support Systems
 InteractiveInteractive
 Uses databases & management science modelsUses databases & management science models
 Address “what if” questionsAddress “what if” questions
 Perform sensitivity analysisPerform sensitivity analysis
Examples include:Examples include:
ERP – Enterprise Resource PlanningERP – Enterprise Resource Planning
OLAP – Online Analytical ProcessingOLAP – Online Analytical Processing
Management Science Models in
Decision Support Systems (DSS)

29. Figure 1.7 A decision support
system
Management Science Models
Decision Support Systems (2 of 2)

30. 1-30
How To Develop aHow To Develop a
Quantitative Analysis ModelQuantitative Analysis Model
A mathematical model of profit:
Profit = Revenue – ExpensesProfit = Revenue – Expenses

31. 1-31
How To Develop a Quantitative AnalysisHow To Develop a Quantitative Analysis
ModelModel
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 =Profit = Revenue – (Fixed cost + Variable cost)Revenue – (Fixed cost + Variable cost)
Profit =Profit = (Selling price per unit)(number of units sold) –(Selling price per unit)(number of units sold) –
[Fixed cost + (Variable costs per unit)(Number[Fixed cost + (Variable costs per unit)(Number
of units sold)]of units sold)]
Profit =Profit = sXsX – [– [ff ++ vXvX]]
Profit =Profit = sXsX –– ff –– vXvX
where
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold

32. 1-32
How To Develop a Quantitative AnalysisHow To Develop a Quantitative Analysis
ModelModel
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 =Profit = Revenue – (Fixed cost + Variable cost)Revenue – (Fixed cost + Variable cost)
Profit =Profit = (Selling price per unit)(number of units(Selling price per unit)(number of units
sold) – [Fixed cost + (Variable costs persold) – [Fixed cost + (Variable costs per
unit)(Number of units sold)]unit)(Number of units sold)]
Profit =Profit = sXsX – [– [ff ++ vXvX]]
Profit =Profit = sXsX –– ff –– vXvX
where
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold
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

33. 1-33
Pritchett’s Precious Time PiecesPritchett’s Precious Time Pieces
Profits =Profits = sXsX –– ff –– vXvX
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
If sales = 0, profits = -f = –$1,000–$1,000.
If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)]
= $4,000

34. 1-34
Pritchett’s Precious Time PiecesPritchett’s Precious Time Pieces
0 =0 = sXsX –– ff –– vX,vX, or 0 = (or 0 = (ss –– vv))XX –– ff
Companies are often interested in the break-evenbreak-even
pointpoint (BEP). The BEP is the number of units sold
that will result in $0 profit.
Solving forSolving for XX, we have, we have
ff = (= (ss –– vv))XX
XX ==
ff
ss –– vv
BEP =
Fixed cost
(Selling price per unit) – (Variable cost per unit)

35. 1-35
Pritchett’s Precious Time PiecesPritchett’s Precious Time Pieces
0 =0 = sXsX –– ff –– vX,vX, or 0 = (or 0 = (ss –– vv))XX –– ff
Companies are often interested in their break-even pointbreak-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 =
f
s – v
BEP =
Fixed cost
(Selling price per unit) – (Variable cost per unit)
BEP for Pritchett’s Precious Time PiecesBEP for Pritchett’s Precious Time Pieces
BEP = $1,000/($10 – $5) = 200 unitsBEP = $1,000/($10 – $5) = 200 units
Sales of less than 200 units of rebuilt springs willSales of less than 200 units of rebuilt springs will
result in a loss.result in a loss.
Sales of over 200 units of rebuilt springs willSales of over 200 units of rebuilt springs will
result in a profit.result in a profit.

36. Advantages of Mathematical ModelingAdvantages of Mathematical Modeling
1.1. Models can accurately represent reality.Models can accurately represent reality.
2.2. Models can help a decision maker formulateModels can help a decision maker formulate
problems.problems.
3.3. Models can give us insight and information.Models can give us insight and information.
4.4. Models can save time and money inModels can save time and money in
decision making and problem solving.decision making and problem solving.
5.5. A model may be the only way to solve largeA model may be the only way to solve large
or complex problems in a timely fashion.or complex problems in a timely fashion.
6.6. A model can be used to communicateA model can be used to communicate
problems and solutions to others.problems and solutions to others.

37. 1-37
Models Categorized by RiskModels Categorized by Risk
 Mathematical models that do not involveMathematical models that do not involve
risk are calledrisk are called deterministicdeterministic models.models.
 All of the values used in the model areAll of the values used in the model are
known with complete certainty.known with complete certainty.
 Mathematical models that involve risk,Mathematical models that involve risk,
chance, or uncertainty are calledchance, or uncertainty are called
probabilisticprobabilistic models.models.
 Values used in the model are estimatesValues used in the model are estimates
based on probabilities.based on probabilities.

38. 1-38
Computers and Spreadsheet ModelsComputers 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

39. 1-39
Computers and Spreadsheet ModelsComputers and Spreadsheet Models
Excel QM’s Main Menu (2010)
 Works automatically within Excel spreadsheets
Program 1.2

40. 1-40
Computers and Spreadsheet ModelsComputers and Spreadsheet Models
Selecting
Break-Even
Analysis in
Excel QM
Program 1.3A

41. 1-41
Computers and Spreadsheet ModelsComputers and Spreadsheet Models
Break-
Even
Analysis
in Excel
QM
Program 1.3B

42. 1-42
Computers and Spreadsheet ModelsComputers and Spreadsheet Models
Using Goal
Seek in the
Break-
Even
Problem
Program 1.4

43. 1-43
Possible Problems in thePossible Problems in the
Quantitative Analysis ApproachQuantitative Analysis Approach
Defining the problemDefining the problem
 Problems may not be easily identified.Problems may not be easily identified.
 There may be conflicting viewpointsThere may be conflicting viewpoints
 There may be an impact on other departments.There may be an impact on other departments.
 Beginning assumptions may lead to a particularBeginning assumptions may lead to a particular
conclusion.conclusion.
 The solution may be outdated.The solution may be outdated.
Developing a modelDeveloping a model
 Manager’s perception may not fit a textbookManager’s perception may not fit a textbook
model.model.
 There is a trade-off between complexity and easeThere is a trade-off between complexity and ease
of understanding.of understanding.

44. 1-44
Possible Problems in thePossible Problems in the
Quantitative Analysis ApproachQuantitative Analysis Approach
Acquiring accurate input dataAcquiring accurate input data
 Accounting data may not be collected forAccounting data may not be collected for
quantitative problems.quantitative problems.
 The validity of the data may be suspect.The validity of the data may be suspect.
Developing an appropriate solutionDeveloping an appropriate solution
 The mathematics may be hard to understand.The mathematics may be hard to understand.
 Having only one answer may be limiting.Having only one answer may be limiting.
Testing the solution for validityTesting the solution for validity
Analyzing the results in terms of the wholeAnalyzing the results in terms of the whole
organizationorganization

45. 1-45
Implementation –Implementation –
Not Just the Final StepNot Just the Final Step
There may be an institutional lack ofThere may be an institutional lack of
commitment and resistance to change.commitment and resistance to change.
 Management may fear the use of formalManagement may fear the use of formal
analysis processes will reduce theiranalysis processes will reduce their
decision-making power.decision-making power.
 Action-oriented managers may wantAction-oriented managers may want
“quick and dirty” techniques.“quick and dirty” techniques.
 Management support and userManagement support and user
involvement are important.involvement are important.

46. 1-46
Implementation –Implementation –
Not Just the Final StepNot Just the Final Step
There may be a lack of commitmentThere may be a lack of commitment
by quantitative analysts.by quantitative analysts.
 Analysts should be involved with theAnalysts should be involved with the
problem and care about the solution.problem and care about the solution.
 Analysts should work with users andAnalysts should work with users and
take their feelings into account.take their feelings into account.

47. TutorialTutorial
Lab Practical : SpreadsheetLab Practical : Spreadsheet
1 - 47

48. Break-Even ExampleBreak-Even Example
 Clock repair shopClock repair shop
 Break-even on repaired springsBreak-even on repaired springs
Profit =Profit = (Selling price per unit)(Selling price per unit)
x (Number of units) – (Fixed cost)x (Number of units) – (Fixed cost)
– (Variable cost per unit)– (Variable cost per unit)
x (Number of units)x (Number of units)
ofit = $10X – $1,000 – $5X

49. Break-Even ExampleBreak-Even Example
Screenshot 1-2A

50. Break-Even ExampleBreak-Even Example
Screenshot 1-2B

51. Using Goal SeekUsing Goal Seek
Screenshot 1-2C

52. Using Goal SeekUsing Goal Seek
Screenshot 1-2C

53. Further ReadingFurther Reading
 Render, B., Stair Jr.,R.M. & Hanna, M.E.
(2013) Quantitative Analysis for
Management, Pearson, 11th
Edition
 Waters, Donald (2007) Quantitative
Methods for Business, Prentice Hall, 4th
Edition.
 Anderson D, Sweeney D, & Williams T.
(2006) Quantitative Methods For
Business Thompson Higher Education,
10th Ed.

54. QUESTIONS?QUESTIONS?