Introduction to Introduction to Quantitative MethodsQuantitative Methods

Introduction to Introduction to Quantitative MethodsQuantitative Methods

BBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESSBBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESS

byStephen Ong

Visiting Fellow, Birmingham City University Business School, UK

Visiting Professor, Shenzhen University

Today’s Overview Today’s Overview

Learning ObjectivesLearning Objectives

1.1. Describe the quantitative analysis approachDescribe the quantitative analysis approach

2.2. Understand the application of quantitative Understand the application of quantitative analysis in a real situationanalysis in a real situation

3.3. Describe the use of modeling in quantitative Describe the use of modeling in quantitative analysisanalysis

4.4. Use computers and spreadsheet models to Use computers and spreadsheet models to perform quantitative analysisperform quantitative analysis

5.5. Discuss possible problems in using quantitative Discuss 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:

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 Analysis How to Develop a Quantitative Analysis ModelModel

1.51.5 The Role of Computers and Spreadsheet The Role of Computers and Spreadsheet Models in the Quantitative Analysis Models in the Quantitative Analysis ApproachApproach

1.61.6 Possible Problems in the Quantitative Possible Problems in the Quantitative Analysis ApproachAnalysis Approach

1.71.7 Implementation Implementation —— Not Just the Final Step Not Just the Final Step

IntroductionIntroduction Mathematical tools have been used Mathematical tools have been used

for thousands of years.for thousands of years. Quantitative analysis can be applied Quantitative analysis can be applied

to a wide variety of problems.to a wide variety of problems. It’s not enough to just know the It’s not enough to just know the

mathematics of a technique.mathematics of a technique. One must understand the specific One must understand the specific

applicability of the technique, its applicability of the technique, its limitations, and its assumptions.limitations, and its assumptions.

The Management Science ApproachThe Management Science Approach

Management science is a scientific approach Management science is a scientific approach to solving management problems.to solving management problems.

It is used in a variety of organizations to solve It is used in a variety of organizations to solve many different types of problems.many different types of problems.

It encompasses a logical mathematical It encompasses a logical mathematical approach to problem solving.approach to problem solving.

Management science, also known as Management science, also known as operations research, quantitative methods, operations research, quantitative methods, etc., involves a philosophy of problem solving etc., involves a philosophy of problem solving in a logical manner.in a logical manner.

The Management Science ProcessThe Management Science Process

Figure 1.1 The management science process

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 Problem Definition of the Problem - problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization.

Model Construction Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.

Model Solution Model Solution - Models solved using management science techniques.

Model Implementation Model Implementation - Actual use of the model or its solution.

Type of ModelsType of Models

• DeterministicDeterministic• All relevant data known with certaintyAll relevant data known with certainty• Mathematical modelsMathematical models

• Probabilistic Probabilistic • Some data uncertainSome data uncertain• Use of probability and statisticsUse of probability and statistics

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 decision makingMay be combined in decision making

Type of ModelsType of Models

Spreadsheets in Decision Spreadsheets in Decision ModelingModeling Computers an integral part of Computers an integral part of

decision modelingdecision modeling Spreadsheets often replace Spreadsheets often replace

specialized softwarespecialized software Excel built-in functions and Excel built-in functions and

add-ins add-ins

Examples of Quantitative AnalysesExamples of Quantitative Analyses

In the mid 1990s, Taco Bell saved over $150 In the mid 1990s, Taco Bell saved over $150 million using forecasting and scheduling million using forecasting and scheduling quantitative analysis models.quantitative analysis models.

NBC television increased revenues by over NBC 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 sales quantitative analysis to develop better sales plans.plans.

Continental Airlines saved over $40 million in Continental Airlines saved over $40 million in 2001 using quantitative analysis models to 2001 using quantitative analysis models to quickly recover from weather delays and other quickly recover from weather delays and other disruptions.disruptions.

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MeaningfulMeaningfulInformationInformation

QuantitativeQuantitativeAnalysisAnalysis

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

What is Quantitative Analysis?What is Quantitative Analysis?

Raw DataRaw Data

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Quantitative factorsQuantitative factors are data that can be are 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 factors Qualitative factors are more difficult to are 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?

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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

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Defining the ProblemDefining the Problem

Develop a clear and concise statement that Develop a clear and concise statement that gives direction and meaning to subsequent gives direction and meaning to subsequent steps.steps.

This may be the most important and difficult step.This may be the most important and difficult step. It is essential to go beyond symptoms and It is essential to go beyond symptoms and

identify true causes.identify true causes. It may be necessary to concentrate on only a few It may be necessary to concentrate on only a few

of the problems – selecting the right problems is of the problems – selecting the right problems is very importantvery important

Specific and measurable objectives may have to Specific and measurable objectives may have to be developed.be developed.

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Developing a ModelDeveloping a Model

Quantitative analysis models are realistic, Quantitative analysis models are realistic, solvable, and understandable mathematical solvable, and understandable mathematical representations of a situation.representations of a situation.

There are different types of models:

$ Advertising

$ S

ales Y = b0 + b1X

Schematic models

Scale models

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Developing a ModelDeveloping a ModelModels generally contain variables Models generally contain variables (controllable and uncontrollable) and (controllable and uncontrollable) and parameters.parameters.

Controllable variables are the Controllable variables are the decision variables and are generally decision variables and are generally unknown.unknown. How many items should be ordered for How many items should be ordered for

inventory?inventory? Parameters are known quantities that Parameters are known quantities that

are a part of the model.are a part of the model. What is the holding cost of the What is the holding cost of the

inventory?inventory?

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.

Garbage Garbage InIn

ProcessProcess

Garbage Garbage OutOut

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Developing a SolutionDeveloping a Solution

The best (optimal) solution to a problem is The best (optimal) solution to a problem is found by manipulating the model variables found by manipulating the model variables until a solution is found that is practical until 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 an Using an algorithmalgorithm – a series of repeating – a series of repeating

steps to reach a solution.steps to reach a solution.

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Testing the SolutionTesting the Solution

Both input data and the model Both input data and the model should be tested for accuracy should be tested for accuracy before analysis and before analysis and implementation.implementation.

New data can be collected to test New data can be collected to test the model.the model.

Results should be logical, Results should be logical, consistent, and represent the real consistent, and represent the real situation.situation.

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Analyzing the ResultsAnalyzing the Results

Determine the implications of the solution:Determine the implications of the solution: Implementing results often requires change in Implementing results often requires change in

an organization.an organization. The impact of actions or changes needs to be The impact of actions or changes needs to be

studied and understood before studied 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.

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Implementing the ResultsImplementing the Results

Implementation incorporates the solution into Implementation 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 failed Many quantitative analysis efforts have failed

because a good, workable solution was not because a good, workable solution was not properly implemented.properly implemented.

Changes occur over time, so even successful Changes occur over time, so even successful implementations must be monitored to implementations must be monitored to determine if modifications are necessary.determine if modifications are necessary.

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Modeling in the Real WorldModeling in the Real World

Quantitative analysis models are Quantitative analysis models are used extensively by real used extensively by real organizations to solve real problems.organizations to solve real problems.

In the real world, quantitative analysis In 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 is Following the steps in the process is an important component of success.an important component of success.

Figure 1.6 Classification of management science techniques

Classification of Management Science Techniques

1.1. Linear Mathematical Programming Linear Mathematical Programming - clear - clear objective; restrictions on resources and objective; restrictions on resources and requirements; parameters known with certainty. requirements; parameters known with certainty.

2.2. Probabilistic Techniques Probabilistic Techniques - results contain - results contain uncertainty.uncertainty.

3.3. Network Techniques Network Techniques - model often formulated - model often formulated as diagram; deterministic or probabilistic. as diagram; deterministic or probabilistic.

4.4. Other Techniques Other Techniques - variety of deterministic and - variety of deterministic and probabilistic methods for specific types of problems probabilistic 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

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 by Applications journal published by Institute for Operations Research and Institute for Operations Research and Management Sciences (INFORMS) Management Sciences (INFORMS)

Business Usage of Management Science

A A decision support system decision support system is a computer-based is a computer-based system that helps decision makers address complex system that helps decision makers address complex problems that cut across different parts of an problems 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 PlanningOLAP – Online Analytical ProcessingOLAP – Online Analytical Processing

Management Science Models in Decision Support Systems (DSS)

Figure 1.7 A decision support system

Management Science ModelsDecision Support Systems (2 of 2)

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How To Develop a How To Develop a Quantitative Analysis ModelQuantitative Analysis Model

A mathematical model of profit:

Profit = Revenue – Expenses Profit = Revenue – Expenses

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How To Develop a Quantitative Analysis How 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

wheres = selling price per unit v = variable cost per unitf = fixed cost X = number of units sold

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How To Develop a Quantitative Analysis How 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 per sold) – [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

wheres = selling price per unit v = variable cost per unitf = 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

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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 = 5Number 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

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Pritchett’s Precious Time PiecesPritchett’s Precious Time Pieces

0 = 0 = sXsX – – ff – – vX, vX, or 0 = (or 0 = (s s – – vv))XX – – ff

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

Solving for Solving for XX, we have, we havef f = (= (ss – – vv))XX

XX = = ff

ss – – vv

BEP = Fixed cost

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

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Pritchett’s Precious Time PiecesPritchett’s Precious Time Pieces

0 = 0 = sXsX – – ff – – vX, vX, or 0 = (or 0 = (s s – – 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 havef = (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 will Sales 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 will Sales of over 200 units of rebuilt springs will result in a profit.result in a profit.

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

5.5. A model may be the only way to solve large A 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 communicate A model can be used to communicate problems and solutions to others.problems and solutions to others.

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Models Categorized by RiskModels Categorized by Risk

Mathematical models that do not involve Mathematical models that do not involve risk are called risk are called deterministicdeterministic models. models. All of the values used in the model are All 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 called chance, or uncertainty are called probabilisticprobabilistic models. models. Values used in the model are estimates Values used in the model are estimates

based on probabilities.based on probabilities.

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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

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Computers and Spreadsheet ModelsComputers and Spreadsheet Models

Excel QM’s Main Menu (2010) Works automatically within Excel spreadsheets

Program 1.2

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Computers and Spreadsheet ModelsComputers and Spreadsheet Models

Selecting Break-Even Analysis in Excel QM

Program 1.3A

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Computers and Spreadsheet ModelsComputers and Spreadsheet Models

Break-Even Analysis in Excel QM

Program 1.3B

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Computers and Spreadsheet ModelsComputers and Spreadsheet Models

Using Goal Seek in the Break-Even Problem

Program 1.4

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Possible Problems in the Possible 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 particular Beginning 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 textbook Manager’s perception may not fit a textbook

model.model. There is a trade-off between complexity and ease There is a trade-off between complexity and ease

of understanding.of understanding.

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Possible Problems in the Possible Problems in the Quantitative Analysis ApproachQuantitative Analysis Approach

Acquiring accurate input dataAcquiring accurate input data Accounting data may not be collected for Accounting 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 validityAnalyzing the results in terms of the whole Analyzing the results in terms of the whole

organizationorganization

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Implementation – Implementation – Not Just the Final StepNot Just the Final Step

There may be an institutional lack of There may be an institutional lack of commitment and resistance to change.commitment and resistance to change.

Management may fear the use of formal Management may fear the use of formal analysis processes will reduce their analysis processes will reduce their decision-making power.decision-making power.

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

Management support and user Management support and user involvement are important.involvement are important.

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Implementation – Implementation – Not Just the Final StepNot Just the Final Step

There may be a lack of commitment There may be a lack of commitment by quantitative analysts.by quantitative analysts.

Analysts should be involved with the Analysts should be involved with the problem and care about the solution.problem and care about the solution.

Analysts should work with users and Analysts should work with users and take their feelings into account.take their feelings into account.

TutorialTutorial

Lab Practical : Spreadsheet Lab Practical : Spreadsheet

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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)

Profit = $10X – $1,000 – $5X

Break-Even ExampleBreak-Even ExampleScreenshot 1-2A

Break-Even ExampleBreak-Even ExampleScreenshot 1-2B

Using Goal SeekUsing Goal Seek

Screenshot 1-2C

Using Goal SeekUsing Goal Seek

Screenshot 1-2C

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.

QUESTIONS?QUESTIONS?