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- 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?

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