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IntroductionChapter 1Introduction toQuantitative AnalysisQuantitative Analysis for Management, Tenth Edition,by Render, Stair, and Hanna 2008 Prentice-Hall, Inc.Traditionally business decisions have beenbased on subjective factorsThough mathematical tools have beenused for thousands of years, the formalstudy of it to make management decisionsbegan in twentieth centuryQuantitative analysis is based on numericdata analysis, modeling and mathematicalcalculationsQuantitative analysis can be used to solvea wide variety of problems in business,government, health care, education, 1–2IntroductionWhat is Operations Management ?It’s not enough to just know how themathematics of a technique (model) worksOne must understand the specificapplicability of the technique (model), itslimitations, and its assumptionsThe terms management science,operations management or research, andquantitative analysis are ofteninterchangeableA set of activities that creates value in theform of goods and services by carefullymanaging the business operations toproduce and distribute products andservices efficiently and effectivelyIncrease profit Reduce cost One of three major functions (marketing,finance, and operations) of anyorganization and is integrally related to allthe other business functions1–31–4

What is Operations Management ?What is Operations Management ?Operations Management (OM) issuch a costly part of an organizationOperations management involvesusing quantitative analysis methodsto help people analyze complicatedbusiness processes and make gooddecisionsA large percentage of the revenue ofmost firms is spent in the OM functionOM provides a major opportunity for anorganization to improve its profitabilityand enhance its service to societyThese techniques are especiallyuseful for helping understand anddeal with business complexity anduncertainty1–51–6What is Quantitative Analysis?Examples of Quantitative AnalysesQuantitative analysis (QA) is a scientificapproach to managerial decision making – nowhim, emotions and guesswork. The heart ofQA is the processing and manipulating of rawdata into meaningful informationTaco Bell saved over 150 million usingdemand forecasting and employeescheduling quantitative analysis modelsNBC television increased revenues by over 200 million by using quantitative analysis todevelop better sales plans for advertisersContinental Airlines saved over 40 millionusing quantitative analysis models to quicklyrecover from weather delays and otherdisruptionsRaw tative analysis involves the investigationof factors in a decision-making problem thatcannot be quantified1–71–8

What is Quantitative Analysis?What is Quantitative Analysis?In most cases quantitative analysiswill be an aid to the decision-makingprocess.The results of quantitative analysiswill be combined with other(qualitative) information in makingthe final decisions.In solving real problems, both quantitativeand qualitative factors must be consideredQuantitative factors might be differentinvestment alternatives, interest rates,inventory levels, demand, or labor costQualitative factors such as the weathercondition, state and federal legislation, theoutcome of an election, technologybreakthroughs, etc.may be difficult to quantify but can affect thedecision-making process1–91 – 10The Quantitative Analysis Approach1. Defining the ProblemDefining the ProblemThe first step is to develop a clear and concisestatement of the problem that gives directionand meaning to the subsequent stepsDeveloping a ModelThis may be the most important and difficult stepIt is essential to go beyond the symptoms of theproblem and identify true causesSeveral problems may exist. It is necessary toconcentrate on only a few of the problems –selecting the right problems is very importantIf the problem is difficult to quantify, specific andmeasurable objectives may have to be developed(e.g. inadequate hospital health care deliveryraise # of beds, doctors, reduce waiting time )Acquiring Input DataDeveloping a SolutionTesting the SolutionAnalyzing the ResultsFigure 1.1Implementing the Results1 – 111 – 12

2. Developing a Model2. Developing a ModelQuantitative analysis models are realistic,solvable, and understandable mathematicalrepresentations of a situationQA Models generally contain variables(controllable and uncontrollable) andparametersVariables are measurable quantities thatare subject to change and are generallyunknown (e.g. sales, advertising)Controllable variables are generally thedecision variables (e.g. advertising)Parameters are known quantities that are apart of the problem (e.g. cost per secondrate for the ads) SalesMathematicmodels AdvertisingThere are other types of modelsScalemodelsSchematicmodels1 – 133. Acquiring Input Data1 – 144. Developing a SolutionThe best (optimal) solution to a problemis found by manipulating the model untila solution is found that is practical andcan be implementedCommon techniques areInput data must be obtained for the model to make ituseful and they must be accurate – GIGO ruleGarbageInSolving equationsTrial and error – trying various approachesand picking the best resultComplete enumeration – trying all possiblevaluesUsing an algorithm – a series of repeatingsteps to reach a solutionProcessGarbageOutData may come from a variety of sources such ascompany reports, company documents, interviews,on-site direct measurement, or statistical samplingThe input data and model determine theaccuracy of the solution1 – 151 – 16

6. Analyzing the Results5. Testing the SolutionDetermine the implications of the solutionBoth input data and the model shouldbe tested for accuracy before thesolution can be analyzed andimplementedImplementing results often requires actionsand changes in an organizationThe impact of actions or changes needs tobe studied and understood beforeimplementationCollect additional data from a differentsource to validate the accuracy of boththe model and model input dataResults should be logical, consistent,and represent the real situationSensitivity analysis determines how muchthe results of the analysis will change ifthe model or input data changesA model is only an approximation of realitySensitive models should be very thoroughlytested to ensure their accuracy and validity1 – 171 – 18Modeling in the Real World7. Implementing the ResultsImplementation incorporates the solutioninto the companyQuantitative analysis models are usedextensively by real organizations to solvereal problemsImplementation can be very difficultPeople can resist changesMany quantitative analysis efforts have failedbecause a good, workable solution was notproperly implementedIn the real world, quantitative analysismodels can be complex, expensive, anddifficult to sellFollowing the steps of quantitative analysisis an important component of success, butnot a guaranteeChanges occur over time, so evensuccessful implementations must bemonitored to determine if modifications arenecessary1 – 191 – 20

How To Develop a QuantitativeAnalysis ModelHow To Develop a QuantitativeAnalysis ModelExpenses can be represented as the sum of fixed andvariable costs and variable costs are the product ofunit costs times the number of unitsDeveloping a model is an important partof the quantitative analysis approachLet’s look at a simple mathematicalmodel of profitProfit Revenue – (Fixed cost Variable cost)Profit (Selling price per unit)(number of unitssold) – [Fixed cost (Variable costs perunit)(Number of units sold)]Profit sX – [f vX]Profit sX – f – vXProfit Revenue – Expenseswheres selling price per unitf fixed costv variable cost per unitX number of units sold1 – 21How To Develop a QuantitativeAnalysis ModelPritchett’s Precious Time PiecesThe company buys, sells, and repairs old clocks andclock parts. 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.Expenses can be represented as the sum of fixed andThe parametersof thismodelvariable costs and variablecosts are theproductofaref,v,andsasthesearetheunit costs times the number of unitsinputs inherent in the modelProfit Revenue – (FixedcostX areVariablecost)Profit andvariablesProfit (Selling price per unit)(number of unitsThe decision variable ofsold) – [Fixed cost (Variable costs perinterest is Xunit)(Number of units sold)]Profit sX – [f vX]Profit sX – f – vXwheres selling price per unitf fixed cost1 – 22s 10f 1,000v 5Number of spring sets sold XProfits sX – f – vX 10X – 1000 – 5XIf sales 0, profits – 1,000If sales 1,000, profits [(10)(1,000) – 1,000 – (5)(1,000)]v variable cost per unitX number of units sold 4,0001 – 231 – 24

Pritchett’s Precious Time PiecesPritchett’s Precious Time Piecesbreak--evenCompanies are often interested in their breakpoint (BEP). The BEP is the number of units soldthat will result in 0 profit.break--evenCompanies are often interested in their breakpoint (BEP). The BEP is the number of units soldBEP for Pritchett’s Precious Time Piecesthat will result in 0 profit.0 sX – f – vX,orBEP –2000 sX – f 1,000/( 10– vX, or – 0 5) (sv)Xunits–f0 (s – v)X – fSalesforof less200 units of rebuilt springsSolvingX, wethanhavewill result in a lossf (s – v)XSales of over 200 unitsfof rebuilt springs willresult in a profit X s–vSolving for X, we havef (s – v)XfX s–vFixed costFixed costBEP (Selling price per unit) – (Variable cost per unit)BEP (Selling price per unit) – (Variable cost per unit)1 – 25Bagels ‘R UsBagels ‘R UsAssume you are the new owner of Bagels R Us and you want todevelop a mathematical model for your daily profits andbreakeven point. Your fixed overhead is 100 per day and yourvariable costs are 0.50 per bagel (these are GREAT bagels). Youcharge 1 per bagel.f 100, s 1, v .50BEP f / (s – v)BEP 100 / ( 1 – .50)Profits Revenue – Expenses(Price per Unit) (Number Sold)1 – 26BEP 200 units– Fixed Cost– (Variable Cost/Unit) (Number Sold)When the number of units sold is equal to 200,the profit is 0.Profits 1*Number Sold – 100 – .50*Number Sold1 – 271 – 28

Advantages of Mathematical ModelingModels Categorized by Risk1. Models can accurately represent reality2. Models can help a decision makerformulate problems3. Models can give us insight and information4. Models can save time and money indecision making and problem solving5. A model may be the only way to solve largeor complex problems in a timely fashion6. A model can be used to communicateproblems and solutions to othersMathematical models that do not involverisk are called deterministic modelsWe know all the values used in the model withcomplete certainty (the outcome is also certain)E.g. – profit and break-even modelsMathematical models that involve risk,chance, or uncertainty are calledprobabilistic modelsValues used in the model are estimates basedon probabilities (the outcome is not certain)E.g. – market for a new product:good (60%), not good (40%)1 – 291 – 30Computers and Spreadsheet ModelsComputers and Spreadsheet ModelsQM for WindowsDeveloping a solution, testing the solution,and analyzing the results are importantsteps in quantitative analysis approachSince mathematical models are used,these steps require mathematicalcalculations.Two computer programs can be used tomake these steps easier:An easy to usedecision supportsystem for use inPOM and QMcoursesThis is the mainmenu ofquantitativemodels1) QM for Windows2) Excel QMProgram 1.11 – 311 – 32

Computers and Spreadsheet ModelsComputers and Spreadsheet ModelsExcel QM’s Main Menu (2003)Excel QM’sMain Menu(2007)Works automatically within Excel spreadsheetsProgram 1.2AProgram 1.2B1 – 33Computers and Spreadsheet Models1 – 34Computers and Spreadsheet ModelsExcel QMfor theBreakEvenProblemExcel QMSolutionto theBreakEvenProblemProgram 1.3AProgram 1.3B1 – 351 – 36