an introduction to model building

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1、AnIntroductiontoModelBuilding1.1AnIntroductiontoModelingOperationsresearch(oftenreferredtoasmanagementscience)issimplyascientificapproachtodecisionmakingthatseekstobestdesignandoperateasystem,usuallyun-derconditionsrequiringtheallocationofscarceresources.

2、Byasystem,wemeananorganizationofinterdependentcomponentsthatworktogethertoaccomplishthegoalofthesystem.Forexample,FordMotorCompanyisasystemwhosegoalconsistsofmaximizingtheprofitthatcanbeearnedbyproducingqualityvehicles.ThetermoperationsresearchwascoinedduringWorldWa

3、rIIwhenBritishmilitaryleadersaskedscientistsandengineerstoanalyzeseveralmilitaryproblemssuchasthede-ploymentofradarandthemanagementofconvoy,bombing,antisubmarine,andminingoperations.Thescientificapproachtodecisionmakingusuallyinvolvestheuseofoneormoremathematicalmod

4、els.Amathematicalmodelisamathematicalrepresentationofanac-tualsituationthatmaybeusedtomakebetterdecisionsorsimplytounderstandtheac-tualsituationbetter.Thefollowingexampleshouldclarifymanyofthekeytermsusedtodescribemathematicalmodels.EXAMPLE1MaximizingWozacYieldEliDa

5、isyproducesWozacinhugebatchesbyheatingachemicalmixtureinapressur-izedcontainer.Eachtimeabatchisprocessed,adifferentamountofWozacisproduced.Theamountproducedistheprocessyield(measuredinpounds).DaisyisinterestedinunderstandingthefactorsthatinfluencetheyieldoftheWozacp

6、roductionprocess.De-scribeamodel-buildingprocessforthissituation.SolutionDaisyisfirstinterestedindeterminingthefactorsthatinfluencetheyieldoftheprocess.Thiswouldbereferredtoasadescriptivemodel,becauseitdescribesthebehavioroftheactualyieldasafunctionofvariousfactors.

7、Daisymightdetermine(usingregressionmethodsdiscussedinChapter24)thatthefollowingfactorsinfluenceyield:ncontainervolumeinliters(V)ncontainerpressureinmilliliters(P)ncontainertemperatureindegreesCelsius(T)nchemicalcompositionoftheprocessedmixtureIfweletA,B,andCbepercen

8、tageofmixturemadeupofchemicalsA,B,andC,thenDaisymightfind,forexample,that22(1)yield300.8V.01P.06T.001T*P.01T.001P11.7A9.4B16.4C