Manufacturing Systems Modeling and Analysis PDF
Preview Manufacturing Systems Modeling and Analysis
Manufacturing Systems Modeling and Analysis Second Edition · Guy L. Curry Richard M. Feldman Manufacturing Systems Modeling and Analysis Second Edition 123 Prof.GuyL.Curry RichardM.Feldman TexasA&MUniversity TexasA&MUniversity Dept.Industrial&Systems Dept.Industrial&Systems Engineering Engineering TAMU3131 TAMU3131 77843-3131CollegeStation 77843-3131CollegeStation Texas Texas 241,Zachry 241,Zachry USA USA [email protected] [email protected] ISBN978-3-642-16617-4 e-ISBN978-3-642-16618-1 DOI10.1007/978-3-642-16618-1 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2010938859 (cid:2)c Springer-VerlagBerlinHeidelberg2009,2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:eStudioCalamarS.L. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Thisbookisdedicatedtothetwoindividuals whokeepusgoing,tolerateourworkethic, andmakelifeawondrousjourney,ourwives: JerrieCurryandAliceFeldman. Preface This textbook was developed to fill the need for an accessible but comprehensive presentation of the analytical approaches for modeling and analyzing models of manufacturing and production systems. It is an out growth of the efforts within theIndustrialandSystemsEngineeringDepartmentatTexasA&Mtodevelopand teachananalyticallybasedundergraduatecourseonprobabilisticmodelingofman- ufacturingtypesystems.Thelevelofthistextbookisdirectedatundergraduateand masters students in engineering and mathematical sciences. The only prerequisite forstudentsusingthistextbookisapreviouscoursecoveringcalculus-basedprob- abilityandstatistics.Theunderlyingmethodologyisqueueingtheory,andweshall develop the basic concepts in queueing theory in sufficient detail that the reader need not have previously covered it. Queueing theory is a well-established disci- plinedatingbacktotheearly1900’sworkofA.K.Erlang,aDanishmathematician, on telephone traffic congestion. Although there are many textbooks on queueing theory,thesetextsaregenerallyorientedtothemethodologicaldevelopmentofthe fieldandexactresultsandnottothepracticalapplicationofusingapproximations inrealisticmodelingsituations.Theapplicationofqueueingtheorytomanufactur- ing type systems started with the approximation based work of Ward Whitt in the 1980’s.HispaperonQNA(aqueueingnetworkanalyzer)in1983isthebasefrom whichmostappliedmodelingeffortshaveevolved. There are several textbooks with titles similar to this book. Principle among these are: Modeling and Analysis of Manufacturing Systems by Askin and Stan- dridge, Manufacturing Systems Engineering by Stanley Gershwin, Queueing The- ory in Manufacturing Systems Analysis and Design by Papadopoulos, Heavey and Browne, Performance Analysis of Manufacturing Systems by Tayfur Altiok, StochasticModelingandAnalysisofManufacturingSystems,editedbyDavidYao, and Stochastic Models of Manufacturing Systems by Buzacott and Shanthikumar. Each of these texts, along with several others contributes greatly to the field. The book that most closely aligns with the motivation, level, and intent of this book is Factory Physics by Hopp and Spearman. Their approach and analysis is highly recommendedreading,however,theirbook’sscopeisonthelargerfieldofproduc- vii viii Preface tionandoperationsmanagement.Thus,itdoesnotprovidethedepthandbreathof analyticalmodelingproceduresthatarepresentedinthistext. Thistextisaboutthedevelopmentofanalyticalapproximationmodelsandtheir useinevaluatingfactoryperformance.Thetoolsneededfortheanalyticalapproach are fully developed. One useful non-analytical tool that is not fully developed in this textbook is simulation modeling. In practice as well as in the development of the models in this text, simulation is extensively used as a verification tool. Even thoughthedevelopmentofsimulationmodelsisonlymodestlyaddressed,wewould encourageinstructorswhousethisbookintheircurriculumafterasimulationcourse to ask students to simulate some of the homework problems so that a comparison canbemadeoftheanalysisusingthemodelspresentedherewithsimulationmod- els. By developing simulation models students will have a better understanding of themodelingassumptionsandtheaccuracyoftheanalyticalapproximations.Inad- dition several chapters include an appendix that contains instructions inthe use of MicrosoftExcelasanaidinmodelingorinbuildingsimplesimulationmodels. Forthissecondedition,suggestionsfromvariousinstructorswhohaveusedthe textbook havebeenincorporated.Becauseoftheimportanceofsimulationmodel- ing,thissecondeditionalsoincludesanintroductiontoevent-drivensimulations. Twospecialsectionsareincludedtohelpthereaderorganizethemanyconcepts containedinthetext.ImmediatelyaftertheTableofContents,wehaveincludeda symbol table that contains most of the notation used throughout the text. Second, immediatelyafterthefinalchapteraglossaryoftermsisincludedthatsummarizes thevariousdefinitionsused.Itisexpectedthatthesewillprovevaluableresources asthereaderprogressesthroughthetext. Many individuals have contributed to this book through our interactions in re- searcheffortsanddiscussions.SpecialthanksgotoProfessorMartinA.Wortman, TexasA&MUniversity,whodesignedandtaughtthefirstpresentationofthecourse forwhichthisbookwasoriginallydevelopedandProfessorBryanL.Deuermeyer, Texas A&M University, for his significant contributions to our joint research ac- tivities in this area and his continued interest and criticism. In addition several in- dividuals have helped in improving the text by using a draft copy while teaching the material to undergraduates including Eylem Tekin at Texas A&M, Natarajan GautamalsoatTexasA&M,andKevinGueatAuburnUniversity.Wealsowishto acknowledgethecontributionsofProfessorsJohnA.Fowler,ArizonaStateUniver- sity,andMarkL.Spearman,FactoryPhysics,Inc.,fortheircontinuedinteractions anddiscussionsonmodelingmanufacturingsystems.AndwethankCiriacoValdez- Flores,aco-authorofthefirstchaptercoveringbasicprobabilityforpermissionto includeitaspartofourbook.Finally,weacknowledgeourthanksthroughthewords ofthepsalmist,“GivethankstotheLord,forHeisgood;Hisloveenduresforever.” (Psalms107:1,NIV) CollegeStation,Texas GuyL.Curry March2008 RichardM.Feldman Contents 1 BasicProbabilityReview........................................ 1 1.1 BasicDefinitions........................................... 1 1.2 RandomVariablesandDistributionFunctions................... 4 1.3 MeanandVariance ......................................... 10 1.4 ImportantDistributions...................................... 13 1.5 MultivariateDistributions.................................... 24 1.6 CombinationsofRandomVariables ........................... 32 1.6.1 FixedSumofRandomVariables ....................... 32 1.6.2 RandomSumofRandomVariables ..................... 33 1.6.3 MixturesofRandomVariables ......................... 35 Appendix ...................................................... 36 Problems ...................................................... 37 References..................................................... 44 2 IntroductiontoFactoryModels.................................. 45 2.1 TheBasics ................................................ 45 2.1.1 Notation,DefinitionsandDiagrams..................... 46 2.1.2 MeasuredDataandSystemParameters .................. 49 2.2 IntroductiontoFactoryPerformance........................... 54 2.2.1 TheModelingMethod................................ 55 2.2.2 ModelUsage........................................ 58 2.2.3 ModelConclusions................................... 59 2.3 DeterministicvsStochasticModels ........................... 60 Appendix ...................................................... 62 Problems ...................................................... 65 References..................................................... 67 3 SingleWorkstationFactoryModels .............................. 69 3.1 FirstModel................................................ 69 3.2 DiagramMethodforDevelopingtheBalanceEquations .......... 73 3.3 ModelShorthandNotation................................... 76 ix x Contents 3.4 AnInfiniteCapacityModel(M/M/1) ......................... 77 3.5 MultipleServerSystemswithNon-identicalServiceRates ........ 81 3.6 UsingExponentialstoApproximateGeneralTimes .............. 85 3.6.1 ErlangProcessingTimes .............................. 85 3.6.2 ErlangInter-ArrivalTimes ............................ 87 3.6.3 PhasedInter-arrivalandProcessingTimes ............... 89 3.7 SingleServerModelApproximations.......................... 90 3.7.1 GeneralServiceDistributions .......................... 91 3.7.2 ApproximationsforG/G/1Systems .................... 93 3.7.3 ApproximationsforG/G/cSystems .................... 95 Appendix ...................................................... 97 Problems ......................................................100 References.....................................................107 4 ProcessingTimeVariability .....................................109 4.1 NaturalProcessingTimeVariability ...........................111 4.2 RandomBreakdownsandRepairsDuringProcessing ............113 4.3 Operator-MachineInteractions ...............................115 Problems ......................................................121 References.....................................................123 5 Multiple-StageSingle-ProductFactoryModels ....................125 5.1 ApproximatingtheDepartureProcessfromaWorkstation.........125 5.2 SerialSystemsDecomposition ...............................128 5.3 NonserialNetworkModels ..................................133 5.3.1 MergingInflowStreams ..............................133 5.3.2 RandomSplittingoftheDepartureStream ...............135 5.4 TheGeneralNetworkApproximationModel....................138 5.4.1 ComputingWorkstationMeanArrivalRates..............139 5.4.2 ComputingSquaredCoefficientsofVariationforArrivals ..141 Appendix ......................................................150 Problems ......................................................152 References.....................................................157 6 MultipleProductFactoryModels ................................159 6.1 ProductFlowRates.........................................160 6.2 WorkstationWorkloads......................................162 6.3 ServiceTimeCharacteristics .................................163 6.4 WorkstationPerformanceMeasures ...........................164 6.5 ProcessingStepModelingParadigm...........................167 6.5.1 ServiceTimeCharacteristics...........................170 6.5.2 PerformanceMeasures ...............................172 6.5.3 AlternateApproaches.................................174 1Section4.3canbeomittedwithoutaffectingthecontinuityoftheremainderofthetext. 2Section6.5.3canbeomittedwithoutaffectingthecontinuityoftheremainderofthetext.
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