computer supported design of flexible kanban system for a multi-stage multi-product manufac

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ComputerSupportedDesignofFlexibleKanbanSystemForAmulti-stageMulti-productManufacturingLines1M.Al-Tahat*,A.Liverani*,F.Persiani**DIEM-UniversityofBologna,V.leRisorgimento2,Bologna40136,Italy.Tel:+39(051)2093452,Fax:+39(051)2093412AbstractAmulti-stagemulti-productKanbanbasedproductionlinewithvariabledemandisconsidered.Theproblemis,tostudyandanalyzetheprocessofdesignaneffectiveFlexibleKanbanpullSystemFKS,andtodesignanddevelopamethodforthepurposeofdeterminingtheoptimumKanbannumbersandtheoptimumKanbansizesofeachmanufacturingstageforanyselectedproductsamongtheproductmix,andtodynamicallyadjusttheKanbannumbersandsizes,tomatchthecurrentoperationconditionsofaproductionline.AnewlyFKScomputerprogramispresented,itisdevelopedforMicrosoftofficeaccessdatabaseandVisualBasicforApplicationVBAplatforms.Thesystemconsistsofthreemainphases,theseare;productionlinedatabase(KnowledgeRepresentationPhase);mathematicalmodelingoftheproductionline;andthecodesofthedevelopedcomputerprogram(InferenceEngine).Thesephasesarelinkedtogethertointegratetheflowofproductionwithitssupply–chainproductmanagement.Anumericalsimulationexamplearecarriedoutwhichallowstudyingthefeasibilityofapplyingthesystem,anditsinfluenceinsynchronizingproductiontoactualdemandanddecreasingproductioncost.FurthermorethesensitivityoftheFKSinresponsetothedifferentproductionvariableshavebeenstudiedandpresented.Ithasbeensuccessfullyconcludedthatthesystemisrealizableandabletocreateasoundresultsforanyreceivedorder.Keywords:KanbanSystem;DesignofManufacturingSystem;SystemsDesign;OperationsPlanningandControl.1.IntroductionTheJITbasicideafirstintroducedon50’sandthesystembeenpopularizedbyTaiichiOhnowhowastryingtodeterminehowthestructureofthesupermarketcouldbeappliedtoamanufacturingenvironment.In1953,TaiichiOhnoappliedtheprinciplesofjust-in-timeandKanbansignalstoToyota’smachiningfactory.TheseprinciplesweresosuccessfulthattheywereappliedtootherfactoriesandtheToyotaKanbansystemevolved.Kanbanstandsforkan-“card”,ban-“signal”.AKanbanisasignalcardcontainingalltheinformationrequiredtobedoneonaproductateachstagealongitspathtocompletionandwhichpartsareneededatsubsequentprocesses.ThesecardsareusedtocontrolWork-In-ProgressWIP,productionandinventoryflow.AKanbanSystemallowsacompanytouseJITproductionandorderingsystems,whichallow1E-mailaddress:mohammad.al-tahat@mail.ing.unibo.it1 themtominimizetheirinventorieswhilestillsatisfyingcustomerdemands.AKanbansystemconsistsofasetofthesecards,withonebeingallocatedforeachpartbeingmanufactured,thattravelbetweenprecedingandsubsequentprocesses.Mr.TaiichiOhno,avicepresidentofToyota,toadapttochangesindemand,andthereforeproductionmorequickly,developedtheKanbansystem.TheKanbanconcepthasaattractedwideinterestduringthelastdecades,andalargeamountofresearchpapersonKanban-basedproductionsystemshasappearedintheliterature,throughthese,literaturehavebeenfoundtoconsiderthedifferentcharacteristicsoftheKanbansystems.SomeofthesepapersconsideringthegeneralphilosophyandreviewofKanban,othersdealwiththemodelingofsuchsystems,aswillasthedevelopmentofmathematicaland/orsimulationmodels.Evaluating,improvingandoptimizingKanbansystemsperformance,aswillasminimizingproductioncost,havebeenaddressedinseveralotherresearchpapers.Also,thereisanimmenseliteraturediscussingandanalyzingthedifferentissuesindeterminingthenumberofkanbans,determiningtheKanbanssizesanddevelopingcontrolschemeforthepurposeofdynamicallyaadjustedandallocatedthenewrequiredkanbans.Moreworkshavebeenconsideredaproductionsystemwithahybridpush/pullproductionsystem;furthermore,aconsiderableattentionhasbeendevotedtothequestionhowothercommonpolicieswouldbehavecomparedtoaKanbanpolicy.2.TheProblemandObjectivesInconventionalproductionlines,rawmaterialswhichissupplyinstantaneouslytheproductionprocessenterthefirstworkstationinlineandthework-in-processWIPflowsthroughtheintermediateworkstationsuntilthefinalfinishedproductdepartstheproductionlinethroughthelastworkstation.InaproductionlineoperatingunderaJust-In-Timeproductionpolicy,theoutputrateofthelastworkstationisgenerallydictatedbythecustomerdemandofthefinalfinishedproductsdemand.Inthisresearch,amulti-stagemultiproductproductionlineisconsideredtoworkunderaJITdeliverypolicy,whichiscontrolledbyaKanbanmechanismbetweentheworkstations.Theproblemis,tostudyandanalyzetheprocessofdesignaneffectiveFlexibleKanbanpullSystemFKS,topresentaKanbanbasedmanufacturingmodel,andtodesignanddevelopamethodforthepurposeofdeterminingtheoptimumKanbannumberstobecirculatedbetweentheworkstations,theoptimumKanbansizes,thenumberofrawmaterialorders,andnumberofshipmentoffinishedproductsforanyselectedproductamongtheproductsmix,andtodynamicallyadjustedtheKanbansystemparameterstoovercomethechangesinthemanufacturingresourcesandoperationsparameters.OncetheparametersofKanbansystemaredetermined,anumericalsimulationwillbecarriedoutwhichallowstostudyandaanalyzethesensitivityofthesystemduetothechangesintheproductionsystemvariablessuchasproductionratedemandratesKanbanwithdrawalcostholdingcostsandmanyothervariable,andtheirinfluencesinsynchronizingproductiontoactualdemandwiththelowestpossibleproductioncost.2.1.ProblemFormulation2 Weconsideramulti-stagesmultiproductsmanufacturingsystemthatprocuresrawmaterials,processestoconvertthemintofinishedproducts,andfinallydeliversthecompletedproductstothecustomers.Theproductionlineiscomposedofmultiworkstations,andaKanbansystemoperatesbetweentwoconsecutiveworkstations.TheKanbanareusedprimarilyasmechanismstofeedbackinformationfromthesucceedingtotheprecedingworkstation,andtotransportmaterialstothesucceedingworkstation.Therawmaterialsarestorednearthedemandpointsontheproductionlinesuchthattheyareavailableimmediatelywheneverneeded.Therawmaterialsarereplenishedatthefirstworkstationoftheproductionlineinstantaneouslyfromasupplierinbatchesatdifferentintervalsoftime.Thedemandoffinishedgoodsatthelastworkstationchangingwithtime.TheproductionrateatanystageisassumedtobeatleastequaltothedemandrateoftheWIPatthatworkstationsoastoensurenoshortageofWIPorthefinalproduct.Sincethedemandofthefinalproductischangingovertime,thesimilarpatternofdemandoftheWIPisreflectedattheintermediatestagesaswell.Becauseofthechangingindemandovertime,thenumberofKanbanateachWIPareasplaysaroleinthetransportingtheWIPfrompreviousstationtothesucceedingstation.ThequantityofWIPtransportedpershipmentislesswiththehighernumberofKanbanincurringlowerinventorycostofWIPtothenextstationandmorecosttotheKanbansystemduetohighernumberofKanban.Ontheotherhand,thequantityofWIPtransportedpershipmentishigherwiththefewernumberofKanbanincurringhigherinventorycostofWIPtothenextstationandlowercosttotheKanbansystemduetofewernumberofKanbanemployedbetweenthestations.Therefore,theseconflictingcharacteristicsofoperationsoftheKanbansystembetweenthestagesresultsinadecisionstrategyofchoosingtheoptimalnumberofKanbanateachWIParea.TheaimofthisstudyistodesignaJIToperationstrategyforthesysteminordertominimizethetotalcostduetoorderingtherawmaterials,storingthem,holdingtheWIPinventory,andfinallydeliveringthemtothebuyers.2.1.1.NotationTomodeltheinteractionsofthedemandoffinishedgoods,rawmaterialandproductionresourcesthefollowingnotationhavebeenused:QR:Rawmaterialordered(Units/Cycle),H:HoldingcostofinventoryatthejthWIParea($/Units/UnitTime),jH:Averageholdingcostofrawmaterials($/Units/UnitTime),RH:Averageholdingcostoffinishedproducts($/Units/UnitTime),FK:NumberofkanbansatthejthKanbanstage(WIParea),jC:Kanbancontainersize,K:Manufacturingshipmentcost($/Batch),FK:Averageorderingcostofrawmaterial($/Order),RW:CostofwithdrawingKanbanfromstagej-1tostagej($/Kanban),jN:NumberofWIPareasintheproductionlinen:Numbersofordersofrawmaterials,3 m:Numberoffullshipmentsoffinishedgoodsfromthelaststation,L:Leadtime(TimeUnits),T:Cycletime(TimeUnits),T:Productiontimeorupdatetime(TimeUnits),1D:Demandattimet=0(Units)0D(t):Demandrateoffinishedgoodsattimet.D:Demandattheendofperiodi(Units)iD:Demandattheendoftheproductioncycle(Units/Cycle)Fw:Rateofchangeofdemandoffinishedgoods(Units/UnitTime)P:Productionrateattimet=0(Units)0p:RateofchangeofProductionperunittime(Units/UnitTime)M:Totalnumbersofproductstobeproducedontheline,u:Istheproductuamongtheproductmixwhere(u=1,....M),B(u):Numberofchangeovertimes(set-times)forproductu,CT(u):Changeovertimeforproductu(UnitTime),CO(u):Changeovercostforproductuperoneset-up($/set-up),OEE:Overallequipmenteffectiveness(%)MTC:Totalproductioncostforproducingproductu($).(n)(u)2.1.2.ModelingAssumptionsThemodelintroducedherehasbeendesignedtosimulatetheintroductionofmultiproductsontoamultiworkstationsproductionlineinapredeterminedsequenceaccordingtothefollowingassumptions;(1)Atanytime,therewillbenoshortagesallowedatanystageinthesystem(p³w);(2)TheWIPareas(Kanbanstages)areassumedtobelargeenoughtoaccommodatetheWIPinventory;(3)Thereisaninstantaneousreplenishmentofrawmaterialsatthefirstworkstationforeachkindofproducts;(4)Thefinaldemandofthefinishedproductsisassumedtoincreaselinearlywithtime.Theadvantageofmodelingwithlineardemandisthatitcananalyzesystemwithincreasing,constantordecreasingdemandofproductsatthetimeofitsmarketintroduction,persistentdemandandlosingthemarketincompetition,respectively.Anotheradvantageisthatitcanroughlycapturethelifecyclepatternofdemandofaproduct;(5)ThequantityofmaterialsconsumedduringtheproductionperiodTisequaltotheamountofrawmaterialssuppliedduringthe1timeperiodTforone-to-oneconversionratio(i.e.,¦=D/Q=1);(6)Each1FRworkstationisconsideredasanequivalentsingleprocessingserver,whichcanprocessesonlyonecontaineratatimeonetypeofproducts;(7)Agenericithstage,consistsof:(a)Aworkstationwithoneprocessingcenter;(b)ProductionKanbanpostcollectingkanabnswaitingforfullcontainersfromtheprecedingstage;(c)Adownstreambuffer,wherefullcontainerswithwithdrawalKanbanatoutputqueueawaitforrequestingkanbansfromthenextstage;(d)Anupstreambuffer,whichcollectfullcontainerwithproductionKanbanwaitingtobeprocessedattheiworkstation;(8)Materialfromeachworkstationmovedtoonlyoneadjoiningth4 workstation;(9)Materialsvisitprocessingstagesonlyonceanditnevercomesagaintothatstage.3.TheDevelopedFlexibleKanbanSystem(FKS.)Inareal-lifeMultistagesmultiproductsmanufacturingenvironment,theKanbansystemissubjectedtovarioustypesofuncertaintiessuchasstochasticvariabledemand,inequalityandmultiplicationsoforderedproducts,productionrates,setupandchangeovertimeetc.Inthissection,anewlydevelopedKanbansystemisdiscussedwhichisusedtodynamicallyandsystematicallymanipulatetheminimumnumbersofKanbaninordertooffsettheblockingandstarvationcausedbythesaiduncertaintiesduringaproductioncycle.ThenewsystemistermedaFlexibleKanbanSystemFKS.ThestepsoftheworkaredetailedandananalysisofFKSisdemonstratedusinganexamples.3.1.SystemArchitectureAsmentionedpreviously,thenewlydevelopedFKSisconsistmainlyofthefollowingthreepartscomponents,theseare;mathematicalmodelingoftheproductionsystem;productionsystemdatabase;thecodeswhichiscontroltheeventsandtheproceduresoftheproductionsystemandtheuserinterface.ThesecomponentsarelinkedtogethertoformtheoverallstructureoftheFKSsysteminthewayshowninFig.1.SystemProductionModelSystemInputOutputInferenceEngineProductionDatabaseUserInterfaceFig.1.OverallstructureofFKS.VisualbasicVBcodesandStructuredQueryLanguagesSQLcodeshavebeenusedtodeveloptheinterfacebetweenfunctionalpartsofthesystem.Thisarrangementhelpsindevelopingeachfunctionalpartseparatelyaswewilljustifyinthefollowingsections.3.1.1.TheNewlyDevelopedProductionModelThemaingoaloftheneededmodelistofindtheoptimalnumberofrawmaterialorders,Kanbanemployedbetweentheworkstations,andbatchesnumbersforproductionoffinishedgoods.Manyformulashavebeenfoundon[2-8]asabasis5 forKanbancalculations.OneofthebestbasicfoundationforKanbansystemseekssingle-productmultistageslinesisgivenbySarkerandBhaba[1],Sarkerhasderivedthefollowingproductionmodelwhichseekssingleproductmulti-stagesMlinesintermsofcostfunctionTC(n)equation(1)fornordersofrawmaterials,Kjkanbansinthestagejthofproduction(j=1,...,N),andmshipments(lots)offinishedproducts.Asabasestohismodelheassumedthatthecomponentofthetotalcostarethecostoffinishedgoods,inventoryCostofwork-in-processinventoryandCostofrawmaterialinventorythereforehedevelopedandsolvedthefollowingmodelforsingleproductproductionlines.ì2æHPT2HpT3öNæaöüTCM=çR01+R1÷ï1+açj÷ï+(n)ç2n2T3n2T÷íavgåçb÷ýèøïîj=1èjøïþ3ì3ì3üHpTïNæaöüïHpTïNæaöï…(1)R1çj÷R1çj÷í1+aavgåç÷ý-3í1+aavgåç÷ý+3nTïj=1èbjøïþ6nTïîj=1èbjøïþîìïNæböüïjnKRí1+bavgåçç÷÷ý+mKF+ïîj=1èajøïþ23HæPTpT(n-1)pTöFç011()1÷+-QT-T-nP-Tç26R102÷èøWheretheproductiontimeandtheproductioncycletimeT;Tcanbe1calculatedbyequation(2)andequation(3)respectively2-D±D+2*w*Q00RT=…(2)w2-P±P+2*p*DT=00F…(3)1pNHNWåjåjj=1HR,j=1KR.…(4)a=b=avgavgNNHWa=j,b=j…(5)jjHKRR*TheoptimalnumberofsetupsmandtheoptimalnumberofkanbansKatj**stagejcanbecalculatedusingtherelationshipsbetweenm,nandKinequation(6)jandequation(7).æHWöK=n*çRJ÷…(6)jç÷KHèRjø2nP+(n-1)pT01m=-1…(7)2D+wT0T=m*L…(8)WherethereareMproductsmovingthroughNworkstationsandwherethereisachangeoverinvolved,thecalculationsbecomemorecomplex,however,theaabovebasicformulasremainsvalidwithsomemodifications.Thefirstrequirementneededtosolvetheabovemodelistodeterminethelead-timeforeachproduct6 L(u)(u=1,...M);thiswillreflectthefrequencywithwhicheachproductisrun.Manyfactorsshouldbetakenintoconsiderationssuchas;OverallEquipmentEffectiveness(OEE=Availability*SpeedUtilisation*QualityRate)andnumbersofset-upsforaproductB(U)(u=1,...M)belongstothenewcomingorder,sequencingofproductionandChangeoverTimeforeachproductCT(u=1,...M).(U)InthismanufacturingenvironmentthewayofcalculatedtheKanbansystemparametersisdifferent.Thecomponentsofthetotalcostarethecostoffinishedgoods,inventorycostofwork-in-processinventory,costofrawmaterialinventoryandchangeovercostduetoproductionchangingfromonetypeofproducttoanothertype.Theoverallproductionlineefficiencyandthechangeovertimewhentogglingfromacertainproducttypetoanother,mustbeconsideredforeachtypeofproductsamongtheproductionorder.Thereforeforanyproductuwhere(u=1,...M)whichispassedthoughtN(u)workstation,cycletimeT(u),productiontimeT1(u),lead-timeML(u),andtotalproductioncostTCn(u)canbecalculatedbyequations(9),(10),(11)and(12)respectively.æ-D±2D2+2*w*Qö1ç0(u)0(u)(u)R(u)÷…(9)T=*+(CT*B)(u)ç(u)(u)÷OEEçw(u)÷èøæ-P±2P2+2*p*Dö1ç0(u)0(u)(u)F(u)÷…(10)T1=*+(CT*B)(u)ç(u)(u)÷OEEçp(u)÷èøT(u)=m(u)*L(u).…(11)ì2æHPT2HpT3öN(u)æaöüTCM=çR0(u)1(u)+R(u)1(u)÷ï1+açj(u)÷ï+(n)(u)ç2n2T3n2T÷íavg(u)åçb÷ýè(u)(u)(u)(u)øïj=1èj(u)øïþî3ìì3üHpTN(u)æaöüHpT3N(u)æaö.…(12)R(u)1(u)ï1+açj(u)÷ï-R(u)1(u)ï1+açj(u)÷ï+íavg(u)åç÷ý3íavg(u)åç÷ý3n(u)T(u)ïj=1èbj(u)øïþ6nuT(u)ïj=1èbj(u)øïþîîìïN(u)æböüïnK1+bçj(u)÷+mK+CO*B+(u)Ríavg(u)åça÷ý(u)F(u)(u)(u)ïîj=1èj(u)øïþ23HFæçP0(u)T1(u)p(u)T1(u)()(n(u)-1)p(u)T1(u)ö÷ç+-QR(u)T(u)-T1(u)-n(u)P0(u)-÷T(u)è262øN(u)HN(u)Wj(u)j(u)ååj=1HR,j=1KR...(13)a=bavg=avg(u)N(u)N(u)(u)HWj(u)j(u)a=,b=…(14)j(u)Hj(u)KRR7 m3ì3üd(TC(n)())Hp()TN(u)æaöuRu1(u)ïçj(u)÷ï=4í1+aavg(u)åç÷ý-dn2n(u)T(u)ïj=1èbj(u)øïîþ223ìN()üæHPT2Hp()TöuæaöçR0(u)1(u)Ru1(u)÷ïçj(u)÷ï…(15)ç3+3÷í1+aavg(u)åç÷ý-èn(u)T(u)3n(u)T(u)øïj=1èbj(u)øïîþHpT3ìN(u)æaöüR(u)1(u)ï1+açj(u)÷ï+3n2Tíavg(u)åçb÷ý(u)(u)ïîj=1èj(u)øïþìN(u)æböüHæpTöKï1+bçj(u)÷ï-FçP-(u)1(u)÷Ríavg(u)åça÷ýTç0(u)2÷ïîj=1èj(u)øïþ(u)èø(m)Whenthevalueoftheequation(15)abovesettozero,dTC(n)andthe=0dn*equationsolvedforn(u),theoptimalnumberofkanbansKj(u)forproductuatstage*j.Alsotheoptimalnumberofshipmentsmforthesameproductcanbe(u)(u)**calculatedusingtherelationshipsbetweenm(u),n(u)andKasdemonstratedinj(u)equation(16),(17)and(18)respectively.æHWöK=n*çRJ(u)÷…(16)j(u)(u)ç÷KHèRj(u)øDF(u)C=…(17)j(u)Kj(u)2n(u)P0(u)+(n(u)-1)p(u)T1(u)…(18)m(u)=-12D+wT0(u)(u)(u)Solvingthemodifiedmodelneedsthedeterminationofalltypesofindependentinputvariables,whichavailableintheproductiondatabase,thesevariablesareclassifiedinto;productslevelvariablesandproductionlinelevelvariables.Productlevelvariables(Processingdetails)thatrelatedtotheproductitself,eachproducthasit’sownindependentvariables.Foreachproduct(u)where(u=1,...M)thefollowingparametersshouldbedeterminedandfedtothedevelopedsystemasaninputvariables,theseare,M,CO(u),w(u),D0(u),DF(u)P0(u),p(u),KF(u),QR(u),N(u),CT(u),B(u)and,Hj(u),Wj(u)"j=1,....N(u).Productionlinelevelvariables(Generaldata)areindependentinputvariablesrelatedtothemanufacturingline,allproductshavethesamevaluesofthesevariables,thesevariablessuchasH,K,H,andOEE.RRFOntheotherhand,theoutputparametersofthemodeln,T,T,m,M(u)(u)1(u)(u)Kj(u)"j(u)=1,....N(u),Cj(u)"j(u)=1,....N(u)andTC(n)(u)couldbeCalculatedbytheinferenceengineofthedevelopedKanbansystemaccordingtoequations(15),(9),(10),(18),(16),(17),and(12)respectivelyassumingthatOEE=100%and(B=1,"u=1,...M).(u)8 3.1.2.InferenceEngineandArithmeticManipulationThemostpowerfultoolofFKSfordevelopmentandgenerationresultofourProposedmodelthroughperformingsophisticatedtargetdrivendatamanipulations,istheinferenceengine,whichallowsrapidconstructionsofsensitiveend-userinterfaces.ThispartoftheFKShasbeendesignedfromthestarttoruninafastwayaccordingtothedailyvariationsindemand,productionresourcesandlimitations.Itintegratesthedatabasewiththeproductionmodel,computesandmanagesdeferentparametervaluesintheircorrespondingqueries.ThesequerieshavebeendesignusingSQLformatandclassifiedintotwotypes;auxiliaryquerieslike“avgsum”,“Fafa”,“Xaxa”,etc;andmainquerylike“StagesDetails”,“minimumcost”,etc.Simply,thisphaseretrievesinputdatafromthedatabase,performstheneededcalculationsandholdstheirvalues,andfinallygeneratesanoutputresult.TheinputvariabledataarethedifferentindependentvariablesoftheFKS,whichare;storedinthedatabaseelementstheseareclassifiedinto;linelevelvariablesorgeneralvariables;andProductlevelvariablesordetailsvariables.Generalindependentvariablesarefoundedinthecostingelementstable,theyarefixedforalltypesofproductionthesevariablesareHR,KR,HF,andOEE.Whilethedetailsvariablesarepo,p,QR,ju,Hj,Wj,,w,DF,D0,n,PP,Bu,CO,CT,u.Thedetailsvariablesarefoundedinthedemanddatatable,productiondatatable,processplanstableandchangeoverdatatable.Inadditiontothatthereisaninputfixeddatainthegenerallevelwhichincludes;productID;productname;customerID;productdescription;unitweight;productdimensions;andremarks,thatrepresentalltheneededinformationaboutanyproduct.Therelatedtablesforthesedataare,drawingtablewhichincludesinformationaboutdrawings,customerstablethatincludedataaboutcustomerssuchas;customerID;companyname;contactnameandcompleteaddresses,employeestable,productmixtableandplansassignmentstable.TheoutputoftheFKShasbeendesignedtoholdthevaluesoftheKanbansystemparameters(thedependentparameters),whicharecorrespondingtotheabove-mentionedinputvariables,thedesiredoutputKanbanparametersaren,m,T,T,TC,K,C"j=1....N&"u=1...M.uuu1uujj3.1.3.ProductionDatabaseAnaccessdatabaseisoneofthemostusefulenvironmentsinwhichtostoreandretrievedataandanidealtooltomanageandmanipulatethatdata.Thebenefitsofawell-structureddatabaseareinfinite,withincreasedefficiencyandtimesavingbeingmoreimmediatelyobviousbenefits.In-depthinvestigationofwhattheKanban-basedproductionlineis,howitworks,andwhatmanualsystemsithasinplace,willitsemployeesneedaccesstothedatabasefromoutinthefield?.Theseandacrowdofotherquestionshavebeenaskedduringtheinitialinvestigation.Theanswersenabledustodesign,create,integrate,anddeveloptheFKSdatabase,whichhasbeenconstructedfromforms,queries,reports,andmenusinanefficientandexclusivewaywiththeminimumdataduplicationandtheeasierrepresentationoftheuser'sperspective.TheFKSdatabasedescribesthedetailsoftheproductioninthetwolevels,productslevelandlinelevel(Factorylevel).Thesemanufacturingknowledgeincludetheproductioncapabilitieswithitscorrespondingcostsrates,Manufacturingprocessplansandtheirdetails,informationaboutdemandand9 demandrate,informationaboutsetupandchangeoverwhenchangingfromproducttoanotherinthemultiproductenvironment,andmanyothergeneralinformation.AlltheseinformationisstoredinMicrosoftaccessdatabaseinatableformattoberetrievedlaterbythesystemtogeneratequeriesthatarenecessarywhenapplyingtheproposedmodeltoperformtherequiredcalculations.3.2.ExpressiveSimulationExamplesTodemonstratemorehowtheFKSworkformulti-stagemultiproductKanbansystem.Weassumedaproductionorderoftwoproducts,product330withtheplanPP=“first”andproduct440withtheplanPP=“Second”,theline330440parametersassumedtobeasH=$1/unit/day,H=$0.5/unit/day,K=$150/order,FRROEE=100%.Thetechnicaldatarelatedtothemanufacturingknowhowofproduct330showsthatthisitemisproducedwitha5-stageprocessplan.ThisplaniscalledFirst(KanbanstagesN330=5),forthisplanB=1changeover,CO=$20/changeover,330330CT=2unittime,K=$135/batchp=10units/day,P=100units/day,330F330330o330H=[0.1,0.02,0.04,0.06,0.08]$/unit/day,andW=[18,18,18,18,18]$/Kanbanj330j330(withdrawalcost).Fromthereceivedordersitfoundthatthedemandchangeratew330=8units/day,andtherequiredquantityDF=2500unitswithaninitialquantity330ofD=80units/day.0330RunningFKSforthattheresultwillbeasfollows.Forj=1,2,3,4,5,330a=[0.2,0.04,0.08,0.12,0.16],b=[0.12,0.12,0.12,0.12,0.12].AsshowninFig.2j330j330theuptimeT1330=16.5days,thecycletimeT330=18.9days.Theminimaltotalcostisreachedforthevalueofn330=2attotalcostTC330=$1349.9withnumberofshipmentsm=1,theKanbannumbersandsizesareshowninFig.3.330Kj=[2,1,3,2,2],CK=[2083,417,833,1250,1667]unitperKanban,thatmeansthat330j330thenumbersofkanbanscirculatedintheKanbanstages1-5are2,1,3,2and2,respectively.ThereasonforvaryingnumberofkanbansatdifferentstagesunderliesintheKanbanorderingandinventorycostsateachstageintheline.EqualityofthecostparametersatdifferentstageswouldhaveresultedinequalnumberofkanbansineachWIParea.ItmaybenotedherethatthemaximumnumberofkanbansiscirculatedinthethirdKanbanstage,whichisRunningFKSforthattheresultwillbeasfollows.Forj=1,2,3,4,5,a=[0.2,0.04,0.08,0.12,0.16],330j330bj=[0.12,0.12,0.12,0.12,0.12].AsshowninFig.2theuptimeT1=16.5days,the330330cycletimeT=18.9days.Theminimaltotalcostisreachedforthevalueofn=2330330attotalcostTC330=$1349.9withnumberofshipmentsm330=1,theKanbannumbersandsizesareshowninFig.3.Kj=[2,1,3,2,2],CK=[2083,417,833,1250,1667]330j330unitperKanban,thatmeansthatthenumbersofkanbanscirculatedintheKanbanstages1-5are2,1,3,2and2,respectively.ThereasonforvaryingnumberofkanbansatdifferentstagesunderliesintheKanbanorderingandinventorycostsateachstageintheline.EqualityofthecostparametersatdifferentstageswouldhaveresultedinequalnumberofkanbansineachWIParea.Itmaybenotedherethatthe10 maximumnumberofkanbansiscirculatedinthethirdKanbanstage,whichisindicatedbyK.Thus,theoptimalnumberofkanbansinthefifthKanbanstageis3330K=3.3330Toproducethesecondordereditem(product440);technicaldatarelatedshowsthatthisitemisproducedwitha3-stageprocessplan.TheplaniscalledSecond(KanbanstagesN440=3),forthisplanB=1changeover,CO=$20per440440changeover,CT=2unittime,K=$135/batchp=20units/day,P=100440F440440o440units/day,H=[0.2,0.1,0.1]$/unit/day,andW=[150,160,195]$/Kanbanj440j440(withdrawalcost).Fromthereceivedordersofproductionitfoundthatthedemandchangeratew=10units/day,andtherequiredquantityforthisiteminthis440orderD=3000unitswithaninitialquantityofD=80units/day.F4400440NoofNoofProductionMinimumPRODUCTProcessCycleTimeOrdersShipmentsTimeTotalCostNOPlan(T=Days)(n)(m)(T1=Days)(TC=$)330FIRST2218.9316.491349.90440Second2219.7715.035896.50Fig.2.FKSoutputresultforn,m,T,T1andTC.AsshowninthepreviousfiguretheuptimeT=15.0days,thecycletime1440T=19.8days.Theminimaltotalcostisreachedforthevalueofn=2attotalcost440440TC440=$5897withnumberofshipmentsm440=1.ButtheKanbannumbersandsizesareKj=[5,11,13],CK=[600,273,231]asshowninthefig.3bellow,thatmeans440j440thenumbersofkanbanscirculatedintheKanbanstages1-3are5,11and13,respectively.ThemaximumnumberofKanbaniscirculatedinthethirdKanbanstage,whichisindicatedbyK.Thus,theoptimalnumberofKanbaninthethird3440KanbanstageisK=13.theaboveresultexplanationareshowninFig.2andinFig.34403asanoutputresultfortheFKS.NoofPRODUCTProcessStageSizeofKANBANKANBANNOPlan(j)(Cj=Unit)K(j)330FIRST122083330FIRST26417330FIRST33833330FIRST421250330FIRST521667440Second15600440Second211273440Second313231Fig.3.FKSoutputresultforKanbannumbersandsizes.11 4.ConclusionsandFutureResearch4.1DiscussionKanbantechniquehasbeenusedtoachievethegoalofJITphilosophyinaproductionenvironmenttominimizetheproductioncostsandtoimprovetheeffectivenessofproductionline.TheresearchissueconsideredhereisoneofthemainproblemsfacedKanban-basedproductionlinesthatoperateinanindustry,whichareverysusceptibletomarketdemand.Thisresearchhasconsideredtheissuesofrawmaterials,finishedgoods,changeovertime,changeovercosts,andWIPinventoryinamulti-stagemultiproductKanban-basedproductionline.ForthatwehavesuggestedanalgorithmforadjustingthedifferentKanbanfactorsinamultistage,multiproductsKanbanbased-productionline.Introducingsimpleandeffectivemultistagepullmechanismsformultipleparttypesystemsbringsthedifficultyofsharingmanufacturingresourcesbetweendifferentparttypes.Inadditiontothedecisionsofwhetherornottoproducethatwereconsidered.Thedevelopedmodelindicatesthattheissuesofrawmaterialorders,WIPinventory,finishedgoodsshipmentsandchangeoverdatahavetobeconsideredtogetherratherthanseparatelyinordertominimizethetotalcostofproduction.Theresearchhasprovedthattheseissuesaredependentononeanother.Thecostparametersofrawmaterials,changeoverbetweenproducts,WIPandfinishedgoodsdictatesthenumberandthesizesofKanbansneededatproductionstageandbatchsizesforshipments.Alogicalandconstructivelinkbetweenproductionlinedatabaseandthesuggestedproductionmodelhasbeendone,thisintegrationresultsinasatisfactoryoutputofthenewlydevelopedFKSthatshowstheimportantbenefitsofsuchintegration.4.2ConclusionsandResultsThenumericalsimulationexamplesshowthatthequalityofthesolutiongeneratedbytheFKSissatisfactory,thesenumericalexamplesleadustofollowingresults:1.ThedevelopedFKShasbeendesignedwiththegoalofbeingusedinthemulti-stagemulti-itemsKanbanbasedproductionlines;ithassuccessfullyindictedthattheconceptisrealizable.Thesystemisabletocreateasoundresultsforanygivenorder.2.ChangeoverproductiondataB,CO,CT:TheFKShasaprovedthatalluKanbanparametersK,C,n,m,T,T1,TCareincreaseasthechangeovernumberisjjincreaseandtheyareincreaseasthechangeovertime(setuptime)isincrease,ontheotherhandthechangeovercostaffectsonlythetotalcostofproduction.3.ProductionvariablesP,p:Iftheinitialproductionquantityisincrease,om,Cwillincrease,K,T1,TC,nwilldecreaseandTremainfixed.WhilethejjincreaseintheendingproductionratewilldecreaseT1,TC,increasemanddoesnotaffectK,C,n,T.ItisconcludedthatKanbanparametershavethehighestjjsensitivitytothechangesofthesetypesofproductionvariables.12 4.CostingelementsHR,HF,KR,OEE:Thechangesinthecostingelementsdonotleadtoanychangesinmorn,butthetotalcostofproductionisalwaysincreaseasanyofthecostingelementsisincrease.Alsoitisconcludedthatastherawmaterialorderingcostincrease,CincreaseandKdecrease,whiletheJjeffectofrawmaterialunitholdingcostistheopposite,astherawmaterialunitholdingcostincrease,Kincreasesand(C)decreases.Intheotherhand,alsoitisjJfoundthatastheoverallefficiencyofthelinedecreasescycletimeandproductiontimeareincreases.5.ProcessplansdetailsHj,Wj:TheincreaseofHjincreasesCjanddecreasesthevalueofKwhiletheincreaseofWhasoppositeaffects,asWisjjjincreaseCincreasesandHdecreases.jj6.DemanddataD,D,w,K:Asthecustomerdemandincreaseswith0FFtimeproductiontotalcost,Kanbannumbersforeachstage,andnumbersofneededordersareincreasewhileproductiontimeandKanbansizesaredecrease.Thechangeinfinalproductshipmentcostaffectsonlythetotalcost.Theincreaseoftheendingdemandincreasestotalcost,productiontime,KanbansizesandnumberoffinalshipmentsanddecreasesKanbannumbers.Itisconcludedalsothattheincreaseoftheinitialdemandincreasestotalcost,KanbannumbersandnumberofordersanddecreasesproductiontimeandKanbansizes.4.3RecommendationsforFutureResearchThepresentstudyislimitedtoonlyamulti-stagemultiproductKanban-basedsingle-lineproductionsystem.Itmaybeworthwhiletofocusfutureresearchonthefollowingissues:1.Thepresentresearchhasconsideredaserialproductionline.Manyissuesmayoccurwhenanassembly-typeproductionlineisconsideredwhenmultiplecomponentsarefedatone-stageforassemblyoperation.Varyingrequirementsofcomponentsfromprecedingstagestoapartatsucceedingstationswillcauseinvaryingdemandsatdifferentstagesonthemainassemblyline.Thusinter-connectingtheseriesconceptoftheKanbansystemmayresultinanimportantstudyforlargeassemblysystem.2.Varyingproductionratesatdifferentstagescapturemorerealisticaspectsofamanufacturingsystem;soinsteadofhavingproductionrateconstantavaryingratemaybeconsidered.5.References[1].BhabaR.Sarker,andChidambaramV.Balan.1999.“Operationsplanningforamulti-stageKanbansystem”.EuropeanJournalofOperationalResearch,Volume112,Issue2,Pages284-303.[2].ChristosG.PanayiotouaandChristosG.Cassandras,(1999).“OptimizationofKanban-basedmanufacturingsystems”.Automatica,Volume35,Issue9,Pages1521-1533.[3].JohnBicheno.September1999.“Kanban:TheOldandTheNew”.InstituteofOperationsManagement,Volume25–No.07.Page:22.Website.13 [4].VitoAlbino,MicheleDassisti,andGeoffreyO.Okogbaa.1995.“ApproximationapproachfortheperformanceanalysisofproductionlinesunderaKanbandiscipline”.InternationalJournalofProductionEconomics,volume40.Pages197-207.[5].BhabaR.Sarker,andChidambaramV.Balan.1996.“OperationsplanningforKanbanbetweentwoadjacentworkstations”.Computersind.Engng,Volume31,No1/2,Pages221-224.[6].ZhaoXiaoboa,andZhaoyingZhou.1999.“Asemi-opendecompositionapproachforanopenqueuingnetworkinageneralconfigurationwithaKanbanblockingmechanism”.InternationalJournalofProductionEconomics,Volumes60-61,Pages375-380.[7].A.A.Andijania.August1998.“AMulti-criterionApproachforKanbanAllocations”.Omega,Volume26,Issue4.Pages483-493.[8].MariaDiMascolo.22February1996.“AnalysisofasynchronizationstationfortheperformanceevaluationofaKanbansystemwithageneralarrivalprocessofdemands”.EuropeanJournalofOperationalResearch,Volume89,Issues1-2.Pages147-163.14