TheThroughputDiagram - An Universal Model for the lIIustration, Control andSupervisionof Logistic Processes

Prat.Dr.-Ing.Hans-PeterWiendahl; Universityat Hanaver - Submittedby Prat. Dr.-Ing. K.Tnshaff (1)Receivedan January 11,1988

~ABSTRACT

Modernmanufacturingconcernsare increasinglyusing the companiesconceptsCIM, Logistics andJust-In-Timefor the permanentilIlJrovementof their flexibility, delivery periodsandscheduleobservance.In doingso, it becomesincreasinglyclearer thata generallyapplicablemodelis neededin arder to describe,representandcontrai the essential targetsof productioncontrai:i.e. LeadTime, lnventory. utilization andScheduleObservance.Sucha modelis proposedin this paper,basedonthe "FunnelModel". It is representedin mathematicalforroin the "ThroughputDiagram"or also called "FlowDiagram".Thethroughputdiagranandits applicationare explainedonthe basis of selectedproductionandassemblyworksystems. Finally, usingthe throughputdiagramand the processbuilding blocks derived therefrom,we attemptto achievethe objective of makingthe piece-goodsproductionprocessevenmoresimilar to a technical flow processo

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KEY WORDS

logistic targets, leadtime, utilization, workin process,duetime-performance,funnel model,throughputdiagram,monitoring,shopfloor controlo"

1. Introduction

Afar-reachingchangein productioncanpresentlybeobservedinali industrial countries. In additionto the introductionDf[iB'/materiaisandproductionprocesses,this principally consists of

reorganising the complete productionprocesswith a view tobeingin a position to react rapidly andflexibly to customerrequirements.

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Theguiding conceptsCIM (ComputerIntegratedManufacturing),

Logistics and Just- In-Time-Productionare today regardedasinitial solutions. A central building blockof ali theseccnceptsis ProductionPlanningandContrai (PPC). It is neverthelessbecomingincreasinglyclear that the previousworkinghypothesesandmethodsare no longeradequate,as they sti II place toa muchrelianceon formerlymoreusual procedures.It is todayfarmorenecessaryto describeproductionprocessandarder through-putin a modelwhichmathematicallydescribesandclarifies thefourcentral logistic targets of LeadTime,ScheduleObservance.lnventoryandUtilization andtheir inter-relationship.

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Thefollowingprerequisitesare necessaryfor sucha model: it

mustbe possibleto obtainthe data necessaryfor constructionof the modelfromthe normalshopdata, includingin particular

basicshopdataandfeedbacks.Themodelmustalso permitgraphicrepresentationof arder throughput,i.e. it mustbe visualizable.Lastly, it mustbe capableof numericaldescription, andthere-fere suitablefor computerapplication.

Themodeltherefore lendsitself to three possibleapplications.ForMonitori ng purposes,a "true-to-I ife" i Ilustration of arder

throughputin the formof graphsandcharacteristic figures canbeinterpreted,supportedby observanceof technicaI production

processes. The task of Oiagnosi s on the basi s of the moni torsystemis to ascertainthe causesof deviationsdetectedbetweenscheduledandactual valuesandto generateremedialmeasures.Finally, with a "proper" arder throughputmodel, it is alsopossibleto achieveproductionsequenceContraI.

2. The Flow Diagram

Theworkingprincipie of themodeldescribedconsists of consid-eringthe productionprocessas a systemof interconnectedfunnelsand illustrating the processesof input andoutputof orders

CIlulativelyover the courseof rime in the formof input andoutputcurves/1/. /

Let us first of ali considera single worksystem. This maybea machine,a craft workshop,or evena store into whichmaterialis loadedandfrom which it is dispatched. Onthe left-hand

lide of Figure 1 this worksystemis illustrated as a funnel

Annals af the CIR? VaI.37/1/1988

with incomingand outgoingorders andorders-in-hand. Onth

right-handside, the input andoutputcurvescanbe seen, illu-strating the eventsin the funnel. Theoutputcurveis plottedby cumulativelyentering the orders dispatchedtogetherwiththeir workcontentassessedin scheduledhoursaccordingto the

respective exit time point, commencingat the origin of thecoordinates. The start of the input curve is determinedby theinitial inventoryexisting in the worksystemat the beginningof the referenceperiod. Fromthis basis, the input curve is

developedby a similar methodto the outputcurve. 80thcurvestogetherdescribethe flow of orders throughthe worksystem;this representationis thereforecalled the ThroughputDiagram.Themoreaccuratethe feedbacktimepoints andthe correspordenceof scheduledtimeswith actual times, the closer the flow diagranwill be to reality. AlI capacity stages, from an individualwork station to a completefactory can be representedwithout

anychangein principie of its structure.

WorkH"

Incoming Orders

~npuIOrdersltYsD

lnventoryLevei

TimeReference Period RP

TStart TEnd

OrdersDespolched

( Oulpul Ihrs!) Funnel Formula:Invenlory

Lead Time; PidUCiion

Fi~ Derivationof a ThroughputDiagramfroma FunnelMode1.

Thenext importantstep in building themodelconsistI of repre-sentingthe four logistic targets in a flow diagramof the worksystem. Figure2 outlines this procedurein four identical flowdiagrams. Inventorycan be calculated at any time from thevertical distancebetweeninputandoutputcurve. TheLeadTimeof the orders in this workplace correspondsto the lengthof

the throughputfactors of eacharder "Ioggedoff". Describedhere as a throughputfactor of anarder in a worksystemis thesquareof lead time timesworkhaurI content. Becauseof the"swoppingover" of orderswhichmostlytakes place in the arderqueuein the workplace, the throughputfactors are not locatedbetweenthe input andoutputcurve. Utilization canberepreserited

by superimposingthe capacity curveonthe outputcurve

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Schedule Deviation can be visibly revealed by superimposing

schedule due-times on actual due-times, in the present case for

"logged-off" orderso Areas to the left of the output curveindicatea delay; areasto the right of the outputcurveindicatetoo-early completion. Inputs can BIso be representedin thesamegraphicformo

InputCurve

Inventory LeadTime

Utilization ScheduleDeviation

Figure2: GraphicIllustration of Inventory,LeadTime,Utilization andScheduleDeviationin a ThroughputDiagram.

3. Examplesof ThroughputDiagrams

To date, the commonestapplicationof the throughputdiagramisfor the graphicrepresentationof workandassemblyplaceswhichare organisedcri the job shopprincipie.

Figure 3, as a typical example,showsthe diagramof a groupofworkstations withNCmachinesln a toei andprecisionengineeringcompanyoveran investigationperiod of 16weekso Theaverage(weighted)lead time of the 35 work operationsloggedoff inthis periodof timewas23workingdays; the unweightedfigurewasaround18workingdayso (Thedifference betweenthese two

figures ist dueto the weighting(multiplication) of eachflowtime by the workcontentof the arder concerned). Sharpfluc-tuations can be seen in input andoutputtrend, dueto 1argedifferencesin workcontentand timewisebadlycontrolled input.Superimposedon this situation are frequentchangesof sequencearder, resulting in a widedispersionof flow time.

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c-E12008 Hrs~'000o~800~

600

Data Basis: NCWorkSystem61446016WeeksInvestigationPeriod

(8 Periods)35WorkOperations

200

400Output Function

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InvestigationPeriod

150 159 169179WorkDayWD209Time

70 90 110 130

Figure 3: ThroughputDiagramof a WorkPlace(PracticalExample).

In contrast, the throughputdiagramr a flexible productionsystemconsistingof four processingceMtresovera two-day

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period is seento be considerablymoreeven(Figure 4) /2/.Processingof the individual workpiecesgaverise to only veryslight dispersionof implementationtimes,with at the sametimea very lowmeanvalue.

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10"E Hrs;:g' 80.~..g60li."ij 40~VI 20

A sy1anc

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1,75 2.25 2,50 3,00Oay 3,25Time

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Figljre 4: ThroughputDiagramfor an FFS with four Processing- Centres.

Inventorytie-up in the systemis limited by the numberof availa-ble workpiece palettes in the system,andfinally, therewerescarcely any changesof sequencearder in the systemo Onlybreakdownsof individual machinetoolsled to deviationsfrom

ideal tren andconsequentlyto lesses of profit. Overall, theperformanceof the systemis characterizedby short flow timeswith little dispersionandlow inventories,with as a consequen-ce, goodscheduleobservance.Theflow performanceof anautomaticassemblysystemcanBIso be illustrated in a similar manner.Such systemsmostly consi st of automatic conveying, assembly and

test/inspection stations, flexibly interlinked by meansof a

conveyorbelt. By"flexibly"wemeanherethat, contrafito arigid interlinkage, althoughthe individual stations are syn-chronisedto the sameclock time, minar interruptions canbebalancedout by filling upor emptyingthe stock of parts locatedbetweenstations. Figure 5 illustrates the flow diagramof asection of the installations of a real assembly planto Therelative data are automaticallycollected in the plant by anexternal sensorsystemandevaluatedbymeansof a programonalinked PC. This producesthe results: MeanBreakdownInterval,MeanBreakdownDuration and MeanFlow Time /3/ o

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4. Application of the ThroughputDiagram

4.1 Monitoring

It tiasalwaysbeenpossible to monitorproductionprocessesbymeansof regularlycalculatedcharacteristic figures. Theseweremostlydefined accordingto the individual workshopandweremainly1imited to productionoutput, uti1ization andcost folla./-up. As comparedwith this, the throughputdiagrammakespossiblea generalillustration of arder flow andan intrinsically con-clusivecalculationof suchcharacteristic figures.

A systemconstructedonthat basis canbe describedas a surveil-lanceor monitoringsystem. The following structural aspectsare important:

Statementsof opinionby the productionmanagement,oonceming

capacities, togetherwith their flow times, uti1ization,scheduledeviationandinventoryare of primaryimportance.

Theclerical staff responsiblefor ordersandconsequentlyfor seles, onthe otherhand,are moreconcemedwithdeliverytime, therefore with arder lead time, duedelivery timeobservanceandorders-in-hand.

Finally, threeaccuracystagesare necessary(Short, mediumandlongterm). Short-termaccuracyis a matterof thY'Ollf1putof orders-in-handto suit time 1imits bymethodsof adjustJrentof short-termcapacity(overtime,extra shifts), aroprioritycontrol. ln themedium-term,onthe other hand,it mustbe

ensuredthat the delivery andworkplaceflow timesacceptedin job-schedulingalso tally, for whichit is necessarytoadjust capacities and inventoriesaccordingto orders re-leased. Finally, in the long-term,i t is a questionofwhethercapacitiescorrespondto the constantlychangingpro-ductionprogramme.

Characteristicfigures of this sort are evaluatedinter aIia ina real factory, by meansof a monitorsystem. Figure6 illustratestheweeklyevaluationof actual andscheduledleadtimefor alI

Overan Movements30

$cheduledOrderlead TimeActualOrderlead Time

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10U1>-"O:;;"c:~Cua. -10O~cJ1

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ScheduleDeviationon arderCompletionScheduleDeviationon arder Release

-2039 42 Week No.46 4740 41 43 44 45

.scheduledLead Time OActuallead Time I g:r~:~n ~ DeviationtlliDeveryFigure6: ContinuousAssessmentof ReferenceFigures in Pro-

duktionbymeansof a Moniter System/Bechte/.

the orders in the companyconcernedandthe scheduledeviationof arder releaseandardercompletion/4, S/. NowwhenscheduledevlatiDosoccur, the managementstaff concentrateonel iminationof the causesas Quickly as possible insteadof wastingtheirtime on suppositionsandallocatingblame. After introductionof the systemandappropriateremediarmeasures,the numberoforderstoa late wasreducedby80 Dercent inside twoyears.

4.2 Diagnosis

Experiencesto datewith monitorsystemsof this typenaveshownthat their interpretationandeffective applicationreQuiresahigh degreeof analytical capability andproductionmanagementskill. For this purpose,therefore, a diagnostic systemisneededwhichschouldbe basedon an expertsystem..Sucha diag-

nostic systemis presentlybeingdevelopedat the lnstitut frFabrikanlagen Factory EQuipmentlnstitute in collaborationwith someindustrial firms whichare alreadyusingthe monitor

systemdescribedin moredetail above,basedon the throughputdiagram. Up to the present, the structure of the systemisenvisagedas follows. Feedbacksoriginating fromthe productionprocess,concerningthe progressof workon the individual pro-duction orders, are first of alI checkedfor completenessandcorrectness, following which periodical reference values arecalculated from themfor flow time, inventory,utilization andscheduleobservance.A checkis carried out at regular intervalsto see if the referencevaluesdeviatefromttie schedulevalues

fixed by the systemuser. If the systemrecognisesthat suchdeviationsexist, it determinesthecausesbymeansof thefumeImodellogic describedin the systemandinformsthe user whichreferencevaluetiasbeenfallen short of or exceededandbywhatamount,whichcapacity groupsandorders are therebyaffectedand what were the presumablemajor causes. Finally, it isplannedthat the systemwi11proposemeasuresfor improvementofthe situation basedonthe factory rules also described/6/.

4.3 ShopFIoor Control

For permanentprocess improvementa knowledgeof the dynamicrelations betweenthe four mentionedlogistic target magnitudesis essential. The throughputdiagramalso formsan effective

basis for this. lt is first of alI necessaryto explainthedependenceof flow time on inventoryand productionoutput.Figure 7 illustrates the real flow diagramof a workplace, onwhichstraight input andoutput lines navebeensuperimposed.If the gradientof the straight input line is the sameas thatof the straight output line, the relationship applies as shownin the hatchedtriangle. Onecan see fromthis, that the meanweightedflow time is eQuaI to meaninventorydividedby meanproductionoutput. This relation describedas the so calledfunnel formulais the moreaccurate,

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b)lOADNG ACCOUNT

UP

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Figure7: Analytical Differentiation betweenLeadTime,OutputandInventoryin Production.

the less tlle averagevolumeof incomingworkdeviatesfromthe volumeof completedwork,

the less and the moreuniform is the workcontentof theindividual orders, and

467

the fewerthe sequencearderchangesin thewai ti ngqueue.

A contrai pracedurealreadyput inta effect in accardancewiththeseprapasalsis laad-arientatedarderrelease,whichcontrais

the input to warkplaces andcansequentlycontrais meanflawtimethraughmeaninventory. Figure8 clarifies thebasicconcept,again in the formof a funnelmede!.Thetheoretical principiesof the methodare documentedin comprehensibleformin /7/, andsevencommercialversionswereavailable on the marketby theendof 1987.

costu(j~~~1::: ) O>J,Requirements

..Capacity"AdjustingR:1rameter(ChangeDemandR:1ra-meter)

..LoadBarrier"AdjustingR:1rameter(Load-in~rcentageR:1ra-meter LIP)

Inventorylevei

..TIme Umit Barrier "AdjustingR:1rameter(ReleaseHorizonR:1ra-meterRH)

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Figur~8: ControlSystemAnalogyof Load-OrientatedarderRelease.

Thefunction of the methodcanbe representedin characteristic

operatingcurves(Figure9). Thetop curverepresentsproductionoutputwhenmeaninventoryin the work systemsis changedbymeansof the "load barrier" control parameter.After a suitableinventorylevei, despitea further increaseof inventory,pro-ductianwill no langerincrease,becauseali worksystemsarebusy. Onlybelowthis valueis productiondecreased,at first

graduallyandthenincreasinglyrapidly, becausewith increasingfrequencymoreandmoreworksystemsno longerhaveworkto do.At the sametimethere is a changein meanweightedflow timethroughtheworksystems.Abovethe appropriateinventoryvalue,therelationship"meanweightedflowtime= meanoutput/mean

WeightedMeanThroughputTime

MeanProduction

Practica!Minimum

TheoreticalMinimum

Inventory

Accordingto lheProductionSchedule

".-/'

/'

/,~anWeightedLeadTime

SuitableValue

Figure9: FundamentalRelationshipbetweenLeadTime,Outputand- Inventoryin Production./Bechte/.

inventory" is followed fairly closely. Belowthat value thetheoretical minimumis approached;this consists of the sumofmeanimplementationtime andmeantransport time. This timecomponentaf lead time (also knownas "processtime") cannot

also be fallen short of by aninventorywhichis similarly low.

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It is thereforea matterin practice of adjustingthe appropriateinventorylevei so that sensible utilization is achievedontheanehandand.unnecessarily high inventoriesavoidedon the other.This at thesametime producesthe practical minimumleadtime.This is achievedin practicebya gradualreductianaf theloadbarrier. Theoreticalbaseshavealso beenworkedout, however,for determiningthis value /7/. Experienceswith the methodtodate have shawnthat inventoryand flow time improvementsofbetween30and50per cent are realistic withoutendangerin9theuti I ization target.

LITERATURE

(1) Kettner, H. Bechte, W., 1981,NewMethodsof ProductionControlbyLoad-OrientatedarderRelease.VDI-Z123,11,p. 459-466.

(2) Wiendahl,H.-P. Dombrowski,U., 1987,ManufacturingRoutineAnalysis for the QuantitativeComparisonof Conventionaland Flexible Manufacturing.The International Journal ofAdvancedManufacturingTechnology,2 (4), 41-62.

Wiendahl,H.-P. Winkelhake,U., 1987, Computer-AssistedStructuringof AutomaticAssemblyInstallations. ZwF82 11,pp. 627-631.

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(4) Bttner, R., 1986,A Control andPlanningSystemfor Load-OrientatedProductianControl in Dialog User Experiences.In: Wiendahl(Hrsg.), ThePractice af Load-OrientatedPro-ductionControl, Munich,pp. 75-88.

Bechte,W., 1986,A Contrai andPlanningSystemfor Load-OrientatedProductionControl in ConversationalMede.ConceptandRealization. In: Wiendahl(Edit.), ThePracticeof Load-OrientatedProductionControl, Munich,pp. 89-118.

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(6) Wiendahl,H.-P. Ludwig,E., 1987,Fundamentsof a modelbasedExpertSystemfor the ShartTermProductionFlowDiagnosis,Proc. Df: ExpertSystemsin Praduction,Munich.

Wiendahl,H.-P., 1987,Load-OrientatedPraductionControl.HanserVerlag, MunichVienna.

(7)

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