Mixed Model Simulation Tutorial 2008

8/8/2019 Mixed Model Simulation Tutorial 2008

1/23

HowtoBuildaCombined

AgentBased/SystemDynamicsModel

LogicinAny

2008XJTechnologieswww.anylogic.com


2/23

HowToBuildaCombinedAgentBased/SystemDynamicsModelinAnyLogic.Tutorial

Contents

Introduction................................................................................................................................................... 3

Theproblemdefinition.................................................................................................................................. 4

Theplan......................................................................................................................................................... 5

Modeldevelopment

......................................................................................................................................

6

Phase1.Create1000agentswithemptybehavior.................................................................................. 6

Phase2.Addsimplestatebasedbehaviortotheagents......................................................................... 9

Phase3.AddtheretailerstockwithsomeinitialamountofproductA................................................. 11

Phase4.AddSDsupplychainfortheproductA..................................................................................... 12

Phase5.Visualizethedynamicsofdemandanduserbase.................................................................... 14

Phase6.Addagentcommunicationtomodelwordofmouth............................................................... 16

Phase7.

Add

product

discards

................................................................................................................

18

Phase8.AddproductBtothemodel..................................................................................................... 19

Phase9.Addproductswitchingtriggeredbywaitingtime.................................................................... 20

Experimentingwiththemodel.................................................................................................................... 23

2008XJTechnologieswww.anylogic.com 2


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Introduction

AnyLogicallowsyoutobuildasimulationmodelusingmultiplemethods:SystemDynamics,AgentBased

andDiscreteEvent(Processcentric)modeling.Moreover,youcancombinedifferentmethodsinone

model:putagentsintoanenvironmentwhosedynamicsisdefinedinSDstyle,useprocessdiagramsor

SDto

define

internals

of

agents,

etc,

etc.

Any

kind

of

mixed

architecture

is

possible

due

to

flexible

object

orientedAnyLogicmodelinglanguage.

Thechoiceofmodelarchitecture(howtopartitionthemodelintocomponents,whattoaggregate,

whichgranularitytouse,whatbehaviorisbestmappedtoaprocessdiagram,andwhattoastatechart,

etc)belongsmainlytothedomainofartandintuitionofthemodelerandisoutsidethescopeofthis

shorttutorial.ThegoalofthistutorialistoshowstepbystephowtobuildacombinedAB+SDmodelin

AnyLogicusingoneparticulararchitecture.Wewillhighlightthepointsofinteractionofagentsand

systemdynamicsandtrytoshowthatmodelelementsbelongingtodifferentapproachesliveasingle

spaceofAnyLogicmodelandcaneasilyaccesseachother.Havingcompletedthistutorialyoushouldbe

abletobuildvariousmultimethodmodelswithmoreconfidenceandefficiency.

ThetutorialdetailslevelassumessomefamiliaritywithAnyLogicmodeldevelopmentenvironment:the

instructionsinmostcasesareofthetype:CreateastatePotentialUserratherthanOpentheModel

palette,clickontheStateitem,thenclickonthecanvasandenterPotentialUserintheeditbox.



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Theproblemdefinition

Wewillbuildamodelofaconsumermarketandasupplychain.

Theassumptionswemakeaboutthemarketaresimilartoonesoftheclassicalmodelsof

product/innovationdiffusion,e.g.ofBassmodelwithdiscardsandreplacements.Wewillhowever

considertwocompetingproductsinsteadofone.

TherearetwoalternativeproductsAandBmanufacturedbydifferent(andcompeting)companies.Theproductsareequivalent,i.e.canreplaceeachother.Theproductpricesare

equalandthereforedonotmatter.

Consumers(thereareTotalPopulation=1000ofthem)initiallyarenotusinganyproductsbutallarepotentiallyinterested(arepotentialusers).

Consumersaresensitivetoadvertizingandtowordofmouth. Advertizinggeneratesthedemandforaproductamongthepotentialusers.Advertizing

Effectiveness=0.011isthepercentofpotentialusersthatbecomereadytobuyaparticular

product(A

or

B)

during

aday.

Both

companies

do

advertizing.

Consumerscontacteachother.AconsumercontactsonaverageaContactRate=5otherpeopleperday.

Duringthosecontactstheusersofproductsmayinfluencepotentialusers.Ifauserofe.g.Acontactsapotentialuser,thelatterwillwanttobuyAwithprobabilityAdoptionFraction=

0.015,sameforB.

AnyproductdiscardsinDiscardTime=uniform(17,23)daysandgeneratestheimmediateneedtobuyareplacementofthesamebrand.

Ifapersonwantstobuye.g.A,butAisnotavailableforMaximumWaitingTime=2days,hebecomesreadytobuyanythingthatisavailable(AorB),sameforB.

Eachcompany(AandB)hasitsownsupplychainthatdeliversproductstotheendconsumers.The

supplychainsareverysimpleandworkasfollows:

Theproductcanbepurchasedbyaconsumeronlyfromtheretailerstock,initiallyholdingacertainamount(InitialRetailerStock=100)ofproduct.

Theproductismanufacturedbyaproducer.AproducermakesProductionRateproductsperday,andthisratemayvary,e.g.itcanbeadjustedaccordingtothedemand(whichisknownto

theproducer)

ThefinishedproductsaredeliveredtotheretailerwithinDeliveryTime=2days.The

output

of

the

model

should

include

the

market

shares

for

A

and

B,

the

demand

(i.e.

the

number

of

peoplewhowanttobuywhiletheproduct(s)arenotavailable)andtheinventorylevelsinthesupply

chains.



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Theplan

WewillmodeltheconsumermarketinAgentBasedway:eachconsumerwillbeanagent.Thesupply

chainsforbothproductsAandBwillbedoneusingSystemDynamics.Pleasenotethattheproblem

definitionallowsmanyotherchoicesthisisjustoneofthem.

TheMarket

The

Supply

Chain

Asyouobviouslyknow,thebestwaytodevelopsimulationmodelsistodoititeratively,i.e.inmultiple

phaseswitharunnablemodelattheendofeachphase.Inourcaseitmakessensetohavethefollowing

order:

1. Startwiththemarketmodelandjustoneproduct(A)a. Buildthebehaviormodelofanindividualconsumerb. Populatethemarketwiththeconsumersc. Assumetheproductisavailable

2. AddsupplychainfortheproductA3. AddproductB



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Modeldevelopment

Phase1.Create1000agentswithemptybehavior

InthisphasewewillcreateanewAnyLogicproject,defineanActiveObjectclassforourconsumers,

drawasimple

animation

of

aconsumer,

define,

create

and

visualize

apopulation

of

1000

consumers.

Theconsumerswillhavenobehavioratthistime,sothemodelwillbedoingnothing.

1. CreateanewprojectMixedMethodModelABMarketandSDSupplyChainAnewprojectalwayshasoneActiveObjectclassMain,whoseeditoropensautomatically.Mainwillbe

thetoplevelofourmodelwherewewilldefinetheinteractionbetweentheagentbasedandsystem

dynamicsparts.Wewillleaveitblankfornowandstartwithdevelopingthemodelofaconsumer.

2. CreateanewActiveObjectclassConsumerWeneedaseparateclassforconsumers,inwhichwewilldefinetheconsumerbehavior.Havingthat

behaviorencapsulatedinaclassenablesustocreatemultipleinstancesofconsumers.Theeditorand

propertiesof

the

class

Consumer

open

when

you

create

it.

3. InthepropertiesoftheclassConsumerspecifythatConsumerisanAgentThiswillenablesomeusefulAnyLogicservicesforagents,forexamplecommunication,space,layout,etc.

TheiconoftheactiveobjectclassConsumerchanges.

4. IntheeditorofConsumerdrawavisualrepresentationofaconsumerusinge.g.aCurveshapenearthecoordinateorigin.Youmaywanttousemaximumzoomforfinepositioningofthecurve

points.SetlinecolorofthecurvetoNoColorandfillcolortogray

Eachconsumerwillbevisualizedbysuchshape.Thecoloroftheshapeaswellasitsotherpropertiescan

bedynamicallysetupbyeachindividualconsumer.

5. DragtheclassConsumerfromtheprojecttreetotheeditorofMain2008XJTechnologieswww.anylogic.com 6


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ThiswaywespecifythatinstanceofConsumerisembeddedinthetoplevelobjectMain.Theiconandthe

presentationofconsumerappearintheeditorofMain.

6. Movethepresentationoftheembeddedconsumertotheposition(50,250)onMainThiswillbethetopleftcorneroftherectangularspacewherewewilllateronvisualizetheconsumer

population.Theothermodelelementswillbelocatedaboveit.

7. SettheReplicationpropertyoftheembeddedconsumerto1000.Changethenameoftheembeddedobjectfromconsumertoconsumers

ThiswaywetellAnyLogicthatinsideMaintherewillbenotonebut1000consumers.consumerswillbe

thenameofthatpopulation.Thesquarebrackets[..]appearnearthenametoindicatethereplication.

8. AddenvironmentobjectfromtheModelpalettetoMain.SetthepropertyEnvironmentoftheconsumer

population

to

environment

Environmenttakescareofspace,layout,network,communicationofagents.Inourcaseweneed

environmenttolayouttheagentpresentationsandtomodelwordofmouthbyagenttoagent

interaction.

9. RunthemodelYoushouldbeabletoseethepicturesimilartotheonebelow.Thereisnodynamicsinthemodel,so

nothingchangesovertime.Inthenextstepwewilladjustthewindowsizeandtheagentspaceborders.



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10.IntheprojecttreeexpandtheexperimentitemSimulation:MainandthenexpanditsPresentationsubitem.ClickonFrametoviewitsproperties.Setthewidthoftheframeto1000

andHeightto600.

Thisisthewayyouspecifytheinitialwindowsizeofthesimulation.

11.IntheeditorofMainclickenvironment.IntheAdvancedpageofitspropertiessetspacewidthto900andspaceheightto300.

Nowtheagentswillbevisualizedinarectangularspacethatfitsthewindow.

12.RunthemodelagainThelayoutshouldlookbetternow.



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Phase2.Addsimplestatebasedbehaviortotheagents

Basedontheproblemdefinition,wewilldefinethebehaviorofaconsumerasasequenceofthree

states:PotentialUser,WantA,UsesA.Wewillassumethattheproductisalwaysavailable,sothe

transitionfromWantAtoUsesAwillbeunconditionalandimmediate.Theeffectofadvertizingwillbe

modeledasstochasticdelayassociatedwithatransitionfromPotentialUsertoWantA.Noproduct

discards

and

no

agent

to

agent

communication

will

be

added

in

this

phase.

1. IntheeditorofConsumerdrawthreestates(topdown):PotentialUser,WantAandUsesA.DrawthestatechartentrypointpointingtothestatePotentialUser.

Thestatesinthestatechartarealternative:theagent(inourcasetheconsumer)canonlybeinonestate

atatime.Thestatechartentrypointmarkstheinitialstate,whichobviouslyisPotentialUser.Thenameof

thestatechartentrypointisthenameofthestatechart.Ingeneral,anActiveObjectinAnyLogicmayhave

multiplestatecharts,butnowweneedonlyone.

2. DrawtransitionfromPotentialUsertoWantAandcallitAdA.DrawtransitionfromWantAtoUsesAandcallitBuyA.CheckthecheckboxShownameforeachtransitionandadjustthe

positionsoflabelsintheeditor

Transitionsdefinehowtheobjectchangesitsstates.Atransitionmaybetriggeredbye.g.amessage

arrival,acondition,ortime.ThetransitionAdAwillmodeltheeffectofadvertizing,andBuyAtheevent

ofpurchasingtheproductA.

3. SpecifythefollowingpropertiesforthetransitionAdA:Triggertype:RateandRate:0.0112008XJTechnologieswww.anylogic.com 9


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TransitionofratetypeinAnyLogicinthiscaseisthesameastransitiontriggeredbyastochastictimeout

distributedexponentially.WhenthestatechartentersthestatePotentialUse,adrawfromtheexponential

distributionismadeandthetimeoutissetup.Therefore,eachconsumerwillhavedifferenttimeof

adoptionbecauseofadvertizing,sothatonaverage1.1%ofpotentialuserswillwanttobuytheproductin

onetimeunit(day).

4. SpecifythefollowingpropertiesforthetransitionBuyA:Trigger:timeoutandTimeout:0.Asweassumethattheproductisalwaysavailable,anybodywhowantstheproductcanimmediatelybuyit

thereforeoncetheconsumerstatechartentersthestateWantA,itwillproceedtostateUsesAwithzero

delay.

5. IntheEntryactionofthestateWantAwrite:curve.setFillColor(pink);In

the

Entry

action

of

the

state

UsesA

write:

curve.setFillColor(

red

);

Thiswaywewillchangethecoloroftheconsumerpresentationtovisualizethechangeofitsstate.Asyou

cansee,allmodelandpresentationelementsoftheactiveobjectclassareaccessibleonefromanother.

NotethatifyouhaveusedotherkindofshapetodrawthepresentationofConsumer,youmayneedto

useothernamefortheshape.

6. Runthemodel.AfterawhileyoumaypresstheVirtualtimebuttontospeedupthemodel.Youshouldbeabletoseehowthepopulationofconsumersgraduallyturnsredthisistheeffectof

advertizing.AlthougheachconsumergoesthroughthestateWantA,inwhichheshouldbepink,youwill

notbeabletoseeitashedoesnotstayinthatstateandimmediatelyproceedstoUsesA.Themodelwill

stopattime100whensomeconsumersareusersandsomearenot.



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7. OpenthepropertiesofexperimentSimulation:Main.OntheGeneralpagesetRandomseed(uniquesimulationruns).IntheModeltimepagesetStoptime:Never.

Asourmodelisstochastic(youmayrememberthatthesourceofstochasticityistheratetransitionAdAin

theconsumersstatecharts),thesimulationresultswilldependontherandomnumbergeneration.By

settingtheRandomseedyoutellAnylogictousedifferentsequencesofrandomnumbersforeachrun.By

settingtheStoptimetoneveryoutellAnyLogictoexecutethemodelinfinitelylong(oruntilthereis

nothingto

execute).

8. RunthemodelagainYouwillseethateventuallyallconsumerswillbuytheproduct.

Phase3.AddtheretailerstockwithsomeinitialamountofproductA

Inthisphasewewilladdthefirst(actuallytheend)elementofthesupplychainforproductA:the

retailerstock.The(SystemDynamics)stockwillhavesomeinitialamountofproduct,sosomeconsumers

willbeabletobuytheproduct.WewillmodifytheconsumerbehaviorsothatthetransitionfromWantA

toUsesAwillonlybepossibleifthethereisatleastoneunitofproductonstock.Asaresultofa

consumertaking

this

transition

the

amount

of

available

product

will

be

decremented.

This

is

the

first

pointofinteractionoftheAgentBasedandtheSystemDynamicscomponentsinthemodel.

1. OpentheeditorofMainandaddastockvariableRetailerStock.Setitsinitialvalueto100.ThisisthefirstSystemDynamicselementinthemodel.WedefineitinMainonthesamelevelwherewe

haveembeddedthepopulationofagentsconsumers.

2. GototheeditorofConsumerandchangethepropertiesofthetransitionBuyA:itshouldnowhavetriggertypeCondition,theCondition:get_Main().RetailerStockA>=1andAction:

get_Main().RetailerStockA;

ThisishowweimplementtheABSDinteraction:wheninthestateWantAaconsumerconstantly

monitorsthestockRetailerStockA;whenthestockcontainsatleastoneproduct,thetransitionistaken

and,

as

a

result,

one

unit

of

product

is

deducted

from

the

stock.

Please

note

that,

as

the

stock

is

located

onelevelupregardingtheconsumerbehavior(attheMainobjectthatcontainstheconsumer),weneed

firstgettoMainandonlythenwecanaccessthestockthatiswhyweusetheprefixget_Main(),which

bringsustothecontainerofConsumeroftypeMain.



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3. Runthemodelinvirtualtime(fast)mode.Youwillseethat100consumerswillbeabletobuyA,whileallotherswilleventuallyturnpinkasthe

retailerisoutofstock.

Phase4.AddSDsupplychainfortheproductA

WewilladdtheremainingpartofthesupplychainforA:productionanddelivery.Thesupplychainwill

beapureSystemDynamicsconstructstartingwithProductionflowintoFactorystockandthenthrough

theDeliveryflowtotheRetailerstock.Wewillfirstmaketheproductionrateconstantandthen

variable,depending

on

the

demand

for

the

product.

This

will

be

asecond

point

of

interaction

between

theABandtheSDpartsofthemodel.TofeedthedemandintotheSDpartwewilladdastatisticsitem

totheconsumerpopulation:itwillcalculatethenumberofconsumersthatareinthestateWantA.The

productionratewillberecalculatedonceadayaccordingtothatnumber.

1. IntheeditorofMainaddthestockFactoryStockAtotheleftofRetailerStockA.DrawflowfromFactoryStockAmtoRetailerStockA(bydoubleclickingthesourcestockandclickingatthesink

stock).CallthecreatedflowDeliveryA.SettheformulaforDeliveryA=FactoryStockA/2

Thiswaywemodelthedeliverydelayof2daysfromthefactorytotheretailerstock.

2. AddtheflowvariableProductionAtotheleftofFactoryStockAandletitflowintoFactoryStockA.LettheProductionA=15.

Wewillassumeaconstantproductionratefornow.



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3. RunthemodelYouwillseethatnowthedemandcanbefullysatisfied,andmoreover,theamountofproducedproductis

muchgreaterthanneeded.Obviously,wheneverybodyhaspurchasedtheproduct,thesupplychain

continuestogrowtheretailerstock.

4. IntheeditorofMainclickontheiconoftheembeddedconsumersandopentheStatisticspageoftheirproperties.AddthestatisticsitemwithnameNWantA.Leavethetypeofstatisticscount.

Intheconditionfieldwrite:item.statechart.isStateActive(item.WantA)

Asourconsumermarketiscompletelydisaggregated,weneedtoiteratethroughallagentstofindout

howmanyofthemwanttobuytheproduct,i.e.areinthestateWantA.Thestatisticsoftypecountdoes

exactlythat:ititeratesthroughthepopulationandcountshowmanyagentssatisfythegivencondition.In

theconditionexpressionitemrepresentsthecurrentagent,statechartisthenameoftheconsumers

statechart,isStateActiveisastandardmethodofstatechart,andWantAisthenameofthestate

definedwithintheagent,thatiswhyitneedstheprefixitem..

5. IntheeditorofMainaddeventnearbytheflowProductionA.CallitupdateProductionA.InthepropertiesoftheeventspecifyTriggertype:timeout,Mode:Cyclic,Recurrencetime:1,Action:

ProductionA=consumers.NWantA();

ByaddingsucheventwebuildyetanotherlinkbetweentheABandSDmodels:nowatthebeginningof

eachdaytheproductionratewillbemodifiedaccordingtothenumberofconsumerswhoarewillingto

buytheproduct.Therecouldbebetterformulasthanrate=demand,butthatsthesimplestone.

NWantA()is

the

statistics

method

we

have

defined

in

the

consumer

population

in

the

previous

step.



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6. IntheformulaforProductionAremove15Nowtheproductionrateisfullycontrolledbytheeventupdatingit,soformulamustberemoved.

7. Runthemodel.ClickontheProductionAtobringupitsinspectwindowandthenclickswitchittochartmodebyclickingthesmallcharticonintheupperrightcorner.

Youshouldbeabletoseethatnowtheproductionrateoscillates,whichistypicalforthesupplychains

withtheirinevitabledelays.

Phase5.Visualizethedynamicsofdemandanduserbase

Inthisphasewewillvisualizethedynamicsofunsatisfieddemandgeneratedbythemarketandthe

numberofusers.Aswearemodelingthemarketinacompletelydisaggregatedway,weneedtoadd

anotherstatisticsitemstothepopulationofconsumers,namelytheonecountingthenumberofagents

thatareinUsesAstate.Also,ifwewanttoseethehistoryoftheseoutputs,weneedtocreateacouple

ofdatasetsandachart,e.g.atimestackchart.

1. IntheeditorofMainclickontheconsumersandgototheirStatisticspage.AddthesecondstatisticsitemNUseAofcounttypewithexpressionitem.statechart.isStateActive(item.UsesA

)(which

you

can

copy

from

the

item

NWantA

and

modify).

2. StayinMainandaddtwodatasetsfromtheAnalysispalette:NWantADSandNUseADS.Tobeabletovisualizethehistoryofacertainvalue,weneedtokeepthathistoryinadatasetobject.



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3. InthepropertiesofNWantADSspecifytheVerticalaxisvalue:consumers.NWantA(),forNUseADScorrespondingly:consumers.NUseA().

DatasetsinAnyLogicarearraysofpairs(x,y).Ashorizontalaxisvalue(x)istimebydefault,thedataadded

tothee.g.NWantADSwillbeoftype(t,demandattimet).Bydefaultthecapacityofadatasetis100

samples.

4.From

the

Analysis

palette

drop

Time

stack

chart

to

the

editor

of

Main

Thebestwaytovisualizethedynamicsoffractionsofthepopulationintimeistimestackchart.

5. Inthepropertiesofthechartaddtwodatasets:NUseADSwithtitleUsersAcolorredandNWantADS

with

title

Demand

for

A

and

color

pink.

Set

the

Vertical

scale

of

the

chart

as

Fixed

to

1000.

Thisdefineswhatwillbeshowninthechart.Bydefaultthetimewindowofthechartis100anditwill

automaticallyupdatethedatasetseach1timeunit.

6. RunthemodelYouwillseehowtheuserbaseforAgrows.Thesupplychainworkswellandthereisonlyasmallslightly

oscillatingunsatisfieddemand.



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Phase6.Addagentcommunicationtomodelwordofmouth

Inthisphaseagentswillstarttalkingtoeachother.Asweareinterestedinusersoftheproducttalking

topotentialusers,wewillsetupacyclictransitioninthestateUsesA.Thetransitionwillbetaken

periodicallyandoneachoccurrencetheagentuserwillbesendingamessagetoarandomotheragent

saying

that

product

A

is

good.

If

another

agent

is

a

potential

user

(i.e.

is

in

the

state

PotentialUser),

he

willreacttosuchamessagebychangingitsstatetoWantA.Obviously,wewillachievethisbeaddinga

transitionfromPotentialUsertoWantAtriggeredbythecorrespondingmessage.

1. GototheeditorofConsumeranddrawatransitioninsidethestateUsesAsuchthatitstartsandendsonthebordersofthestateandallitssegmentsareinsidethestate.CallitContactA.Set

thetriggertypeofthetransitiontoRatewithrate=5*0.015.SetitsActiontosend("BuyA!",

RANDOM);

Theinternaltransitionisacyclictransitionthatdoesnottakethestatechartoutofthestateinwhichitis

defined.InthiscasethetransitionContactAwilloccurwiththespecifiedrate.Thevalueofrate(5*0.015)

needstobefurtherexplained.Wecouldmodelallcontactsstraightforwardly,i.e.5contactsperday,in

whichcase

the

rate

would

be

5.

But

we

know

that

not

all

contacts

are

successful,

i.e.

convince

potential

userstobuyA.Thereforeherewemodelonlyasuccessfulfractionofcontactsandmakethemmorerare

bymultiplyingby0.015.Intheactionofthetransitiontheconsumerchoosesanotherrandomconsumer

(notnecessarilythepotentialuser!)andsendshimatextmessageBuyA!.

2. GototheAgentpageofthepropertiesoftheConsumerclass.IntheOnmessagereceivedfieldwritestatechart.receiveMessage(msg);



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Inthepreviousstepwehavesetuptheagentsuserstoperiodicallycontactotheragentsbysendingthem

themessageBuyA!.InthesectionOnmessagereceivedwecanspecifythereactionontheincoming

messages.Thecodeforwardsthemessagetothestatechart,wherewewillspecifyoneadditional

transitioninthenextstep.

3. AddonemoretransitiontothestatechartoftheConsumer:fromPotentialUsertoWantAandcallitWomA.SetthetriggerofthetransitiontoMessage,thetypeofthemessage:String,and

letthetransitiontofireIfmessageequalsBuyA!.

Thisisthelaststepinmodelingthewordofmouth.Themessagethatcomesfromanotheragentis

forwardedthestatechart,and,ifthestatechartisinthestatePotentialUser,causesanimmediate

transitiontoWantA.Inallotherstatesthemessageisignored.

4. Runthemodel.Youshouldseethatthemarketsaturationisachievedalotfasternow.ThechartshowsthewellknownS

shapedcurveoftheproductadoption.Theunsatisfieddemandduringthepeakofinteresttotheproduct

isquitesignificant.



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Phase7.Addproductdiscards

Thisisaverysimplephase.Astheproductisdiscardedafteracertainperiodandtheuserneedstobuya

replacement,wewilladdatransitionfromUsesAtoWantAtriggeredbyaconstanttimeoutDiscard

Time.HavingdefinedsuchtransitionwerestrictthesojourntimeinthestateUsesAbyDiscardTime.

1. InthestatechartofaconsumeraddatransitionfromUsesAtoWantA,callitDiscardA.SetthetriggertoTimeoutwithvalueuniform(17,23).

WhenthestatechartentersthestateUsesA,asampleofstochastictimeoutisevaluatedandcountdownis

startedforthetransitionDiscardA.Thetimeofusingaparticularproductitem(i.e.thetimespentin

UsesA)thereforewillbedistributeduniformlyfrom17to23.PleasenotethatthetransitionContactAwill

notberesettingthattimeoutasitisaninternaltransition.AftertakingDiscardAtheconsumerwillenter

WantAstate,whichmeansheimmediatelyiswillingtobuyareplacement.

2. RunthemodelAfterthemarketissaturated(everybodyisusingtheproduct),youwillobservetheperiodicshortagesin

theproductsupplycausedbytheproductexpirationatthemajorityofusers.Thesupplychainasitisset

upnowisnotcapableofsatisfyingthesepeaksofdemand.



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Phase8.AddproductBtothemodel

NowwecanaddtheproductBthatcompeteswithproductA.Wewilldoitbysimplycopyingthesupply

chainforAandrenamingitselements.Theproductspecificpartoftheconsumersstatechartwillalso

becopiedsothatPotentialUserwillhavetwoalternatives:transitiontoWantAortoWantB.Atthistime

we

will

not

model

the

maximum

waiting

time

for

a

product.

Two

new

statistics

items

and

two

datasets

willbeneededtoshowthedynamicsofthemarket.

1. IntheeditorofConsumerselecttwostatesWantAandUsesAandalltransitions(inotherwords,selectallstatechartelementsexceptforthestatePotentialUserandthestatechartentrypoint.

Makeacopyoftheselectionandarrangethetransitionsasshowninthescreenshotbelow.

RenameA1thatappearsintheendingsofthecopiedelementstoB.

InthetransitionsWomBandContactBchangeBuyA!toBuyB!.

InthepropertiesofthetransitionBuyBchangeRetailerStockBtoRetailerStockB.

IntheEntryactionsofstatesWantBandUsesBchangethecolorstolightBlueandblue.

Inthisstepwehavedefinedanalternativepathoftheconsumerbehavior.Weassumethesame

advertizingeffectivenessforproductB(0.011)andsamecontactrateandadoptionfraction(obviouslywe

canchangeanyofthoseparameters).Notethatthenewstatechartstructureallowsonlyinitialchoiceof

productbyapotentialuser;oncetheinitialchoicehasbeenmade,thereisnowayforaconsumerto

switch.

2. IntheeditorofMainclickontheconsumersandgototheStatisticspage.Addtwomorestatisticitems:NWantBandNUseBwithconditions



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item.statechart.isStateActive(item.WantB)anditem.statechart.isStateActive(item.UsesB)

correspondingly

ThesestatisticsitemswillcountthedemandandthenumberofusersoftheproductB.

3. IntheeditorofMainselectthewholesupplychainforproductA(allSDelements)andalsotheeventupdateProductionA,copyitandpastetotheright.Rename:

eventupdateProductionA1

to

updateProductionB,

stock

ProductionA1

to

ProductionB,

etc.

ChangetheactionofupdateProductionBtoProductionB=consumers.NWantB();

ChangeAtoBinallformulasinthesupplychainforproductB.

Needlesstosay,allthatcopyingandrenamingdoesnotlookelegant.Andindeed,AnyLogicoffersmuch

betterwayofreplicatingpiecesofmodel:youcanpackthesupplychainandthecorrespondingeventinto

anewActiveObjectclass,parameterizeitwithe.g.demand,andinstantiateittwiceinMain:onceforA

andonceforB.Forsimplicityhoweverwearenotdoingitinthistutorial.

4. IntheeditorofMainmakeacopyofthetwodatasets.ChangethenamesofthenewitemstoNWantBDSandNUseBDS.Changetheirvaluestoconsumers.NWantB()and

consumers.NUseB().AddthesedatasetstothechartwithtitlesDemandforBandUsersB.

5. RunthemodelYouwillseethesymmetricdiffusiondynamicsforAandB.Pleasenotethatthemarketshareisdefined

onlybytheinitialadoptionandcannotchangelateronbecauseoftheconsumersstatechartstructure.

Phase9.Addproductswitchingtriggeredbywaitingtime

Accordingtoourproblemdefinition,ifaconsumerwaitstoolongforaparticularproduct,hebecomes

impatientandwillbuywhateverisavailable(AorB),soproductswitchingispossible.Theconsumer



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statechartcaneasilybemodifiedtocapturethis:weshouldaddtwotimeouttransitionsfromWantA

andWantBtoanewstateWantAnything.Fromthatstate,inturn,therewillbetwoalternative

conditiontypetransitionstoUsesAandUsesBtriggeredbythepurchaseofthecorrespondingproduct.

1. AddanewstateWantAnythinginthemiddleoftheconsumersstatechart.DrawtwotransitionsfromWantAandfromWantBtothenewstate.CallthemGiveUpWainingAand

GiveUpWaitingB.BothtransitionsshouldbeofTimeouttypewithtimeout2.Makeacopyofthe

transitionBuyA(itwillbecalledBuyA1)andplaceitfromWantAnythingtoUsesA.Similarly,

createacopyofBuyB.Leavethetriggersofthosetransitionsastheyare.IntheEntryactionof

WantAnythingwritecurve.setFillColor(gold);

Thetimeouttransitionsrestrictthewaitingtimeforaparticularproductto5.Oncetheconsumergetsto

thestateWantAnything,hestartsmonitoringavailabilityofbothproductsandwillbuywhateverbecomes

availablefirst.

2. IntheeditorofMainclickontheconsumersandaddyetanotherstatisticsitemNWantAnywithconditionitem.statechart.isStateActive(item.WantAnything).Addthecorrespondingdataset

NWantAnyDSwith

Vertical

axis

value

consumers.NWantAny()

and

add

that

dataset

to

the

chart

withgoldcolor.

3. RunthemodelYouwillseethattheunsatisfieddemandgrowsovertime.Thisiscausedbythewrongdemand

estimationsmadebythesupplychains:theproductionrateforeachproductdependsonlyonthenumber

ofconsumersthatarewaitingforthatparticularproductanddoesnottakeintoaccountthosewhoarein

thestateWantAnything.



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4. ModifytheactionsofeventsupdateProductionAandupdateProductionBinthefollowingway:writeProductionA=consumers.NWantA()+consumers.NWantAny();andProductionB=

consumers.NWantB()+consumers.NWantAny();.

Thiswaywetakeintoaccountthedemandofthoseconsumerswhoarereadytobuyanyproduct.

5. RunthemodelNow

the

supply

chains

work

better,

although

there

are

slight

periodic

shortages.

You

can

also

see

that

the

marketsharesfluctuatealittlebit,i.e.theproductswitchingoccurs.ButthebalancebetweenAandB

staysaround50/50becausethemodeliscompletelysymmetric.



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Experimentingwiththemodel

Atthistimethemodelfullyreflectstheproblemdefinitionandyoucandovariousexperimentswithit.

Forexample,youcanplaywiththesupplychainpoliciesandexplorehowtheyaffecttheresulting

marketshares.Itmightmakesensetomonitornotonlythedemandsatisfactionbutalsotheinventory

levelatthestocks(which,obviously,youwishtokeepatminimumlevel).

Thesupplychaincanbemodeledusingdiscreteeventorprocesstechnology(withAnyLogic

EnterpriseLibraryblocks)insteadoftheSD.Thenitwillbealoteasiertomodelthedeliverytimeand

granularity.

Anotherinterestingsetofexperimentscanbedonewiththeconsumerbehaviorandconsumer

population.Youcanaddasocialnetworkintothemodelwherecontactscanonlyoccurbetweenpeople

whoknoweachother.Thiswillobviouslyaffectthediffusionprocess.Youcanaddheterogeneitytothe

consumersattheparameterslevel(e.g.differentsensitivitytoadvertisingandtowordofmouth,

differentlevelofbrandloyalty),oratthebehaviorpatternlevel(e.g.someconsumersmaybecome

frustratedwith

the

product,

spread

negative

information,

etc.).

Documents

Mixed Model Simulation Tutorial 2008