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ArtificialAgentsPlaytheBeerGameEliminatetheBullwhipEffectandWhiptheMBAsStevenO.KimbroughD.-J.WuFangZhongFMEC,Philadelphia,June2000;file:beergameslides.pptTheMITBeerGame•Players–Retailer,Wholesaler,DistributorandManufacturer.•Goal–Minimizesystem-wide(chain)long-runaveragecost.•Informationsharing:Mail.•Demand:Deterministic.•Costs–Holdingcost:$1.00/case/week.–Penaltycost:$2.00/case/week.•Leadtime:2weeksphysicaldelayTiming1.Newshipmentsdelivered.2.Ordersarrive.3.Fillordersplusbacklog.4.Decidehowmuchtoorder.5.Calculateinventorycosts.GameBoard…TheBullwhipEffect•Ordervariabilityisamplifiedupstreaminthesupplychain.•Industryexamples(P&G,HP).ObservedBullwhipeffectfromundergraduatesgameplayingRetailer'sOrder0102030401234567891011121314151617181920212223242526272829WeekOrderWholesaler'sOrder0102030401234567891011121314151617181920212223242526272829WeekOrderDistributor'sOrder0102030401234567891011121314151617181920212223242526272829WeekOrderFactory'sOrder0102030401234567891011121314151617181920212223242526272829WeekOrderBullwhipEffectExample(P&G)Leeetal.,1997,SloanManagementReviewAnalyticResults:DeterministicDemand•Assumptions:–Fixedleadtime.–Playersworkasateam.–Manufacturerhasunlimitedcapacity.•“1-1”policyisoptimal--orderwhateveramountisorderedfromyourcustomer.AnalyticResults:StochasticDemand(Chen,1999,ManagementScience)•Additionalassumptions:–OnlytheRetailerincurspenaltycost.–Demanddistributioniscommonknowledge.–Fixedinformationleadtime.–Decreasingholdingcostsupstreaminthechain.•Order-up-to(basestockinstallation)policyisoptimal.Agent-BasedApproach•Agentsworkasateam.•Noagenthasknowledgeondemanddistribution.•Noinformationsharingamongagents.•Agentslearnviageneticalgorithms.•Fixedorstochasticleadtime.ResearchQuestions•Cantheagentstrackthedemand?•CantheagentseliminatetheBullwhipeffect?•Cantheagentsdiscovertheoptimalpoliciesiftheyexist?•Cantheagentsdiscoverreasonablygoodpoliciesundercomplexscenarioswhereanalyticalsolutionsarenotavailable?FlowchartAgentsCodingStrategy•Bit-stringrepresentationwithfixedlengthn.•Leftmostbitrepresentsthesignof“+”or“-”.•Therestbitsrepresenthowmuchtoorder.•Rule“x+1”means“ifdemandisxthenorderx+1”.•Rulesearchspaceis2n-1–1.Experiment1a:FirstCup•Environment:–Deterministicdemandwithfixedleadtime.–FixthepolicyofWholesaler,DistributorandManufacturertobe“1-1”.–OnlytheRetaileragentlearns.•Result:RetailerAgentfinds“1-1”.Experiment1b•AllfourAgentslearnundertheenvironmentofexperiment1a.•Überrulefortheteam.•Allfouragentsfind“1-1”.ResultofExperiment1bAllfouragentscanfindtheoptimal“1-1”policyArtificialAgentsWhiptheMBAsandUndergraduatesinPlayingtheMITBeerGameAccumulatedCostComparisonofMBAsandouragents010002000300040005000123456789101112131415161718192021222324252627WeekAccumulatedCostMBAGroup1MBAGroup2MBAGroup3AgentUnderGradGroup1UnderGradGroup2UnderGradGroup3Stability(Experiment1b)•Fixanythreeagentstobe“1-1”,andallowthefourthagenttolearn.•Thefourthagentminimizesitsownlong-runaveragecostratherthantheteamcost.•Noagenthasanyincentivetodeviateoncetheothersareplaying“1-1”.•Therefore“1-1”isapparentlyNash.Experiment2:SecondCup•Environment:–Demanduniformlydistributedbetween[0,15].–Fixedleadtime.–AllfourAgentsmaketheirowndecisionsasinexperiment1b.•AgentseliminatetheBullwhipeffect.•Agentsfindbetterpoliciesthan“1-1”.ArtificialagentseliminatetheBullwhipeffect.024681012141618201357911131517192123252729313335WeekOrderRetailerWholeSalerFactoryDistributerArtificialagentsdiscoverabetterpolicythan“1-1”whenfacingstochasticdemandwithpenaltycostsforallplayers.AccumulatedCostvs.Week0100020003000400050001357911131517192123252729313335WeekAccumulatedCostAgentCost1-1CostExperiment3:ThirdCup•Environment:–Leadtimeuniformlydistributedbetween[0,4].–Therestasinexperiment2.•Agentsfindbetterpoliciesthan“1-1”.•NoBullwhipeffect.•ThepolicesdiscoveredbyagentsareNash.Artificialagentsdiscoverbetterandstablepoliciesthan“1-1”whenfacingstochasticdemandandstochasticlead-time.ArtificialAgentsareabletoeliminatetheBullwhipeffectwhenfacingstochasticdemandwithstochasticleadtime.AgentslearningWinnerStrategiesGenerationRetailerWholesalerDistributorManufacturerTotalCost0x–0x–1x+4x+273801x+3x–2x+2x+578562x–0x+5x+6x+369873x–1x+5x+2x+361374x+0x+5x–0x–261295x+3x+1x+2x+338866x–0x+1x+2x+030717x+2x+1x+2x+126948x+1x+1x+2x+125559x+1x+1x+2x+1255510x+1x+1x+2x+12555TheColumbiaBeerGame•Environment:–Informationleadtime:(2,2,2,0).–Physicalleadtime:(2,2,2,3).–InitialconditionssetasChen(1999).•Agentsfindtheoptimalpolicy:orderwhateverisorderedwithtimeshift,i.e.,Q1=D(t-1),Qi=Qi-1(t–li-1).OngoingResearch:MoreBeer•Valueofinformationsharing.•Coordinationandcooperation.•Bargainingandnegotiation.•Alternativelearningmechanisms:Classifiersystems.Summary•AgentsarecapableofplayingtheBeerGame–Trackdemand.–EliminatetheBullwhipeffect.–Discovertheoptimalpoliciesifexist.–Discovergoodpoliciesundercomplexscenarioswhereanalyticalsolutionsnotavailable.•Intelligentandagilesupplychain.•Multi-agententerprisemodeling.Aframeworkformulti-agentintelligententerprisemodelingExecutiveCommunity(StrategyFinde