chaos economics

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IStrategicManagement ournal, Vol. 15, 167-178 1994)

CHAOSTHEORY ND STRATEGY:HEORY,APPLICATION.ND MANAGERIALMPLICATIONSDAVIDLEVYDepartment of Management, lJniversity of Massachusetfs BostonBoston, Massachusetts, U.S.A.

This paper argues that chaos theory provides a useful theorectical framework forunderstanding the dynamic evolution of industries and the complex interactions amongindustry actors. It is argued that industries can be conceptualized and modeled as complex,dynamic systems, which exhibit both unpredictability and underlying order. The relevanceof chaos theory for strategy is discussed, and a number of managerial implications aresuggested. To illustrate the application of chaos theory, a simulation model is presentedthat depicts the interactions between a manufacturer of computers, its suppliers, and itsmarket. The resuhs of the simulation demonstrate how managers might underestimate thecosts of international production. The paper concludes that, by understanding industries ascomplex systems, managers con improve decision making and search for innovativesolutions.

INTRODUCTIONOne of the enduring problemsfacing the fieldof strategicmanagment s the lack of theoreticaltools available to describe and predict thebehaviorof firms and industries.For example,even f we know that oligopolistic ndustriesarelikely to experience eriodsof stabilityalternatingwith periodsof intense competition, we do notknow when they will occur or what will be theoutcome. Similarly, it is almost impossible opredict the impact of the advent of a newcompetitor or technology n an industry. Thefundamental roblem s that industries volve na dynamicway over time as a resultof complexinteractionsamong firms, government, abor,consumers, financial insti tutions, and otherelementsof the environment.Not only doesindustry structure influence firm behavior, but

Key words: Chaos heory,simulation, nternational,supply chainccc 0143209594tB01.67r2@)1994 y JohnWiley & Sons, td.

firm behavior n turn can alter the structure ofan industry and the contours of competition.Existing theoreticalmodels, however, tend toassume relatively simple linear relationshipswithout eedback. ndeed,manystrategic heoriesattempt to classify irms and industries and todescribeappropriate strategies or each class;examplesnclude the Boston ConsultingGroupmatrix for resource allocation and Bartlett'sclassification f internationalstrategies Bartlettand Ghoshal,1989).Although thesemodelsarebasedon recurrentpatterns hat we recognize nthe real world, there are usually far too manyexceptionsor the models o havemuchpredictivevalue.Chaos heory, which s the studyof nonlineardynamic systems, promises to be a usefulconceptual ramework that reconciles he essen-tial unpredictability f industrieswith the emer-genceof distinctivepatterns(Cartwright, 991).Although chaos heory was originallydevelopedin the contextof the physical ciences, adzicki(1990)and Butler (1990)amongstothers have


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168 D. Levynoted that social, ecological, and economicsystemslso end o be characterizedy nonlinearrelationshipsndcomplexnteractionshatevolvedynamically ver time. This recognitionhas edto a surgeof interest n applyingchaos heorytoa numberof fields, ncluding cology Kauffman,l99l), medicine Goldberger,Rigneyand West,1990) nternational elations(Mayer-Kress ndGrossman,1989),and economics Baumol andBenhabib, 1989; Kelsey, 1988).t Despite theapparent pplicability f chaos heory o the fieldof business trategy',here hasbeensurprisinglylittle work in this area.This paper ntroduceseaders o chaos heory,and discussests relevanceo the socialsciencesin general nd o aspects f strategyn particular,including planning and forecasting,and theimpact of changeon firms and industries.Theapplication f chaosheory o a businessituationis illustratedusing a simulationmodel of aninternational upplychain.The model,which sbasedon the author's research nto the supplychainof a California-basedomputercompany,depicts the complex interactionsbetween thefirm, ts suppliers, nd tsmarkets. he simulationresults llustrate he managerialmplicationsofapplyingchaos heory to strategicmanagement.The model demonstrates ow small disruptionsto the supplychain interact o make the chainhighlyvolatile, mposingsignificant ostson theorganization.Although orecastings verydifficultin the supply chain, distinct patterns emergewhich are useful or managers. he simulationalso shows that by understandinghe supplychainas a complexdynamic ystem,t is possibleto identify managerialapproacheshat lower thecost of operating he supplychain.

AN INTRODUCTION TO CHAOSTHEORYChaos heory s the studyof complex,nonlinear,dynamicsystems.The field was pioneeredbyLorenz (1963),who was studying he dynamicsof turbulent flow in fluids. Although we al lrecognizehe swirlsand vortices hat characterizeturbulent low, thecomplexities f turbulent lowt See also special issues of. Journal of Economic Theory,40(1), 1986,and Journal of Economic Behavior and Organiza-t ion,8(3), 1987.

have confoundedmathematiciansor years.Asimilar problem afflictssomeonewho is tryingto calculate the path of an object in thegravitational ul l of two or more bodies.Whilewe canusesimpleNewtonian quationso predictthe orbitsof planetsaround he sunwith a highdegreeof accuracy,he mathematicsnvolved nthecase f two or more suns'becomentractable.The problemcan be illustratedon a terrestriallevelby observinghe motionof a simple oy, ametalball suspendedver two or more magnets.The ball will tracea series f patterns hat neverexactly epeat hemselves,nd yet aie not totallyrandom.The paradox here is that the motion of themetal ball is driven by the same Newtonianequations s he well understood aseof a singlegravitational ttractor. f we knew preciselyheoriginal location, speed,and direction of theball, we ought o be able o predict ts pathwitha reasonabledegree of accuracy.How is itthat deterministic systems can give rise tounpredictability?The explanation s that tinyvariationsn the motionof the ball are magnifiedevery time it swingsby one of the magnets. tis a combinationof this divergenceand therepeated nteractionshat give rise to 'chaotic'behavior. Mathematically, haotic systemsarerepresentedy differentialequationshat cannotbe solved,so that we are unable o calculatehestateof the systemat a specificuture time 't'.At the limit, chaotic ystemsan become rulyrandom.A toss of a coin or the roll of a dieare, in theory, deterministic ystems, ut yieldmore or lessrandom outcomes.Not only is itimpossible o toss a coin twice in exactly thesameway, but on each oss he coin is subjectto slightly different air currents, hemselvesresultof turbulentair flow (Ford, 1983).To overcomehe problemof intractablediffer-ential equations, esearcherssuallymodel sys-tems as discrete difference equations,whichspecifywhat the stateof the systemwill be attime 't * 1' given he stateof the systemat time't.' Computersimulations an then be used toseehow the system volves ver time.One of themajorachievementsf chaosheoryis its ability to demonstrate ow a simplesetofdeterministicelationshipsanproducepatternedyet unpredictableoutcomes.Chaotic systemsnever return to the sameexact state, yet theoutcomes re boundedand createpatterns hat


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embody mathematicalconstants Feigenbaum,1983). t is the promiseof findinga fundamentalorder and structurebehindcomplexevents hatprobablyexplains he great nterest haos heoryhasgeneratedn so many fields.

Chaos heory and the social sciencesProponents f chaos heory enthusiasticallyeesignsof it everywhere, ointing o the ubiquityof complex,dynamicsystemsn the socialworldand he resemblanceetween atterns eneratedby simulatednonlinear systemsand real timeseries of stock exchangeor commodityprices.From a theoreticalperspective, haos heory iscongruouswith the postmodernparadigm,whichquestions eterministic ositivismas t acknowl-edgeshe complexity nddiversityof experience.While postmodernismas had a profound nflu-ence on many areasof social scienceand thehumanities,t hasbeenneglected y organizationtheorists ntil veryrecently Hassard nd Parker,1ee3).Despite ts attractions,he application f chaostheory o the socialsciencess still in its infancy,and thereare thosewho think that expectationsare too high (Baumol and Benhabib, 1989).Althoughreal ife phenomenamay resemblehepatternsgenerated y simplenonlinearsystems,that does not mean that we can easily modeland forecast these phenomena; t is almostimpossible o take a set of data and determinethe system of relationships hat generates t(Butler, 1990). In fact, there is considerabledebate in the economicsand finance iteratureabout how one testsa data series o determineif it is chaotic or simply subject to randominfluences Brock and Malliaris, 1989; Hsieh,1991).Moreover, it is important to recognizethat many systemsare not chaotic, and thatsystemscan transition between chaotic andnonchaotic tates.Chaos heory s perhaps etterseen as an extensionof systems heory (Katzand Kahn 1966; hompson,1967)nto the realmof nonlinear dynamics ather than as a totalparadigm hift.It is possible hat the applicationof chaostheory o socialscience as been constrained ythe fact that it has developed n relation tophysical systems,without taking into accountfundamentaldifferencesbetweenphysicalandsocial cience.n the socialworld, outcomes ften

Chaos Theory and Strategy t69reflect ery complexunderlying elationshipshatinclude the interaction of several potentiallychaoticsystems; rop prices, or example,areinfluencedby the interaction of economicandweathersystems. he search or a simpleset ofequations o explain complexphenomenamaybe a futile attempt to construct grand 'meta-theory,'a project hat s rejected n the postmod-ern paradigm.The applicationpresentedhereusesa different approach; ield study researchsused to derive a set of relationshipsamongvariablesand the influence of external systemsis modeledprobabilistically, methodsuggestedby Kelsey 1988).Socialand physicalsystems lso differ in thesource of unpredictability. In the physicalworld, unpredictabilityarises due to manyiterations,nonlinearity,and our inability todefinestartingconditionswith infiniteprecision.In the social world, far less accuracy ispossiblen defining tarting onditions, nd hespecificationof the system structure itself ismuch essprecise.A final difference is that physical systemsareshaped y unchangingatural aws,whereassocial systemsare subject to intervention byindividualsand organizations.nvestigations feconomic ime seriesby chaos heoristshaveusuallyassumed hat relationships mong eco-nomic actors are fixed over time. In reality,methods of stabilizing the economy havechanged from the use of the gold standardand balanced budgets to Keynesian demandmanagement nd , later, to monetarist onto ls.Human agencycan alter the parametersandvery structures of social systems, and it isperhapsunrealistically mbitious o think thatthe effectsof such intervention can be endo-genized in chaotic models.2 Nevertheless,chaotic models can be used to suggestwaysthat people might intervene o achievecertaingoals. The applicationpresented here, fo rexample,showshow management an reducethe volatility of the supply chain to improveperformance.

2 To some extent, the distinction between endogenous andexogenous variables in a model is one of convenience; afactor that is exogenous in a simple model might becomeendogenous in a more complex and comprehensive one.Exogenous factors can be included as random variables inchaotic systems or modeling purposes (Kelsey. 1988).


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170 D.LevyRELEVANCE OF CHAOS THBORY TOSTRATEGYTo understand he relevanceof chaos heory tostrategy,we need to conceptualizendustriesascomplex, dynamic, nonlinear systems.Firmsinteractwith eachother and with other actors ntheir environment, uchas consumers,abor, hegovernment,and financial institutions. Theseinteractions are strategic in the sense thatdecisionsby one actor take into accountantici-pated reactions by others, and thus reflecta recognition of interdependence.Althoughinterfirm behaviorhas beenmodeled ormally ineconomicsand businessstrategy using gametheory (Camerer, I99L), these models end topresume he emergence f equilibriumand donot adequatelyreflect industry dynamics. AsPorter (1990) emphasizes, he evolution ofindustriess dynamicandpathdependent: orpor-ate (and country-level) capabilities acquiredduring previouscompetitiveepisodes hape hecontext or futurecompetitivebattles.Moreover,the accumulationof competitiveadvantage anbe self-reinforcing,suggesting t least one wayin which industriesare nonlinear. f industriesdo behave as chaotic systems,a number ofimplications or strategycan be drawn.Long-term planning is very difficultIn chaoticsystems, mall disturbancesmultiplyover time because f nonlinear elationships ndthe dynamic, epetitive atureof chaotic ystems.As a result,suchsystems reextremely ensitiveto initial conditions,which makes forecastingvery difficult. This is a problem that hasconfronted meteorologists rying to model theweather: he fundamentalproblem is trying touse finite measurementsn an infinite world.A related problem is that as systemsevolvedynamically, hey are subject to myriad smallrandom or perhas haotic) nfluenceshat cannotbe incorporatednto the model.Formulatinga long-termplan is clearlya keystrategic ask facing any organization.Peopleinvolved n planning,whether n business, co-nomics,or someother area,havealways nownthat models realwaysust models, hat orecastsare uncertain,and that uncertaintygrowsovertime.Nevertheless.ur conventional nderstand-ing of linearmodelsand he influence f random

errorswould leadus to think that better modelsand a more accuratespecificationof startingconditionswould yield better forecasts,usefulfor perhapsmonths f not years nto the future.Chaos heory suggests therwise; he payoff interms of better forecastsof building morecomplex ndmoreaccuratemodelsmaybe small.Similarly,we cannot earn too much about thefuture by studying he past: f history s the sumof complex and nonlinear interactionsamongpeopleand nations, hen historydoesnot repeatitself. Concerningurban planning, Cartwright(1991)has noted that we have to acknowledgethat 'a completeunderstanding f some of thethingswe plan may be beyondal l possibility.'The notion hat ong-termplanning or chaoticsystems is not only difficult but essentiallyimpossible asprofound mplicationsor organi-zations trying to set strategy based on theiranticipationof the future. Rather than expendlargeamountsof resources n forecasting, tra-tegic planning needs to take into account anumber of possiblescenarios.Moreover, toonarrow a focus on a firm's core productsand markets might reduce the ability of theorganizationo adapt and be flexible n the faceof change.The proliferation of joint-venturesand the acquisition by large firms of stakesin entrepreneurial nterprises an perhapsbeunderstoodas attempts o keep a foothold in anumber of potential scenarios n the face ofuncertainty nd acceleratinghange.Industries do not reach a stableequilibriumThe traditional approach o understandingheinfluenceof industry structureon firm behaviorand competitive outcomes has been derivedfrom microeconomics,with its emphasisoncomparative tatics nd equilibrium.More recentapplicationsof game theory have attempted oaccount or interactionsamongsmall numbersoffirms (usually wo), yielding predictionsabout,for example, investments n R&D or plantcapacity to seize first-mover advantages.Eventhe most complexgame heoreticmodels,how-ever, are only considered seful f they predictan equilibrium outcome. By contrast, chaoticsystemso not reacha stable quilibrium;ndeed,they can neverpass hrough he sameexactstatemore than once. If they did, they would cycleendlessly hrough the same path because hey


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are driven by deterministic relationships.Theimplication s that industriesdo not 'settledown'and any apparent tability, or example n pricingor investment atterns,s likely to be short ived.Chaos theory also suggests hat changes nindustrystructures anbeendogenous. orporatedecisions o enter or exit the market, or todevelopnew echnologies, lter the verystructureof the industry, which in turn influences uturefirm behavior.One of the most provocativeandcontroversialelementsof chaos theory is thatchaoticsystems an spontaneously elf-organizeinto more complex tructuresAllen, 1988).Thenotion has been applied to biologicalevolution(Laszlo, 1987)as well as to economicsystems(Mosekilde ndRasmussen,986). n the contextof business trategy,he concept ouldpotentiallybe applied o the evolution of complexorganiza-tional relationshipssuch as long-term contractsand technical cooperation with suppliers, andhybrid forms of organizationalcontrol such asjoint ventures.Chaos heory suggestshat new,more complex organizational orms will appearmore frequently than if they were simply theresultof random mutations.Dramatic changecan occur unexpectedlyTraditionalparadigms f economics nd strategy,which are generallybased upon assumptions flinear relationships nd the use of comparativestatic analysis, ead to the conclusion thatsmall changes n parametersshould lead tocorrespondinglymall changesn the equilibriumoutcome.Chaos heory orcesus o reconsiderhisconclusion.Large fluctuationscan be generatedinternally by deterministic haoticsystems.Mod-els of population growth based on the logisticdifferenceequation llustrate how sudden, argechangesn population levelscan arise from thedynamics of the system rather than from theinfluenceof externalshocks Radzicki, 1990).3Similarly, if economicsystemsare chaotic thenwe do not need to search or wars or natural

3The logistic difference equation has the form:P,* t : P , * R* (1-P,)P, a fraction between0 and 1, represents he populationlevel as a proportionof the maximumcarryingcapacityofthe environment.R is the growth rate from one cycle o thenext. Population rowth s constrained y the factor 1-P,,whichcan be understood s a resource onstraint.

Chaos Theory and Strategy I7tdisasterso account or economicdepressionsra crash n the stock market.The size of fluctuations rom one period tothe next in chaoticsystems ave a characteristicprobabilitydistribution(Bak and Chen, 1991).Under this distribution, large fluctuationsoccurmore frequently than under the normal distri-bution, suggestinghat managersmight underesti-mate the potential for large changesn industryconditions r competitors' ehavior.Small exogenousdisturbanceso chaotic sys-temscan alsocauseunexpectedlyargechanges.The implication for business trategy s that theentry of one new competitoror the developmentof a seeminglyminor technologycan have asubstantialmpacton competitionn an ndustry.An example hat comes o mind s the way Dell'smail order strategy in the personal computerindustryforced other companies o reduce heirpricesand reexamine heir traditional high-costsalesand service hannels.Short-term forecastsand predictionsof patternscan be madeAlthough the unpredictability nd instabilityofchaotic systems as been emphasized,here isalso a surprising degree of order in chaoticsystems. Short-term forecasting is possiblebecause n a deterministicsystem, given theconditions at time 't,' we can calculate heconditions t time 't+1.' A carefullyconstructedsimulation model of a complex system withaccurately pecified tartingconditionscan yielduseful orecasts t least or several ime periods.Weather forecastsbasedon sophisticated om-putermodelsusingmeasurementsrom thousandsof points around the globe do provide usefulforecastsor a few days,which susuallysufficientfor purposessuch as hurricanewarnings. f weimagine hat strategicdecisionsn companies remadeon a monthlyor even annualcycle, henindustry s imulation models might be able tomake useful predictionsover a time horizon ofseveralmonths or possiblyyears.Another featureof chaotic systems hat lendsthem a degreeof order is that they arebounded;outcomevariables uchpricingor investmentsnnew capacity luctuatewithin certainbounds hatare determined by the structure of the systemand its parameters ut not its initial conditions.In the context of businesstrategy hesebounds


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t72 D. Levymight be set by feedback loops such as theentrance of new firms or antitrust action bythe government in responseto monopolisticconditions.Although we cannot orecast he precisestateof a chaoticsystem n the longer term, chaoticsystems race repetitive patterns which oftenprovide useful information. According to Rad-zicki (1990),deterministic haos is characterizedby self-sustained scillationswhose period andamplitudeare nonrepetitiveand unpredictable,yetgenerated y a system evoidof randomness.'For example, while we do not know exactlywhere or when tornadoes and hurricaneswillstrike,we do know what conditionsead o theiroccurrence,when and where they are mostfrequent,and heir ikely paths. n a similarway,we know that oligopolistic ndustries end toalternatebetweenperiodsof intensecompetitionandperiods f morecooperative ehavior,houghwe do not know when an industry will make thetransition rom one state o another.To give athird example,we know that the economy yclesthrough recessionsnd booms, houghwe cannotpredict very well the depth or duration of aparticular recession Butler, 199). Observingpatterns s especiallyuseful if we can associatedifferentphases f the systemwith other charac-teristics; or example,here sa strong elationshipbetweenbusiness yclesand other variables uchas demand, interest rates, the availability ofcredit, vendor ead times, and the tightness fthe labor market.An intriguingaspectof the patterns racedbychaoticsystemss that they are independentofscale; n otherwords,similarpatternsare tracedby a systemwhateverhorizon s used o view t.Economic time seriesoften appear to displaythisproperty.Stockprices, or example, isplayaremarkably imilarpatternwhetherone observesdaily changes ver 1 year or minute-by-minutechanges ver a day. These magesof patternswithin patterns are termed fractals when theyare generated y chaoticsystems. n the naturalworld, ractals anbe found n manyphenomena,from the shapeof coastlineso ice crystals.Theimplicationsor businesstrategy renot entirelyclear.One nterpretations that previous xperi-ences n an industry are likely to recur on amuch larger scale. A second nterpretation sthat similar patterns of behavior might beexpected whether one examinescompetition

between ountries, etween irms n an industry,or even betweendepartmentsn a firm.Guidelinesare needed o cope with complexityand uncertainty'Strategy'can refer to a set of guidelines hatinfluence decisionsand behavior. It is thecomplexityof strategicnteractions,whether nchess,soccer, or in business, hat makes itessentialo adopt simplifyingstrategieso guidedecisions; ven he most powerfulcomputersareunable o track all possiblemovesand counter-moves n a chess ame.GeneralElectric'swellknownstrategy f beingnumberone or numbertwo in every industry in which it participatessa simple exampleof a guidelinewhich may begenerallyuseful but is not alwaysoptimal inevery situation. We need general guidelinesbecause t is impossible o specify the optimalcourseof action for everypossiblescenario.It is important to distinguish he guidelinesand patternsof behavior hat constitutestrategyfrom the underlying rules of the game. In agame of chess, or example,knowing the rulesfor playing the game does not necessarily iveone insights nto strategies or successful lay.One can only learn thesestrategies fter experi-encing the complexitiesof interactionson thechess oard. Indeed,because f the complexityof strategic nteractions,one does not alwaysknow why a particularstrategy s successful.While the complexity of industry systemsdictates he need or broadstrategies,he dynamicnatureof chaoticsystemsmandateshat strategiesadapt.As industrystructures volveand competi-tors change heir strategies, firm clearly needsto change ts own guidelinesand decision ules.The problemhere is that there is no simplewayof derivingoptimalstrategiesor a givensystem.Indeed, n a complexsystem he best strategiesmight achievegoals ndirectly and even appearcounter-intuitive. hebestway o improvequalityis not necessarilyo checkeveryproductseveraltimes: t may be to improve abor relationsandthus gain abor'scooperationn finding ways oreduce defects. IBM's decision in 1981 tolet other 'clone' manufacturers se the DOSoperating ystem or personal omputers elpedcompetitorsbut also indirectly helped IBM tobuild market share by creating the industrystandard.


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Chaos Theory and Strategy t73In order to understand ndirect or counter-intuitive means o an end, a systemneeds o be I I/ENDoRS I Iunderstood as a whole. If systems are very I | !t lt lcomplex, then simulation models might pronl J i Ihelpful in finding the most effective way to cor{poNENTachieve a goal. The example discussed later in Il{\tBNtclRY vs. TARGET Nv. iIIthis paper llustrates ow the best way to cutinventoryn a supplychainmight be to reduce I i idisruptions to the chain rather than shorten lead I TARGET oMPoNENT --- II TNvENToRY itrmes. v i

!I nnooucrroN l


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174 D.Levycation can be delayed,and information can bemisunderstood.A second mportantdimensionof the supplychain system s the time relationshipamongthe stages.As a result of the time lags incommunication, roduction,and distribution,adisruption o one elementgenerates sequenceof changesn other parts of the system.Forexample,demand fluctuationscausechangesnsales orecasts, roductionschedules, nd orderto vendors.Disruptionsoriginating n any onepart of the system, n effect, propagate orwardsand backwardsalongthe chain. Disruptionscaninteract; for example, a production problemcould occur in a month when demand wasunexpectedly igh, causingsome demand o gounmet.A numberof researchersnvestigatingaspectsof the supply chain have recently turned tosimulationmodels,mostof whichattempt o findcost-minimizingolutions sing inearor nonlinearprogramming e.g., Breitman and Lucas, 1987;Cohenand Lee, 1989;HodderandJucker,1985;Hodder and Dincer, 1986).These models donot, however,deal adequatelywith uncertaintyin a dynamic,multiperiodsetting.The simulationmodel developedor this studyis describedn more detail in the Appendix andin Levy (1992). The model assumesa set ofdecision ules and linkagesamong the stagesofthe supply chain, which are used to determinethe production plan and other variables eachmonth.Eachstageof the supplychain s subjectto random luctuations,and the chainevolves na dynamic ashion rom month to month.Resultsand implicationsFigure 2 showssimulated nventory levelsovera period of lffi months basedon a version ofthe model representing roduction n Singaporefor the U.S. market, which entails 30 daysshipping ime. Inventory levels are expressed sa proportionof monthly demand,and negativevaluesndicate hat demandcannotbe met frominventory hat month.The most obvious feature of the graph isthe volatility of inventory levels. These largefluctuations llustratewell how relativelysmalldisruptions o the supplychain can nteractwithorganizational ecisionprocesses nd lead timesin the system o produce arge and unpredictable

t ,,"r,"iir"r, tooFigure . Simulatednventoryevels, roducthippedfromSingaporeo U.S.

outcomes.CCT's managers id not expect hisvolatility, becausehe strategic ecisiono sourcefrom Singaporewas taken using cost estimatesthat assumed stablesupplychain. n fact, theinstability of the chain imposed substantialunexpectedcostson CCT, primarily related tothe expense of using air-freight to expediteshipments,he opportunity ostof lostsales, ndthecostof holdingexcessnventories.n addition,CCT incurredexpenseselating o the communi-cation and managerial ime needed o managethe unstable supply chain. These costs wereal l underestimated ecausemanagersdid notappreciate he impact of complex interactionsalong he supplychain,and tended o treateachdisruptionas a one-timeevent.The simulation does reveal some patternswithin the fluctuating inventory levels. Peakinventory evelsare reached,on average, very5 months, hough he numberof monthsbetweenpeaks varies from 21 months; the system isclearly aperiodic.Moreover, there is a relation-ship between the average ime between peakinventory evelsand shipping ime: when pro-duction is available or sale the same month(representingroductionn the U.S. for the U.S.market), average ime betweenpeak inventorylevels alls to around4 months.Note also thatinventory evelsare lessvolatileand that peaksare lower, as would be expectedwhen deliverytimesare shorter.As well as illustrating the volatility of thesupplychainand its associatedosts, he model

oZ .=u,o-FzO 2=FF ' IzUJz o

INVENTORY O DEMANDRATIOFOR OOMONTHS


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INVENTORYO DEMANDRATIOFO R1OOMONTHS2 . e2 . 62 . 42 2-z

t r 1 .9o . . 8J 4 . 4F 1 . 26 1= o ' ot o . BO o. . rz 0 . 2llj7 -o.z

- 0 . 4- o . 3- o . 8

TIME (MONTHSI

Figure 3. Simulated inventory levels, product madeand sold in U.S.

can be used to guide decisions concerningproduction location, sourcing, and optimuminventory levels. Used for this purpose, thesimulation model demonstrates ow complexsystems eed o be understood s a whole, andhow goalscan be achieved hrough indirect andnonobviousmeans.For example, he simulationmodel enables he cost of offshore sourcing obe estimatedn termsof the ncrementalnventoryneeded o maintaindemand ulfillmentat somespecifiedevel. It was estimated hat in order tomaintainan averageevel of 95 percentdemandfulfillment when sourcing rom Singapore atherthan California for the U.S. market, averagesystem nventory levels would have to increaseby more than 2 monthsof sales.The underlying order in the supply chainsystem an be glimpsedn Figure4. The X-axisshows he value of a parameter epresentinghestandarddeviation of the monthly percentagechange in demand, a measure of demandinstability. The range of values was chosen oreflect the instability observed or CCT's pro-ducts. The Y-axisshows he averageproportionof demand hat could not be fulfilled over 100iterations f a 36-monthperiod.Thereappears o be a thresholdbeneathwhichdemand instability does not have a significanteffect; n this region, he system oesnot exhibitchaos.Once he nstability arameter pproaches0.1, the proportionof demandunfulfilledbeginsto rise rapidly but smoothly and exceeds10

ChaosTheory and Strategy 175

Figure 4. Impact of demand stability on unfulfilleddemands

percentof demand for productswith the mostunstable emand.While the simulationmodel llustrateshe costsand difficultiesof an unstablesupply chain, italso suggests pproaches o solving theseprob-lems. The simulationmodel could be used todetermineoptimal nventory evels or differentproductsand components, nd to identify thosewhich need to be manufactured ocally, basedon the level of volatility associated ith them.Although CCT's managershad always beenaware hat unstable roducts houldbe producedlocally, hey ended o underestimatehese osts.The simulationprovideda tool to analyzemorepreciselywhich productswere stableenough oroffshore manufacture.Another approach,using the insight gainedfrom Figure 4 above, would be for managersto attempt to improve the accuracy of salesforecastingn order to reduce he costof offshoremanufacture.Similarly, managers ould try toreducedisruptions o the supplychain rom othersources,by working with suppliers o improvequality and reduce ead times, and by reducingthe occurrence f internalproductionproblems.Volatility can alsobe reducedby interveningatthe boundaries of the system to change itsstructure.CCT, for example,hasparticipatednthe widely observedrend oward ewer suppliers.Using hese echniques,managementouldsim-plify and stabilize he system, ossiblymaking tnonchaotic.It should be noted that the approaches o

o . 1 t2 o ' r= o . o euJ! o .o .lr,=l o.07u-j 0 .08l.LZ o.osf$ o.orf o .o ,ulf , o.o"

0. 01

STD. DEV. OF MONTHLY % CHANGE IN DEMAND


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176 D. Levymanaging omplexsystems escribedabovecon-stitute eyelements f leanproduction Womack,Jones,and Roos, 1990).Lean productioncanthus be conceptualized s a way to simplify andreduce he varianceof complex dynamicsupplychain systems,making their behavior morepredictable. ndeed, this research uggestshat,contrary to the prevailing notion that leanproductionmethodsconstrain nternationalpro-duction (Hoffman and Kaplinsky, 1988;Jonesand Womack, 1985), lean production couldactually facilitate international operations byreducingvolatility along the supply chain.

CONCLUSIONSChaos theory is a promising framework thataccountsor the dynamicevolution of industriesand the complex interactions among industryactors. By conceptualizingndustries as chaoticsystems,a number of managerial mplicationscan be developed. Long-term forecasting isalmost impossible for chaotic systems, anddramatic change can occur unexpectedly;as aresult, flexibility and adaptiveness re essentialfor organizationso survive.Nevertheless,haoticsystems xhibit a degreeof order, enablingshort-term forecastingo be undertakenandunderlyingpatterns can be discerned. Chaos theory alsopoints o the importanceof developing uidelinesand decision ules to copewith complexity,andof searching or nonobviousand indirect meansto achievinggoals.The simulation model presentedhere demon-strates hat chaos heory haspracticalapplicationto issuesof business trategy.The simulationillustrates how managementcan underestimatethe impact of disruptions to an internationalsupplychain,generating ubstantial nanticipatedcosts. It also demonstrateshow managementmight interveneto reduce the volatility of thesupply chain and improve its performance,byreducing he extent of disruptionsand changingthe structureof the supply chain system.

APPENDIXThe supply chain was simulatedusinga spread-sheet model, with columns representingthevariables n the system, and rows representing

successivemonths. In order to model thestochastic atureof the supply hain,a simulationpackage alled RISK'was used,which allowsavariety of probabilitydistributionso be assignedto each cell of the spreadsheet.Actual dataand decisioncriteria from CCT were used todetermine the structure of the model and therangeof values o be used or variousparameters.For example,monthly bookings data revealedthat the level of bookingseach month could bemodeledby taking he previousmonth'sdemandplus a percentagechange hat was a normallydistributed andomvariablewith meanzero.Three sets of input parameterswere used orthe model. The first set representshe level ofdisruptionsaffectingdemand,supplierdeliveries,and production. The secondset representshetarget levels of system and component nven-tories.The standardvalues or thesewere set athalf a month's sales or systems, xcludinganyinventory n transit, and 1 week'sproduction orcomponents. he third groupof input parametersrepresents he impact of distanceon shippingtime for finishedgoods,and of different vendorlead times. The main output variables of thesystemwere the levelsof systemand componentinventoriesand the level of demand ulfillment.Using theseparameters,he model simulates36-month ime period.The model beginsat timezero with a nominal level of demand andproductionof 100units, but thesevaluesevolveover time. The simulationpackageenables hespreadsheeto be recalculated specified umberof times. On each teration, he entire 36-monthspreadsheets recalculatedwith a new set ofrandom numbers.A large number of iterationscan thus be used to build up a probabilitydistribution for these output variables and tocalculatea mean (expected)value. The resultspresented ere were obtainedusingone hundrediterationsfor each simulation. Each simulationof lffi iterationswas run using a different set ofinput parameters.A list of variables ecalculatedon a monthly basis s given n the Appendix.Three main performancemeasureswere cap-tured as output variables.Average system andaveragecomponent inventory levels over 100iterationsof the 36-monthperiodwereexpressedin terms of months' sales.Demand fulfillmentwas measuredby summing he total number ofunits of demandwhich could not be met due toinadequatenventory,and dividing his total by


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total demand o givea ratio indicatingunfulfilleddemand.The effect of distanceon shipping imes and ENDINGof different vendor lead times was modeled by SYSTEM INV:using different versionsof the basicmodel. Thesimulationsused or this paperuseda version nwhich production in Singapore s available orsale n the U.S. the followingmonth (i.e., 30days o ship and clearcustoms)and vendor eadtimes are 60 days. TARGETSYSTEMINV:

Chaos Theory and Strategy I77dependingon the version,lessa randompercentage.Systemnventory at the endof eachmonth was equal tothe inventory the previousmonth less sales plus pro-duction the same or thepreviousmonth, dependingon the modelversion.The target level of systeminventorywas adjusted achmonth to equala proportionof the currentsales orecast.The production plan for thefollowing month was basedon the sales forecast,adjusted for the differencebetweenactualand plannedsystemnventory.System production eachmonth was equal to theproduction plan of the pre-viousmonth, lessa randompercentage, nd constrainedby the availabilityof materialinventory.Unfulfilled demandequalledmonthly demand lessmonthlv sales.

VARIABLES RECALCULATED ONMONTHLY BASISFOR SIMULATIONMODELACTUALDEMAND:

ENDINGCOMP. INV.:

TARGET The target level of compo-COMP. INV.: nent inventorywas adjustedeachmonth to equal a pro-portion of the current salesforecast.ORDERS Orders to vendors wereTO VENDORS: basedon the sales orecast,the productionschedule orthe following month, and acomparison of actual withtarget component nventorylevels.

PRODUCTIONPLAN:

ACTUALSALES:

SALESFORECAST:

DEL. FROMVENDORS:

Demand for systems eachmonth was equal to theprevious month's demandplus a random percentage ACTUALchange. PRODUCTION:Salesof systems achmonthwereequal o demand nlessconstrained y lack of inven-tory.The best sales orecast forthe next month was the UNFUL.previous month's demand, DEMAND:as no trend was built intodemand luctuations.The level of component (ormaterial) inventory each REFERENCESmonth was the level theprevious month plus deliver- Allen, P. M. (1988). Dynamicsmodelsof evolvingies from vendors less what- systeryl" SystemDynamics Review' 4' Summer'ever was consumedn pro- ""flt.t"tiJtilbn"r (1991).self-organizedcriticality',duction. ScientificAmerican, 2&(l), pp. 4G53.

Deliveries each monthequalled orders placed 1. or2 months previously,

Bartlett, C. A. and S. Ghoshal (1989). ManagingacrossBorders TheTransnationat olution. HarvardBusiness choolPress,Boston,MA.Baumol,W. and J. Benhabib 1989). Chaos:Signifi-cance, mechanism, and economic applications'.Journal of Economic Perspectives, , pp. 77-105.Breitman,R. L. andJ. M. Lucas 1987).PLANETS:Amodelingsystem or business lanning', nterfaces,r7(1),pp. 94-106.Brock, W. and A. Malliaris (1989). DffirentialEquations,Stabilityand Chaos n Dynamic Systems.North-Holland,New York.Butler, A. (1990). A methodological pproach ochaos:Are economistsmissing he point?', FederalReserve ank of St.Louis, 72(13),pp. 3G48.Camerer,C. F. (1991). Doesstrategy esearch eedgame heory?', StrategicManagement ournal, 12,Winter Specialssue,pp . 137-153.


12/12

I78 D.LevyCartwright,T. J. (1991).Planning nd chaos heory',Journal of the American Planning Association,57(l), pp. 44-56.Cohen, M. A. and H. L. Lee (1989). Resourcedeploymentanalysisof global manufacturinganddistribution networks', Journal of Manufacturingand OperationsManagement, , pp.81-104.Eisenhardt,K. M. (1989). Building theories romcase study research', Academy of ManagementReview, 4(4), pp. 532-550.Feigenbaum,M. J. (May 1983).Universalbehaviorin nonlinearsystems',Physica,7, pp. IG39.Ford, J. (April 1983). How random s a coin toss?'Physics oday,36, pp . 4M7.Goldberger,A. L., D. R. Rigney and B. J. West(February1990).Chaosand fractals n physiology',ScientificAmerican, 263, pp. 4A9.Hassard, . and M. Parker (eds.)(1993).Postmodern-ismand Organizations. age,ThousandOaks, CA.Hodder,J. E. andJ. V. Jucker 1985). Internationalplant location under price and exchange rateuncertainty', Engineering Costs and ProductionEconomics,9, pp. 225129.Hodder,J. E. and M. C. Dincer 1986).A multifactormodel or international acility locationand financ-ing under uncertainty',Computers nd OperationsResearch,3(5), pp. 601-609.Hoffman, K. and R. Kaplinsky(1988).Driving Force.WestviewPress,Boulder,CO.Hsieh,D. A. (1991). Chaosand nonlineardynamics:Application to financial markets', Journal ofFinance,46(5), pp. 1839-1877.Jones,D. T. and J. P. Womack(1985). Developingcountries nd he utureof the automobile ndustry',World Development, 3(3), pp. 393407.Kauffman,S. A. (1991). Antichaosand adaptation',Scientific merican, 265(2),pp. 78-84.Katz,D. andR. L. Kahn (1966).TheSocialPsychologyof Organizations.ohnWiley andSons,Chichester.

Kelsey, D. (1988). The economics f chaosor thechaosof economics',Oxford Economic Papers,4{1,pp. 1-31.Lant, T. K. and S. J. Mezias (1990). Managingdiscontinuous hange:A simulation tudyof organi-zational learning and entrepreneurship',StrategicManagement ournal, Summer Special ssue, ll,pp . 147-179.Laszlo, E. (1987). Evolution: The Grand Synthesis.Shambhala, oston,MA.Levy, D. (1992). 'The costs of coordinating nter-national production'. DBA Dissertation,HarvardUniversity Graduate Schoolof BusinessAdminis-tration.Lorenz, E. N. (March 1993). Deterministicnon-periodic flow', Journal of theAtmosphericSciences,20, pp. 13f141.Mayer-Kress,G. and S. Grossman 1989). Chaosinthe international arms race', Nature, 337, pp.70r-704.Morecroft, J. D. (1984). Strategysupportmodels',StrategicManagement ournal, 5(3), pp. 215-229.Mosekilde,E. and S. Rasmussen1986). Technical

economic uccession nd the economic ong wave',EuropeanJournal of OperationalResearch, 5, pp.27-38.Porter, M. E. (1990).The CompetitiveAdvantageofNations.Free Press,New York.Radzicki,M. J. (1990). Institutionaldynamics, eter-ministicchaos,and self-organizingystems',ournalof Economic Issues, 4(l), pp. 57-102.Sterman,J. D. (1989). Deterministicchaos n anexperimentaleconomic system',Journal of Eco-nomic BehaviorandOrganization,12(29),p. 1-28.Thompson, J. D. (1967). Organizations n Action.McGraw-Hill, New York.Womack, J. P., D. T. Jonesand D. Roos (1990).The Machine that Changed the World. RawsonMacmillan.New York.

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