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Strategic Management Journal, Vol. 15, 167-178 (1994)

CHAOS THEORY AND STRATEGY: THEORY,APPLICATION. AND MANAGERIAL IMPLICATIONSDAVID LEVYDepartment 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.

INTRODUCTION

One of the enduring problems facing the fieldof strategic managment is the lack of theoreticaltools available to describe and predict thebehavior of firms and industries. For example,even if we know that oligopolistic industries arelikely to experience periods of stability alternatingwith periods of intense competition, we do notknow when they will occur or what will be theoutcome. Similarly, it is almost impossible topredict the impact of the advent of a newcompetitor or technology in an industry. Thefundamental problem is that industries evolve ina dynamic way over time as a result of complexinteractions among firms, government, labor,consumers, financial institutions, and otherelements of the environment. Not only doesindustry structure influence firm behavior, but

Key words: Chaos theory, simulation, international,supply chain

ccc 0143 -2095 t94tB01.67 -r2@) 1994 by John Wiley & Sons, Ltd.

firm behavior in turn can alter the structure ofan industry and the contours of competition.Existing theoretical models, however, tend toassume relatively simple linear relationshipswithout feedback. Indeed, many strategic theoriesattempt to classify firms and industries and todescribe appropriate strategies for each class;examples include the Boston Consulting Groupmatrix for resource allocation and Bartlett'sclassification of international strategies (Bartlettand Ghoshal, 1989). Although these models arebased on recurrent patterns that we recognize inthe real world, there are usually far too manyexceptions for the models to have much predictivevalue.

Chaos theory, which is the study of nonlineardynamic systems, promises to be a usefulconceptual framework that reconciles the essen-tial unpredictability of industries with the emer-gence of distinctive patterns(Cartwright, 1991).Although chaos theory was originally developedin the context of the physical sciences, Radzicki(1990) and Butler (1990) amongst others have

168 D. Levy

noted that social, ecological, and economicsystems also tend to be characterized by nonlinearrelationships and complex interactions that evolvedynamically over time. This recognition has ledto a surge of interest in applying chaos theory toa number of fields, including ecology (Kauffman,l99l), medicine (Goldberger, Rigney and West,1990) international relations (Mayer-Kress andGrossman, 1989), and economics (Baumol andBenhabib, 1989; Kelsey, 1988).t Despite theapparent applicability of chaos theory to the fieldof business strategy', there has been surprisinglylittle work in this area.

This paper introduces readers to chaos theory,and discusses its relevance to the social sciencesin general and to aspects of strategy in particular,including planning and forecasting, and theimpact of change on firms and industries. Theapplication of chaos theory to a business situationis illustrated using a simulation model of aninternational supply chain. The model, which isbased on the author's research into the supplychain of a California-based computer company,depicts the complex interactions between thefirm, its suppliers, and its markets. The simulationresults illustrate the managerial implications ofapplying chaos theory to strategic management.The model demonstrates how small disruptionsto the supply chain interact to make the chainhighly volatile, imposing significant costs on theorganization. Although forecasting is very difficultin the supply chain, distinct patterns emergewhich are useful for managers. The simulationalso shows that by understanding the supplychain as a complex dynamic system, it is possibleto identify managerial approaches that lower thecost of operating the supply chain.

AN INTRODUCTION TO CHAOSTHEORY

Chaos theory is the study of complex, nonlinear,dynamic systems. The field was pioneered byLorenz (1963), who was studying the dynamicsof turbulent flow in fluids. Although we allrecognize the swirls and vortices that characterizeturbulent flow, the complexities of turbulent flow

t 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 confounded mathematicians for years. Asimilar problem afflicts someone who is tryingto calculate the path of an object in thegravitational pull of two or more bodies. Whilewe can use simple Newtonian equations to predictthe orbits of planets around the sun with a highdegree of accuracy, the mathematics involved inthe case of two or more 'suns' become intractable.The problem can be illustrated on a terrestriallevel by observing the motion of a simple toy, ametal ball suspended over two or more magnets.The ball will trace a series of patterns that neverexactly repeat themselves, and yet aie not totallyrandom.

The paradox here is that the motion of themetal ball is driven by the same Newtonianequations as the well understood case of a singlegravitational attractor. If we knew precisely theoriginal location, speed, and direction of theball, we ought to be able to predict its path witha reasonable degree of accuracy. How is itthat deterministic systems can give rise tounpredictability? The explanation is that tinyvariations in the motion of the ball are magnifiedevery time it swings by one of the magnets. Itis a combination of this divergence and therepeated interactions that give rise to 'chaotic'

behavior. Mathematically, chaotic systems arerepresented by differential equations that cannotbe solved, so that we are unable to calculate thestate of the system at a specific future time 't'.

At the limit, chaotic systems can become trulyrandom. A toss of a coin or the roll of a dieare, in theory, deterministic systems, but yieldmore or less random outcomes. Not only is itimpossible to toss a coin twice in exactly thesame way, but on each toss the coin is subjectto slightly different air currents, themselves aresult of turbulent air flow (Ford, 1983).

To overcome the problem of intractable differ-ential equations, researchers usually model sys-tems as discrete difference equations, whichspecify what the state of the system will be attime 't* 1' given the state of the system at time't.' Computer simulations can then be used tosee how the system evolves over time.

One of the major achievements of chaos theoryis its ability to demonstrate how a simple set ofdeterministic relationships can produce patternedyet unpredictable outcomes. Chaotic systemsnever return to the same exact state, yet theoutcomes are bounded and create patterns that

embody mathematical constants (Feigenbaum,1983). It is the promise of finding a fundamentalorder and structure behind complex events thatprobably explains the great interest chaos theoryhas generated in so many fields.

Chaos theory and the social sciences

Proponents of chaos theory enthusiastically seesigns of it everywhere, pointing to the ubiquityof complex, dynamic systems in the social worldand the resemblance between patterns generatedby simulated nonlinear systems and real timeseries of stock exchange or commodity prices.From a theoretical perspective, chaos theory iscongruous with the postmodern paradigm, whichquestions deterministic positivism as it acknowl-edges the complexity and diversity of experience.While postmodernism has had a profound influ-ence on many areas of social science and thehumanities, it has been neglected by organizationtheorists until very recently (Hassard and Parker,1ee3).

Despite its attractions, the application of chaostheory to the social sciences is still in its infancy,and there are those who think that expectationsare too high (Baumol and Benhabib, 1989).Although real life phenomena may resemble thepatterns generated by simple nonlinear systems,that does not mean that we can easily modeland forecast these phenomena; it is almostimpossible to take a set of data and determinethe system of relationships that generates it(Butler, 1990). In fact, there is considerabledebate in the economics and finance literatureabout how one tests a data series to determineif it is chaotic or simply subject to randominfluences (Brock and Malliaris, 1989; Hsieh,1991). Moreover, it is important to recognizethat many systems are not chaotic, and thatsystems can transition between chaotic andnonchaotic states. Chaos theory is perhaps betterseen as an extension of systems theory (Katzand Kahn , 1966; Thompson,1967) into the realmof nonlinear dynamics rather than as a totalparadigm shift.

It is possible that the application of chaostheory to social science has been constrained bythe fact that it has developed in relation tophysical systems, without taking into accountfundamental differences between physical andsocial science. In the social world, outcomes often

Chaos Theory and Strategy t69

reflect very complex underlying relationships thatinclude the interaction of several potentiallychaotic systems; crop prices, for example, areinfluenced by the interaction of economic andweather systems. The search for a simple set ofequations to explain complex phenomena maybe a futile attempt to construct grand 'meta-

theory,' a project that is rejected in the postmod-ern paradigm. The application presented hereuses a different approach; field study research isused to derive a set of relationships amongvariables and the influence of external systemsis modeled probabilistically, a method suggestedby Kelsey (1988).

Social and physical systems also differ in thesource of unpredictability. In the physicalworld, unpredictability arises due to manyiterations, nonlinearity, and our inability todefine starting conditions with infinite precision.In the social world, far less accuracy ispossible in defining starting conditions, and thespecification of the system structure itself ismuch less precise.

A final difference is that physical systemsare shaped by unchanging natural laws, whereassocial systems are subject to intervention byindividuals and organizations. Investigations ofeconomic time series by chaos theorists haveusually assumed that relationships among 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 and, later, to monetarist contols.Human agency can alter the parameters andvery structures of social systems, and it isperhaps unrealistically ambitious to think thatthe effects of such intervention can be endo-genized in chaotic models.2 Nevertheless,chaotic models can be used to suggest waysthat people might intervene to achieve certaingoals. The application presented here, forexample, shows how management can 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 for modeling purposes (Kelsey. 1988).

170 D. Levy

RELEVANCE OF CHAOS THBORY TOSTRATEGY

To understand the relevance of chaos theory tostrategy, we need to conceptualize industries ascomplex, dynamic, nonlinear systems. Firmsinteract with each other and with other actors intheir environment, such as consumers, labor, thegovernment, and financial institutions. Theseinteractions are strategic in the sense thatdecisions by one actor take into account antici-pated reactions by others, and thus reflecta recognition of interdependence. Althoughinterfirm behavior has been modeled formally ineconomics and business strategy using gametheory (Camerer, I99L), these models tend topresume the emergence of equilibrium and donot adequately reflect industry dynamics. AsPorter (1990) emphasizes, the evolution ofindustries is dynamic and path dependent: corpor-ate (and country-level) capabilities acquiredduring previous competitive episodes shape thecontext for future competitive battles. Moreover,the accumulation of competitive advantage canbe self-reinforcing, suggesting at least one wayin which industries are nonlinear. If industriesdo behave as chaotic systems, a number ofimplications for strategy can be drawn.

Long-term planning is very difficult

In chaotic systems, small disturbances multiplyover time because of nonlinear relationships andthe dynamic, repetitive nature of chaotic systems.As a result, such systems are extremely sensitiveto initial conditions, which makes forecastingvery difficult. This is a problem that hasconfronted meteorologists trying to model theweather: the fundamental problem is trying touse finite measurements in an infinite world.A related problem is that as systems evolvedynamically, they are subject to myriad smallrandom (or perhas chaotic) influences that cannotbe incorporated into the model.

Formulating a long-term plan is clearly a keystrategic task facing any organization. Peopleinvolved in planning, whether in business, eco-nomics, or some other area, have always knownthat models are always just models, that forecastsare uncertain, and that uncertainty grows overtime. Nevertheless. our conventional understand-ing of linear models and the influence of random

errors would lead us to think that better modelsand a more accurate specification of startingconditions would yield better forecasts, usefulfor perhaps months if not years into the future.Chaos theory suggests otherwise; the payoff interms of better forecasts of building morecomplex and more accurate models may be small.Similarly, we cannot learn too much about thefuture by studying the past: if history is the sumof complex and nonlinear interactions amongpeople and nations, then history does not repeatitself. Concerning urban planning, Cartwright(1991) has noted that we have to acknowledgethat 'a complete understanding of some of thethings we plan may be beyond all possibility.'

The notion that long-term planning for chaoticsystems is not only difficult but essentiallyimpossible has profound implications for organi-zations trying to set strategy based on theiranticipation of the future. Rather than expendlarge amounts of resources on forecasting, stra-tegic planning needs to take into account anumber of possible scenarios. Moreover, toonarrow a focus on a firm's core productsand markets might reduce the ability of theorganization to adapt and be flexible in the faceof change. The proliferation of joint-venturesand the acquisition by large firms of stakesin entrepreneurial enterprises can perhaps beunderstood as attempts to keep a foothold in anumber of potential scenarios in the face ofuncertainty and accelerating change.

Industries do not reach a stable equilibrium

The traditional approach to understanding theinfluence of industry structure on firm behaviorand competitive outcomes has been derivedfrom microeconomics, with its emphasis oncomparative statics and equilibrium. More recentapplications of game theory have attempted toaccount for interactions among small numbers offirms (usually two), yielding predictions about,for example, investments in R&D or plantcapacity to seize first-mover advantages. Eventhe most complex game theoretic models, how-ever, are only considered useful if they predictan equilibrium outcome. By contrast, chaoticsystems do not reach a stable equilibrium; indeed,they can never pass through the same exact statemore than once. If they did, they would cycleendlessly through the same path because they

are driven by deterministic relationships. Theimplication is that industries do not 'settle down'and any apparent stability, for example in pricingor investment patterns, is likely to be short lived.

Chaos theory also suggests that changes inindustry structures can be endogenous. Corporatedecisions to enter or exit the market, or todevelop new technologies, alter the very structureof the industry, which in turn influences futurefirm behavior. One of the most provocative andcontroversial elements of chaos theory is thatchaotic systems can spontaneously self-organizeinto more complex structures (Allen, 1988). Thenotion has been applied to biological evolution(Laszlo, 1987) as well as to economic systems(Mosekilde and Rasmussen, 1986). In the contextof business strategy, the concept could potentiallybe applied to the evolution of complex organiza-tional relationships such as long-term contractsand technical cooperation with suppliers, andhybrid forms of organizational control such asjoint ventures. Chaos theory suggests that new,more complex organizational forms will appearmore frequently than if they were simply theresult of random mutations.

Dramatic change can occur unexpectedly

Traditional paradigms of economics and strategy,which are generally based upon assumptions oflinear relationships and the use of comparativestatic analysis, lead to the conclusion thatsmall changes in parameters should lead tocorrespondingly small changes in the equilibriumoutcome. Chaos theory forces us to reconsider thisconclusion. Large fluctuations can be generatedinternally by deterministic chaotic systems. Mod-els of population growth based on the logisticdifference equation illustrate how sudden, largechanges in population levels can arise from thedynamics of the system rather than from theinfluence of external shocks (Radzicki, 1990).3Similarly, if economic systems are chaotic thenwe do not need to search for wars or natural

3 The logistic difference equation has the form:P,* t : P, * R* (1-P, )P, a fraction between 0 and 1, represents the populationlevel as a proportion of the maximum carrying capacity ofthe environment. R is the growth rate from one cycle to thenext. Population growth is constrained by the factor 1-P,,which can be understood as a resource constraint.

Chaos Theory and Strategy I7t

disasters to account for economic depressions ora crash in the stock market.

The size of fluctuations from one period tothe next in chaotic systems have a characteristicprobability distribution (Bak and Chen, 1991).Under this distribution, large fluctuations occurmore frequently than under the normal distri-bution, suggesting that managers might underesti-mate the potential for large changes in industryconditions or competitors' behavior.

Small exogenous disturbances to chaotic sys-tems can also cause unexpectedly large changes.The implication for business strategy is that theentry of one new competitor or the developmentof a seemingly minor technology can have asubstantial impact on competition in an industry.An example that comes to mind is the way Dell'smail order strategy in the personal computerindustry forced other companies to reduce theirprices and reexamine their traditional high-costsales and service channels.

Short-term forecasts and predictions of patternscan be made

Although the unpredictability and instability ofchaotic systems has been emphasized, there isalso a surprising degree of order in chaoticsystems. Short-term forecasting is possiblebecause in a deterministic system, given theconditions at time 't,' we can calculate theconditions at time 't+1.' A carefully constructedsimulation model of a complex system withaccurately specified starting conditions can yielduseful forecasts at least for several time periods.Weather forecasts based on sophisticated com-puter models using measurements from thousandsof points around the globe do provide usefulforecasts for a few days, which is usually sufficientfor purposes such as hurricane warnings. If weimagine that strategic decisions in companies aremade on a monthly or even annual cycle, thenindustry simulation models might be able tomake useful predictions over a time horizon ofseveral months or possibly years.

Another feature of chaotic systems that lendsthem a degree of order is that they are bounded;outcome variables such pricing or investments innew capacity fluctuate within certain bounds thatare determined by the structure of the systemand its parameters but not its initial conditions.In the context of busines strategy these bounds

t72 D. Levy

might be set by feedback loops such as theentrance of new firms or antitrust action bythe government in response to monopolisticconditions.

Although we cannot forecast the precise stateof a chaotic system in the longer term, chaoticsystems trace repetitive patterns which oftenprovide useful information. According to Rad-zicki (1990), deterministic chaos 'is characterizedby self-sustained oscillations whose period andamplitude are nonrepetitive and unpredictable,yet generated by a system devoid of randomness.'For example, while we do not know exactlywhere or when tornadoes and hurricanes willstrike, we do know what conditions lead to theiroccurrence, when and where they are mostfrequent, and their likely paths. In a similar way,we know that oligopolistic industries tend toalternate between periods of intense competitionand periods of more cooperative behavior, thoughwe do not know when an industry will make thetransition from one state to another. To give athird example, we know that the economy cyclesthrough recessions and booms, though we cannotpredict very well the depth or duration of aparticular recession (Butler, 199). Observingpatterns is especially useful if we can associatedifferent phases of the system with other charac-teristics; for example, there is a strong relationshipbetween business cycles and other variables suchas demand, interest rates, the availability ofcredit, vendor lead times, and the tightness ofthe labor market.

An intriguing aspect of the patterns traced bychaotic systems is that they are independent ofscale; in other words, similar patterns are tracedby a system whatever horizon is used to view it.Economic time series often appear to displaythis property. Stock prices, for example, display aremarkably similar pattern whether one observesdaily changes over 1 year or minute-by-minutechanges over a day. These images of patternswithin patterns are termed fractals when theyare generated by chaotic systems. In the naturalworld, fractals can be found in many phenomena,from the shape of coastlines to ice crystals. Theimplications for business strategy are not entirelyclear. One interpretation is that previous experi-ences in an industry are likely to recur on amuch larger scale. A second interpretation isthat similar patterns of behavior might beexpected whether one examines competition

between countries, between firms in an industry,or even between departments in a firm.

Guidelines are needed to cope with complexityand uncertainty'Strategy' can refer to a set of guidelines thatinfluence decisions and behavior. It is thecomplexity of strategic interactions, whether inchess, soccer, or in business, that makes itessential to adopt simplifying strategies to guidedecisions; even the most powerful computers areunable to track all possible moves and counter-moves in a chess game. General Electric's wellknown strategy of being number one or numbertwo in every industry in which it participates isa simple example of a guideline which may begenerally useful but is not always optimal inevery situation. We need general guidelinesbecause it is impossible to specify the optimalcourse of action for every possible scenario.

It is important to distinguish the guidelinesand patterns of behavior that constitute strategyfrom the underlying rules of the game. In agame of chess, for example, knowing the rulesfor playing the game does not necessarily giveone insights into strategies for successful play.One can only learn these strategies after experi-encing the complexities of interactions on thechess board. Indeed, because of the complexityof strategic interactions, one does not alwaysknow why a particular strategy is successful.

While the complexity of industry systemsdictates the need for broad strategies, the dynamicnature of chaotic systems mandates that strategiesadapt. As industry structures evolve and competi-tors change their strategies, a firm clearly needsto change its own guidelines and decision rules.The problem here is that there is no simple wayof deriving optimal strategies for a given system.Indeed, in a complex system the best strategiesmight achieve goals indirectly and even appearcounter-intuitive. The best way to improve qualityis not necessarily to check every product severaltimes: it may be to improve labor relations andthus gain labor's cooperation in finding ways toreduce defects. IBM's decision in 1981 tolet other 'clone' manufacturers use the DOSoperating system for personal computers helpedcompetitors but also indirectly helped IBM tobuild market share by creating the industrystandard.

Chaos Theory and Strategy t73

In order to understand indirect or counter-intuitive means to an end, a system needs to be I

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INI|ENSORY VS. TARGBT INV. !The simulation of an international supply chaindemonstrates how chaos theory can be appliedto the understanding of a real managerial issue.The example is drawn from the author's researchinto the costs of coordinating the internationalsupply chain of a personal computer companycalled California Computer Technology (CCT).4Following Eisenhardt (1989), a case approachwas used to build and test theory in an iterativemanner.

The research led to a conceptualization of thesupply chain as a complex, dynamic, nonlinearsystem. The system is subject to external disrup-tions, and the stages of the chain are linked byflows of goods and information, with time lagsand feedback mechanisms. The complexity ofinteractions along the supply chain is such thatone cannot easily predict how the system willoperate under various conditions, but a computermodel of these processes can simulate theoutcome (Lant and Mezias, 1990; Morecroft1984). Figure 1 is a simplified representation ofCCT's supply chain, showing in schematic formthe flows of goods and information within themodel. Solid lines represent flows of goods,dotted lines flows of information.

In reality, supply chains are often much morecomplex than this. CCT, for example, hashundreds of vendors, three production sites, anddistributors and warehouses in many countries.Corporate headquarter functions interact withvendors, the field sales organization, and theproduction sites. Nevertheless, the diagram does

a The name of the company has been disguisedproprietary information.

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capture the essence of the supply chain. Materialsmove along the chain in one direction, gainingvalue at each stage. Information is exchanged inboth directions among the organizations alongthe chain. This simple representation is veryuseful in analyzing the potential sources ofcoordination costs in a supply chain and theimpact of geographically separating stages of thechain. It is also valuable as a tool for designingstrategies that improve the performance of asupply chain.

There are two important dimensions to thissystem, uncertainty and time relationships.Rather than performing as a stable, ready statesystem, each stage of the chain is potentiallysubject to disruptions, or 'shocks.' Demandfluctuates in an unpredictable way, productionproblems can affect output, and suppliers do notalways deliver on time. When demand andproduction are rising, delivery and productionproblems are more likely. As a result of theuncertainty at each stage, flows of materialsand finished systems fluctuate in volume, andinventories need to be adjusted to cope with the

to prorecr uncertainty, The linkages themselves are alsosubject to disruption. Shipments and communi-

174 D. Levy

cation can be delayed, and information can bemisunderstood.

A second important dimension of the supplychain system is the time relationship amongthe stages. As a result of the time lags incommunication, production, and distribution, adisruption to one element generates a sequenceof changes in other parts of the system. Forexample, demand fluctuations cause changes insales forecasts, production schedules, and orderto vendors. Disruptions originating in any onepart of the system, in effect, propagate forwardsand backwards along the chain. Disruptions caninteract; for example, a production problemcould occur in a month when demand wasunexpectedly high, causing some demand to gounmet.

A number of researchers investigating aspectsof the supply chain have recently turned tosimulation models, most of which attempt to findcost-minimizing solutions using linear or nonlinearprogramming (e.g., Breitman and Lucas, 1987;Cohen and Lee, 1989; Hodder and Jucker, 1985;Hodder and Dincer, 1986). These models donot, however, deal adequately with uncertaintyin a dynamic, multiperiod setting.

The simulation model developed for this studyis described in more detail in the Appendix andin Levy (1992). The model assumes a set ofdecision rules and linkages among the stages ofthe supply chain, which are used to determinethe production plan and other variables eachmonth. Each stage of the supply chain is subjectto random fluctuations, and the chain evolves ina dynamic fashion from month to month.

Results and implications

Figure 2 shows simulated inventory levels overa period of lffi months based on a version ofthe model representing production in Singaporefor the U.S. market, which entails 30 daysshipping time. Inventory levels are expressed asa proportion of monthly demand, and negativevalues indicate that demand cannot be met frominventory that month.

The most obvious feature of the graph isthe volatility of inventory levels. These largefluctuations illustrate well how relatively smalldisruptions to the supply chain can interact withorganizational decision processes and lead timesin the system to produce large and unpredictable

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outcomes. CCT's managers did not expect thisvolatility, because the strategic decision to sourcefrom Singapore was taken using cost estimatesthat assumed a stable supply chain. In fact, theinstability of the chain imposed substantialunexpected costs on CCT, primarily related tothe expense of using air-freight to expediteshipments, the opportunity cost of lost sales, andthe cost of holding excess inventories. In addition,CCT incurred expenses relating to the communi-cation and managerial time needed to managethe unstable supply chain. These costs wereall underestimated because managers did notappreciate the impact of complex interactionsalong the supply chain, and tended to treat eachdisruption as a one-time event.

The simulation does reveal some patternswithin the fluctuating inventory levels. Peakinventory levels are reached, on average, every5 months, though the number of months betweenpeaks varies from 21 months; the system isclearly aperiodic. Moreover, there is a relation-ship between the average time between peakinventory levels and shipping time: when pro-duction is available for sale the same month(representing production in the U.S. for the U.S.market), average time between peak inventorylevels falls to around 4 months. Note also thatinventory levels are less volatile and that peaksare lower, as would be expected when deliverytimes are shorter.

As well as illustrating the volatility of thesupply chain and its associated costs, the model

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can be used to guide decisions concerningproduction location, sourcing, and optimuminventory levels. Used for this purpose, thesimulation model demonstrates how complexsystems need to be understood as a whole, andhow goals can be achieved through indirect andnonobvious means. For example, the simulationmodel enables the cost of offshore sourcing tobe estimated in terms of the incremental inventoryneeded to maintain demand fulfillment at somespecified level. It was estimated that in order tomaintain an average level of 95 percent demandfulfillment when sourcing from Singapore ratherthan California for the U.S. market, averagesystem inventory levels would have to increaseby more than 2 months of sales.

The underlying order in the supply chainsystem can be glimpsed in Figure 4. The X-axisshows the value of a parameter representing thestandard deviation of the monthly percentagechange in demand, a measure of demandinstability. The range of values was chosen toreflect the instability observed for CCT's pro-ducts. The Y-axis shows the average proportionof demand that could not be fulfilled over 100iterations of a 36-month period.

There appears to be a threshold beneath whichdemand instability does not have a significanteffect; in this region, the system does not exhibitchaos. Once the instability parameter approaches0.1, the proportion of demand unfulfilled beginsto rise rapidly but smoothly and exceeds 10

Chaos Theory and Strategy 175

Figure 4. Impact of demand stability on unfulfilleddemands

percent of demand for products with the mostunstable demand.

While the simulation model illustrates the costsand difficulties of an unstable supply chain, italso suggests approaches to solving these prob-lems. The simulation model could be used todetermine optimal inventory levels for differentproducts and components, and to identify thosewhich need to be manufactured locally, basedon the level of volatility associated with them.Although CCT's managers had always beenaware that unstable products should be producedlocally, they tended to underestimate these costs.The simulation provided a tool to analyze moreprecisely which products were stable enough foroffshore manufacture.

Another approach, using the insight gainedfrom Figure 4 above, would be for managersto attempt to improve the accuracy of salesforecasting in order to reduce the cost of offshoremanufacture. Similarly, managers could try toreduce disruptions to the supply chain from othersources, by working with suppliers to improvequality and reduce lead times, and by reducingthe occurrence of internal production problems.Volatility can also be reduced by intervening atthe boundaries of the system to change itsstructure. CCT, for example, has participated inthe widely observed trend toward fewer suppliers.Using these techniques, management could sim-plify and stabilize the system, possibly making itnonchaotic.

It should be noted that the approaches to

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176 D. Levy

managing complex systems described above con-stitute key elements of lean production (Womack,Jones, and Roos, 1990). Lean production canthus be conceptualized as a way to simplify andreduce the variance of complex dynamic supplychain systems, making their behavior morepredictable. Indeed, this research suggests that,contrary to the prevailing notion that leanproduction methods constrain international pro-duction (Hoffman and Kaplinsky, 1988; Jonesand Womack, 1985), lean production couldactually facilitate international operations byreducing volatility along the supply chain.

CONCLUSIONS

Chaos theory is a promising framework thataccounts for the dynamic evolution of industriesand the complex interactions among industryactors. By conceptualizing industries as chaoticsystems, a number of managerial implicationscan be developed. Long-term forecasting isalmost impossible for chaotic systems, anddramatic change can occur unexpectedly; as aresult, flexibility and adaptiveness are essentialfor organizations to survive. Nevertheless, chaoticsystems exhibit a degree of order, enabling short-term forecasting to be undertaken and underlyingpatterns can be discerned. Chaos theory alsopoints to the importance of developing guidelinesand decision rules to cope with complexity, andof searching for nonobvious and indirect meansto achieving goals.

The simulation model presented here demon-strates that chaos theory has practical applicationto issues of business strategy. The simulationillustrates how management can underestimatethe impact of disruptions to an internationalsupply chain, generating substantial unanticipatedcosts. It also demonstrates how managementmight intervene to reduce the volatility of thesupply chain and improve its performance, byreducing the extent of disruptions and changingthe structure of the supply chain system.

APPENDIX

The supply chain was simulated using a spread-sheet model, with columns representing thevariables in the system, and rows representing

successive months. In order to model thestochastic nature of the supply chain, a simulationpackage called 'RISK'was used, which allows avariety of probability distributions to be assignedto each cell of the spreadsheet. Actual dataand decision criteria from CCT were used todetermine the structure of the model and therange of values to be used for various parameters.For example, monthly bookings data revealedthat the level of bookings each month could bemodeled by taking the previous month's demandplus a percentage change that was a normallydistributed random variable with mean zero.

Three sets of input parameters were used forthe model. The first set represents the level ofdisruptions affecting demand, supplier deliveries,and production. The second set represents thetarget levels of system and component inven-tories. The standard values for these were set athalf a month's sales for systems, excluding anyinventory in transit, and 1 week's production forcomponents. The third group of input parametersrepresents the impact of distance on shippingtime for finished goods, and of different vendorlead times. The main output variables of thesystem were the levels of system and componentinventories and the level of demand fulfillment.Using these parameters, the model simulates a36-month time period. The model begins at timezero with a nominal level of demand andproduction of 100 units, but these values evolveover time. The simulation package enables thespreadsheet to be recalculated a specified numberof times. On each iteration, the entire 36-monthspreadsheet is recalculated with a new set ofrandom numbers. A large number of iterationscan thus be used to build up a probabilitydistribution for these output variables and tocalculate a mean (expected) value. The resultspresented here were obtained using one hundrediterations for each simulation. Each simulationof lffi iterations was run using a different set ofinput parameters. A list of variables recalculatedon a monthly basis is given in the Appendix.

Three main performance measures were cap-tured as output variables. Average system andaverage component inventory levels over 100iterations of the 36-month period were expressedin terms of months' sales. Demand fulfillmentwas measured by summing the total number ofunits of demand which could not be met due toinadequate inventory, and dividing this total by

total demand to give a ratio indicating unfulfilleddemand.

The effect of distance on shipping times and ENDINGof different vendor lead times was modeled by SYSTEM INV:using different versions of the basic model. Thesimulations used for this paper used a version inwhich production in Singapore is available forsale in the U.S. the following month (i.e., 30days to ship and clear customs) and vendor leadtimes are 60 days. TARGET

SYSTEM INV:

Chaos Theory and Strategy I77

depending on the version,less a random percentage.System inventory at the endof each month was equal tothe inventory the previousmonth less sales plus pro-duction the same or theprevious month, dependingon the model version.The target level of systeminventory was adjusted eachmonth to equal a proportionof the current sales forecast.The production plan for thefollowing month was basedon the sales forecast,adjusted for the differencebetween actual and plannedsystem inventory.System production eachmonth was equal to theproduction plan of the pre-vious month, less a randompercentage, and constrainedby the availability of materialinventory.Unfulfilled demand equalledmonthly demand lessmonthlv sales.

VARIABLES RECALCULATED ONMONTHLY BASIS FOR SIMULATIONMODEL

ACTUALDEMAND:

ENDINGCOMP. INV.:

TARGET The target level of compo-COMP. INV.: nent inventory was adjusted

each month to equal a pro-portion of the current salesforecast.

ORDERS Orders to vendors wereTO VENDORS: based on the sales forecast,

the production schedule forthe following month, and acomparison of actual withtarget component inventorylevels.

PRODUCTIONPLAN:

ACTUALSALES:

SALESFORECAST:

DEL. FROMVENDORS:

Demand for systems eachmonth was equal to theprevious month's demandplus a random percentage ACTUALchange. PRODUCTION:Sales of systems each monthwere equal to demand unlessconstrained by lack of inven-tory.The best sales forecast forthe next month was the UNFUL.previous month's demand, DEMAND:as no trend was built intodemand fluctuations.The level of component (ormaterial) inventory each REFERENCES

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