Forthcoming in The Bullwhip Effect in Supply Chains. O. Carranza and F. Villegas, (eds.) Palgrave McMillan.

Operational and Behavioral Causes of Supply Chain Instability*

John D. Sterman Sloan School of Management

Massachusetts Institute of Technology Cambridge, MA 02142

jsterman@mit.edu web.mit.edu/jsterman/www

The central core of many industrial companies is the process of production and distribution. A recurring problem is to match the production rate to the rate of final consumer sales. It is well known that factory production rate often fluctuates more widely than does the actual consumer purchase rate. It has often been observed that a distribution system of cascaded inventories and ordering procedures seems to amplify small disturbances that occur at the retail level... How does the system create amplification of small retail sales changes?... [W]e shall see that typical manufacturing and distribution practices can generate the types of business disturbances which are often blamed on conditions outside the company.

—Jay W. Forrester (1961) Industrial Dynamics, p. 22

Supply chain instability is a pervasive and enduring characteristic of market economies. Production, inventories, employment, revenue, profit and a host of other indicators fluctuate, irregularly but persistently, throughout the economy, in industries from A to Z—Aircraft to Zinc (e.g., W. Mitchell 1971, Zarnowitz 1985, Sterman 2000). Supply chain instability harms firms, consumers, and the economy through excessive inventories, poor customer service, and unnecessary capital investment. Instability in employment erodes skill and worsens labor-management relations. Volatility in revenue and profit increases risk and raises the cost of capital. Instability diverts leadership attention from the design of successful new products and strategies to firefighting and crisis management.

Despite the undoubted benefits of the lean manufacturing and supply chain revolutions of the past decade, supply chain instability continues. Examples include record inventory write-offs, excess capacity, price cuts, layoffs, and bankruptcies in computers, semiconductors, telecommunications, and other high-tech industries after 2000, and waves of zero-interest financing, employee discounts for all, and cash-back incentives accompanying surplus inventory in the automobile market.

Supply chain instability is often described as the bullwhip effect, the tendency for variability to increase at each level of a supply chain as one moves from customer sales to production (Lee et al. 1997, Chen et al. 2000). While amplification from stage to stage is important, supply chain instability is a richer and more subtle phenomenon. The economy, and the networks of supply * I acknowledge the contributions of Ed Anderson, Octavio Carranza, Rachel Croson, Gokhan Dogan, Karen Donohue, Paulo Gonçalves, Elena Katok, and Rogelio Oliva. Financial support provided by the Project on Innovation in Markets and Organizations at the MIT Sloan School.

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chains embedded within it, is a complex dynamic system and generates multiple modes of behavior. These include business cycles (oscillation), amplification of orders and production from consumption to raw materials (the bullwhip), and phase lag (shifts in the timing of the cycles from consumption to materials). High product returns and spoilage are common in industries from consumer electronics to hybrid seed corn (Gonçalves 2003). Many firms experience pronounced hockey-stick patterns in which orders and output rise sharply just prior to the end of a month or quarter as the sales force and managers rush to hit revenue goals. Boom and bust dynamics in supply chains are often worsened by phantom orders—orders customers place in response to perceived shortages in an attempt to gain a greater share of a shrinking pie (T. Mitchell 1923, Sterman 2000, ch. 18.3, Gonçalves 2002, Gonçalves and Sterman 2005).

What are the causes of supply chain instability? Why does supply chain instability persist, despite the lean revolution and tremendous innovations in technology? What can be done to stabilize supply chains and improve their efficiency?

Here I describe the origins of supply chain instability from a complex systems perspective. The dynamics of supply chain networks arise endogenously from their structure. That structure includes both operational and behavioral elements. Operational causes refer to the physical and institutional structure. Physical structure includes the placement of inventories throughout the network of suppliers and customers and time delays in production, order fulfillment, transportation, and so on. The institutional structure includes the degree of horizontal and vertical coordination and competition among and within firms, the availability of information to each organization and department, and the incentives faced by each decision maker. Behavioral causes encompass the mental models of the decision makers, including their attitudes, attributions about other actors, and the heuristics and routines they use to interpret the information they have and make decisions such as production, capacity and pricing.

The operations management literature emphasizes the physical and institutional structure, assuming decision makers are rational agents who make optimal decisions given their local incentives and the information available to them. For example, the bullwhip can arise from rational behavior if there are quantity discounts that encourage bulk purchases. However, supply chain instability is also, and crucially, a behavioral phenomenon. The mental models and decision rules people use to manage supply chains are far from optimal. Decision makers are, at best, boundedly rational, typically relying on mental models that grossly simplify the environment, incorporate few feedback processes, ignore or underestimate time delays, and fail to account for key stock and flow structures. The same bounds on rationality slow learning, enabling supply chain instability to persist. I review the extensive experimental and field data documenting these misperceptions of feedback and discuss how they can be overcome.

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Oscillation, Amplification, and Phase Lag

Exhibit 1 shows industrial production in the US. The data exhibit several modes of behavior. First, the long-run growth rate of manufacturing output is about 3.4%/year. Second, as seen in the bottom panel, production fluctuates significantly around the growth trend. The dominant periodicity is the business cycle, a cycle of prosperity and recession of about 3–5 years in duration, but exhibiting considerable variability.

The amplitude of business cycle fluctuations in materials production is significantly greater than that in consumer goods production (exhibit 2). The peaks and troughs of the cycle in materials production also tend to lag behind those in production of consumer goods. Typically, the amplitude of fluctuations increases as they propagate from the customer to the supplier, with each upstream stage tending to lag behind its customer. These three features, oscillation, amplification, and phase lag, are pervasive in supply chains.

Oscillation, amplification, and phase lag are even more pronounced in specific industries. The top panel in exhibit 3 shows the petroleum supply chain (the figures show the annualized growth rate; all monthly data are shown as 12-month centered moving averages to filter out the high-frequency month-to-month noise). Oil and gas drilling activity fluctuates about three times more than production, imposing large boom and bust cycles on suppliers of drill rigs and oil field services. The middle panel shows the machine tool industry. Fluctuations in economic growth lead to much larger swings in motor vehicle sales. During recessions, sales fall as people keep old cars longer, causing unanticipated inventory accumulation and forcing even larger production cutbacks. The automotive industry generates a large share of total machine tool orders. During a production downturn, the auto companies postpone or cancel their capital investment plans, causing even larger drops in the orders they place for machine tools. During the next upswing they scramble to build capacity and orders surge. The phase lag between vehicle production and the induced changes in machine tool orders is clearly visible. The bottom panel shows the semiconductor industry. Semiconductor production is at the upstream end of the computer and electronics supply chain and fluctuates far more than industrial production as a whole.

Prior research offers two categories of explanation for the bullwhip effect, each motivating distinct recommendations to dampen it. The first category focuses on operational causes of the problem, such as production lags and order processing delays, procedures for demand forecasting, order batching to take advantage of scale economies or quantity discounts, rational responses to product shortages, and price fluctuations caused by promotions. Many of these were documented and modeled by Forrester (1958, 1961); see also Lee et al. (1997). Techniques to eliminate them are now an important part of the tool kit for supply chain design (e.g., Simchi-Levi et al. 1999).

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The second category, first introduced by Forrester (1958, 1961), emphasizes behavioral causes of instability. Behavioral explanations emphasize the bounded rationality of decision makers, particularly the failure to account for feedback effects, accumulations, and time delays. Studies in dynamic decision making consistently show that people do not understand the stock and flow structure of systems and do not adequately account for time delays, feedbacks, and nonlinearities (Booth Sweeney and Sterman 2000, Dörner 1996, Brehmer 1992). Specifically, people tend to place orders based on the gap between the target level of inventory and their current, on-hand stock, while giving insufficient weight to the supply line of unfilled orders (the stock of orders placed but not yet received). Supply line underweighting is sufficient to cause the instability observed in both experimental and real supply chains (Sterman 1989a, 2000).

Supply chains are of course not restricted to manufacturing or even management settings. Service industries such as insurance have supply chains for recruiting customers, writing policies, and processing claims (Anderson and Morrice 2005, Fitzsimmons et al. 2003). Labor supply chains provide employees through processes of vacancy creation, recruitment, and training; product development provides new products through requirements definition, high-level design, detailed design, testing, and so on. Even the supply of glucose providing the energy required for your metabolic activity is the output of a supply chain encompassing food consumption, insulin synthesis, glucose metabolism and waste excretion (see Sturis et al. 1991 for a system dynamics model of the human glucose-insulin system). Like manufacturing supply chains, these systems include multiple time delays and are prone to instability and oscillation.

The Stock Management Problem

Supply chains consist of networks of firms, each receiving orders and adjusting production and production capacity to meet changes in demand. Each link in a supply chain maintains stocks of materials and finished product. To understand the behavior of a supply chain and the causes of instability, it is first necessary to understand the structure and dynamics of a single link, that is, how an individual firm manages its resources as it attempts to balance production with orders.

In such stock management tasks, managers seek to maintain a stock (the state of the system) at a particular target level or within an acceptable range. Stocks are altered only by changes in their inflow and outflow rates. Typically, the manager must set the inflow rate to compensate for losses and usage and to counteract disturbances that push the stock away from its desired value. Usually there are lags between the initiation of a control action and its effect and lags between a change in the stock and the perception of that change by the decision maker. The duration of these lags may vary and may be influenced by the manager’s own actions.

Stock management problems occur at many levels of aggregation. At the level of a firm,

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managers order parts and raw materials to maintain inventories sufficient for production to proceed at the desired rate. They must adjust for variations in the usage of these materials and for changes in their delivery delays. At the individual level, you regulate the temperature of the water in your morning shower, guide your car down the highway, and manage your checking account balance. At the macroeconomic level, the US Federal Reserve seeks to manage the stock of money to stimulate economic growth and avoid inflation, while compensating for variations in credit demand, budget deficits, and international capital flows.

The stock management control problem can be divided into two parts: (1) the stock and flow structure of the system and (2) the decision rule used by the managers to control the acquisition of new units (Exhibit 4). Consider first the physical structure. The stock to be controlled, S, is the accumulation of the acquisition rate AR less the loss rate LR:

!

S = (AR – LR)dt" (1)

Losses include any outflow from the stock and may arise from usage (as in a raw material inventory) or decay (as in the depreciation of plant and equipment). The loss rate must depend on the stock itself—losses must approach zero as the stock is depleted—and may also depend on other endogenous variables X (e.g., prices, marketing campaigns, competitor responses) and exogenous variables U (e.g., weather). Losses may be nonlinear and may depend on the age distribution of the stock:

LR = f(S, X, U) (2)

In general the decision maker cannot acquire units directly; rather there is a time delay between ordering units and delivery. Hence there is a supply line of unfilled orders—the stock of orders placed but net yet received. The supply line accumulates the Order Rate, OR, less the acquisition rate:

!

SL = (OR – AR)dt" (3)

In general, the acquisition of new units involves time delays (e.g., the time required to fill orders, fabricate subassemblies, or build capital plant). Hence acquisition depends on the supply line and the average Acquisition Lag, λ.

AR = L(SL, λ) (4)

where the lag functional L(.) denotes a material delay. The acquisition lag λ is itself endogenous. The acquisition of new units requires resources: Production requires labor and equipment; deliveries require materials handling systems and transportation resources. These resources may themselves be dynamic and endogenous. The resources available at any moment impose capacity constraints. The acquisition lag λ depends on the supply line relative to the capacity of the process to delivery, which in turn depends on other endogenous and exogenous variables.

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Often, the average acquisition lag is relatively constant up to the point where the required acquisition rate exceeds the capacity of the process, as for example when the desired construction rate for capital plant exceeds the capacity of the construction industry. The acquisition lag can also be influenced by management, as when a firm speeds construction through overtime, or expedites materials procurement by paying premium freight. Thus the acquisition lag depends on the supply line and these other endogenous and exogenous variables:

λ = f(SL, X, U) (5)

When the acquisition rate is constrained by the capacity of the supplier the actual delivery time for items in the supply line rises, causing deliveries to be delayed and product to be rationed among competing customers. The consequences of such rationing are discussed below.

The stock management structure is quite general. The system is nonlinear (nonlinearities arise from nonnegativity constraints and capacity limits on acquisition). There may be arbitrarily complex feedbacks among the endogenous variables, and the system may be influenced by a number of exogenous forces, both systematic and stochastic. Exhibit 5 maps common examples into the generic form. In each case, the manager must choose the order rate over time so as to keep the stock close to a target. Oscillation and instability are common in these systems.

In most realistic stock management situations the complexity of the feedbacks among the variables precludes the determination of the optimal strategy. The order decision model proposed here assumes that managers, unable to optimize, instead exercise control through a locally rational heuristic. The model thus falls firmly in the tradition of bounded rationality as developed by Simon (1982), Cyert and March (1963), and others. Cognitive limitations are recognized, as are information limitations caused by organizational structures such as task factoring and subgoals (for a discussion of local rationality in the context of simulation models see Morecroft 1983, 1985 and Sterman 2000).

The hypothesized decision rule utilizes information locally available to the decision maker and does not presume that the manager has global knowledge of the structure of the system. Managers are assumed to choose orders so as to: (1) replace expected losses from the stock; (2) reduce the discrepancy between the desired and actual stock; and (3) maintain an adequate supply line of unfilled orders. To formalize this heuristic, first observe that orders in most real-life situations must be nonnegative:1

OR = MAX(0, IO) (6) 1 Order cancellations are sometimes possible and occasionally exceed new orders (e.g. the U.S. nuclear power industry in the 1970s, telecommunications equipment in 2001). Cancellations are subject to different costs and administrative procedures than new orders and should be modeled as a distinct outflow from the supply line rather than as negative orders.

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where IO is the indicated order rate, the rate indicated by other pressures.

The indicated order rate is based on the anchoring and adjustment heuristic (Tversky and Kahneman 1974). Anchoring and adjustment is a common strategy in which an unknown quantity is estimated by first recalling a known reference point (the anchor) and then adjusting for the effects of other factors which may be less salient or whose effects are obscure, requiring the decision maker to estimate these effects by what Kahneman and Tversky (1982) call mental simulation. Anchoring and adjustment occurs a wide variety of decision-making tasks (Plous 1993). Here the anchor is the expected loss rate Le. Adjustments are then made to bring the stock and supply line in line with their desired levels:

IO = Le + AS + ASL (7)

where AS, the Adjustment for the Stock, corrects discrepancies between the desired and actual stock, and ASL, the Adjustment for the Supply Line, corrects discrepancies between the desired and actual supply line.

Why does the order rate depend on expected losses rather than the actual loss rate? The sales of a company right now cannot be measured. Instead sales are accumulated over some interval of time such as a week, month, or quarter. The reported sales rate is the average over the reporting interval, and sales right now usually differ from the average over the interval. Even in a supply chain with bar code scanning or RFID, the reported flows always differ from their instantaneous values. Further, the more frequently sales data are reported, the more high-frequency noise they contain. Managers seeking to determine whether a change in orders is a temporary blip to be quickly reversed or a trend requiring changes in production, employment, and capital investment must therefore wait until more data become available, creating additional delay between data reporting and action. Indeed, the more frequently data are sampled and reported, the more noise they will contain, and the longer the decision maker must wait before being able to separate signal from noise.

Forecasts of the loss rate (e.g., shipments from inventory) may be formed in various ways. Common forecasting methods include moving averages, exponential smoothing, and trend extrapolation. Even when apparently sophisticated market research methods and econometric models are used, forecasters tend to massage the data in such a way that the resulting forecasts are often indistinguishable from simple smoothing and extrapolation (Sterman 1987).

The bottom of Exhibit 4 shows the feedback structure of the ordering heuristic. The adjustment for the stock AS creates a negative feedback loop that regulates the stock. For simplicity the adjustment is linear in the discrepancy between the desired stock S* and the actual stock:

AS = αS(S* – S), (8)

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where the stock adjustment parameter αS is the fraction of the discrepancy ordered each period. The adjustment for the supply line is formulated analogously as

ASL = αSL(SL* – SL), (9)

where SL* is the desired supply line and αSL is the fractional adjustment rate for the supply line. The desired supply line in general is not constant but depends on the desired throughput Φ* and the expected acquisition lag λe:

SL* = λeΦ*. (10)

By Little’s Law, the longer the expected delay in acquiring goods or the larger the throughput desired, the larger the supply line must be. For example, if a producer wishes to add 10,000 widgets per week to finished inventory and production requires 8 weeks, there must be 80,000 widgets in various stages of work in process inventory to ensure an uninterrupted flow of production. The adjustment for the supply line creates a negative feedback loop that adjusts orders so as to maintain an acquisition rate consistent with expected throughput and the acquisition lag. Without such a feedback production would be initiated even after the supply line contained sufficient orders to correct stock shortfalls, producing overshoot and instability (as shown below, this is precisely what happens). The supply line adjustment also compensates for changes in the acquisition lag. If the acquisition lag doubled, for example, the supply line adjustment would induce sufficient additional orders to restore the desired throughput. As in the formation of expected losses, there are a variety of possible representations for λe and Φ*, ranging from constants through sophisticated forecasts (Dogan and Sterman 2005). In particular, it takes time to detect changes in delivery times. Customers often do not know that goods they ordered will be late until after the promised delivery time has passed. Hence changes in λe tend to lag changes in the actual acquisition lag.

Behavior: The Endogenous Emergence of Instability

The simple stock management structure yields important insight into the sources of amplification observed in supply chains. To illustrate, exhibit 6 shows the policy structure diagram for a simple model of a manufacturing firm operating a make-to-stock system. The structure is an example of the general stock management structure described above. The firm maintains a stock of finished inventory and fills orders as they arrive. Production takes time. The stock of WIP (work in process) is the supply line. WIP is increased by production starts and decreased by production. A key decision for the firm is production scheduling: managers must set production starts to replace expected losses from inventory (shipments), keep inventory at an appropriate level to provide good customer service, and maintain an adequate supply line of WIP inventory to do so. If inventory is inadequate, some items will be out of stock and shipments fall below

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orders, degrading customer service (in this initial model I assume customers are delivery sensitive; unfilled orders are lost to competitors). The firm adjusts production starts to move the levels of inventory and WIP toward their desired levels. Exhibit 7 shows illustrative parameters. The manufacturing cycle time, from the receipt of raw materials to the completion of finished product, is set to 8 weeks. To provide excellent customer service, the firm seeks to maintain inventory coverage of four weeks. They attempt to correct gaps between desired and actual inventory in 8 weeks (αS = 1/8 of the gap per week) to smooth production and minimize costly swings in output, and correct gaps between the desired and actual level of WIP inventory over two weeks (αSL = 1/2 of the gap per week). Exponential smoothing of actual orders, a widely used method, forms the demand forecast.

To illustrate how supply chain instability arises endogenously through the interaction of a firm’s own structure and policies, in this initial model demand is exogenous and materials, plant, equipment and labor are assumed to be ample so the production process is uncapacitated. Hence the lag between production starts and completion is constant (these and other simplifying assumptions are relaxed in Sterman 2000 and Gonçalves et al. 2005). The resulting dynamics arise entirely within the firm itself as it manages its inventories and production.2

Exhibit 8 shows the firm’s response to an unanticipated 20% step increase in customer orders (the initial customer order rate is 10,000 widgets per week). The firm is initially able to fill nearly all the incoming orders, despite the increase. However, since production continues at the initial rate of 10,000 widgets/week, inventory falls. As inventory falls, so too does the firm’s ability to ship. Shipments drop below orders, causing the firm to lose business (and its reputation as a reliable supplier). The growing gap between desired and actual inventory forces desired production above expected orders. The quantity of work in process required to meet the higher production goal also grows, opening a gap between the desired and actual level of WIP. Desired production starts therefore rise even more than desired production.

As time passes the firm recognizes that the change in demand is not a mere random blip and gradually raises its demand forecast. As expected orders rise, so too does desired inventory, further increasing the gap between desired and actual inventory and further boosting desired production. Though customer orders jump 20%, production starts peak more than 42% higher than the initial rate about 4 weeks after the shock. A useful measure of supply chain instability is the amplification ratio, defined as the ratio of the maximum change in the output to the maximum change in the input. The amplification ratio for production starts is 42%/20% = 2.1.

2 The model is fully documented in Sterman (2000), Chapter18, and is available at www.mhhe.com/business/opsci/sterman/models.mhtml; file <widgets>.

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A 1% increase in desired capacity induces a peak surge in production starts of more than 2%.

The rapid increase in production starts soon fills the supply line of WIP, but production lags behind. Production does not surpass shipments until more than 6 weeks have passed; until then inventory continues to fall even as desired inventory rises. Inventory stops falling when production first equals shipments. The system is not yet in equilibrium, however, because of the large gap between desired and actual inventory and between orders and expected orders. Production eventually rises above shipments, causing inventory to grow. Production falls back as inventory reaches the new, higher desired level. The peak of production comes about one-quarter year after the change in orders, far longer than the eight week production delay.

The simulation reveals several fundamental aspects of supply chain behavior. First, the production delay means additions to finished inventory continue at the original rate long after demand changes. When shipments unexpectedly rise an initial drop in inventory is inevitable—it is a fundamental consequence of the physical structure of the system. Second, an increase in demand means the firm must increase the inventory it carries to maintain adequate coverage and good service. The firm’s inventory falls at the same time it seeks to hold more.

Second, amplification of the demand shock is unavoidable. The only way to increase inventory back to its initial level is for production to exceed shipments. Production must overshoot the shipment rate long enough and by a large enough margin to build inventory back to its initial level. Production starts must overshoot orders even more to build inventory to the new desired level, and still further to build WIP up to a level consistent with the higher throughput rate.

Third, amplification is temporary. In equilibrium, production starts rise precisely as much as demand. But restoring inventory and then building inventory and WIP to their desired levels requires a transient increase in production starts above demand. The temporary overshoot of production starts is then passed upstream to suppliers through orders for materials. Though final demand does not overshoot, suppliers face a boom and bust in the orders they receive.

Fourth, changes in production starts must lag the change in customer orders. The inventory gap reaches its maximum about when inventory reaches its minimum. Inventory bottoms out only after production has finally risen enough to equal shipments, an event that must lag the change in orders. Like amplification, this phase lag, characteristic of many real supply chains, is a fundamental and inevitable consequence of the physical stock and flow structure.

The stock management structure thus explains why supply chains generate amplification and phase lag. Given the structure of the system (in particular, production delays and forecast adjustment delays), production and production starts must overshoot, amplify, and lag unanticipated changes in demand, no matter how rational the managers of the firm may be.

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While the amount of amplification and length of the phase lag depend on the parameters, their existence does not. Less aggressive stock adjustments would reduce amplification, but lengthen the time required to restore inventory to the desired level, thus harming customer service.

The model developed so far constitutes a generic model of a firm’s manufacturing process. An industry supply chain can be modeled by linking several of the single firm models together. Each member of the supply chain is then represented by the same structure, though of course the parameters can differ. The generic modules can be linked in an arbitrary network to capture the structure of an industry or economy, including multiple suppliers, competitors, and customers.

To illustrate, consider a supply chain consisting of two firms (or units within a vertically integrated firm). As before, the customer order rate received by the downstream firm (the producer) is exogenous. The model has been augmented to include backlogs of unfilled orders and an explicit stock of raw materials. The upstream (supplier) firm’s orders are determined by materials orders placed by the downstream firm. Deliveries to the downstream firm depend on the supplier’s ability to ship. As is common, the producer does not share its point of sale data, or data on its inventory and WIP levels, with the supplier. For both firms capacity is again assumed to be ample and never constrains production. For purposes of exposition, the parameters of the two firms are assumed to be identical.3

Exhibit 9 shows the response of the linked model to a 20% step increase in customer orders. Performance is far worse than the case where materials can be acquired fully and without delay. The producer’s materials orders reach a peak of about 18,000 units/week, an amplification ratio of 4.1. Though customer demand does not fluctuate, the supplier is whipsawed through large amplitude fluctuations. The delivery of materials to the supplier reaches a peak of more than 28,000 units/week, an amplification ratio relative to customer orders greater than a factor of nine. The surge in orders received by the supplier causes a severe inventory shortage at the supplier, boosting the supplier’s delivery lead time to a peak 75% greater than normal. Those shortages constrain the downstream firm’s ability to produce, degrading customer service.

The transient surge in orders for materials placed by the downstream firm compounds the supplier’s problems. Though the supplier smooths incoming orders to filter out short-term fluctuations, the supplier’s forecast of orders significantly overshoots the final equilibrium. Because information is not shared, the supplier does not know final sales and cannot tell which orders reflect an enduring change in consumer demand and which reflect temporary inventory and supply line adjustments. Consequently, the supplier first finds itself with far too little

3 Full documentation is provided in Sterman 2000, chapter 18; the model, <W2Stage_w_DD_FB.mdl> is available at www.mhhe.com/business/opsci/sterman/models.mhtml.

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inventory and materials, and aggressively boosts production. But just as the tap begins to flow, orders received from the producer fall, leaving the supplier with huge surplus stocks and forcing supplier production starts far below producer orders. The delays and stock adjustments cause supplier production to be nearly completely out of phase with producer orders. Supplier output reaches its peak just about the time incoming orders fall to their low point.

The simulated supply chain, though it represents only two links, exhibits all three phenomena observed in real supply chains: oscillation, amplification, and phase lag. Most important, these attributes arise endogenously. The supplier experiences oscillation in output even though the external environment does not oscillate at all. The dynamics emerge from the interaction of the physical structure of the supply chain with the bounded rationality of the managers.

Of course, the step increase in customer demand is not realistic. The step is analogous to striking a bell with a single tap of the clapper. The step in demand suddenly knocks the system out of equilibrium, allowing us to observe how the system responds to a single shock. In the real world, of course, supply chains are not struck once but are continuously perturbed by changes in customer orders (and random variations in other key rates, such as production and materials deliveries). These random shocks constantly knock systems out of equilibrium, eliciting a characteristic response determined by their feedback structure. Exhibit 10 shows the response of the two-firm model when customer orders vary randomly around a constant value. The random shocks in customer orders cause the supply chain to ring like a bell. The rate at which the supplier acquires raw materials fluctuates with much larger amplitude and much longer period than the changes in customer orders. The standard deviation of customer orders is less than 5%, but the standard deviation of the supplier’s materials acquisition rate is more than seven times greater. And while most of the random fluctuation in customer orders consists of day-to-day or week-to-week variations, the response of the supply chain is a longer cycle—the system resonates at a characteristic frequency determined by its structure.

The purpose of inventory is to buffer the system against unforeseen fluctuations in demand. The simulated supply chain does a good job of absorbing the very rapid random fluctuations in customer orders. However, management policies significantly strengthen the slower variations in demand, leading to persistent, costly fluctuations. These fluctuations are progressively amplified by each stage. The system selectively attenuates high-frequency variations in demand while amplifying low frequencies. As seen in the petroleum, machine tool and semiconductor industries (Exhibit 3), small perturbations in final demand cause huge swings upstream.

Evidence from the lab and field

A large number of experimental and field studies document the bounds on rationality and

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dysfunctional behavior of managers in supply chains and other dynamically complex systems. Indeed, the evidence shows that the behavior of even experienced managers is often less rational than assumed in the models above.

The Beer Distribution Game is a role-playing simulation of a supply chain originally developed by Jay Forrester in the late 1950s to introduce managers to the concepts of system dynamics and computer simulation.4 Since then the game has been played all over the world by tens of thousands of people ranging from high school students to supply chain professionals and chief executive officers. The game is also used extensively in experimental studies of dynamic decision making and supply chain management (e.g., Sterman 1989a, Chen and Samroengraja 2000, Croson and Donohue 2002, 2003, Croson et al. 2005, Steckel, Gupta and Banerji 2004, Wu and Katok 2005, Dogan and Sterman 2005, Oliva and Gonçalves 2005).

The game is played on a board portraying a typical supply chain (Exhibit 11; many universities and experimental studies use computer implementations). Markers and chips represent orders for and cases of beer. Each brewery consists of four sectors: retailer, wholesaler, distributor, and factory (R, W, D, F). One person manages each sector. A deck of cards represents customer demand. Each week, customers demand beer from the retailer, who fills the order out of inventory. The retailer in turn orders beer from the wholesaler, who ships the beer requested from wholesale stocks. Likewise the wholesaler orders and receives beer from the distributor, who in turn orders and receives beer from the factory. The factory produces the beer. At each stage there are order processing and shipping delays. Each sector has the same structure.

The players’ objective is to minimize total costs for their company. Inventory holding costs are usually set to $0.50 per case per week, and stockout costs (costs for having a backlog of unfilled orders) are $1.00 per case per week. The task facing each player is a clear example of the stock management problem. Players must keep their inventories as low as possible while avoiding backlogs. Incoming orders deplete inventory, so players must place replenishment orders and adjust their inventories to the desired level. There is a delay between placing and receiving orders, creating a supply line of unfilled orders.5

The game is far simpler than any real supply chain. There are no random events—no machine breakdowns, transportation problems, or strikes. There are no capacity constraints or financial limitations. The structure of the game is visible to all. Players can readily inspect the board to

4 Instructions and materials are available from the System Dynamics Society at <systemdynamics.org>. Many firms have customized the game to represent their industry. 5Minimum costs are obtained when inventory is zero, but when incoming orders are uncertain and backlogs are more costly than inventories, it is optimal to set desired inventory to a small positive number.

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see how much inventory is in transit or held by their teammates, essentially creating the full information sharing firms in the real world still struggle to achieve. The game is typically played with a very simple pattern for customer demand. Starting from equilibrium, there is a small, unannounced one-time increase in customer orders, from 4 to 8 cases per week.

Despite the simplicity of the game, people do extremely poorly. Among first-time players average costs are typically an astonishing 10 times greater than optimal. Exhibit 12 shows representative results. In all cases customer orders are constant (except for the small step increase near the start). In all cases, the response of the supply chain is unstable. The oscillation, amplification, and phase lag observed in real supply chains are clearly visible in the experimental results. The period of the cycle is 20-25 weeks. The average amplification ratio of factory production relative to customer orders is a factor of four, and factory production peaks some 15 weeks after the change in customer orders.

Most interesting, the patterns of behavior generated in the game are remarkably similar (there are, of course, individual differences in magnitude and timing). Starting with the retailer, inventories decline throughout the supply chain, and most players develop a backlog of unfilled orders (negative net inventory). In response, a wave of orders moves through the chain, growing larger at each stage. Eventually, factory production surges, and inventories throughout the supply chain start to rise. But inventory does not stabilize at the cost-minimizing level near zero. Instead, inventory significantly overshoots. Players respond by slashing orders, often cutting them to zero for extended periods. Inventory eventually peaks and slowly declines. These behavioral regularities are all the more remarkable because there is no oscillation in customer demand. The oscillation arises as an endogenous consequence of the way the players manage their inventories. Though players are free to place orders any way they wish, the vast majority behave in a remarkably uniform fashion.

Analyses of the beer game and related experiments (Sterman 1989a, b; Diehl and Sterman 1995) show why. In brief, participants tend to place orders without regard to the supply line of unfilled orders. The only thing most players care about is whether there is enough inventory right now. Ignoring the time delays creates oscillation and instability, and raises costs far above potential.

To understand the role of the supply line adjustment in the origin of oscillations more formally I estimated the parameters of the stock management decision rule for a large sample of players in the beer game. To do so, I assumed that the desired stock S* and desired supply line SL* are constant.6 Defining β = αSL/αS and S´ = S* + βSL*, collecting terms, and allowing for an additive disturbance term ε yields 6 Dogan and Sterman (2005) relax the assumption of constant desired stocks, finding no significant change in results.

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OR = MAX(0, Le + αS[S´ – S – βSL) + ε] (11)

Note that since S*, SL*, αS and αSL are all ≥ 0, S´ ≥ 0. Further, subjects are unlikely to place more emphasis on the supply line than on inventory itself: the supply line does not directly affect costs nor is it as salient as inventory. Therefore it is probable that αSL ≤ αS, meaning 0 ≤ β ≤ 1. Thus β can be interpreted as the fraction of the supply line subjects take into account. If β = 1, managers give the supply line as much weight as inventory on hand. If β = 0, goods on order are ignored. It is easily shown that the optimal value of β is one: managers should fully account for both on-hand and on-order inventory when placing new orders. Failure to count the supply line of on-order inventory means managers attempting to correct an inventory shortfall would continue to place orders even after sufficient goods to fully correct the problem are in the supply line. Inventory would overshoot the desired level, leading to oscillation and high costs.

While it is folly to ignore the supply line the estimation results show this is precisely what happens. The decision rule in eq. (11) explains 71% of the variance in the order decisions of the subjects (Sterman 1989a). The estimated parameters showed that most were using grossly suboptimal cue weights. The average weight on the supply line was only 0.34. Only 25% of the subjects considered more than half the supply line and the estimated value of β was not significantly different from zero for fully one-third. Exhibit 13 compares simulated and actual behavior for the factory in an actual game. The estimated stock adjustment rate αS is 0.80 weeks—the player reacted aggressively to inventory shortfalls, ordering nearly the entire inventory shortfall each week. At the same time, the subject completely ignored the supply line (β = 0). Because it takes 3 weeks to produce beer ordered today, the player ordered nearly three times more than needed to correct the inventory shortfall. Aggressively reacting to current inventory while completely ignoring the supply line leads to severe instability and high costs.

These results have been repeatedly confirmed by subsequent experiments, and alternative explanations have been tested and ruled out. The standard protocol for the beer game eliminates most of the operational explanations for amplification cited in, e.g., Lee et al. (1997), including order batching (because there are no fixed ordering costs or quantity discounts), gaming in response to shortages (because each player orders from and ships to only one supplier and production capacity is infinite), and promotions or forward buying (because prices are fixed and customer demand is exogenous). However, in the standard game players do not know the pattern of customer demand, so it is possible that the bullwhip arises from the way subjects forecast demand. Croson and Donohue (2002, 2003) tested this possibility by running the game (in a computerized implementation) so that demand was a stationary, uniform random process, varying from 0 to 8 cases/week. Further, all subjects were informed of the demand distribution in advance. The results were nearly identical to the standard game with unknown demand.

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Subjects generated oscillation, amplification, and phase lag. Estimation of the subjects’ decisions showed that they ignored the supply line much as in the original experiment.

It may still be objected that subjects did not know the realization of demand—if they had perfect information on actual demand, rather than only its distribution (e.g., by making point of sale data available throughout the system), then the bullwhip would disappear. To test this possibility Croson, Donohue, Katok and Sterman (2005) made customer demand completely constant at four cases per week, and all players were publicly informed of this fact in advance. When demand is constant and known to all, and with initial inventory set at the cost minimizing level, there should never be any bullwhip effect. Surprisingly, however, among more than 250 subjects, amplification, oscillation and phase lag were pervasive. Estimation results showed subjects significantly underweighted the supply line much as in the original study. Supply line underweighting and the resulting instability persisted even when subjects were allowed to play a second time. Exhibit 14 shows a typical second game. Demand is constant at four cases/week, publicly announced to all players in advance, and subjects were paid in proportion to their profit. Nevertheless, the classic pattern of oscillation, amplification, and phase lag is clearly visible. Indeed, the amplitude of the cycle is still growing after nearly 50 weeks.

The tendency to ignore feedbacks and time delays is robust to information availability, incentives, opportunities for learning and the presence of markets (Sterman 1989b; Diehl and Sterman 1995; Brehmer 1992, Kampmann and Sterman 1998, Bakken 1993, Paich and Sterman 1993). In the standard beer game supply line information is not displayed; subjects must keep track of the supply line themselves. Many people assume that providing supply line information would eliminate the problem. However, in Sterman 1989b, Diehl and Sterman (1995), and Kampmann and Sterman (1998) the supply line was made as prominent in the information display as the inventory level, yet subjects ignored it anyway. Our mental models condition the cues we use in decision-making. Subjects who don’t recognize the presence of a time delay or understand its function in the system are unlikely to account for it even if the information needed to do so is available. Another critique relates to learning: perhaps first time players make these errors, but surely people would rapidly learn to recognize and account for the supply line. Unfortunately the experimental evidence shows this is false. Diehl and Sterman (1995), Wu and Katok (2005), Paich and Sterman (1993) and Croson et al. (2005) show that learning from repeated play in the beer game and related dynamic decision making tasks is slow and uneven. People often learn false and harmful lessons. Performance remains significantly below optimal even after the equivalent of years or decades of simulated experience.

Many players find these results disturbing. They argue that they took a wide range of information into account when placing orders and that their subtle and sophisticated reasoning

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cannot be captured by a model as simple as equation 11. After all, the decision rule for orders only considers three cues (incoming orders, inventory, and the supply line)—how could it possibly capture the way people place orders? Actually, players’ behavior is highly systematic and is explained well by the simple stock management heuristic. People are often surprised how well simple decision rules can mimic their behavior.

In fact, one of the games shown in Exhibit 12 is a simulation, not actual play. Each player’s orders are generated by the decision rule in equation 11. The parameters of the rule, for all four players, were set to the average values estimated in Sterman (1989a). A small amount of random noise was added to the order rate. Which is the simulation?7

Why Do We Ignore the Supply Line?

The beer game clearly shows it is folly to ignore the time delays in complex systems. Consider the following situation. Your car is stolen and never recovered. Insurance settlement in hand, you visit a dealer and select a new car, but the model you want is not in stock—delivery will take 4 weeks. You pay your deposit and leave. The next morning, noticing that your driveway is empty—Where’s my car!—you go down to the dealer and buy another one. Ridiculous, of course. No one would be so foolish as to ignore the supply line. Yet in many real life situations people do exactly that. Consider the following examples (Exhibit 5 shows how they map into the stock management structure):

• You cook on an electric range. To get dinner going as soon as possible, you set the burner under your pan to “high.” After a while you notice the pan is just hot enough, so you turn the heat down. But the supply line of heat in the glowing coil continues to heat the pan even after the current is cut, and your dinner is burned anyway.

• You are surfing the worldwide web. There is no response to your last mouse click. You click again, then again. Growing impatient, you click on some other buttons—any buttons—to see if you can get a response. After a few seconds, the system executes all the clicks you stacked up in the supply line, and you end up far from the page you were seeking.

• You arrive late and tired to an unfamiliar hotel. You turn on the shower, but the water is freezing. You turn up the hot water. Still cold. You turn the hot up some more. Ahhh. Just right. You step in. A second later you jump out screaming, scalded by the now too-hot water. Cursing, you realize that, once again, you’ve ignored the time delay for the hot water to heat

7Simulated orders were generated by eq. 11 with the average parameters found in Sterman (1989a): S’ = 17 units, αS = 0.26/week, and β = 0.34. Le

t was formed by first-order exponential smoothing of the incoming order rate with smoothing time constant τ = 1.82 weeks. The error term εt ~ N(0, σ2) with σ set to the mean of the standard errors of the estimated equation over the sample.

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the cold pipes and get to your shower.

• You are driving on a busy highway. The car in front of you slows slightly. You take your foot of the gas, but the distance to the car in front keeps shrinking. Your reaction time and the momentum of your car create a delay in responding to changes in the speed the car ahead. To avoid a collision, you have to slam on the brakes. The car behind you is forced to brake even harder. You hear the screech of rubber and pray you won’t be rear-ended.

• You are young, and experimenting with alcohol for the first time. Eager to show your friends you can hold your liquor, you quickly drain your glass. You feel fine. You drink another. Still feeling fine. You take another and another. As consciousness fades and you fall to the floor, you realize—too late—that you ignored the supply line of alcohol in your stomach and drank far too much.8

Few of us can say we’ve never burned our dinner or been scalded in the shower, never drunk too much or braked hard to avoid a collision.

Recognizing and accounting for time delays is not innate. It is behavior we must learn. When we are born our awareness is limited to our immediate surroundings. Everything we experience is here and now. All our early experiences reinforce the belief that cause and effect are closely related in time and space: When you cry, you get fed or changed. You keep crying until mother or father appears, even when you hear your parents say, “We’re coming” (that is, despite knowledge that your request for attention is in the supply line). As all parents know, it takes years for children to learn to account for such time delays. When my son was two he might ask for a cup of juice: “Juice please, Daddy.” “Coming right up,” I’d say, taking a cup from the shelf. Though he could see me getting the cup and filling it up, he’d continue to say, “Juice, Daddy!” many times—ever more insistently—until the cup was actually in his hand.

Learning to recognize and account for time delays goes hand in hand with learning to be patient, to defer gratification, and to trade short-run sacrifice for long-term reward. These abilities do not develop automatically. They are part of a slow process of maturation. The longer the delay and the greater the uncertainty in seeing the results of our corrective actions, the harder it is to account for the supply line. More subtly, our childhood experiences reinforce the idea that there is no cost to ignoring the supply line. Though my son may have said “Juice, Daddy” ten times before I could fill his “order,” I brought him only one cup. He didn’t take the supply line into account, but I did. In that situation, there is no cost to overordering, while patience might not work (dad might get distracted and forget to bring the juice; others might get fed while the one 8Tragically, young people die every year from alcohol poisoning induced by aggressive drinking and failure to account for the supply line of alcohol they’ve already ingested.

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who accounts for the supply line goes hungry). What is adaptive and evolutionarily advantageous for the individual is dysfunctional for modern social systems where there is no central authority to account for time delays and prevent overordering.

One might argue that by the time we become adults we have developed the requisite patience and sensitivity to time delays. There may be no cost to demanding “juice” a dozen times, but surely when the stakes are high we would quickly learn to consider delays. You don’t burn yourself in your own shower at home—you’ve learned where to set the hot water faucet to get the temperature you like and to wait long enough for the water to warm up. Most people soon learn to pay attention to the supply line of alcohol in their system and moderate their drinking. The conditions for learning in these systems are excellent. Feedback is swift and the consequences of error are highly salient (particularly the morning after). There is no doubt in either case that it was the way you made decisions—the way you set the faucet or drank too fast—that caused the problem. These conditions are usually not met in business, economic, environmental, and other social systems. Cause and effect are obscure, creating ambiguity and uncertainty. The dynamics are far slower, and the time required for learning often exceeds the tenure of individual decision makers. Ignoring time delays is also sometimes rational for the individual. In a world of short time horizons, of annual, quarterly, or even monthly performance reviews, the incentives people face often mean it is rational for them to be aggressive and ignore the delayed consequences of their actions (of course, those short evaluation time horizons themselves reflect failure by the principals to understand the time delays between the actions of their subordinates and outcomes).

The economist Albert Aftalion recognized in the early 1900s how failure to account for the time delays could cause business cycles. Using the familiar fireplace as an analogy, his description explicitly focuses on the failure of decision makers to pay attention to the supply line of fuel:

If one rekindles the fire in the hearth in order to warm up a room, one has to wait a while before one has the desired temperature. As the cold continues, and the thermometer continues to record it, one might be led, if one had not the lessons of experience, to throw more coal on the fire. One would continue to throw coal, even though the quantity already in the grate is such as will give off an intolerable heat, when once it is all alight. To allow oneself to be guided by the present sense of cold and the indications of the thermometer to that effect is fatally to overheat the room.9

While Aftalion argued that “the lessons of experience” would soon teach people not to “continue to throw coal,” he argued that business cycles in the economy arose because individual entrepreneurs focused on current profitability and failed to account for the lags between the initiation of new investment and its realization, leading to collective overproduction. Yet even if individuals can’t learn effectively, shouldn’t the discipline imposed by the market quickly weed 9Quoted in Haberler (1964) pp. 135–136.

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out people who use suboptimal decision rules? Those who ignore the supply line or use poor decision rules should lose money and go out of business or be fired, while those who use superior decision rules, even by chance, should prosper. The selective pressures of the market should quickly lead to the evolution of optimal decision rules.

To the contrary, learning and evolution in real markets appear to be slow, despite decades of experience and the huge sums at stake. Part of the problem is lack of information. Individual firms frequently do not share full information on their incoming orders, inventories, WIP, and supply lines with their supply chain partners or competitors, many of whom are ordering from the same suppliers. Part of the problem is a mismatch in time horizons, with managers evaluated over periods much shorter than the time required for the full impacts of their decisions to manifest. The tenure of individual managers is often short relative to the time frame over which supply chain dynamics unfold. Expertise is diluted by the entry of new firms and new managers who lack experience. Part of the problem is the narrow boundary of the mental models used by many managers. Many firms view themselves as small relative to the market and treat the environment as exogenous, thereby ignoring all feedbacks from prices to supply and demand. The individual firm may not know or give sufficient weight to the supply lines of all firms in the industry or the total capacity of all plants under construction. Firms tend to continue to invest and expand as long as profits are high today, even after the supply line of new capacity under construction is more than sufficient to cause a glut and destroy profitability. Each investor takes market conditions as exogenous, ignoring the reactions of others. Field study of the telecom, real estate, shipbuilding and other industries document the failure to consider these feedbacks and the supply lines of capacity under construction (e.g. Sterman 2000, Shi 2002).

Instability and Trust in Supply Chains

It is worth pausing to consider the effect of supply chain instability on the beliefs and behaviors of managers in the different firms. In the unstable world illustrated by the simulations and data shown here, trust among partners in a supply chain can rapidly break down. Downstream firms find their suppliers to be unreliable. Delivery quotes will often not be met, and producers too often find suppliers place hot selling products on allocation (where each customer receives less than their full order due to a shortage of supply). In turn, suppliers find the ordering patterns of their customers to be volatile and capricious. Forecasts of incoming orders are rarely correct and always changing. As shown in exhibit 9, the supplier’s forecast of incoming orders (the expected order rate) reaches its peak just as actual incoming orders fall below their equilibrium level and begin to approach their minimum. Before long, the forecasts, which are typically produced by the sales and marketing organization, lose all credibility with the production and operations people. The marketing organization, in turn, complains that unreliable production

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makes forecasting, not to mention selling, difficult. The endogenous instability caused by the structure of a supply chain—in particular, management’s own policies—can breed blame and mistrust within and between firms in a supply chain.

Blame and mistrust then feed back to worsen the instability in a vicious cycle. One common manifestation of such distrust is the phenomenon of phantom orders or lead-time gaming. During upswings in demand, suppliers are unable to boost production fast enough to keep pace. Product becomes scarce, and customers are placed on allocation. Customers often respond to longer delivery times and unreliable supplier deliveries by increasing their desired inventory levels, ordering farther ahead, and placing multiple orders through different distributors. Such hedging is particularly likely when the supplier serves multiple customers. Suppose the supplier runs short of product and places the customers on allocation: Each will only receive, say, 80% of its order. Customers are likely to respond by ordering 125% or even more of what they actually require. Firms that fail to play this allocation game will likely lose market share to their aggressive competitors.

Contrary to basic economic intuition, scarcity causes an increase in demand as each customer scrambles to get a bigger slice of the shrinking supply pie. The result is a positive feedback loop, a vicious cycle of scarcity, increased orders by customers desperate to gain a larger share of available supplies, and still longer delivery times and smaller allocations. Suppliers, experiencing a huge increase in demand just when supplies are tightest, scramble to add capacity and expedite production. Once they succeed, however, delivery times return to normal and allocations are increased. Customers, now able to get product quickly, cancel the phantom orders they placed, leaving the supplier with excess inventory, excess capacity, and large losses. Phantom orders played a major role in the overshoot and collapse of the telecommunications equipment supply chain in the late 1990s, causing record losses, layoffs, and stock price declines at firms such as Lucent, Nortel, Cisco, and JDS Uniphase (Gonçalves 2002, Shi 2002).

On the surface, it appears that the supplier bears most of the excess costs created by phantom orders. However, these costs must eventually be passed on to the downstream firms in higher prices or poor customer service and product quality. Firms have a strong incentive to improve the stability of their suppliers. Nevertheless, the parochial, local incentives facing individual functions and firms often lead to actions that degrade the stability of the entire supply chain.

Why would customers place phantom orders when doing so is ultimately harmful to both their suppliers and themselves? Phantom orders are locally rational. To ensure delivery of needed goods, the purchasing department must maintain a supply line proportional to the delivery delay. Failure to respond to changes in lead times could result in costly accumulation of excess

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inventories, or, worse, shortages that could shut down production. The mental models of the purchasing managers in downstream firms typically treat supplier lead times as outside their control. Each firm reasons that it is responsible for only a small part of the supplier’s total demand, so changes in its orders won’t affect supplier lead times. Organizational routines such as updating the supplier lead time assumptions of the materials requirement planning system based on recent delivery experience implicitly presume that the resulting changes in materials orders won’t affect supplier lead times. But when all customers act in a similar fashion a vicious cycle (positive feedback loop) is closed. The mismatch between the mental models of the supplier, in which lead times are exogenous, and the actual situation, in which lead times are strongly affected by the ordering behavior of the downstream firms, further degrades supply chain performance and reinforces the view of the different organizations that their partners are unpredictable and untrustworthy.

What can be done? There are now many useful tools to redesign supply chains for improved stability, agility and efficiency (Simchi Levi et al. 1999). These include changes to the physical structure (lean manufacturing, platform-based product architectures, multi-modal transport, third-party warehousing) and changes in information technology (point of sale data, ERPs, RFID, etc.). Yet the continued oscillation and amplification, boom and bust, in high tech, real estate, shipbuilding, automobiles, and other industries suggests that these technical solutions are not sufficient to eliminate supply chain instability. Enduring, comprehensive improvements require managers to address the behavioral causes: improving mental models and redesigning decision making processes to recognize the interdependencies, feedbacks, time delays, and other elements of dynamic complexity in modern organizations. While space does not permit description, the list of successful examples is growing (e.g., Sterman 2000, Ch. 11.6, 18.3).

Summary

Supply chains are fundamental to a wide range of systems and many exhibit persistent instability. Every supply chain consists of stocks and the management policies used to manage them. These management policies are designed to keep the stocks at their target levels, compensating for usage or loss and for unanticipated disturbances in the environment. Often there are important delays between the initiation of a control action and the result, creating a supply line of unfilled orders.

This paper developed a generic model of the stock management structure and showed how it can be customized to various situations. The model was used to explain the sources of oscillation, amplification, and phase lag observed in supply chains. Supply chain instability arises from both operational and behavioral causes. Field and experimental studies show that people often fail to

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account for the feedback effects of their actions and ignore important time delays. These misperceptions of feedback are robust to incentives, experience, information availability, and the presence of market institutions. Experimental studies show clearly that supply chain instability remains even after all operational causes such as quantity discounts are eliminated. Instability is a behavioral phenomenon arising from the failure to account for feedbacks, time delays, and the supply line of unfilled orders.

There is no single cause for the failure to account for feedback, time delays and the supply line. A range of factors, from information availability to individual incentives, all contribute. But behind these apparent causes lies a deeper set of behavioral causes, causes rooted in our imperfect mental models and poor inquiry skills. True, the supply line is often inadequately measured, but if people understood its importance they would invest in data collection and measurement systems to provide the needed information. True, compensation incentives often encourage people to ignore the distal and delayed consequences of today’s actions, but if managers and shareholders understood the structure and dynamics of the market they could redesign incentives so their agents would focus on long-term performance. Our mental models affect the design of our institutions, information systems, and incentive schemes. These, in turn, feed back to our mental models. The failure to account for the supply line reflects deeper defects in our understanding of complex systems. Failure to understand the role of time delays worsens the instability we face and leads to more surprises—usually unpleasant—strengthening the belief that the world is inherently capricious and unpredictable, slowing learning, and further reinforcing the harmful short-term focus. Innovative managers who redesign the physics of their systems, their information systems, and, most importantly, the mental models guiding decision making and strategy are creating breakthrough improvements in performance.

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ate

(%

/year) Oil and Gas

Well Drilling

Oil and Gas Production

-60

-40

-20

0

20

40

60

80

1970 1975 1980 1985 1990 1995

Fra

cti

on

al G

row

th R

ate

(%

/year)

Machine ToolOrders

MotorVehicleSales

GDP

-20

0

20

40

60

1955 1965 1975 1985 1995 2005

Fra

cti

on

al G

row

th R

ate

(%

/year)

Semiconductors

Industrial Production

Exhibit 3. Oscillation, amplification, and phase lag in supply chains Top: Oil and gas drilling fluctuates far more than production. The graph shows 12-month centered moving averages of the annualized fractional growth rate calculated from the monthly data. Source: US Federal Reserve, series G211 and N213111. Middle: Orders for machine tools fluctuate far more than the production of their major customer (the auto industry). Graph shows annual growth rates. Source: Anderson, Fine & Parker (2000). Bottom: Semiconductor production fluctuates far more than aggregate industrial production. Twelve-month centered moving averages of the annualized fractional growth rate calculated from the monthly data. Source: Federal Reserve, series B50001 and B53122.

11/30/05 28

StockS

Order RateOR

-

AcquisitionRateAR

Loss RateLR

IndicatedOrders

IO

Adjustmentfor Supply

LineASL

DesiredSupply

LineSL* Adjustment

for StockAS

DesiredStock

S*

ExpectedLoss Rate

AcquisitionLag

OtherEndogenous

VariablesX

ExogenousVariables

U

+

++

+

+

++

+

+

-

-

+

B

Supply Line Control

B

Stock Control

Stock and Flow Structure

Ordering Heuristic

Supply LineSL

Exhibit 4. The generic stock management structure. The determinants of the desired supply line are not shown (see text).

Business Dynamics DRAFT Manufacturing Supply Chains

John Sterman 11/30/05 29

System Stock Supply Line Loss Rate Acquisition Rate Order Rate Typical Behavior Inventory management

Inventory Goods on order Shipments to customers

Arrivals from supplier

Orders for goods Business cycles

Capital investment Capital plant Plant under construction

Depreciation Construction completion

New contracts Construction cycles

Equipment Equipment Equipment on order

Depreciation Equipment delivery

New equipment orders

Business cycles

Human resources Employees Vacancies & trainees

Layoffs and quits Hiring rate Vacancy creation Business cycles

Cash management

Cash balance Pending loan applications

Expenditures Borrowing rate Loan application rate

Cash flow cycles

Marketing Customer base Prospective customers

Defections to competitors

Recruitment of new customers

New customer contacts

Boom and bust in customer base

Hog farming Hog stock Immature and gestating hogs

Slaughter rate Maturation rate Breeding rate Hog cycles

Agricultural commodities

Inventory Crops in the field Consumption Harvest rate Planting rate Commodity cycles

Commercial real estate

Building stock Buildings under development

Depreciation Completion rate Development rate Real estate booms and busts

Cooking on electric range

Temperature of pot

Heat in coils of range

Diffusion to air Diffusion from coils to pot

Setting of burner Overcooked dinner

Driving Distance to next car

Momentum of car Friction Velocity Gas and brake pedals

Stop-and-go traffic

Showering Water temperature

Water temp. in pipes

Drain rate Flow from showerhead

Faucet settings Burn then freeze

Personal energy level

Glucose in bloodstream

Sugar and starch in GI tract

Metabolism Digestion Food consumption Cycles of energy level

Social drinking Alcohol in blood Alcohol in stomach

Metabolism of alcohol

Diffusion from stomach to blood

Alcohol consumption rate

Drunkenness

Exhibit 5. Examples of the stock management structure

Business Dynamics DRAFT Manufacturing Supply Chains

John Sterman 11/30/05 30

Production

Rate

Shipment

Rate

Production

Start Rate

Production

Scheduling

Customer

Order Rate

Stockout

InventoryControl

B

WIP Control

Work in

Process

Inventory

Inventory

Order

Fulfillment

Demand

Forecasting

B

B

Exhibit 6. The policy structure of inventory management in a manufacturing firm

Parameter Value (Weeks) Normal Inventory Coverage 4 Manufacturing Cycle Time (acquisition delay for inventory) 8 Inventory Adjustment Time 8 WIP Adjustment Time 2 Time to Average Order Rate (demand forecast smoothing time) 8

Exhibit 7. Main parameters for the production model

Business Dynamics DRAFT Manufacturing Supply Chains

John Sterman 11/30/05 31

9,000

10,000

11,000

12,000

13,000

14,000

15,000

0 10 20 30 40 50

Wid

gets

/Week

Weeks

Shipments

Desired Shipments

Lost Orders

9,000

10,000

11,000

12,000

13,000

14,000

15,000

0 10 20 30 40 50

Wid

ge

ts/W

ee

k

Weeks

Production

ExpectedOrders

ProductionStarts

Customer Orders

DesiredProduction

0

1

2

3

4

5

0 10 20 30 40 50

Inv

en

tory

Co

ve

rag

e(w

ee

ks

)

Weeks 30,000

50,000

70,000

90,000

110,000

0 10 20 30 40 50

Wid

ge

ts

Weeks

WIP

Desired Inventory

DesiredWIP

Inventory

Exhibit 8. Response of manufacturing model to a 20% step increase in orders

Business Dynamics DRAFT Manufacturing Supply Chains

John Sterman 11/30/05 32

9,000

10,000

11,000

12,000

13,000

14,000

15,000

0 10 20 30 40 50

Widgets/Week

Weeks

SupplierExpectedOrders

CustomerOrders

ExpectedCustomerOrders

9,000

10,000

11,000

12,000

13,000

14,000

15,000

0 10 20 30 40 50

Wid

ge

ts/W

ee

k

Weeks

Supplier Shipment Rate

CustomerOrders

Shipment Rate

10,000

12,000

14,000

16,000

18,000

0 10 20 30 40 50

Wid

gets

/Week

Weeks

Shipments

Orders forMaterials

ProductionStarts

Production

5,000

10,000

15,000

20,000

25,000

30,000

0 10 20 30 40 50

Wid

ge

ts/W

ee

k

Weeks

Supplier Order Rate

SupplierMaterial Deliveries

SupplierProduction Starts

SupplierProduction

2.0

2.4

2.8

3.2

3.6

0 10 20 30 40 50

De

liv

ery

De

lay

(w

ee

ks

)

Weeks

SupplierDelivery Delay

Delivery Delay

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50

Inv

en

tory

Co

ve

rag

e (

we

ek

s)

Weeks

SupplierInventory Coverage

InventoryCoverage

Supplier Materials Inventory CoverageMaterials

InventoryCoverage

Exhibit 9. Response of two-stage supply chain to a 20% unanticipated demand increase

Business Dynamics DRAFT Managing the Supply Chain

John Sterman 11/30/05 33

0

5,000

10,000

15,000

20,000

0 50 100 150 200

Un

its/W

eek

Weeks

Supplier MaterialDelivery RateCustomer

Orders

Exhibit 10. Response of the two-stage supply chain to random variations in customer orders

Business Dynamics DRAFT Managing the Supply Chain

John Sterman 11/30/05 34

ShippingDelay

ShippingDelay

ProductionRequests

IncomingOrders

OrdersPlaced

ProductionDelay

RawMaterials

UsedOrderCards

Orders Soldto Customers

WHOLESALER DISTRIBUTOR FACTORY

ShippingDelay

ShippingDelay

ShippingDelay

ShippingDelay

CurrentInventory

IncomingOrders

OrdersPlaced

IncomingOrders

OrdersPlaced

CurrentInventory

RETAILER

CustomerOrders

ProductionDelay

CurrentInventory

CurrentInventory

4 4 4 4 4 4 4

Exhibit 11. The Beer Distribution Game

The game is a role-play simulation. Each player manages one of the links in the distribution chain from Retailer to Factory. In the game, chips of various denominations represent cases of beer and move through the supply chain from Raw Materials to Customers. Customer orders are written on a deck of cards. Each week players place orders with the supplier on their left and the factory sets the

production schedule. The orders, written on slips of paper, move upstream (left to right). The initial configuration is shown.

Business Dynamics DRAFT Managing the Supply Chain

John Sterman 11/30/05 35

0 10 20 30

Cases/W

eek

0

0

0

0

Team 1

0 10 20 30

Team 2

0

0

0

0

0 10 20 30

Team 3

0

0

0

0

0 10 20 30

Team 4

0

0

0

0

0 10 20 30

Team 5

F

R

W

D

0

0

0

0

0 10 20 30

Cases

Team 1

0

0

0

0

0 10 20 30

Team 2

0

0

0

0

0 10 20 30

Team 3

0

0

0

0

0 10 20 30

Team 4

0

0

0

0

0 10 20 30

Team 5

F

R

W

D

0

0

0

0

Exhibit 12. Typical results of the Beer Distribution Game

Top: Orders. Bottom: Net inventory (Inventory – Backlog). Graphs show, bottom to top, Retailer, Wholesaler, Distributor, and Factory. Vertical axis tick marks denote 10 units. Note the characteristic oscillation, amplification, and phase lag as the change in customer orders propagates from retailer to factory.

Business Dynamics DRAFT Managing the Supply Chain

John Sterman 11/30/05 36

0

10

20

30

40

0 5 10 15 20 25 30 35

Cases/W

eek

Simulated

ActualFactory Orders

(R2 = 0.87)

Weeks

Exhibit 13. Estimated vs. actual behavior in the beer game Factory orders for an actual player compared to estimated orders. Parameters: Smoothing time for forecast of customer orders, 1.82 weeks; desired total stock on hand and on order, 9 cases; αS = 0.80, β = 0. Source: Sterman (1989b).

0

10

20

30

40

50

0 10 20 30 40 50

R OrdersW OrdersD OrdersF Orders

Ord

ers

(c

as

es

/we

ek

) T5G2

Week

-100

-50

0

50

100

0 10 20 30 40 50

R InventoryW InventoryD InventoryF Inventory

Net

Inven

tory

(cases)

Week

T5G2

Exhibit 14. Typical experimental results when customer demand is constant and known. Demand is 4 cases/week, and this is publicly announced to all players in advance (Croson et al. 2005). The supply chain is initialized in the optimal equilibrium with throughput of 4/cases/week and zero inventory. The data show the players’ second game.