Measuring the Bullwhip Effect

Termpaper for International Logistics

WS14/15

Lecturer: Christian Deckert

Johannes Wolff

BA13, International Business , International Trade

1132214046

Table of Contents

List of Figures.......................................................................................................................................... ii

1. Introduction..........................................................................................................................................1

2. The Bullwhip Effect as a Supply Chain Phenomenon.........................................................................1

2.1. Managing the Supply Chain.........................................................................................................1

2.2. The Bullwhip Effect as Supply Chain Dynamics........................................................................2

2.3. The Bullwhip Effect as an Inevitable Consequence of Supply Relations—The Beer Game......3

2.4. The Reasons for the Bullwhip Effect...........................................................................................3

2.5. Studying the Bullwhip Effect in Data..........................................................................................5

3. Formal Analysis of the Bullwhip Effect..............................................................................................7

3.1. Models Based on Serially Correlated Demand............................................................................7

3.2. Measuring the Effect of Transparency.........................................................................................8

4. Mitigating the Bullwhip Effect............................................................................................................8

4.1. Information Policy.......................................................................................................................8

4.2. Reducing Lead Time....................................................................................................................8

4.3. Collaboration of Retailers............................................................................................................9

5. Summary..............................................................................................................................................9

References..............................................................................................................................................10

Appendix................................................................................................................................................12

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List of Figures

Figure 1: Order fluctuations in the beer supply chain..................................................................12

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1. Introduction

The US-American telecommunications company CISCO depreciated 2.25 million US dollars

in the third quarter of 2001 due to excess stock (Beer, 2014, p. 1). According to Beer (2014,

p. 3.) the bullwhip effect is the probably most important reason for this depreciation. The

bullwhip effect affects production and leads to a shortage of stocks or excess stocks, drops in

sales, increases inventory costs and instability of planning (Beer, 2014, p. 3). Productivity

losses due to the bullwhip effect are between 10 and 30%, according to Beer (2014, p. 3).

Thus, eliminating the bullwhip effect is one of the most important goals of supply chain

management. Since the length of production chains has increased over the last decades, due

to the implementation of cost-reducing outsourcing and since new inventory strategies are

implemented to increase efficiency, the importance of overcoming the bullwhip effect has

gained additional importance.

This paper deals with the reasons for the bullwhip effect and shows some approaches that

might be able to mitigate the effect. The rest of the paper is structured following this goal.

First, the bullwhip effect is explained, and selected scientific literature addressing the effect is

presented. The discussion of reasons for the bullwhip effect is added with empirical findings

that show the existence and scope of the effect. Chapter three deals with the formal

description of the model and chapter four presents some of the proposals often discussed in

literature to mitigate the bullwhip effect. Chapter five summarizes the presented arguments.

2. The Bullwhip Effect as a Supply Chain Phenomenon

2.1. Managing the Supply Chain

A supply chain is a channel where firms are ranked by their supplier–purchaser relationship

to produce a final good that needs defined raw materials at a given production stage.

Depending on the research topic, the focus on studying this channel varies; it may cover all or

selected stages, single or multiple suppliers, value chains and procurement procedures (Beer,

2014, pp. 15–16). How to deal with supply chains is discussed in network sourcing, supply

pipeline management, value chain or value stream management and demand chain

management scientific literature. For example, Internet-based commerce and third party

logistics are recently discussed problems that may lead to channel conflicts (Tsay &

Agrarwal, 2004, p. 93). Since management of the supply chain provokes or eliminates related

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phenomenon within the context of procurement and inventory, the underlying definition of

supply chain management is critical for discussing these problems. Supply chain management

may be defined as a “set of approaches used to efficiently integrate suppliers, manufacturers,

warehouses, and stores so that merchandise is produced and distributed at the right quantities,

to the right locations, and at the right time. . .” (Simchi-Levi, Kaminsky & Simchi-Levi,

2004, as quoted by Beer, 2014, p. 16). Thus, even if supply chains consist of already

efficiently integrated firms, some mismatching problems still exist. That is because the

upstream and downstream flow of products, information and finances happens between three

or more suppliers and customers, which are called echelons in supply chain management

literature, coordination the chain is no simple task. While early studies assumed irrational

behavior of a single supplier being the main reason for coordination mismatch in the chain,

the coordination itself has come under investigation in the meanwhile.

2.2. The Bullwhip Effect as Supply Chain Dynamics

The bullwhip effect refers to the variability, fluctuation, variations, oscillation and even

delays within a supply chain (Beer, 2014, p. 19). Forrester (1961) first identified the effect as

part of his studies of system dynamics (Shen et al., 2014, p. 539). Forrester related the effect

to the impact of changes in retail sales to factory production, the impact of clerical delays to

management decisions and the impact of management strategies at one stage of the chain to

the efficiency of procurement and inventory (Forrester, 1958, as quoted by Alicke, 2005, p.

101). Following Lee, Padmanabhan and Whang (1997, p. 94), the variability in retailers’

orders to the wholesalers’ is spiked, even if the consumer sale does not vary at all. Discussing

the variability of orders within a supply chain with constant demand, they find fluctuations on

the upstream site are always larger than on the downstream site. Their seminal works ask for

studies focusing on overcoming the bullwhip effects by counteracting measurements as

information sharing, coordination and collaboration (Lee, Padmanabhan & Whang, 1997, p.

95). Since then, the literature on the bullwhip effect has increased and the effect itself has

“the first law of supply chain dynamics” (Kouvelis, Chambers, & Wang, 2006, p. 450). Since

the bullwhip effect can cause excess inventory as well as suboptimal capacity that go along

with rising costs, the phenomenon is well known in scientific research, both in theoretical and

empirical studies.

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2.3. The Bullwhip Effect as an Inevitable Consequence of Supply Relations—The Beer Game

The famous beer game, demonstrating the bullwhip effect first-hand in teaching, was inverted

and brought into the classroom by Forrester (1961) to teach students of the Massachusetts

Institute of Technology (MIT) how structures create behavior (Riemer, 2007, p. 1). The

game, which is explained in detail by Riemer (2007, p. 1.), can be used as a role-play

simulation game. Students enact a four-stage supply chain to produce and deliver beer. The

chain consists of a factory and three suppliers. Orders flow upstream and deliveries flow

downstream in the supply chain, and delivery takes time. It requires two rounds until orders

are delivered to the next stage. Students receive incoming orders and deliveries, coordinate

their sheets that cover outstanding deliveries and inventory, send out their materials and

decide on the amount to be ordered. The rules are quite simple. Every order must be fulfilled

and inventory and backlog that are deliveries must be taken back from the next stage. Since

communication and collaboration is not allowed, orders fluctuate with inefficient amplitude

so that cost minimization is not reached even within this simple supply chain (Riemer, 2007,

p. 1). The typical result shown in a graph, which is included in the Appendix, is a highly

fluctuated amount of orders within the chain with higher amplitudes for the factory. Thus,

this result is in line with Lee, Padmanabhan and Whang’s (1997, p. 95) general findings and

the assumption that order variability increases along the supply chain.

2.4. The Reasons for the Bullwhip Effect

Reasons that may lead to the bullwhip effect have been categorized by Lee, Padmanabhan

and Whang (1997, p. 93), who base their findings on empirical studies with constant demand.

Since varieties in the order along the supply chain seem to be irrational at first glance, Lee,

Padmanabhan and Whang (1997, p. 95) claim the bullwhip effect occurs even if all managers

behave rationally. When ordering the categories, they find four main reasons for the bullwhip

effect: (1) the demand forecast updating, (2) the order batches, (3) the price fluctuation and

(4) the rationing and shortage gaming. These reasons are explained in detail as follows:

1. Demand Forecast Updating (Lee, Padmanabhan & Whang, 1997, p. 95)

Since scheduling and planning necessitates demand forecasting, the way this forecast is

obtained is important. For example, managers can base their forecasts on judgments,

opinions, intuition, emotions, or personal experiences (Makridakis & Wheelwright, 1989, p.

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15). Thus, forecasting is very subjective in nature. Moreover, even if all managers base their

forecasts on their experience, and apply time series, their methods may differ, depending on

the importance they equate to the data and the complexity of the method. They can use

regressions or move averages and exponential smoothing (Makridakis & Wheelwright, 1989,

p. 30). Altogether, demand information might be distorted due to erratic orders, unforeseen

and variable lead times, and unanticipated production times.

2. The Order Batching (Lee, Padmanabhan & Whang, 1997, p. 96)

Methods of inventory control or procurement approaches may differ between companies

within a supply chain. Lee, Padmanabhan and Whang (1997, p. 96) discuss two types of

order batching—periodic ordering and push ordering. The impact of fixed costs and other

economies of scale considerations play an important role in batching orders. Managers can

combine orders to optimize their inventory capacity or minimize their transportation costs.

Splitting orders often causes higher delivery and inventory costs (Henn, Koch & Wäscher,

2011, p. 6). Moreover, Lee, Padmanabhan and Whang (1997, p. 96) mentioned material

requirement planning systems that often run monthly so that orders are placed following the

planning system period without considering stabilizing effects.

3. Price Fluctuations (Lee, Padmanabhan & Whang, 1997, p. 97)

Due to dynamic pricing and promotional campaigns, customers often place large orders that

do not equal the amount of material they need for just-in-time production. Thus, peaks and

valleys caused by changes in the demand of the final consumer are not adequately reached in

the chain. Forward buying arrangements, introduced in parts of the chain, can lead to costs

for the complete supply chain.

4. Rationing and Shortage Gaming (Lee, Padmanabhan & Whang, 1997, p. 98)

When managers experience periods of shortages and overstocks, they often react to this

experience without using a more period-covering inventory strategy. Thus, peaks and valleys

can cause bullwhip effects, since managers can come to believe that system constraints

change over time. Demand cycles can change a manager’s point of reference.

Summarizing these reasons shows the bullwhip effect as failure in coordinating the supply

chain. This failure is based on local decisions instead of considering the entire chain (Alicke,

2005, p. 102). The orders and forecasts are not coordinated since the supply chain is often not

transparent and suppliers are not familiar with the complete chain (Alicke, 2005, p. 102).

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2.5. Studying the Bullwhip Effect in Data

Since the length of supply chains increases due to the implementation of optimizing

processes in production, outsourcing and the implementation of optimized procurement, or

logistic and inventory approaches, more recent empirical studies analyze the reasons for the

extent of the bullwhip effect. There are different findings. For example, Chen et al. (2000, p.

442) find evidence that information sharing does not eliminate the effect but may lead to

reduced variability amplitude. As amplitudes are assumed to be related to total procurement

costs in supply chains, different studies research this type of relation. This branch of research

studies finds that the simple reduction of orders does not seem to proportionally affect total

costs (Chen & Samroengraja, 2004, p. 721). Moreover, eliminating the bullwhip effect does

not necessarily increase a supply chain’s efficiency.

Another research area contributes to the mathematical description and the formula of the

bullwhip effect. It is assumed that order variability spreads along the supply chain, since

“demand distortion propagates upstream with amplification occurring at each echelon”

(Warburton, 2004, p. 150). Thus, formal analyses tend to gain complexity with each link in

the chain. However, the assumption of increasing amplitudes along the chain leads to higher

amplitudes upstream for the final producer, which has been proposed as a kind of law by Lee

et al. (1997, p. 94), has recently been challenged by Sucky (2009, p. 311), who find firms at

the downstream do not always have more stable orders. The role of information may not be

as simple as assumed. Sucky (2009, p. 322) argues that pooling effects in supply chains

structured as networks may lead to reduced amplitudes of order variability. Thus, although

the bullwhip effect must be in effect in all order-up-to systems, its scale depends “on the

statistical correlation of the regarded demands” (Sucky, 2009, p. 322).

Coordination mismatches as the bullwhip effect are based on manager’s behavior. Empirical

studies find the scope of bullwhip effects depends on the forecasting technique used by the

managers. Simple forecasting techniques as the perpetuation of the last order period into the

future may increase the effect (Watson & Zheng, 2008, p. 1). Chen et al. (2000, p. 442) find

proof for the total effect may be based on the forecasting techniques itself. Recent literature

often debate the bullwhip effect using lead time forecasting techniques.

In a recently published empirical study, Shan et al. (2014, p. 549) estimated the bullwhip

effect for companies in China. They based their study on the data of the production and sales

series for over 1,200 publicly-listed Chinese companies. The data have been collected

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quarterly, from 2002 to the second quarter of 2009, for every company to avoid masking the

bullwhip effect, due to industry level aggregation. They test three hypotheses. First, they

assume that “the firm-level amplification ratio is positively associated with the inventory

days of the firm” (Shan et al., 2014, p. 540). Since the days in inventory measures, the time

length from inventory acquisition to its sale, companies with longer inventory turnover cycles

tend to order high batch sizes. Second, they assume “the firm-level amplification ratio being

negatively associated with the seasonality ratio of demand” (Shan et al., 2014, p. 540). The

reason for this hypothesis is that companies facing stronger seasonality might have more

knowledge about how to deal with demand volatility. Cachon et al. (2007) argue in this way,

while employing findings on US industry-level data (Cachon et al., 2007, as quoted by Shan

et al., 2014, p. 549). The last hypothesis they test is the relationship between firm-level

amplification ratio and the persistence of demand shocks. Altogether, Shan et al. (2014, p.

549) find “that volatility of production is larger than volatility of sales (demand) in a majority

(67%) of the companies.” However, estimations show a declining trend in the intensity of the

bullwhip effect for at least up to 2007. Shan et al. (2014, p. 549) argue that the companies of

which data they analyzed, tend to be the more efficient, large companies, so that they

introduced measurements to avoid the bullwhip effect or to diminish it. Testing the link

between the bullwhip effect and inventory days, seasonality and persistence of demand

shocks, they find less variable demand when companies must generally deal with seasonality.

Besides this, they also find a stable link between firm-level bullwhip effects and “average

inventory days and a firm’s persistence of demand shocks” (Shan et al., 2014, p. 549).

However the reasons for these findings are not so clear at all, since the data are aggregated on

a time and product level. Since companies are multi-product firms and orders and delivery

takes place within the quarter, the bullwhip effect occurring at the product level or in a

shorter time interval could be masked. The impact of product and time aggregation discussed

in scientific literature ranges from findings that time and product aggregation does not have

an effect at all, up to the claim that “the severity of the bullwhip effect tends to be masked

with product and time aggregation” (Chen & Lee, 2012, as quoted by Shan, 2014, p. 549).

Exploring the effect of time aggregation, they find no significant hint that the bullwhip effect

changes when time aggregation is introduced (Shan et al., 2014, p. 549). Thus, their findings

show evidence that the bullwhip effect is also in force in China.

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3. Formal Analysis of the Bullwhip Effect

3.1. Models Based on Serially Correlated Demand

Based on a serially correlated demand, Lee, Padmanabhan and Whang (1997) quantify the

bullwhip effect by analyzing the ratio of the variance between demand and orders (as quoted

by Alicke, 2005, p. 103). Bullwhip effects are often calculated for a given period and on firm

or industry levels. The following calculus starts with a time dependent demand function

(1) Dt=D+ρ Dt−1+e t

with

t=¿time period

D=¿mean of demand

ρ=¿ correlation coefficient with −1 ≤ p≤1

e t=¿normally distributed factor N (0 ,σ )

Furthermore, let

Var (x ) = variance of the order

Var (D) = variance of the demand

¿=¿lead time

(2) Var ( x )=Var (D )+ 2 p (1−p¿+1)(1−p¿+2)(1+ p)¿¿

for p>0

If lead time equals zero, then the formula reduces to

Var ( x )=Var (D )+2 p σ2

For all distributions where demands are not serially correlated that are not defined by last

periods demand, the variance of the order equals the variance of the demand (Alicke, 2005, p.

103).

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3.2. Measuring the Effect of Transparency

Chen et al. (2000, p. 441) extend the Lee, Padmanabhan and Whang approach by introducing

central information showing that lead time is the main reason for bullwhip effects when

demand is not serially correlated, which is ρ=0. These effects are still in function, even if all

retailers use the same forecasting techniques, if the demand information is centralized and

every stage uses the same inventory policy (Chen et al., 2000, p. 442).

(3) Var (xk)Var (D)

≥ 1+¿

with

p=¿ Number of observations used in the moving average

k=¿Number of stages

Proving that equation (3) holds for all k , they have shown that “the bullwhip effect is not

completely eliminated by centralizing customer demand information” (Chen et al., 2000, p.

442).

4. Mitigating the Bullwhip Effect

4.1. Information Policy

Studying countermeasures to mitigate the bullwhip effect, Beer (2014, p. 205) find that

transparency and equally shared information between retailers are often discussed in

literature. Within this debate, not only is information related to the order policy addressed,

but also capacity, the stock and the forecasting method. All information related to the causes

of the effect might be relevant.

4.2. Reducing Lead Time

Some studies find positive relations between lead time and scope of the bullwhip effect.

Therefore, proposals on how to mitigate the bullwhip effect also address lead time (Beer,

2014, p. 205). However, lead time does not necessarily provoke a bullwhip effect. Especially

since the lead times are common knowledge, the connection between lead times and the

bullwhip effect might be overcome by simple adaptation of forecast methods.

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4.3. Collaboration of Retailers

The collaboration of retailers by Vendor Managed Inventory’s (VMI) may reduce the

bullwhip effect, since inventory strategies that do not apply on a local stage, but take the

chain itself into account, might help to address the true causes. A further approach is the

standardization of inventory and forecasting strategies (Beer, 2014, p. 206). In particular, the

countermeasures that help to minimize the events of rationing and shortage gaming may help

to overcome the bullwhip effect. Furthermore, by avoiding discounts for large orders and

price fluctuations within the chain, the coordination of the chain might become easier (Beer,

2014, p. 207). However, collaboration does not work in every industry, but planning and

scheduling in the supply chains are especially important in manufacturing (Kreipl & Pinedo,

2004, p. 77).

5. Summary

The bullwhip effect represents a coordination failure in supply chains and leads to order

fluctuations with different amplitudes, even if the final demand does not vary at all. The

effect, which has been studied for different countries and industries, is based on demand

forecast updating, order batching, price fluctuations, rationing and shortage gaming (Lee,

Padmanabhan & Whang, 1997, p. 96). Thus, the effect happens even if all retailers behave

rationally. Recent empirical studies show evidence that this phenomenon is also in force in

China. A formal analysis suggests that the effect is still working if information is centralized.

Countermeasures discussed in literature address the main reasons and propose that an

enriched information policy improves transparency as well as the collaboration of retailers.

Coordination of supply chains is of increasing interests to companies, since the potential for

reducing costs and increasing efficiency are assumed to be very high (Werner, 2014, p. 3).

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References

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Unternehmensübergreifendes Supply Chain Management. 2., neu bearb. u. erw. Aufl.

Berlin: Springer VDI-Buch.

Beer, A. (2014). Der Bullwhip-Effekt in einem komplexen Produktionsnetzwerk. Entwicklung

eines realitätsadäquaten Simulationsmodells in Anlehnung an ein Realbeispiel und

Quantifizierung der Wirksamkeit von Maßnahmen gegen den Bullwhip-Effekt.

Information-Organistion-Produktion. Wiesbaden: Springer Gabler.

Chen, F. & Samroengraja, R. (2004). Order volatility and supply chain costs. Operations

Research, 52(5), 707–722.

Chen, F., Drezner, Z., Ryan, J. K., & Simchi-Levi, D. (2000). Quantifying the Bullwhip

Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and

Information. Management Science, 46(3), 436–443.

Forrester, J. (1961). Industrial Dynamics. John Wiley and Sons, New York, New York.

Henn, S., Koch, S., & Wäscher, G. (2011). Order Batching in Order Picking Warehouses: A

Survey of Solution Approaches. Otto von Guericke Universität Magdeburg, Faculty of

Economics and Management. Working Paper Series. Working Paper No. 01/2011.

Kouvelis, P., Chambers, C., & Wang, H. (2006). Supply Chain Management Research and

Production and Operations Management: Review, Trends, and Opportunities.

Production and Operations Management, 15(3), 449–469.

Kreipl, S. & Pinedo, M. (2004). Planning and Scheduling in Supply Chains: An Overview of

Issues in Practice. Production and Operations Management. Vol. 13, No. 1, 77–92.

Lee, L.H., Padmanabhan, V., & Whang, S. (1997). The bullwhip effect in supply chains. MIT

Sloan Management Review, 38(3), 93–102.

Makridakis S. & Wheelwright S. C. (1989). Forecasting Methods for Management. 5th ed.

New York [u.a.]: John Wiley & Sons.

Riemer, K. (2007). The Beer Game Portal. Available at URL: http://www.beergame.org/.

Shan, J., Yang, S., Yang, S., & Zhang, J. (2014). An Empirical Study of the Bullwhip Effect

in China. Production and Operations Management, 23(4), 537–551.

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Tsay, A. A. & Agrarwal, N. (2004). Channel Conflict and Coordination in the E-Commerce

Age. Production and Operations Management, 13(1), 93–110.

Werner, H. (2014). Kompact Edition: Supply Chain Controlling. Grundlagen, Performance

Messung und Handlungsempfehlungen. Wiesbaden: Springer Gabler.

Watson, N. H. & Zheng, Y. (2008). Over-reaction to demand changes due to subjective and

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Harvard University, Boston, MA.

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Appendix

Figure 1: Order fluctuations in the beer supply chain

Source: Riemer, K. (2007). Typical Results. Available at: http://www.beergame.org/the-game/typical-results , p. 1.

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I/we herewith declare that the following work I/we have prepared is my/our own without the use of materials other than those cited.

Place, date, signature

Köln, 27.11.2014, Johannes Wolff

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