Bullwhip Effect by Means of Numerical Simulation CUOA International MBA

Paolo Vaona

paolo.vaona@gmail.com

Abstract

The object of this papers to provide an overview of what the bullwhip effect is and try to better

understanding it by the means of agent base simulation.

The article is divided in four section. First a brief overview of the bullwhip effect is provided.

In the second section the Cisco 2001 case is discussed, showing how relevant is this problem in

the life of a company.

In the third section it is illustrated a code written in NetLogo, a multi-agent programmable modeling

environment, that simulate the Beer Game. In this way it is possible to study how different behavior

of the actor of the process can affect the outcome of the simulation. Some possible way to mitigate

the effect are investigated.

Finally in the conclusion some possible advantage for firm are considered.

The Bullwhip Effect

The bullwhip effect it is also known as Forrester Effect, is at the base of a lot of studies in the

supply chain management. It could be studied form different point of view but what comes out at a

first glance of some graph of the orders of retailers, wholesalers and manufacturers is the

increasingly volatility in the graph.

The easiest and safe way to experience the bullwhip effect is the beer game. In the game one can

experience the increasing in orders, the empty inventory, tremendous backlog. This happen for all

the participants of the game, with an increase in fluctuation. All these fluctuation are amplified

moving upstream of the flow.

Supply chains are often referred to as pipelines of product (and sometimes service) flow. Supply

chains rarely do, even when they are supposed to. This is because supply chains have their own

dynamic behavior patterns which tend to distort the smooth flow of information up the chain and

product moving down the chain. In practice, flow in supply chains can be turbulent, with the activity

levels in each part of the chain differing significantly and the flow of products, services and

information varying, even when demand at the end of the chain is relatively stable. A definition of

bullwhip effect then could be that small changes in one part of the chain can cause seemingly

erratic behavior in other parts.

It is important to understand it, for although it is essentially a short-term phenomenon, the

measures that operations try to put in place in order to deal with it have more strategic implications.

There are several reason for the bullwhip effect. Some of these are:

Demand forecast updating. Forecasting is often based on the order history from the

company immediate customer and usually the information exchanged between the actors

are the order. When a downstream operation place an order the upstream process that

piece of information as a signal of future demand. This underline a mismatch between what

upstream and downstream see.

Order batching. This is something related by the way usually downstream makes orders.

Generally downstream batches or accumulate demands before placing an order. Periodic

ordering amplify the effect of the bullwhip effect. The effect on the upstream of this behavior

is, even with a steady demand, to have concentrated orders. Another example of these

behaviors could be found in the hockey stick effect.

Price fluctuation. Usually forward buying results from price fluctuation ( due to currency,

materials, due to wholesaler that want to clear the inventory or even due to trade

promotions because of the impact on the manufacturer’s stock performance). I this way the

costumer consumer’s buying pattern doesn’t reflect its consumption pattern. A famous

example is the one that involved Volvo during the 90s. At that time Volvo had an excess of

green cars. To move them along marketing and selling began offering special deals.

Nobody told the manufacture department about the discount and so once they saw the

increase the demand for green car they ramped up production. Another famous case study

in this field is Barilla.

Rationing and shortage gaming This generally happen when demand exceeds supply.

Under such circumstances, a supplier may ration supplies to its customers. For example, it

might allocate a fixed proportion of each customer’s orders for delivery to them. Of course,

if the customer is aware that this is happening, it is in their interests to place a larger order

in the hope that they will still get what they need, even after the order has been rationed

down. This has the effect of killing the supplying operation’s marketing information.

These are the main cause, known by long time, that could generate the bullwhip effect. Although

they are acquainted by more than 30 years, still some firms face the closure due to them.

What went wrong at Cisco in 2001

The easy solution mention in all the textbook to avoid the bullwhip effect is sharing information.

And for sure a company that declare itself the leader in networks should be prepare to manage in

its supply chain changes and avoid negative effects. In practices what Cisco faced in 2001 was a

major downturn due not only to the economic downturn but also to a wrong management of its

supply chain.

2001 has been a year that Cisco has fixed in his memory. During the year they face the beginning

of one of the biggest change in the organization design in order to face the 2001 Internet bubble

burst.

According to CEO John Chambers: "We never built models to anticipate something of this

magnitude." That something was 2001 economic downturn. Chambers surveyed the wreckage and

compared it to an unforeseeable natural disaster. In his mind, the economy not his company’s

software nor its management was clearly to blame. But other networking companies, with far less

sophisticated tools started downgrading their forecasts months earlier. They saw the downturn

coming. Cisco did not. Other companies cut back on inventory. Cisco did not. Other companies

saw demand declining. Cisco saw it rising.

The IT system with Cisco manage the supply chain was at the time view as one of the most

advance and as source of real competitive advantage. It was said that the system was able to

manage everything in all the process of the company. What Cisco’s systems didn’t do was model

what would happen if one critical assumption was removed from both their forecasts and their

mind-sets. If Cisco had run even modestly declining demand models, Chambers and others

managers might have seen the consequences of betting on more inventory. But Cisco had enjoyed

more than 40 straight quarters of stout growth. In its immediate past were three quarters of

extreme growth as high as 66 percent. The numbers the virtual close presented to the eye of the

Cisco executives painted a picture of the present lovely and pleasant. According to many

observers, Cisco’s fundamental blunder was to rely on that pretty picture to assume the future

would be equally pretty.

During the 2000 some components for Cisco’s networking equipment were rumored to be in short

supply. Privately, Cisco was already twitchy because lead times on delivering its routers and

switches were extending. Eventually those lead times would reach nearly six months on some

products. Not having the components could push those delivery dates out even further. This was

mainly due to the precedent choice of the company to heavily outsource the production of all his

products. Due to the increasing lead time Cisco decided to build up its components inventory.

Doing that would accomplish two things: It would reduce the wait time for its customers, and it

would give the manufacturers of Cisco’s switches and routers a reserve to draw on if components

makers ran out.

Of course, everyone else wanted those components and the manufacturing capacity to build the

networking devices too. So in order to get both, to make sure they would have them when they

needed them (and they knew they’d need them; the virtual close told them so), Cisco entered into

long-term commitments with its manufacturing partners and certain key components makers.

Promise us the parts, Cisco said, and we promise to buy them. No matter what.

In the summer of 2000, Solectron’s Shah had customers from every corner begging for more

manufacturing capacity. Even so, his forecasts were slowly diverging from his networking partners’,

including Cisco. His were less optimistic, based on what he saw in the general economy. There

were meetings about it, but nothing was resolved about the growing disparity between what Shah

and his customers thought was happening and what Cisco said was happening. Here, the very

core of Cisco’s infrastructure its much-vaunted outsourced manufacturing model worked against

the company because Cisco’s partners were simply not as invested in delivering a loud wake-up

call as an in-house supplier would have been.

By year’s end, the economy was foundering. It was neither a "U" nor a "V" buy a cliff. The biggest

company halted capital spending. Alternative telecommunications carriers disappeared, along with

many of the dotcoms that had been so feverishly buying Cisco gear. That equipment ended up on

a gray market; barely-used Cisco switches could be had for 15 cents on the dollar, and Cisco lost

money every time one was snapped up. Traditional telecom companies stopped spending too. In

short, demand vanished. Cisco finally threw on the brakes Dec. 15. Cisco, the networking

industry’s big engine, went over the edge.

Cisco try to deny and blame for problems to uncontrollable forces, as if the historic $2.2 billion

inventory write-off and the steep decline of the company’s stock had nothing to do with the men at

the top or the systems they trusted. But after that moment they start working more closely with

supplier and try to integrate more and more and develop alliance with their partner to really

integrate the supply chain.

Cisco decided to provide its partners with the same tools it used, as stated in Value Added Retail

Business News “Partner Access OnLine (PAL) leverages the same technology Cisco uses

internally to monitor and score customer satisfaction levels. The idea is that the partners can use

the data, which they can access via the Web 24 hours a day, to get a better understanding of the

relationship they have with customers and identify the specific areas where they need

improvement.”

Bullwhip effect by means of agent modelling

Probably the famous application of the bullwhip effect can be seen playing at the Beer Game.

The beer distribution game(also known as the beer game) is an experiential learning business

simulation game created by a group of professors at MIT Sloan School of Management in early

1960s to demonstrate a number of key principles of supply chain management. The game is

played by teams of at least four players, often in heated competition, and takes from one to one

and a half hours to complete. A debriefing session of roughly equivalent length typically follows to

review the results of each team and discuss the lessons involved. The purpose of the game is to

understand the distribution side dynamics of a multi-echelon supply chain used to distribute a

single item, in this case, cases of beer.

Using NetLogo it is possible to create a program where each agent involved( customer, retailer,

wholesaler, distributor and factory) follow a strategy. Some part of the code has been taken from

an existing model of the beer game for human players. The variable set up in the model allow to

change the following features:

Demand style – Step , Sine, Random

Who place first the order – Retail or Factory

Visibility – this option could be swich on or off and allow the upstream to know what the

next order will be.

Duration ( yearly-52 week,104 week and so on)

Order first – allow to place the order before or later the costumer order is received.

Order Style – Could be costumer driven or modeled according to Sterman Model

The program consider each time step as a week and

It takes one step (1 week) for an order to be received by the upstream supplier, and two time slots

(2 weeks) for an order to be filled by that supplier, thus a three week lag in all. The cost of

inventory is set in the same way of the beer game ( 0.5$ for inventory and 2$ for backlog).

With all these variable set it is possible to show and test some of the possible misbehavior that

lead to bullwhip effect.

In the picture below the way in which the program calculate the different demands is shown:

In the picture below the way in which the program model possible behaviors according to Sterman

models is shown.

Here a picture of how the program looks like before the simulation start.

In the following paragraph an analysis of how the different variables influence the game is shown.

In general a 104 week period is considered. Always the order is driven from retailer.

No human behavior – the customer driven supply chain

In this case the simulation consider to have no interpretation of the information.

If the variable visibility is set to off, meaning there is no exchange of the order and each player

moves upstream the order information as it is the supply chain is influenced only by the lag that

takes to fill the order.

At first the simulation is run with a step model from customer.

As can be seen from the order windows the order all follow the customer order.

It is interesting to underline how even under different shape of the costumer order, for example

sine or random the supply chain works efficiently.

In these models, setting visibility on or off doesn’t change the behavior of the supply chain, since

all the players are able to see the real information coming from the customer, since no additional

noise is added.

This situation is of course the best supply chain designable, able to efficiently transmit the

information upstream.

Then the case has no real interest but it could be considered as benchmark for supply chain

optimization.

Human behavior – How different biases affect the supply chain.

In this case the order style is switched to Sterman. Here 4 variables, alpha, beta, theta and Q,

allow to module the behavior of the player. Each of these variables add some information to the

order, in this way increasing the noise in the information that travel upstream trough the supply

chain.

Alpha

The alpha coefficient is inserted in order to modify the expectation based on an amplification of the

expectation due to an order. As can be see this effect has its peak every time the order change

and then it is difficult to dispose the excess of inventory. As seen in the first section, this could lead

to a price fluctuation. The use of visibility could help to mitigate this effect.

Same simulation but with visibility on had a substantial decrease in the total inventory cost.

Beta

Beta regulate the fraction of the supply line taken into account. In this case since is the retailer the

one who experience the order it ignore partially the order and then the inventory of the retailer is

always in backlog. In this case since the other variable are zero the effect is concentrated. Since it

is multiplied by alpha, a value different from 0 need to be used (0.07 set)

Having the visibility and constant order it can be seen how the information travel trough the supply

chain and actually beta could help to optimize the cost reducing the inventory at the lowest level.

Of course, under the step demand it easy to optimize the minimum inventory, while under random

demand it could lead to extra cost. In the picture below could be seen the result of the visibility

increase dramatically the efficiency of the supply chain with beta.

Theta

The theta represent the phase lag in the order, between the expectation and the last order. For this

reason it is useful to show the result of the simulation under the sine demand instead of the

constant demand. This lead to a slightly lag between the orders an with this kind of demand lead to

an increase in the inventory ( since beta is zero and didn’t allow to stop the orders and consume

the inventory.) It could also represent the reactivity of the supply chain to the changes.

Adding the visibility of the order to the whole supply chain reduce the lag between costumer order

and the other others. Also it is interesting to note that in this case the inventory doesn’t incur in

scarcity period(inventory graph).

Q

Q represent a fixed quantity that it is added to the orders. As per the case of beta it is needed to

have the alpha value set different from zero. In this way can be seen that at each order a fix quota

is added, this increase the more upstream the information travel, and therefore the factory takes

more time to come up the orders. This effect add another phase lag to the system.

Again the visibility allow the supply chain to be more immediate in the response and to limit the

increase in the effect of the impulsive change from the customer, which is to say that increase the

damping of the system.

Here the results with visibility on.

Real case model

Now it is possible try to simulate a real case, defining first of all the characteristics of the Supply

chain.

In order to represent a real situation the following values are applied:

Alpha = 0.25 a low level of increase the changes

Beta = 1 strong influence of the pending order

Theta=0.1 low level of reactiveness

Q= 6 medium value of influence in the order

We will consider a sine demand and a random demand, always with visibility off.

For a sine demand the result is the following:

It is interesting to note that increasing theta the cost decrease because the factory is more reactive

in providing the good, then reducing the period of backlog , more costly. This is an obvious

conclusion that with a more reactive supply chain cost should generally decrease.

Adding the visibility , as expected the reduce the maximum unfilled orders in all players inventory.

Before analyzing the final case, the random demand it have to be clarify that for this type of demand it is not possible to compare easily the quantitative results obtained between one case and another because each pattern of order is different from the previous. As indication, what has been obtained from the sine model should be followed as example of optimization, since a random pattern could be decomposed in a series of sine and cosine demand. One thing that it is interesting to note is that under the random demand it is the retail inventory is more correlated with the oscillation of the wholesaler. At the same time with no visibility and low level of theta the orders don’t follow the order of customer.

Also in this case increasing the theta help the orders to be more attached to the order of the costumer.

It is interesting to note that, with the visibility, repeating the simulation for 10 times, the average cost of the inventory it is slightly less than the sine one. This is probably due to the chance to empty the inventory less frequently due to the period of 0 order.

Conclusions

The paper has tried to illustrate the bullwhip effect bot from the theoretical point of view and from a

real case study. In the third section a code is analyzed and explained in order to show a way to

model possible behaviors that could be encountered in the supply chain. The intent is not to

simulate every time a real supply chain, which due to the complexity and the number of variable is

probably almost impossible, but to provide an easy tool to test possible scenario.

It is important as a tool also because it allows to see if between theoretical data and real data there

are some possible trend unseen, such as in the case of Cisco. Since the variable are a lot not anly

a combination of parameters exists, and then having the chance to test the all could help to study

better a real time situation, testing in a quick way possible solution.

In any case, the model proof empirically the fundamental importance of communication between

the actor or player of the supply chain.

This is because a supply chain is not a fix entity but something that evolves with time, and it is then

fundamental to continually monitor it and all conclusion that one could find in a supply chain are

temporary and have to be continually tested.

References

Global Operations Strategy: Fundamentals and Practice, Yeming Gong, 2013

Operations Strategy, Slack,Lewis, 2011

Cisco Unauthorized, Jeffrey Young ,Prima Publishing, 2001

Lee, H.L., Padmanabhan, V. and Whang, S. The Bullwhip Effect in Supply Chains. Sloan

Management Review

Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making

Experiment, Sterman J.D., Management Science 35(3), 321-339, 1988.