Soft computing and the bullwhip effect

Soft computing and the bullwhip effect΢ȗ
Christer Carlsson and Robert Full´er
IAMSR, ˚
Abo Akademi University,
Lemmink¨ainengatan 14B, FIN-20520 ˚
Abo, Finland
e-mail: {christer.carlsson, robert.fuller}@ra.abo.fi
Abstract: We consider a series of companies in a supply chain, each of which orders from its
immediate upstream members. Usually, the retailer’s order do not coincide with the actual
retail sales. The bullwhip effect refers to the phenomenon where orders to the supplier tend
to have larger variance than sales to the buyer (i.e. demand distortion), and the distortion
propagates upstream in an amplified form (i.e. variance amplification). We show that if the
members of the supply chain share information, and agree on better and better fuzzy estimates
(as time advances) on future sales for the upcoming period, then the bullwhip effect can be
essentially reduced.
Keywords: supply chain, bullwhip effect, fuzzy number, variance of fuzzy numbers
1
Introduction
The Bullwhip Effect has been the focus of systematic theoretical work only in recent
years. The first articles to report on research results in a more systematic fashion [5]
have been published only recently. The effect is often identified with the simulation
experiment, The Beer Game, which is used to demonstrate the effects of distorted in-
formation in the supply chain (which is the cause of the bullwhip effect).
There are some examples published which demonstrate the bullwhip effect: (i) P & G
has over the years been successful producers and sellers of Pampers, and they have seen
that babies are reliable and steady consumers; (ii) the retailers, however, show fluctu-
ating sales, although the demand should be easy to estimate as soon as the number of
babies is known; (iii) P & G found out that the orders they received from distributors
showed a strong variability, in fact much stronger than could be explained by the fluc-
tuating sales of the retailers; finally, (iv) when P & G studied their own orders to 3M for
raw material they found these to be wildly fluctuating, actually much more than could
be explained by the orders from the distributors.
The context we have chosen for this study is the forest products industry and the mar-
kets for fine paper products. The supply chain is thus a business-to-business chain, and
∗In: Economics and Complexity, Vol. 2, No. 3, Winter 1999-2000 1-26.
1

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Soft computing and the bullwhip effect
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we will show that the bullwhip effect is as dominant as in the business-to-consumer
supply chain.
The key driver of the bullwhip effect appears to be that the variability of the estimates
or the forecasts of customer demand seems to amplify as the orders move up the sup-
ply chain from the customer, through retailers and wholesalers to the producer of the
product or service. This is called the bullwhip, the whiplash or the whipsaw effect.
In a number of studies, it appears that the bullwhip effect will have a number of negative
effects and that it will cause significant inefficiencies:
1. Excessive inventory investments throughout the supply chain as retailers, distrib-
utors, logistics operators and producers need to safeguard themselves against the
variations.
2. Poor customer service as some part of the supply chain runs out of products due
to the variability and insufficient means for coping with the variations.
3. Lost revenues due to shortages, which have been caused by the variations.
4. The productivity of invested capital in operations becomes substandard as rev-
enues are lost.
5. Decision-makers react to the fluctuations in demand and make investment de-
cisions or change capacity plans to meet peak demands. These decisions are
probably misguided, as peak demands may be eliminated by reorganisations of
the supply chain.
6. Demand variations cause variations in the logistics chain, which again cause
fluctuations in the planned use of transportation capacity. This will again produce
sub-optimal transportation schemes and increase transportation costs.
7. Demand fluctuations caused by the bullwhip effect may cause missed produc-
tion schedules, which actually are completely unnecessary, as there are no real
changes in the demand, only inefficiencies in the supply chain.
There are some studies [5], which have revealed four key reasons for the occurrence
of the bullwhip effect. These include (i) the updating of demand forecasts, (ii) order
batching, (iii) price fluctuations and (iv) rationing and shortage gaming.
The updating of demand forecasts appears to be a major source of the bullwhip effect.
The parties of the supply chain build their forecasts on the historical demand patterns
of their immediate customers. In this way, only the retailers build on the actual demand
patterns of the customers, the other parties adjust to (unmotivated) fluctuations in the
ordering policies of those preceding them in the supply chain. Another effect will also
occur: if everybody reacts to fluctuations with smoothing techniques (like exponential
smoothing), the fluctuations will amplify up through the supply chain. It appears that

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Soft computing and the bullwhip effect
3
safety stocks, which are popular smoothing devices, will actually amplify the bullwhip
effect.
The order batching will appear in two different forms: (i) periodic ordering and (ii)
push ordering. In the first case there are a number reasons for building batches of
individual orders. The costs for frequent order processing may be high, which will
force customers into periodic ordering; this will in most cases destroy customer de-
mand patterns. There are material requirement planning systems in use, which are run
periodically and thus will cause that orders are placed periodically. Logistics operators
often favor FTL-batches and will determine their tariffs accordingly. These reasons
for periodic ordering are quite rational, and will, when acted upon, amplify variability
and contribute to the bullwhip effect. Push ordering occurs, as the sales people em-
ployed by the producers try to meet their end-of-quarter or end-of-year bonus plans.
The effect of this is to amplify the variability with orders from customers overlapping
end-of-quarter and beginning-of-quarter months, to destroy connections with the actual
demand patterns of customers and to contribute to the bullwhip effect.
The producers initiate and control the price fluctuations for various reasons. Customers
are driven to buy in larger quantities by attractive offers on quantity discounts, price
discounts, coupons or rebates. Their behavior is quite rational: to make the optimal
use of opportunities when prices shift between high and low. The problem introduced
by this behavior is that buying patterns will not reflect consumption patterns anymore,
customers buy in quantities which do not reflect their needs. This will amplify the
bullwhip effect. The consequences are that producers (rightfully) suffer: manufacturing
is on overtime during campaigns, premium transportation rates are paid during peak
seasons and products suffer damages in overflowing storage spaces.
The rationing and shortage gaming occurs when demand exceeds supply. If the pro-
ducers once have met shortages with a rationing of customer deliveries, the customers
will start to exaggerate their real needs when there is a fear that supply will not cover
demand. The shortage of DRAM chips and the following strong fluctuations in de-
mand was a historic case of the rationing and shortage game. The bullwhip effect will
amplify even further if customers are allowed to cancel orders when their real demand
is satisfied. The gaming leaves little information on real demand and will confuse the
demand patterns of customers.
It is a fact that these four causes of the bullwhip effect may be hard to monitor, and even
harder to control in the forest products industry. We should also be aware of the fact
that the four causes may interact, and act in concert, and that the resulting combined
effects are not clearly understood, neither in theory nor in practice. It is also probably
the case that the four causes are dependent on the supply chain’s infrastructure and on
the strategies used by the various actors.
The factors driving the bullwhip effect appear to form a hyper-complex, i.e. a system
where factors show complex interactive patterns. The theoretical challenges posed by
a hyper-complex merit study, even if significant economic consequences would not
have been involved. The costs incurred by the consequences of the bullwhip effect

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Soft computing and the bullwhip effect
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offer a few more reasons for carrying out serious work on the mechanisms driving the
bullwhip. Thus, we have built a theory to explain at least some of the factors and their
interactions, and we have created a support system to come to terms with them and to
find effective means to either reduce or eliminate the bullwhip effect.
With a little simplification there appears to be three possible approaches to counteract
the bullwhip effect:
1. Find some means to share information from downstream of the supply chain with
all the preceding actors.
2. Build channel alignment with the help of some co-ordination of pricing, trans-
portation, inventory planning and ownership - when this is not made illegal by
anti-trust legislation.
3. Improve operational efficiency by reducing cost and by improving on lead times.
The first approach can probably be focused on finding some good technology to accom-
plish the information sharing, as this can be shown to be beneficial for all the actors
operating in the supply chain.
The second approach can first be focused on some non-controversial element, such as
the co-ordination of transportation or inventory planning, and then the alignment can
be widened to explore possible interactions with other elements.
The third approach is probably straight-forward: find inefficiencies in operations in
selected strategic business units (SBUs), find ways to reduce costs and to improve on
lead times, and explore if these solutions can be generalised for more actors in the
supply chain.
The most effective - and the most challenging - effort will be to find ways to combine
elements of all three approaches and to find synergistic programs, which will have the
added benefit of being very resource-effective, to eliminate the bullwhip effect.
2
The Bullwhip Effect in the Forest Products Industry
The two corporate members of the EM-S Bullwhip consortium had observed the bull-
whip effects in their own markets and in their own supply chains for fine paper products.
They also readily agreed that the bullwhip effect is causing problems and significant
costs, and that any good theory or model, which could give some insight into deal-
ing with the bullwhip effect, would be a worthwhile effort in terms of both time and
resources.
There are several reasons why the bullwhip effect occurs in the fine paper products
market. The first reason is to be found in the structure of the market (cf. fig. 1):
The paper mills do not deal directly with their end-customers, but fine paper products
are distributed through wholesalers, merchants and retailers. The paper producers may

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Soft computing and the bullwhip effect
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Silvaculture & Timber Farming
Logging & Chipping
Pulp Manufacturing
Paper Manufacturing
Converting Operations
Merchanting & Distribution
End-Users [Printing houses, etc.]
Figure 1: The supply chain of the market for fine paper products.
(i) own some of the operators in the market supply chain, (ii) they may share some
of them with competitors or (iii) the operators may be completely independent and
bound to play the market game with the paper producers. The operators in the market
supply chain do not willingly share their customer and market data, information and
knowledge with the paper producers.
Thus, the paper producers do not get neither precise nor updated information on the
real customer demand, but get it in a filtered and/or manipulated way from the mar-
ket supply chain operators. Market data is collected and summarised by independent
data providers, and market forecasts are produced by professional forest products con-
sultants and market study agencies, but still it appears that these macro level studies
and forecasts do not exactly apply for the markets of a single paper producer. The
market information needed for individual operations still needs to come from the indi-
vidual market. Here the operators of the market supply chain control access to the data
sources, and the paper producer is forced to build his demand forecasts on the numbers
he get from the wholesaler or merchant part of the market supply chain.
The second reason for the bullwhip effect to occur is found earlier in the supply chain.
The demand and price fluctuations of the pulp markets dominate also the demand and
price patterns of the paper products markets, even to such an extent, that the customers
for paper products anticipate the expectations on changes in the pulp markets and act
accordingly. If pulp prices decline, or are expected to decline, demand for paper prod-
ucts will decline, or stop in anticipation of price reductions. Then, eventually, prices
will in fact go down as the demand has disappeared and the paper producers get ner-

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Soft computing and the bullwhip effect
6
vous. The initial reason for fluctuations in the pulp market may be purely speculative,
or may have no reason at all. Thus, the construction of any reasonable, explanatory
cause-effect relationships to find out the market mechanisms that drive the bullwhip
may be futile. If we want to draw an even more complex picture we could include the
interplay of the operators in the market supply chain: their anticipations of the reactions
of the other operators and their individual, rational (possibly even optimal) strategies
to decide how to operate. This is a later task, to work out a composite bullwhip effect
among the market supply chain operators, as we cannot deal with this more complex
aspect here.
The third reason for the bullwhip effect is order batching. The logistics systems favour
the shipping of larger batches of paper products, the building of inventories in the
supply chain to meet demand fluctuations and push ordering to meet end-of-quarter
or end-of-year financial needs. The logistics operators are quite often independent of
both the paper producers and the wholesalers and/or retailers, which will make them
want to operate in such a way that their result and financial goals are met. Thus they
decide their own tariffs in such a way that their operations are effective and profitable,
which will - in turn - affect the decisions of the market supply chain operators, including
the paper producers. The adjustment to proper shipload or FTL batches will drive the
bullwhip effect.
There is a fourth reason for the bullwhip effect, which is caused by the paper producers
themselves. There are attempts at influencing or controlling the paper products markets
by having occasional low price campaigns or special offers. The market supply chain
operators react by speculating in the timing and the level of low price offers and will
use the (rational) policy of buying only at low prices for a while. The nervous reactions
and speculations of all the players drive the bullwhip effect.
There is a fifth and final explanation for the bullwhip effect, the so-called rationing
and shortage game. This would be the case when demand in paper products markets
outgrow the production capacity and the supply chain operators cannot fill their orders.
If they get less than their needs in some period, they will try to compensate for this
in their next order by anticipating the rationing and ordering more than their actual
needs. If the policy allows for not taking delivery of excessive orders, or if there is
sufficient inventory capacity, the rationing game will drive the bullwhip effect. It is
questionable if this factor will play any role in the paper products market, as the rule
for the last decade seems to have been that there is more production capacity available
than needed.
The bullwhip effect may be illustrated as in fig.2. The variations shown in fig.2 are
simplifications, but the following patterns appear: (i) the printer (an end-customer)
orders once per quarter according to the real market demand his has or is estimating;
(ii) the dealer meets this demand and anticipates that the printer may need more (or
less) than he orders; the dealer acts somewhat later than his customer; (iii) the paper
mill reacts to the dealer’s orders in the same fashion and somewhat later than the dealer.
The resulting overall effect is the bullwhip effect.

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Soft computing and the bullwhip effect
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60
50
40
Printer
Retailer
30
Wholes.
20
Mill
10
0
Month1Month2Month3Month4Month5Month6Month7Month8Month9
Month10
Month11
Month12
Figure 2: The bullwhip effect in the paper products market.
In the following section, we will present the standard theory for explaining the bullwhip
and for coming to terms with it.
3
Explanations for the bullwhip effect: Standard Results
The first detailed, theoretical discussion of the bullwhip effect was published by Lee et
al [5] in Management Science (April 1997) and in a more popular, empirical version in
the Sloan Management Review [6] (Spring 1997). These two papers were continuations
of earlier studies of the benefits of co-ordination among members of a supply chain,
which comprises manufacturers, distributors, wholesalers and retailers.
A key mechanism for the co-ordination is the information flows among members of the
supply chain, as they have a direct impact on production scheduling, inventory control,
delivery planning and logistics solutions among the individual members of the supply
chain. If this information flow gets distorted or interrupted the consequences will be
felt in the production plans and the production scheduling, which will cause inventories
to either grow rapidly or empty out, which again disrupts delivery planning and causes
expensive logistics solutions. The dynamics behind this series of events - if mastered -
will have a profound effect on how the supply chain is managed and will point the way
to more productive and effective operations in all parts of the supply chain.
The supply chain management is an important issue for the Finnish forest products
industry as supply chain mismanagement, with a total turnover of more than 100 BFIM,
has consequences costing 100-200 MFIM per year.
Lee et al focus their study on the demand information flow and work out a theoretical
framework for studying the effects of systematic information distortion as information

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Soft computing and the bullwhip effect
8
works its way through the supply chain. The distortion becomes visible when the
retailer’s orders to the wholesaler do not coincide with the actual retail sales. As the
wholesaler reacts to his retailers orders by adding a similar ”safety margin” (a positive
margin for growing demand, a negative margin for declining demand) when ordering
from the producer, the distortion grows in magnitude.
This means that the orders to a supplier will have larger variance than the sales to a
buyer. The theory demonstrates and proves that the distortion propagates upstream in
an amplified form, i.e. the variances grow as we move upstream in the supply chain.
This phenomenon is known as the bullwhip or whiplash effect.
Lee et al simplifies the context for the theoretical work by defining an idealised situ-
ation. They start with a multiple period inventory system, which is operated under a
periodic review policy. They include the following assumptions: (i) past demands are
not used for forecasting, (ii) re-supply is infinite with a fixed lead time, (iii) there is no
fixed order cost, and (iv) purchase cost of the product is stationary over time. If the
demand is stationary, the standard optimal result for this type of inventory system is to
order up to S, where S is a constant. The optimal order quantity in each period is ex-
actly equal to the demand of the previous period, which means that orders and demand
have the same variance (and there is no bullwhip effect).
This idealised situation is useful as a starting point, as is gives a good basis for working
out the consequences of distortion of information in terms of the variance, which is the
indicator of the bullwhip effect. By relaxing the assumptions (i)-(iv), one at a time, it
is possible to produce the bullwhip effect.
3.1
Demand Signal Processing
Lets focus on the retailer-wholesaler relationship (the framework applies also to a
wholesaler-distributor or distributor-producer relationship). Now we consider a mul-
tiple period inventory model where demand is non-stationary over time and demand
forecasts are updated from observed demand.
Lets assume that the retailer gets a much higher demand in one period. This will be
interpreted as a signal for higher demand in the future, the demand forecasts for future
periods get adjusted, and the retailer reacts by placing a larger order with the whole-
saler. As the demand is non-stationary, the optimal policy of ordering up to S also gets
non-stationary. A further consequence is that the variance of the orders grows, which
is starting the bullwhip effect. If the lead-time between ordering point and the point
of delivery is long, uncertainty increases and the retailer adds a ”safety margin” to S,
which will further increase the variance and add to the bullwhip effect.
Lee et al simplifies the context even further by focusing on a single-item, multiple
period inventory, in order to be able to work out the exact bullwhip model.
The timing of the events is as follows: At the beginning of period t, a decision to order
a quantity zt is made. This time point is called the ”decision point” for period t. Next
the goods ordered ν periods ago arrive. Lastly, demand is realized, and the available

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Soft computing and the bullwhip effect
9
inventory is used to meet the demand. Excess demand is backlogged. Let St denote
the amount in stock plus on order (including those in transit) after decision zt has been
made for period t. Lee at al assume that the retailer faces serially correlated demands
which follow the process
Dt = d + ρDt−1 + ut
where Dt is the demand in period t, ρ is a constant satisfying −1 < ρ < 1, and ut is
independent and identically normally distibuted with zero mean and variance σ2. Here
σ2 is assumed to be significantly smaller than d, so that the probability of a negative
demand is very small. The existence of d, which is some constant, basic demand, is
doubtful; in the forest products markets a producer cannot expect to have any ”granted
demand”. The use of d is technical, to avoid negative demand which will destroy the
model, and it does not appear in the optimal order quantity. After formulating the cost
minimization problem Lee et al proved the following theorem,
Theorem 3.1. [5] In the above setting, we have:
1. If 0 < ρ < 1, the variance of retails orders is strictly larger than that of retail
sales; that is,
Var(z1) > Var(D0)
2. If 0 < ρ < 1, the larger the replenishment lead time, the larger the variance of
orders; i.e. Var(z1) is strictly increasing in ν.
This theorem has been proved using the relationships
ρ(1 − ρν+1)
z∗1 = S1 − S0 + D0 =
(D
1 − ρ
0 − D−1) + D0
(1)
and
2ρ(1 − ρν+1)(1 − ρν+2)
Var(z∗1) = Var(D0) +
> Var(D
(1 + ρ)(1 − ρ)2
0)
where z∗1 denotes the optimal amount of order. Which collapses into
Var(z∗1) = Var(D0) + 2ρ
for ν = 0.
The optimal order quantity is an optimal ordering policy, which sheds some new light
on the bullwhip effect. The effect gets started by rational decision making, i.e. by
decision makers doing the best they can. In other words, there is no hope to avoid the
bullwhip effect by changing the ordering policy, as it is difficult to motivate people to
act in an irrational way. Other means will be necessary (cf. Section 5).

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Soft computing and the bullwhip effect
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3.2
The Rationing Game
For the second reason for the bullwhip effect, we have to change the context. Now
we have the situation that the demand potentially exceeds supply due to limitations
of production capacity, uncertainty of production yield, or limitations or disturbances
of the logistics system. We will focus on limitations of production capacity, we will
work with a single-product, one-period inventory model, and we will assume multiple
retailers. This is also known as the newsvendor problem, after a classical inventory
problem in operations research.
In the forest products industry limitations of production capacity, to the extent that
demand exceeds production capacity, is rather rare. Thus the rationing game does not
occur very often, but we have included the theory in order to make the theoretical
framework complete.
Lets assume that a producer supplies a single product to n identical retailers. Retailer i
observes the demand distribution Φ(·), and places an order zi at time 0. Here we have
a demand, which is known through its probability distribution, and the retailer tries to
anticipate what the demand is going to be. The producer delivers the order at time 1;
the producer’s delivery m is a random variable, distributed according to F (·).
In the newsvendor problem, in which old newspapers are worthless and no backorders
are possible, the optimal policy is to estimate the expected demand and its variance,
and then to find an order quantity for which the marginal profit for adding one more
newspaper to the order exactly balances the expected loss of leaving the order one
newspaper short. Let us assume that this optimal order quantity is z .
If the total amount of orders received from the n retailers exceeds the production quan-
tity m, the producer will allocate products to the retailers in relation to their orders; if
the total amount of orders is less than m, then all retailers will get the amounts they
ordered. The question now is what the optimal order quantity zi of retailer i should be?
The model gets rather complicated as it turns out that the retailer should not only try to
estimate the expected demand and its variance, and then use the newsvendor solution,
but should also in ordering try to anticipate what the other n − 1 retailers will do. The
policy would be to order more than the expected demand in anticipation of rationing
in order to make sure that the actual delivery will satisfy the expected demand. The
only problematic issue is to decide how much to exaggerate and also to find out if
the coming period will be one in which the production capacity will not b enough to
satisfy all retailers. The model to be used for this is the classical Nash equilibrium
model, which shows how to decide the optimal ordering policy (minimising expected
cost = holding cost + ordering cost + shortage cost) when n − 1 other rational decision
makers optimal decisions are given. There is an optimal ordering policy for retailer i,
which is found at an equilibrium point - the so-called Nash equilibrium - which ensures
that none of the retailers should try to exaggerate more than any other retailer.
The result is that the z∗ ≤ z
i
, and that the inequality hold strictly if F (·) and Φ(·) are
strictly increasing. The retailer should thus exaggerate the order to the producer and

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