Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information

Abstract

The tendency of orders to increase in variability as one moves up a supply chain is commonly known as the 'bullwhip effect.' We study this phenomenon from a behavioral perspective in the context of a simple, serial, supply chain subject to information lags and stochastic demand. We conduct two experiments on two different sets of participants. In the first we find the bullwhip effect still exists when normal operational causes (e.g., batching, price fluctuations, demand estimation, etc.) are removed. The persistence of the bullwhip effect is explained, to some extent, by evidence that decision-makers consistently under-weight the supply line when making order decisions. In the second experiment we find that the bullwhip, and the underlying tendency of underweighting, remains when information on inventory levels is shared. However, we observe that inventory information helps somewhat to alleviate the bullwhip effect by helping upstream chain members better anticipate and prepare for fluctuations in inventory needs downstream. These experimental results support the theoretically suggested notion that upstream chain members stand to gain the most from information sharing initiatives.

Full text

MANAGEMENT SCIENCE
Vol. 00, No. 0, Xxxxx 2005, pp. 1–14
issn 0025-1909eissn 1526-55010500000001
informs®
doi 10.1287/mnsc.1050.0436
© 2005 INFORMS
Behavioral Causes of the Bullwhip Effect and
the Observed Value of Inventory Information
Rachel Croson
Department of Operations and Information Management, The Wharton School, University of Pennsylvania,
Philadelphia, Pennsylvania 19104-6366, crosonr@wharton.upenn.edu
Karen Donohue
Department of Operations and Management Science, The Carlson School, University of Minnesota,
Minneapolis, Minnesota 55455-9940, kdonohue@csom.umn.edu
The tendency of orders to increase in variability as one moves up a supply chain is commonly known as
the bullwhip effect. We study this phenomenon from a behavioral perspective in the context of a simple,
serial, supply chain subject to information lags and stochastic demand. We conduct two experiments on two
different sets of participants. In the first, we find the bullwhip effect still exists when normal operational causes
(e.g., batching, price fluctuations, demand estimation, etc.) are removed. The persistence of the bullwhip effect
is explained to some extent by evidence that decision makers consistently underweight the supply line when
making order decisions. In the second experiment, we find that the bullwhip, and the underlying tendency
of underweighting, remains when information on inventory levels is shared. However, we observe that inven-
tory information helps somewhat to alleviate the bullwhip effect by helping upstream chain members better
anticipate and prepare for fluctuations in inventory needs downstream. These experimental results support the
theoretically suggested notion that upstream chain members stand to gain the most from information-sharing
initiatives.
Key words: supply chain management; bullwhip effect; behavioral experiments; information sharing; dynamic
decision making
History: Accepted by Abraham Seidmann, decision analysis; received June 24, 1999. This paper was with the
authors for 3 revisions.
1. Introduction
In recent years there has been a vast increase in the
quality and quantity of information shared across
supply chains. This increase is driven in part by
improvements in the technology available for gather-
ing and sharing data. The advent of enterprise logis-
tics software, such as SAP, now allows companies to
maintain and share inventory information for mul-
tiple supply points on a common database (Stein
1998). Many industry analysts claim that such sys-
tems offer tremendous savings for integrated supply
chains, despite their significant investment cost. In
the auto industry, for example, analysts project that
improvements in the quality of information shared
between OEMs up through the highest level in the
supply chain will save $1 billion in supply-chain inef-
ficiencies over the next few years alone (Scheck 1998).
One explanation given for why information sharing
leads to lower costs is that it may reduce the bullwhip
effect.
The bullwhip effect refers to the tendency of orders
to increase in variation as one moves up a sup-
ply chain. Forrester (1958) was the first to point out
this effect and its possible causes. Increased variation
is a concern for distribution chains since it leads
to increased costs in the form of increased inven-
tory requirements, expediting, or customer short-
ages. In the last few years, supply chain managers
as well as academics have focused attention on
the operational causes of the bullwhip effect. These
causes include demand signal processing, inventory
rationing, order batching, and price variations (Lee
et al. 1997a, b). Ways to alleviate these operational
problems include improved demand forecasting tech-
niques (Chen et al. 1998), capacity allocation schemes
(Cachon and Lariviere 1999), staggered order batching
(Cachon 1999), and everyday low pricing (Sogomonia
and Tang 1993).
The goals of this paper, in contrast, are to shed
light on the behavioral causes of the bullwhip and
investigate the potential benefit inventory informa-
tion sharing offers for overcoming these problems. We
report on the results of two controlled experiments,
each patterned after the well-known beer distribu-
tion game (Sterman 1992), where players make order-
ing decisions within a simple, linear, supply chain
subject to information and shipment lags. Our first
experiment reveals that the bullwhip effect still exists
1

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
2Management Science 00(0), pp. 1–14, © 2005 INFORMS
when traditional operational causes are removed and
the demand distribution is known by all parties.
This seemingly “irrational” behavior is in line with
previous behavioral research (e.g., Kahneman and
Lovallo 1993, Schotter and Weigelt 1992, Schweitzer
and Cachon 2000), which shows that individuals often
exhibit some form of decision bias in business set-
tings. We test for the existence of one particular type
of bias, underweighting the supply line, which was
first identified by Sterman (1989a) in his study of the
bullwhip effect. Results from our first study confirm
that decision makers still exhibit this bias in a con-
trolled setting where demand information is known
and stationary.
In our second study we examine the behavioral
impact of inventory tracking systems, which expose
the inventory position of each member of the sup-
ply chain and therefore may help to overcome this
underweighting bias. We find that exposure to real
time inventory information helps reduce the bullwhip
effect but not in the manner expected. Decision mak-
ers continue to exhibit the bias, even though stock
is now in full view. As a result, exposure to such
information has little impact on the variance of orders
of downstream chain members. On the other hand,
this information appears to substantially reduce the
variance of orders for upstream members. We pos-
tulate that exposure to inventory information helps
these chain members better prepare for fluctuations
in orders downstream.
This observation has important implications for
companies looking to invest in inventory tracking sys-
tems. From a behavioral point of view, our results
suggest that upstream members stand to gain the
most from such an investment. The results also sug-
gest that humans are still prone to decision biases
when such an investment is made, even in this sim-
plified supply chain setting. As one anonymous ref-
eree points out, this gives further credence to the use
of automated ordering systems, such as those often
bundled with inventory tracking software.
Sterman (1989a) was the first to use the beer dis-
tribution game to rigorously test the existence of the
bullwhip effect in an experimental context. His exper-
iments rely on a simple, nonstationary retail demand
function (beginning at four cases per period and
jumping to eight) unknown to chain members. In this
sense, his experiments control for three out of the four
operational causes cited by Lee et al. (1997b): inven-
tory rationing, order batching, and price fluctuations.
However, demand signal processing still looms as
an operational issue because the demand distribution
is nonstationary and unknown. Within this environ-
ment, Sterman provides evidence that the bullwhip
effect exists and may be caused by participants’ ten-
dency to underweight inventory in the supply line.
That is, participants place orders in one period, but do
not account for them in their inventory calculations
when placing orders in the next period. Thus inven-
tory that has been ordered but not yet received (i.e.,
is in the supply line) is underweighted in the decision
to order more. We build on this research by show-
ing, in our first study, that both the bullwhip effect
and underweighting still occur when all operational
causes are removed (i.e., when the demand distribu-
tion is stable and known to chain members).
Subsequent researchers have used the beer distri-
bution game to test various strategies for reducing
the bullwhip effect (e.g., Kaminsky and Simchi-Levi
1998, Steckel et al. 2004). Common strategies include
reducing order lead times, sharing POS data, and cen-
tralizing ordering decisions. Anderson and Morrice
(2000) study a novel service-oriented supply chain
game in a similar manner, showing that sharing con-
sumer demand (in the form of customer orders feed-
ing into a make-to-order mortgage service) can lead
to improvements in capacity fluctuations and cost.
Our research is the first to examine the behavioral
impact of sharing echelon inventory information in a
supply chain. Our research also differs from previous
experimental studies in its level of control. We use
a computerized version of the game, like Kaminsky
and Simchi-Levi (1998) and Steckel et al. (2004), that
avoids accounting errors and carefully controls what
information is available to each participant and when.
In addition, we add two more controls to eliminate
other, less interesting, factors from the analysis. First,
we control for demand signal processing errors by
sharing knowledge of the retail demand distribution
with all participants. In this sense, our version of
game is similar to the stationary beer game recently
developed by Chen and Samroengraja (1998) for class-
room use. Second, we utilize an incentive scheme
that avoids problems of collusion and reduced effort
over time.
Although this paper is the first to examine the
behavioral implications of inventory information
sharing, some important theoretical work exists in this
area. Chen (1998) studies the impact of information
sharing by quantifying the costs achieved using opti-
mal echelon base stock and installation base stock
in a multiechelon inventory system. He found that
echelon base-stock policies (which require access to
global inventory information) lead to lower cost than
installation policies (which require only local informa-
tion). Because both echelon and installation base-stock
policies imply that participants place orders equal to
the orders/demand they receive, the bullwhip effect
does not emerge in either information state. Other
researchers have theoretically examined the costs and
benefits of sharing inventory and demand informa-
tion in two-echelon systems consisting of one man-
ufacturer and one or more retailers (e.g., Bourland

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 3
et al. 1996, Lee et al. 2000, Cachon and Fisher 2000,
Gavirneni et al. 1999). Even though the assumed set-
tings and order policies differ between these papers,
all conclude that the supplier enjoys larger cost sav-
ings from information sharing than his retailers. The
results of our second study confirm that this dispar-
ity holds true behaviorally. In particular, when infor-
mation is available, upstream players enjoy a larger
reduction in the variance of orders than downstream
players.
The paper continues in §2 with a description of our
experimental setting. Section 3 reports on the results
of our first study, which demonstrates the existence of
the bullwhip effect while controlling for operational
causes. Section 4 describes the results of our second
study, which focuses on the impact of sharing inven-
tory information. Section 5 provides final conclusions
and a framework for future research.
2. Methods
In this section, we briefly introduce necessary nota-
tion, describe the mechanics of the beer distribution
game, and explain the protocol followed in conduct-
ing the experiments.
2.1. Design
The beer distribution game mimics the mechanics of a
decentralized, periodic review, inventory system with
four, serial echelons. Each supply chain team consists
of four players, denoted by i=14, correspond-
ing with the four echelon levels. Figure 1 provides an
illustration. Each participant is responsible for plac-
ing orders to his upstream supplier and filling orders
Figure 1 Distribution System Used in the Beer Distribution Game
Incoming orders Incoming orders Incoming orders
On-hand inv.
distributor (i= 3)
On-hand inv.
wholesaler (i= 2)
12
On-hand inv.
factory (i= 4)
44 44
4
(Ot,Ot–1,Ot–2)
4g4g4g
44
12
12
(Ot,Ot–1)
44 Production orders
On-hand inv.
retailer (i= 1)
12
1g
(It )2g
(It )4g
(It)
3g
(It )
4 4 4 4 4 4
Shipments
in process
Shipments
in process
Shipments
in process
(St–1,St )
1g1g(Ot,Ot–1)
2g2g(Ot,Ot–1)
3g3g
2g2g(St–1,St )
3g3g(St–1,St )
4g4g
Note. The numbers listed indicate the initial quantities (of outstanding orders, on hand inventory, and shipments in process) at the start of the game.
placed by his downstream customer, over a series of
time periods t=1T.
To illustrate the specifics of the game, consider the
dynamics of a single team g, where g=1G,
and Gis the number of teams in a particular exper-
iment. Each participant ireceives orders placed by
its downstream customer i −1and places orders
for additional inventory from its upstream supplier
i +1. For each echelon level and order period,
we define inventory as Iig
t, where Iig
t≥0 represents
on-hand inventory and Iig
t<0 represents orders in
backlog. Note that when we refer to sharing “inven-
tory” information we mean sharing Iig
t(i.e., both
on-hand inventory and backlog information). We also
define the quantity shipped to the downstream cus-
tomer by Sig
t, the order placed to the upstream sup-
plier by Oig
t, and retail demand in period tby Dt.
Events within each period unfold as follows. First,
shipments arrive from upstream suppliers. Second,
new orders arrive from downstream customers. In the
case of the retailer, the order received at time tis sim-
ply retail demand, Dt. Third, these new orders are
filled, if possible, from current inventory and shipped
out. If an order cannot be filled, it is placed in back-
log. The period ends with each participant placing
an order, Oig
t, with his upstream supplier. These are
the sole decision variables in the game. Our analysis
focuses on how Oig
tvaries between roles i=14
and with the availability of inventory information.
The system is complicated by order processing
and product shipment delays between each sup-
plier/customer pair. We assume delay times in keep-
ing with the traditional beer distribution game setup

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
4Management Science 00(0), pp. 1–14, © 2005 INFORMS
(i.e., two period order and shipment delays between
echelons i=13 and a three period manufactur-
ing delay at echelon i=4; see Figure 1). The order
quantity filled and shipped by level iat the end of
period tis thus
Sig
t=minDtmaxIig
t−1+Si+1g
t−20 for i=1 (1)
=minOi−1g
t−2maxIig
t−1+Si+1g
t−20 for i=23 (2)
=minOi−1g
t−2maxIig
t−1+Oig
t−30 for i=4(3)
where
Iig
t=Iig
t−1+Si+1g
t−2−Dtfor i=1
=Iig
t−1+Si+1g
t−2−Oi−1g
t−2for i=23
=Iig
t−1+Oig
t−3−Oi−1g
t−2for i=4
Participants are encouraged (through an incentive
scheme, described in §2.2) to choose orders in a man-
ner that minimizes their team’s cumulative chain cost.
Chain cost for each period tis defined as the sum of
holding and backlog costs across the four echelon lev-
els. Using our notation, chain cost through period T
for group gis simply
CgT  =
4

i=1
T

t=1himaxIig
t0−simin−Iig
t0 (4)
where siand hiare the unit backlog and inventory
holding costs incurred at level i, respectively. Note
that this supply chain structure controls for three of
the four operational causes of the bullwhip effect:
inventory allocation (since there are no competing
customers and manufacturing capacity is infinite),
order batching (since setup times are zero), and price
fluctuations (since prices are constant over time).
2.2. Procedure
The game was implemented in Java to run off a Web
server, with each participant within a team working
off a separate computer. Kalidindi (2001) provides a
detailed overview of the software.
In both studies, participants arrived in the exper-
imental lab at a predetermined time and were
randomly assigned to a computer terminal, which
determined their role iand supply chain assign-
ment g. Participants were told not to communicate
with anyone during the experiment, as is standard
practice in experimental economics. Once seated, par-
ticipants were oriented to the rules and objectives of
the game. They were instructed that each role would
incur unit holding costs of $0.50 hiand unit backlog
costs of $1 siper period, as normally assumed in the
board version of the beer distribution game (Sterman
1989a). They were also told that retail demand was
uniformly distributed between 0 and 8 cases per
period and independently drawn between periods.
This allows us to control for the remaining opera-
tional cause of the bullwhip effect, demand signal
processing.
One might question whether all subjects under-
stood the meaning of a “uniform distribution.” To
overcome this problem, we briefed the subjects about
the implications of a uniform 08distribution and
wrote the phrase “Demand is U08meaning (0, 1,
2, 3, 4, 5, 6, 7, or 8) is equally likely in each period” in
large letters on the front board. We left this phrase on
the board, in clear view, during the entire experiment.
Each echelon began with an initial inventory level
of 12, outstanding orders of 4 for the last two peri-
ods, and an incoming shipment of 4 in the next two
periods, as shown in Figure 1. Participants were not
informed how many periods the experiment would
run to avoid end-of-game behavior that might trigger
over- or underordering. The actual number of peri-
ods was T=48 for all experiments. All experiments
also used the same random number seed to gener-
ate demand, i.e., Dt,t=1T, was identical across
groups. This allowed us to isolate variations due to
ordering behavior from variations due to different
demand streams.
We used a continuous incentive scheme to reward
participants for their play, which was also announced
at the beginning of the experiment. The incentive
scheme provided a base compensation of $5 for each
participant along with a bonus of up to $20 per par-
ticipant. The bonus for each member of group gwas
calculated as follows, based on the cumulative chain
profit of the group
bg=$20 maxgCg−Cg
maxgCg−mingCg(5)
where Cg=Cg48is defined by (4). This bonus was
computed separately for each treatment.
This incentive scheme has a number of attractive
properties. First, it provides a continuous incentive for
participants to minimize cost in the game. In contrast
to previous experimental implementations in which
the best-performing group won a fixed prize (e.g.,
Sterman 1989a), under this payment method, each
group has an incentive to control their costs, even
if they cannot get into first place by doing so. Sec-
ond, this design discourages collusion among partic-
ipants to artificially raise the earnings of all teams
together. This is in contrast to the scheme used in
Steckel et al. (2004) which paid participants a mul-
tiple of their earnings, and thus removed competi-
tion between groups. Third, this payment represents
the benchmarked cost of an integrated supply chain
“firm,” which is a metric of performance often used
in industry.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 5
2.3. Participants
Study participants were drawn from a pool of
undergraduate business students at the University
of Minnesota enrolled in an introductory opera-
tions management course. The subject pool consisted
of 51% women and 49% men, with 24% of students
in their senior year, 56% in their junior year, and 20%
in their sophomore year. Study I and II used 44 sub-
jects each and were both performed on the same day
(April 30, 2002) back-to-back. To further avoid con-
tamination, participants were told not to share infor-
mation about the game with anyone.
Some may claim that these participants are from a
different subject pool than people who actually make
inventory decisions for a living and thus the impli-
cations of the results are limited. This is a problem
common to most experimental work. Our response is
that today’s business students are tomorrow’s inven-
tory professionals. Presumably experiments run with
students pull from the same population sample as
inventory professionals, and thus we are not select-
ing a different set of people to study. Of course, there
is a question about training. Since inventory profes-
sionals have had more practice and experience in this
problem, perhaps they would not exhibit the biases
as (untrained) students.
To gauge this impact, we also ran a more infor-
mal version of Study I with members of the Twin
Cities chapter of the Council of Logistics Management
(CLM), a professional organization of logistics man-
agers. This study was informal in the sense that the
participants were not paid and were not randomly
chosen from a pool of professionals. Indeed, many of
the participants where familiar with the beer distribu-
tion game and came to the seminar because they were
interested in learning how to run the game within
their own organizations. These experiments were per-
formed with five teams (20 people) during the chap-
ter’s monthly meeting on December 9, 2003. Results
are consistent with those from the student popula-
tion. These results are briefly highlighted in §3, and
described in greater detail in Appendix 2.
3. Study I: Stationary and
Known Demand
In previous experimental studies of the bullwhip
effect (e.g., Sterman 1989a, Steckel et al. 2004), par-
ticipants reacted to demand processes that were both
unknown and nonstationary.1Participants of the tradi-
tional beer distribution game (used by Sterman 1989a)
often cite the combination of a changing demand
1We define a stationary demand process as one that is drawn from
a stable demand distribution, with natural variation but no auto-
correlation between draws.
pattern and lack of basic distribution information
(e.g., demand minimum, maximum, and mode) as
the cause of the bullwhip effect. The question exam-
ined in our first study is whether the bullwhip effect
remains when these operational complications are
removed, i.e., when the demand distribution is com-
monly known and stationary. Subsection 3.1 describes
our design and develops hypotheses for this setting,
while §3.2 describes our experimental results.
3.1. Design and Hypotheses
Theoretical research suggests that rational decision
makers will induce the bullwhip effect when the
demand distribution is either nonstationary or un-
known to supply chain members. For example, when
demand is nonstationary and a simple order-up-to
policy is used, a rational decision maker will adjust
order-up-to levels dynamically in each order period.
Lee et al. (1997b) show analytically that such a strat-
egy invokes the bullwhip effect in a two-echelon
system. This occurs even when the retailer makes
order decisions with full knowledge of the under-
lying (nonstationary) demand distribution. Graves
(1999) uncovers a similar result assuming demand fol-
lows an autoregressive, integrated moving average
(ARIMA) process. In this case, he develops an explicit
expression for the magnitude of amplification, which
appears independent of the level of information pro-
vided to upstream stages.
When the demand distribution is stationary but
unknown, it makes sense to use a stationary fore-
casting technique to estimate demand. Chen et al.
(1998) show that the bullwhip effect can occur when
managers follow a simple order-up-to policy that is
updated in each period based on current demand
information. Their results suggest that the bullwhip
effect will be largest during transient periods, when
little demand information is available, and may
diminish once enough demand information is avail-
able to provide an accurate forecast. Anderson and
Fine (1998) give further credence to the hypothesis
that demand signal updating induces the bullwhip
effect through an analysis of real industry data.
If the demand distribution is both stationary and
commonly known, theory suggests that no bullwhip
effect will exist. Chen (1999) shows that a base-stock
policy is optimal in a serial inventory system with
fixed order and shipment delays. This policy was also
shown to be optimal for serial systems without delays
by Clark and Scarf (1960) and Federgruen and Zipkin
(1984). A base-stock policy implies that participants
place orders equal to the orders they receive. Thus,
we hypothesize that decision makers will not induce
the bullwhip effect in our first study where demand
is known and stationary.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
6Management Science 00(0), pp. 1–14, © 2005 INFORMS
Hypothesis 1. The bullwhip effect will not occur when
the demand distribution is known and stationary.
As we see in the next subsection, our experimental
results are not consistent with this prediction.
3.2. Results
Figure 2 illustrates an example of the trend of orders
placed for a typical team. Recall that the bullwhip
effect is defined as an increase in the variance of
orders placed at a given echelon level, relative to
the orders received at that level. This implies that
the variance of orders is amplified as one moves
up the supply chain. Hypothesis 1 implies instead
that the variance of orders across levels will remain
stable. Figure 3 graphs the variance of orders placed
for the 44 participants. By inspection, it appears that
some amplification in order variance occurs as one
moves up the chain. If we look at the ratio of average
variances between roles, we find that the whole-
saler/distributor pairing exhibit the largest magni-
tude of amplification: 2
2/2
1=173, 2
3/2
2=211,
2
4/2
3=148, where 2
iis the average variance for
role i. One explanation for the weaker increase in
order variance between the distributor and the man-
ufacturer is that the manufacturer enjoys a constant
delivery delay of 3 weeks, while all the other players
face a minimum delay of 4 weeks (which increases
further when their supplier is out of stock). The exper-
imental results of Sterman (1989a) show a similar pat-
tern (his ratios, calculated from Table 3 of Sterman
(1989a), are 2
2/2
1=177, 2
3/2
2=196, 2
4/2
3=160).
3.2.1. Evidence of the Bullwhip Effect. A simple
nonparametric sign test confirms that amplification is
present in this setting. The test works as follows. For
each supply chain, we code an increase in the vari-
ance of orders placed between each role as a success
and a decrease as a failure. More details on the sign
test can be found in Seigel (1965), p. 68 and Table D.
The data reveals an 82% success rate, i.e., 82% of the
observations involve an increase in variance of orders
placed between roles. This is significantly different
than the null hypothesis (50%) implied by Hypothe-
sis1(N=33, x=6, p<00001). This is a conservative
estimate because if the order variance at the whole-
sale level is higher than variance at the retail level (for
example) then the probability that variance at the dis-
tributor level is greater than variance at the wholesale
level is actually less than 50% due to regression to the
mean (although the exact rate is difficult to estimate).
This result leads us to reject Hypothesis 1. The
bullwhip effect still exists when retail demand is sta-
tionary and commonly known. This result is also
supported by our professional data (see Appendix 2),
although the magnitude of the effect is less signifi-
cant for this group (success rate of 75%, p=00530).
Figure 2 Orders Placed for Group 1 in Study I (Base Case)
Retailer
0
5
10
15
20
25
30
35
Wholesaler
0
5
10
15
20
25
30
35
Distributor
0
5
10
15
20
25
30
35
Manufacturer
0
5
10
15
20
25
30
35
This is not surprising given that many of the pro-
fessional participants had prior knowledgeable of the
game; nevertheless, these results raise an interesting
question about the role of training in counteracting
the magnitude of the bullwhip effect, a fertile area
for future research. For now, we return to the ques-
tion at hand: Why do decision makers continue to
exhibit bullwhip behavior when demand is station-
ary and known? In the next subsection, we test the
existence of one type of decision bias identified by

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 7
Figure 3 Variance of Orders for Study I
0
20
40
60
80
100
120
140
160
Retailer (i = 1) Wholesaler (i = 2) Distributor (i= 3) Manufacturer (i = 4)
Role
Variance
Sterman (1989a) that may contribute to this seemingly
irrational behavior.
3.2.2. Evidence of Underweighting the Supply
Line. Sterman (1989a) found that participants fail to
take proper assessment of their current outstanding
order level when making order decisions subject to
an unknown and nonstationary retail demand distri-
bution. In other words, they underweight the supply
line. Our purpose here is to test whether this deci-
sion bias holds when the retail demand distribution is
known and stationary. One might expect participants
to pay closer attention to the supply line in this more
stable setting. Therefore, we seek to test the following
hypothesis:
Hypothesis 2. Participants will not underweight the
supply line when demand is known and stationary.
Following Sterman’s analysis, we test participants’
perception of the supply line as a whole (i.e., all out-
standing orders) by running a set of regressions, one
for each participant in our experiment. Each regres-
sion compares orders placed in period tagainst the
participant’s on-hand inventory level, orders received,
and outstanding orders in period t. The regression
equation for a given participant i, in group g,at
time t,is
Oig
t=max0
0+IIig
t−1+RRig
t+SSig
t
+NNig
t+tt+(6)
where Iig
t−1denotes the inventory held last period,
Rig
tdenotes orders received from the downstream
customer (i.e., Rig
t=Oi−1g
t−2,Sig
tdescribes the ship-
ments received from his upstream supplier (defined
by Equations 1–3), Nig
tdenotes the participant’s total
outstanding orders (i.e., Nig
t=Oig
t−1−min0Ii+1g
t+
Si+1g
t+Si+1g
t−1), and tserves as a control for any time
trends.2
If the bullwhip effect did not exist, a partici-
pant’s order quantity would simply equal the orders
received from his downstream customer. In our
regression equation, this implies R=1 after the ini-
tial transient period ends (i.e., once the participant
has a chance to either deplete excess initial inventory
or raise the initial inventory level to the order-up-to
level). An exogenous shock increasing inventory on
hand in the supply line, or in shipments received,
should reduce orders by one unit in order to retain
the order-up-to level. This implies I=N=S=−1.
Note that if the participants were ordering according
to the optimal order-up-to policy, 0would reflect the
optimal order-up-to level.
We ran this regression for each of the 44 par-
ticipants in our study (4 roles ×11 groups), using
the data from all but the last two periods of the
2One may notice that the regressions we run to test Sterman’s
hypothesis are simpler than the ones used in his paper. Sterman’s
original analysis included a number of assumptions concerning
the heuristics used by his participants. For example, he assumed
that participants anchored in their choice of desired stock, with the
anchor estimated separately for each subject. Thus each subject was
thought to order up to a fixed inventory level in each time period.
Sterman also assumed participants used adaptive expectations to
forecast the orders they would receive. Neither of these assump-
tions seemed reasonable in our setting, where participants knew
the demand distribution facing the retailer. Our regression expres-
sion (6) is an attempt to capture Sterman’s insight without relying
on his assumptions of anchoring and forecasting.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
8Management Science 00(0), pp. 1–14, © 2005 INFORMS
game.3Appendix 1 provides a summary of each
individual regression for the interested reader. The
average R2(adjusted) statistic over all regressions
was 0.6827. Overall, the regressions were highly sig-
nificant with only one participant’s F-statistic indi-
cating his choices could be equally well explained
by a constant order amount (and that participant’s
regression was marginally significant, with p=008).
The coefficient for on-hand inventory Iwas signif-
icantly higher than the optimal value of −1 for all but
8 of the 44 regressions (at the p<005 level or bet-
ter) with an average value of −02368. Similarly, the
coefficient on the orders received term, R, was sig-
nificantly lower than the optimal value of +1 for all
but 10 of the 44 regressions (again at the p<005 level
or better) with an average value of 0.3312. Similar
results hold for the profession data (see Appendix 2
for details).
If participants are accurately accounting for the
supply line, the coefficient on orders outstanding
should be the same as the coefficient on inventory.
If Sterman’s conjecture holds (i.e., participants are
underweighting the supply line), then we should find
N>
I. We found that the average value for N
was −00302 compared to −02368 for I. All of the
44 participants placed less weight on their supply line
than on their inventory positions N>
I, and thus
underweighted their supply line. We can easily reject
Hypothesis 2 (which implies an equal likelihood of
N>
Iand N<
I) using a sign test (N=44, x=0,
p<00001). Thus, we conclude that a supply line
underweighting bias still occurs when retail demand
is stationary and known. It is interesting to note
that our estimated regression parameters are simi-
lar to those derived by Sterman (1989a). For exam-
ple, Sterman reports an average inventory coefficient
of −026 (versus our −02368) and an average sup-
ply line coefficient of −00884 (versus our −00302). It
appears that having a stable and known demand dis-
tribution does little to alleviate subjects’ tendency to
underweight the supply line. This result also holds for
the professionals from CLM (see Appendix 2), imply-
ing that underweighting behavior is robust to profes-
sional experience.
Previous experimental research offers some clues to
why participants continue to underweight the supply
line even when demand is known and stationary. In a
literature review, Sterman (1994) notes that dynamic
settings render decision making difficult, even when
only one decision maker is involved, due to reduced
saliency of feedback. Saliency refers to the strength of
3In the last two periods of the game, the shipments that an
upstream counterpart could send were not determined because
they depended, in part, on the orders that counterpart would have
placed had the game continued.
the tie between feedback and the decision (Hogarth
1987). Diehl and Sterman (1995), Paich and Sterman
(1993), Sterman (1989b, c) provide specific examples
and experimental evidence in individual decision-
making tasks. When decisions are made in a decen-
tralized fashion across multiple parties, such as in our
supply chain setting, the interaction of decisions and
outcomes further degrades the saliency of feedback
(Hogarth 1987). Other authors suggest that the type
of feedback available is critical to the learning pro-
cess, and that outcome feedback (rather than process
feedback) causes inefficiencies (e.g., Sengupta and
Abdul-Hamid 1993). Still other explanations involve
arecency effect. Participants overweight more recent
information relative to information they received in
the distant past (see, e.g., Hogarth and Einhorn 1992).
Thus, orders that were placed three periods ago may
be underweighted relative to the current inventory
position.4
One type of feedback missing in this and many
other supply chain settings is a forewarning of when
upstream suppliers (or downstream customers) are
running short on inventory. Without this information,
a participant cannot be certain that the shipments
they receive will correspond to orders they actu-
ally placed. A decision maker’s connection between
cause and effect (here, orders requested and ship-
ments received) is broken whenever his supplier is
out of stock. Having access to the inventory lev-
els of upstream members could improve a decision
maker’s ability to anticipate supply shortages and
thus increase the salience of feedback. If the par-
ticipant knew when (and why) stock outs occurred,
his understanding of the relationship between orders
placed and orders received might improve. This infor-
mation might also combat the supply line under-
weighting tendency just observed, since it provides a
clear view of one critical component of a participant’s
supply line (his supplier’s inventory level). This is the
behavioral motivation behind Study II. Study II is of
interest for operational reasons as well, as it sheds
light on the behavioral impact of inventory tracking
systems being implemented in practice.
4. Study II: Sharing Dynamic
Inventory Information
4.1. Design and Hypotheses
The purpose of our second study is to measure what
improvement is gained by sharing current inventory
information across the supply chain. Conditions in
this experiment were identical to Study I except that
the participants also had access to dynamic inventory
4We thank an anonymous referee for calling our attention to the
recency effect explanation and related literature.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 9
information. This information was displayed in a bar
chart with four bars representing the inventory posi-
tions of the four members of their group. The chart
was automatically updated at the beginning of each
period so all members had access to the same infor-
mation when making their order decisions. Before
discussing the results of the experiment, we briefly
outline our hypotheses.
Our main hypothesis is that sharing inventory
information will help reduce the bullwhip effect. We
can measure reductions to the bullwhip effect in two
ways: reduced order oscillations at a given supply
level, and reduced amplification across levels. The
first measure reflects efficiency improvements to the
chain as a whole, while the second focuses on the rate
of change between levels. Theoretical research sug-
gests that inventory information can improve the pro-
curement process for a supplier serving one or more
retailers (e.g., Bourland et al. 1996, Lee et al. 2000,
Cachon and Fisher 2000, Gavirneni et al. 1999) and
for multiple decision makers in a serial supply chain
(Chen 1998). We hypothesize that inventory informa-
tion will help in our setting as well by reducing order
oscillations throughout the chain. This leads to the
following hypothesis:
Hypothesis 3. Sharing dynamic inventory informa-
tion across the supply chain will decrease the level of order
oscillation.
Whether the amplification of order oscillations will
decrease between levels as a result of inventory expo-
sure is less clear. Theory suggests the bullwhip will
not occur when the demand distribution is known
and stable, whether or not inventory information is
shared (Chen 1998). However, we saw in Study I that
the bullwhip effect does appear when inventory infor-
mation is not available. We hypothesize that inven-
tory information may help alleviate the supply line
underweighting bias reported in §3.2.2 by increasing
the saliency of feedback between orders placed and
shipments received and thus decreasing the ampli-
fication of orders. This leads to the following two
hypotheses:
Hypothesis 4. Sharing dynamic inventory informa-
tion across the supply chain will decrease the amplification
of order oscillation between each supply chain level.
Hypothesis 5. Sharing dynamic inventory informa-
tion will cause participants to no longer underweight the
supply line.
Another interesting question to ask is who ben-
efits the most from information sharing.5Theoreti-
cal research of two-echelon inventory systems (e.g.,
5Of course, the fact that one member yields greater opera-
tional improvements (such as reduced order oscillations) does not
Bourland et al. 1996, Lee et al. 2000, Cachon and
Fisher 2000, Gavirneni et al. 1999) suggests that man-
ufacturers enjoy most of the operational benefits.
Indeed, once inventory information is shown, the
improvement in demand information is most pro-
found for upstream participants. Access to down-
stream information allows suppliers to manage their
orders based on echelon inventory level rather than
the order quantity placed by his immediate customer
(Chen 1998), which effectively eliminates the order
amplification component of the bullwhip effect.
On the other hand, for downstream participants,
inventory information offers an opportunity to bet-
ter anticipate supply shortages and possibly increase
their understanding of the ordering process used by
their suppliers. This may also help correct a retailer’s
tendency to underweight the supply line. In partic-
ular, it may reduce his tendency to overorder when
shipments begin to fall short of previous order levels.
If this is the main benefit of inventory information,
we may find downstream partners have more to gain.
To test the relative benefits achieved by upstream
and downstream participants, we divide the supply
chain into two segments. This leads to the following,
competing, hypotheses:
Hypothesis 6a. Sharing dynamic inventory informa-
tion across the supply chain will lead to a greater reduction
in order oscillations for manufacturers and distributors
than for retailers and wholesalers.
Hypothesis 6b. Sharing dynamic inventory informa-
tion across the supply chain will lead to a lower reduction
in order oscillations for manufacturers and distributors
than for retailers and wholesalers.
The next subsection tests these hypotheses by com-
paring a new set of experiments against the results of
Study I.
4.2. Results
Figure 4 illustrates the variance of orders placed for
the participants. It appears that the bullwhip effect
still exists, but may be less severe than that observed
in Study I (i.e., Figure 3).
4.2.1. Impact on Overall Chain. Focusing first
on Hypothesis 3, we use a nonparametric two-
tailed Mann-Whitney University test (also called the
Wilcoxon test)6to compare how the oscillation com-
ponent of the bullwhip effect compares across the two
treatments. The test confirms that order variances are
guarantee this same member will enjoy a larger share of the mon-
etary gains. In a market economy, these cost improvements could
very well be transferred to a more powerful channel member or
passed on to final customers in the form of lower prices.
6Seigel (1965) discusses the Mann-Whitney University test starting
on p. 116.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
10 Management Science 00(0), pp. 1–14, © 2005 INFORMS
Figure 4 Variance of Orders for Study II (Inventory Shown)
0
20
40
60
80
100
120
140
160
Retailer (i= 1) Wholesaler (i= 2) Distributor (i= 3) Manufacturer (i= 4)
Role
Variance
significantly less when inventory is known, compared
with the control treatment (n=44, m=44, z=192,
p=0028), providing support for the hypothesis.
While order variances may be lower, it is interest-
ing to note that the bullwhip effect still persists when
inventory information is shown. Using the same sign
test discussed in §3.2.1, we find that the variability
of orders placed between each role increased 69%
of the time (i.e., exhibited a 69% success rate) when
inventory information was commonly known. This
is significantly different than the 50% success rate
of the null hypothesis if no amplification existed
(N=33, x=10, p=00107), but is significantly lower
than the 82% rate of increase observed previously
p =00344. This suggests that the amplification com-
ponent of the bullwhip effect is reduced, but still
present, when inventory information is commonly
known.
To examine this amplification aspect of the bull-
whip effect more rigorously, we perform a Mann-
Whitney University test on the ratio of the vari-
ances between each of the two roles (e.g., the vari-
ance of a wholesaler’s orders divided by the vari-
ance of his retailer’s orders) between the two treat-
ments. A Mann-Whitney University test using all the
levels of the chain (33 observations from the control
treatment and 33 observations from the inventory-
shown treatment) suggests no significant difference
(n=33, m=33, z=0468, p=0320) between the
two treatments. However, a similar test performed
separately on each customer/supplier link shows
some evidence of amplification reduction between
roles. In particular, there is a significant reduction in
amplification between the wholesaler and distribu-
tor (n=11, m=11, z=1609, p=0044) across the
two treatments. In contrast, the retailer/wholesaler
(n=11, m=11, z=0164, p=0435) and distribu-
tor/manufacturer (n=11, m=11, z=1145, p=0125)
links show no significant difference between treat-
ments. These tests suggest that while the impact of
information sharing on reducing amplification is not
significant overall (rejecting Hypothesis 4), it may
offer some benefit to upstream players. We revisit this
issue in §4.2.3.
4.2.2. Impact on Supply Line Weighting. To test
whether participants continue to underweight the
supply line in this setting, we ran the same indi-
vidual regressions on each of the 44 participants
in this study. Appendix 1 provides a summary of
each individual regression for the interested reader.
The average R2(adjusted) statistic for these regres-
sions was 0.5636. The average inventory weight was
−01939, while the average weight placed on the sup-
ply line was −00288. Forty-two out of 44 participants
underweighted the supply line. As before, this pat-
tern of results is significantly different than would
be expected if the supply line were being weighted
equally as inventory using a sign test (N=44, x=2,
p<00001). These results are similar to those in the
first study, allowing us to reject Hypothesis 5.7Our
results suggest that participants’ underweighting of
the supply line is robust to the additional informa-
tion in this experiment (i.e., the inventory position of
other firms). This result supports the work of Diehl
and Sterman (1995) and Sterman (1989b), who found
that additional information does not counteract the
7Additionally a t-test comparing the distribution of the individual
Iand Nparameters reveals no significant differences between
Study I and Study II (p=0194 for Iand p=0968 for N).

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 11
underweighting tendency in other experimental set-
tings. It appears that downstream customers do not
use inventory information to their full advantage.
If supply line underweighting is still prevalent
when inventory information is shown, then what is
causing the improvement in performance? The next
subsection suggests that while inventory information
is not being used by downstream members to adjust
for outstanding orders, it could be used by upstream
members of the supply chain to anticipate and adjust
for downstream members’ orders. This use coun-
teracts the underweighting of the supply line and
improves overall performance.
4.2.3. Impact on Upstream and Downstream
Members. Table 1 compares the average order vari-
ance for the two studies by role. Here we see that the
magnitude of improvement due to information shar-
ing appears much larger for upstream supply chain
members (i.e., the distributor and manufacturer). To
test the significance of this improvement for upstream
versus downstream members, we once again use a set
of Mann-Whitney University tests. Grouping distrib-
utors and manufacturers together reveals that sharing
inventory information leads to a significant reduction
in the variance of orders at upstream sites (n=22,
m=22, z=182, p=0043). Grouping retailers and
wholesalers together reveals an insignificant differ-
ence between the treatments (n=22, m=22, z=124,
p=0110).
Table 1 also reports the percentage reduction in
order variance enjoyed by each role with the introduc-
tion of inventory information, both compared with
Study I and compared with the benchmark of no bull-
whip effect. These calculations highlight the asym-
metric improvement observed between upstream and
downstream members of the supply chain.
Together these results suggest that members near
the beginning of the chain exhibit a different impact
from inventory information than those near the end.
Table 1 Comparison of Average Order Variance, by Role, Across the
Two Studies
Average variance of
orders iImprovement
Base Inventory relative to
case shown Improvement “no bullwhip”
Role (Study I) (Study II) (%) benchmark∗(%)
1. Retailer 10.73 10.13 56111
2. Wholesaler 18.56 16.98 85119
3. Distributor 47.83 23.18 515580
4. Manufacturer 57.95 36.37 372410
∗In the “no bullwhip” benchmark, the order variance at each role matches
the variance of customer demand (which is 5.33 for our uniform 08distri-
bution). This improvement statistic is thus i1−i2/i 1−533, where
ik is the average variance for role iin study k.
In particular, our results suggest that inventory infor-
mation may be more useful as one moves fur-
ther away from end user demand. This behavior is
consistent with Hypothesis 6a and concurs with pre-
vious theory (e.g., Bourland et al. 1996, Lee et al.
2000, Cachon and Fisher 2000, Gavirneni et al. 1999).
Upstream members exhibit a significant reduction in
order oscillations, while downstream members show
relatively little improvement.
Note that one key difference between competing
Hypotheses 6a and 6b is the extent to which they pre-
dict underweighting of the supply line. Hypothesis 6b
suggests that sharing inventory information will trig-
ger retailers and wholesalers to stop underweighting
the supply line due to upstream information. We saw
in §4.2.2 that this was not the case. Our individual
results here suggest that inventory information is of
limited value in alleviating this behavioral cause of
the bullwhip effect. Nonetheless, inventory informa-
tion counteracts this bias and improves performance
by allowing manufacturers and distributors to antici-
pate and interpret orders placed by their downstream
customers.
5. Discussion
This paper reports the results of two experimen-
tal studies on the behavioral causes of the bullwhip
effect. We find participants continue to exhibit the
bullwhip effect (the amplification of oscillation of
orders higher in the supply chain) even under con-
ditions where it should not occur. This suggests that
cognitive limitations contribute to the bullwhip effect,
even in ideal and controlled settings like the lab.
We also observe that transmitting dynamic inventory
information lessens the bullwhip effect, particularly at
higher echelon levels. We argue that this information
allows upstream members to better interpret orders
on the part of their customers and prevents them
from overreacting to fluctuations when placing their
own orders. These studies provide several important
implications for managerial practice and for guiding
the development of inventory theory.
Results from our first study suggest that the bull-
whip effect is not solely a result of operational compli-
cations such as seasonality or unpredictable demand
trends. Indeed, the effect remains even under the most
optimistic demand scenario, when the demand distri-
bution is stationary and commonly understood. The
reason has to do with cognitive limitations on the part
of managers and difficulties inherent in managing a
complex dynamic system. One particular limitation
appears to be that participants underweight the sup-
ply line, tending to discount orders they have placed
but which have not been delivered. This tendency was
significant even for subjects who were trained logis-
tics professionals.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
12 Management Science 00(0), pp. 1–14, © 2005 INFORMS
Many companies are in the process of implement-
ing integrated information systems to manage their
distribution processes. Our results indicate that these
systems have the potential to decrease the severity
of the bullwhip effect. Further analysis revealed this
potential is significantly larger for upstream members.
This result suggests several implementation philoso-
phies, which warrant further study. For example,
these results lead us to speculate that the critical part
of an inventory-sharing information system is not
communicating the inventory position of the man-
ufacturer to the retailer, but rather communicating
the inventory position of the retailer to the manu-
facturer. This implies that the biggest “bang for the
buck” from these systems may lie in tracking and
sharing downstream inventory information, i.e., infor-
mation closest to the final customer. Because the cost
of inventory tracking is quite high, particularly at
manufacturing sites, one might do well to implement
such systems first at the retail and wholesale level.
We predict diminishing returns as such systems are
implemented further up the supply chain. We also
conjecture that an inventory-sharing system may still
be effective even if upstream firms are reluctant or
Appendix 1. Individual Regression Details
Baseline Inventory shown
Role R2adj. INRole R2adj. IN
Retailer 0.5922 −026 −009 Retailer 0.6633 −019 −001
Retailer 0.4262 −027 010 Retailer∗0.1470 −005 007
Retailer 0.6289 −026 −009 Retailer 0.2770 −025 −001
Retailer 0.5804 −023 004 Retailer 0.2438 −013 011
Retailer 0.7214 −028 004 Retailer 0.5327 −035 −020
Retailer 0.7238 −038 −001 Retailer 0.8036 −032 −010
Retailer 0.6246 −025 −004 Retailer 0.4722 −043 −018
Retailer 0.6631 −110 −093 Retailer 0.2765 −032 −016
Retailer∗0.1181 −014 −013 Retailer 0.6094 −025 −004
Retailer 0.5935 −021 000 Retailer 0.1789 −019 −013
Retailer 0.6700 −023 −003 Retailer∗0.0095 −015 −009
Wholesaler 0.4072 −016 −005 Wholesaler 0.8000 −037 −033
Wholesaler 0.5897 −026 020 Wholesaler 0.3194 −024 −009
Wholesaler 0.8004 −012 001 Wholesaler 0.2612 −007 003
Wholesaler 0.6066 −017 003 Wholesaler 0.4162 −031 −002
Wholesaler 0.6902 −025 −013 Wholesaler 0.6900 −010 004
Wholesaler 0.7623 −018 −006 Wholesaler 0.7584 −018 −005
Wholesaler 0.5764 −013 −003 Wholesaler 0.5234 −014 −006
Wholesaler 0.3519 −032 −005 Wholesaler 0.4958 −018 002
Wholesaler 0.7552 −011 006 Wholesaler 0.7616 −037 −019
Wholesaler 0.5737 −005 007 Wholesaler 0.4691 −020 −015
Wholesaler 0.6772 −025 −004 Wholesaler 0.4961 −008 006
Distributor 0.8411 −024 −023 Distributor 0.5432 −009 005
Distributor 0.6298 −009 005 Distributor 0.7493 −007 002
Distributor 0.8017 −028 −016 Distributor 0.5277 −030 −011
Distributor 0.7392 −056 −016 Distributor 0.6894 −009 012
Distributor 0.7155 −011 −005 Distributor 0.7800 −007 015
Distributor 0.8520 −014 001 Distributor 0.6856 −007 008
Distributor 0.7599 −018 −012 Distributor 0.7200 −029 −001
Distributor 0.5540 −044 −024 Distributor 0.4899 −007 015
unable to share their inventory positions with down-
stream firms.
With respect to inventory theory, our results point
to the need for more theoretical research that incor-
porates the biases of individual decision makers. In
our experience, these factors are often overlooked
when assessing the expected benefits of investments
in information technology. Our results suggest that
models based on unboundedly rational actors may
not reflect actual decision-making behavior and thus
may undervalue the benefit from investments in infor-
mation technology. We hope this research stimulates
new theoretical models which better capture supply
line decision biases, the boundedly rational nature of
supply chain managers, and the impacts of these limi-
tations not only on actions taken within one particular
informational structure, but the choice of informa-
tional structure itself.
Acknowledgments
The first author’s research was supported by NSF Grant
#SBR 9753130. The second author’s research was supported
by NSF Career Award #SBR 9602071.

Croson and Donohue: Behavioral Causes of the Bullwhip Effect and the Observed Value of Inventory Information
Management Science 00(0), pp. 1–14, © 2005 INFORMS 13
Appendix 1. (Continued)
Baseline Inventory shown
Role R2adj. INRole R2adj. IN
Distributor 0.7730 −024 −007 Distributor 0.4662 −026 −010
Distributor 0.5603 −017 −007 Distributor∗0.0947 −002 −001
Distributor 0.7612 −021 010 Distributor 0.5971 −023 003
Manufacturer 0.5699 −044 000 Manufacturer 0.6168 −028 018
Manufacturer 0.7772 −052 −035 Manufacturer 0.8477 −009 030
Manufacturer 0.9448 −001 008 Manufacturer 0.5100 −027 −016
Manufacturer 0.7941 −011 036 Manufacturer 0.8912 −030 008
Manufacturer 0.8536 −018 −010 Manufacturer∗∗ 0.7089 −017 −023
Manufacturer 0.7045 −031 −011 Manufacturer 0.8662 −013 013
Manufacturer 0.8907 −018 027 Manufacturer 0.7848 002 005
Manufacturer 0.8145 −024 008 Manufacturer∗∗ 0.6581 004 −021
Manufacturer 0.7624 −011 024 Manufacturer 0.7966 −023 −009
Manufacturer 0.8656 009 016 Manufacturer 0.8785 −048 −039
Manufacturer 0.9411 −014 011 Manufacturer 0.6914 −021 018
Average 0.6827 −02368 −00302 Average 0.5636 −01939 −00288
St. dev. (0.1597) (0.1813) (0.1933) St. dev. (0.2274) (0.1207) (0.1414)
∗This regression was not significant at the p<005 level.
∗∗This participant did not underweight the supply line relative to on-hand inventory.
Appendix 2. Results of Study I Using Professional
Subjects
To check for external validity, we conducted an informal
version of Study I with professionals from the Twin Cities
Chapter of the Council of Logistics Management (CLM) on
December 9, 2003. Twenty people (five teams) took part in
the experiment. Data from one team was eliminated due to
revealed collusion on the part of the distributor and man-
ufacturer, leaving data from four teams (16 people). It is
interesting to note that this deleted team also had the worst
performance of the group despite its collusion (crime does
not pay).
Figure 5 displays the average order variance for each par-
ticipant. The bullwhip effect appears to still exist, although
it is dampened compared with the student data. The ratio
of average variances is now 2
2/2
1=114, 2
3/2
2=155,
2
4/2
3=131 compared with 1.73, 2.11, and 1.48 respectively
for students. Applying the same statistical tests outlined
in §3.2.1, we find that 75% of the observations involve an
increase in variance of orders placed between roles. This
is marginally significantly different from the null hypothe-
sis (50%) implied by Hypothesis 1 p =00530. Recall that
this is a conservative estimate and its lower significance
Figure 5 Variance of Orders (Professional Data)
0
5
10
15
20
25
30
35
Retailer
(i= 1)
Wholesaler
(i= 2)
Distributor
(i= 3)
Manufacturer
(i= 4)
Role
Variance
(compared with the student group) is partly a result of the
smaller sample size.
To test whether these professionals also underweight the
supply line, we ran individual regressions on each of the
16 participants. The average R2(adjusted) statistic for these
regressions was 0.4935 with only one participant’s F-statistic
indicating his choices could be equally well explained by
a constant order amount. The average inventory weight was
−01781, while the average weight placed on the supply line
was −00156. Fifteen out of 16 participants underweighted
the supply line. This pattern of results is significantly dif-
ferent than would be expected if the supply line were being
weighted equally as inventory using a sign test (N=16,
x=1, p<00002). These results are consistent with those
of our student participants in Study I, allowing us to reject
Hypothesis 5.
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