020-0131
AN EXPERIMENTAL INVESTIGATION OF THE EFFECTS OF
SUPPLY UNCERTAINTY ON SUPPLY CHAIN PERFORMANCE
Ancarani A.1, Di Mauro C.2, D’Urso D.3
1 Dipartimento di Ingegneria Civile e Ambientale, Università di Catania – aancaran@dica.unict.it +390957382715
2 D.A.P.P.S.I., Università di Catania – cdimauro@unict.it - +3909570305216
3 Dipartimento di Ingegneria Industriale e Meccanica, Università di Catania - ddurso@diim.unict.it +390957382712
POMS 22 nd Annual Conference
Reno, Nevada, U.S.A.
April 29 to May 2, 2011
Abstract: We present a series of controlled human experiments investigating the impact of
supply uncertainty on buyers’ inventory management. The experiments focus on one specific
source of SC risk, namely stochastic lead times, within the framework of the “beer game”.
Specifically, we study the impact of stochastic lead times on supply chain performance and on
the formation of the bullwhip effect. Next, the impact of players’ SCM skills and game
experience is investigated. Two between subject treatments were run, a standard beer game
(SBG) and a beer game with stochastic lead times (SLT). A total of 104 MBA students and 24
purchasing managers participated. Results show that SLT gives rise to higher costs and a
more marked bullwhip effect than the SBG. Both effects decrease with experience in the
game. However, they do not disappear, even when real managers are involved in the game.
Keywords: Experiments, Beer Game, SCM
1. Introduction
Today’s supply chains are more complex than they used to be. There are various reasons for
supply chain complexity, such as higher levels of R&D and manufacturing outsourcing,
supplier–supplier relationships in supplier networks, increased dependence on supplier
capabilities, new technologies, regulatory requirements, shorter product life-cycles due to
rapidly changing customer preferences, and international market and production expansion
(Wagner and Neshat, 2010). Further, as firms try to reduce costs through the rationalization
and reduction of the supply base, the aim to secure an interrupt flow of materials has become
more difficult to achieve (Harland et al., 2003). Finally, global trends towards leaner supply
chains have taken place at the cost of increased vulnerability due to fewer buffers. Since lean
supply chains reduce the margin for human errors, it is more likely that disruptions or supply
chain instability result from those errors (Tang, 2006)).
As a consequence, the instability of supply chains has increased (Geary et al., 2006). The
Bullwhip Effect (BWE) is a paradigmatic representation of SC instability. The BWE is
generally triggered by demand uncertainty (Forrester, 1958), and it entails that as external
demand passes upstream through the SC from the downstream to the upper stream levels of
the chain, the variance of orders is amplified. This behaviour can imply substantial costs in
terms of stock-out costs and in inventory and obsolescence costs.
The BWE is documented empirically in several industries (Blanchard, 1983; Lee et al. 1997,
2000 among many others) and has been studied in a large number of experiments, either
numerical or carried out with human subjects. Controlled human experiments have gained
importance as a methodology for the study of the BWE since Sterman’s (1989) finding that
the BWE is a problem arising mainly as a consequence of human decision making. In
particular, Sterman posited that due to the lags in acquiring materials and reacting to changes
in demand, individuals involved in SC management amplify unanticipated changes in demand
and have a biased perception of the flows in transit through the SC pipeline. The volatility
thus generated is further amplified by feedback effects across the network. The experiments
conducted with human subjects have further demonstrated that the BWE is especially strong
when the SC is non-integrated (Croson and Donohue, 2002), and have pinpointed the
advantages of introducing information sharing (Croson and Donohue, 2006) and coordination
across the various layers of the SC (Wu and Katok, 2006).
Most of the extant literature on the BWE has focused on the impact of uncertainty in demand,
while ignoring the impact of other sources of uncertainty (process side, supply-side, controlside). Among the supply-side sources of uncertainty, lead times variability is one of the most
relevant, as the assumption of deterministic lead-time is especially restrictive since lead times
are not deterministic in many supply chains. Moreover, some authors have posited that the
BWE reduction is best enabled via implementation of the principles of smooth material flow
and the reduction of actual or perceived shortage risk (Geary et al., 2002; 2006). Only a small
number of numerical simulations have investigated the effects of lead time uncertainty on the
formation, extent and consequences of the BWE (Chatfield et al., 2004; Truong et al., 2008),
showing that stochastic lead times do contribute to worsen BWE.
In light of the discovery of the importance of biases in human decision making for SC
performance, it is even more surprising that negligible attention has been paid to the effects of
supply uncertainty on the BWE and SC costs. Human experiments on the BWE have shown
that human behavior deviates from a model that accounts only for rational interactions and the
dynamics of the system, and thus there are grounds for positing that natural aversion to
uncertainty may bias the performance of the SC under uncertain lead times. Further, since
people learn “to live with risk”, a human experiment can also provide insight into the path
that individual behavior follows as they experience a highly variable environment.
To the best of our knowledge a test of the impact of uncertainty in lead time using human
subjects is still lacking. In this paper, we explore the behavior of members of a SC in the face
of supply uncertainty, that we make operational through uncertainty in lead times, and
contrast the performance of a SC with stochastic lead times with that of a SC with
deterministic lead times. We carry out the study within the framework of the beer distribution
game, a simulated serial supply chain with four echelons (retailer, wholesaler, distributor, and
factory).
The research questions we investigate are the following:
1. What is the impact of stochastic lead times in supply chains?
2. To what extent the different performance (if any) of the supply chain under known vs.
stochastic lead times is caused by inexperience of those who manage the supply chain?
3. How does out-of-task experience affect performance? Both classroom and managerial
experience can be expected to influence judgment and information handling. Task
experience gained in the classroom exposes participants to the broad principles
underlying inventory control and SC management. Managerial experience provides
intensive exposure to practical problems, so it is likely that students and managers
behave differently (Bolton et al., 2008).
The paper is organized as follows: Section 2 reviews the relevant literature that underpins the
hypotheses tested through the experiment, Section 3 discusses the experimental design, while
Section 4 presents the results. Section 5 concludes the paper summarizing the main findings
and highlighting implications for future research and SC management.
2. Factors investigated and hypotheses tested
2.1 The bullwhip effect with stochastic lead times
The BWE has been widely studied in the context of the so-called “beer game”. In the classic
beer distribution game (Forrester, 1961) the supply chain normally consists of four echelons
(retailer-wholesaler-distributor-factory). Inventory is managed according to the periodic
review inventory model (order-up-to). During the game each i-participant, i [1,...,4], places
orders, Oi(t), to the immediate upstream supplier and fills downstream customer’s orders,
Di(t). At each level, when a buyer places an order a delay of one week (LTI) occurs before
this latter is known to the upstream supplier, Di(t) = Oi-1(t-1); a two weeks lead time (LTD) is
requested to ship orders to the downstream echelon and the same happens to the factory when
beer is brewed (LTP). At each level, goods received at time t, Ri(t), correspond to the ones
which were shipped by the upstream supplier two weeks before, Si+1(t-2). During the game
each player must respect an inventory balance: Ii(t) = Ii(t-1) + Ri(t) – Si(t), where Ii(t) is the on
hand quantity; customer orders are filled if Ii(t) ≥ Di(t) otherwise Si(t) < Di(t) and backorders
occur, Bi(t) = Di(t) – Ii(t-1) + Ri(t).
If external demand is variable, larger oscillations of orders occur as one moves upstream the
SC, giving rise to the BWE. Most of the extant literature on the BWE has focused on the
standard case described above, i.e. variable customer demand and constant lead times, thus
ignoring the impact of other sources of uncertainty on the BWE (process side, supply-side,
control-side).
A few papers in the last ten years have addressed the problem of the BWE and of SC
performance relaxing the assumption of deterministic lead times. Chatfield et al. (2004) use
simulation to investigate the effects of stochastic lead times in a k-node SC. In particular,
through a factorial design, the effect of various levels of lead time variability is crossed with
that of four levels of information quality and updating rules, and absence/presence of
information sharing. The authors show that as the variance of lead time increases, in the case
of a normally distributed customer demand, BWE worsens. This result is confirmed by
Truong et al. (2008) assuming either an AR(1) or an ARMA(1,1) model for customer
demand.
Chatfield et al. (2004) further show that the amplification of order variances is higher when
historical information on lead times variances is used to update inventory parameters than
when this information is not used (due to misperception of the variability or indifference
towards uncertainty). This finding seems to be consistent with that of Chen et al. (2000) who
verified that the BWE would not exist if there were no forecast-based orders attempting to
capture the latest demand information.
Kim et al. (2006) present a model with stochastic lead time in which the case of information
sharing (customer demand is common knowledge for all echelons of the chain) is contrasted
with that of no sharing. Results show that the variance of orders increases nearly linearly in
echelon stage with information sharing, and exponentially without information sharing. One
managerial implication of this result is that the sharing of information on customer demand by
all echelons is an effective way to reduce BWE also under conditions of supply uncertainty.
However, information sharing per se does not eliminate BWE, which remains higher than
under condition of deterministic lead time.
Heydari et al. (2009) try to isolate the impact of lead time uncertainty from that of demand
uncertainty by simulating a four-stage SC in which customer demand is constant. Results
show that the uncertainty in lead time increases the variance of orders at each echelon but
does not worsen BWE. Further, order variance is positively correlated to the variance of
inventory levels and the amounts of stock-out. However, results of this study are not directly
comparable with those already discussed, since Heydari et al. (2009) assume that if the
supplier holds insufficient inventory to satisfy an order, the unavailable quantity will be lost.
Similarly, all delayed orders will be lost. Further, the uppermost level of the chain does not
face stochastic lead time.
Chaharsooghi and Heydari (2010) study the impact of two classes of policies (implemented
either through supplier selection or investment strategies) meant to reduce supply risk under
stochastic lead time: policies aimed at reducing the mean lead time and policies addressing
the reduction of the variance. The former make the customer get the product quickly, the latter
make the lead time more predictable. Results of simulations carried out by the authors on a
four-stage SC suggest that reduction in lead time variance reduces stock-out size, whereas
mean lead time reduction reduces BWE, with the effect of the former on SC performance
much greater than the effect of the latter. The simulations are run under the same assumptions
(in particular constant demand) of Heydari et al. (2009).
The above discussion suggests the following hypotheses:
Hypothesis 1: in the presence of both customer demand uncertainty and stochastic lead time,
the BWE will be higher than in the case when only demand uncertainty is considered and the
lead time is deterministic.
2.2 The effect of experience and learning-by-doing in BWE experiments
Several experimental studies have focused on the impact of the amount of information about
the SC and of information sharing on SC performance and the bullwhip effect using the beer
game. For instance, Croson and Donohue (2003) study the impact of Point of Sale (PoS) data
sharing and find that information sharing mitigates the bullwhip effect by reducing the
oscillations of orders of upstream members. Similar results are obtained by Steckel et al.
(2004). Gupta et al. (2002) study the beer game under three different demand scenarios (a
step-up function, a S-shaped function, and a S-shaped plus error function) and show that PoS
information results in improved performance only in the simplest scenario (the step-up
demand). Machuca and Barajas (2004) find that significant savings can accrue from the
implementation of an electronic data interchange (EDI) across the entire supply chain. Cantor
and Macdonald (2009) show that information availability about the supply line (local vs.
system-wide) interacts with the problem-solving approach (abstract/flexible rules versus
concrete/fixed rules) in determining the performance of the supply chain.
A different strand of research has focused on the learning process of the actors involved in the
game. Wu and Katok (2006) study the effect of learning-by-doing on SC performance and
find that experience of the game significantly reduces the bullwhip effect only when it is
“system wide”, i.e. it concerns the whole structure of the game, whereas ambiguous effects
are reported when role specific experience is given to participants in the experiment. The
implication is that training (i.e. repetition of the task) may improve individuals’ knowledge
and understanding of the system. However, it does not improve SC performance unless
supply chain partners are allowed to communicate and coordinate through knowledge sharing.
The effect of learning-by-doing has also been explored in the context of the newsvendor
problem. Bolton and Katok (2008) find that knowledge gained through personal experience
leads to a significant improvement in performance. Similarly, Ben-Zion et al. (2008) find that
game experience is important in improving profits and leads to stationary orders. Although in
the earlier stages of the game orders exhibited a bias towards mean demand, this effect was
significantly reduced as the game unfolded. Bostian et al. (2008) test and find evidence in
favour of a learning model with recency effects, i.e. in which subjects respond to recent gains
and losses, and inertia. This model adds to previous studies since it incorporates demand
chasing in a framework where expected payoffs also matter. Gavirneni and Isen (2010) carry
out a verbal protocol analysis to explore the reasons underlying recency effects. They observe
that participants had difficulty dealing with the abstractness of the task and tried to identify
anchors for their decision-making process, the most common of which was average demand.
Further, the players focused on the basic information relevant to the decision and ignored
some of the advanced information that would have helped them make a better decision.
Finally, performance in ordering decision may be tied to professional experience of the
players. Bolton et al. (2008), comparing the ordering behaviour of students at different level
of education with that of expert procurement managers, find the anchoring bias toward
average demand is observable whatever the level of experience the subjects have. Rather than
professional experience, it is the exposure to varying levels of information and task training
that has a significant effect on performance.
Thus, on the basis of the above literature, we formulate the following hypotheses:
Hypothesis 2: task experience in presence of demand variability reduces the bullwhip effect
both under conditions of variability of lead times and with deterministic lead time.
Hypothesis 3: Out of task experience has a lower impact than task experience on SC
performance.
3. Experimental design
a. Students’ experiment
In this experiment, two treatments were run. The first treatment (SBG hereafter)
reproduced a beer game with four echelons (i = 1,...,4), i.i.d. normally distributed external
demand with parameters known to all echelons (µ = 100, σ = 20), known and constant lead
times equal to 3 (LTI = 1, LTD = 2). This design differs from Sterman’s experiments, in
which the retail demand is completely unknown and non-stationary, and is represented by a
simple step-function whereby demand starts at 4 units and jumps to 8 units after the eighth
game period. However, subsequent studies by Croson and Donohue (2006) have shown that
even with stationary and known demand distributions, the BWE arises. Thus, we expect the
BWE to arise also in our setting.
In the second treatment (SLT henceforth) lead times of all suppliers in the chain (including
the factory’s brewery) are uniformly distributed in the interval (1, 2, 3) periods. Thus, in
addition to demand uncertainty, players face also supply uncertainty stemming from
stochastic lead times.
In both treatments, an order placed with the supplier can be partially fulfilled with a
continuous distribution, depending on the supplier’s inventory availability. The histories of
incoming demands, of past shipments and past purchases are available to each player. From
this information, the history of lead times can be worked out in SLT. Also, because of
stochastic lead times, in SLT order cross-over can occur.
Summing up, the game can be assumed to mimic a non-integrated supply chain in which
each buyer has a single supplier; no information sharing about actual demand, inventories,
backlogs, and own lead times, is allowed among SC participants; and the retailer is the only
echelon of the chain that observes external demand.
Behaviour in both treatments was observed for a number of periods (T), from 36 up to 50.
Players were not informed of the final period of the game to avoid end-of-game behaviour
that might trigger over- or under-ordering.
Each echelon began with an initial inventory level Ii(t=1) = 300, outstanding orders Oi(t=
0, -1) = 100 for the previous two periods, and an incoming shipment Si(t=2, 3) = 100 in the
following two periods. All experiments also used the same random number seed to generate
demand, i.e., Di(t), t=1, …..T was identical across groups. This allowed us to isolate
variations due to ordering behaviour from variations due to different demand streams.
In order to assess the impact of task experience, each player participated in two different
beer game sessions, the second taking place about one month after the first. In the second
session, each player kept the same role he/she had been assigned in the first game but was
assigned to a different chain. This setting allowed to study the effect of role-specific task
experience and avoided the risk that members of the same chain during the first session
agreed on a specific strategy, which would have changed the SC from a non-integrated chain
to a coordinated one.
Participants in both treatments were MBA students who had attended at least one course in
Operations Management. This was done in order to enhance the chances that the experimental
subjects may be considered “tomorrow’s inventory professionals (Croson and Donohue,
2006). Participants were randomly assigned to either of the two treatments. Participants were
told not to communicate with anyone during the experiment. Once seated, participants were
oriented to the rules and objectives of the game by means of a tutorial. They were instructed
that each role would incur unit inventory costs of €0.50 and unit backlog costs of €1 per
period (Sterman, 1989).
Table 1 summarizes the distribution of players across the different cells of the experiment.
Table 1 – Participants in the different treatments/sessions
1st session
2nd session
Treatment 1 - SBG
13 chains
10 chains
Treatment 2 - SLT
13 chains
11 chains
The incentive used in the game was both monetary and in terms of coursework grades.
Participants were instructed that the members of the supply chain team with the lowest total
costs (inventory + backlog costs) shared a final prize of €77. In addition, they received an
extra course grade (out of a total of 30 grades).
The version of the beer game here adopted was developed in a Googledocs® software
application which enables Excel® spreadsheets to be shared by different SC players.
b. Managers’ experiment
The two treatments were also run with a sample of 24 purchasing managers working for a
large manufacturer of automotive components.
Participants played both treatments sequentially, first SBG and then SLT in the course of a
day session. The behavior of 6 chains was observed for 20 periods. Given the small number of
participants and the high heterogeneity in experience and seniority levels, rather than
assigning players to chains randomly, we preferred to build the teams in a stratified fashion,
considering experience, seniority level, and age.
4. Numerical simulation
In order to generate predictions of the BWE and SC performance using the same structure
and parameters of the two games described in section 3, we codified two numerical models of
the game scenarios, corresponding to the two experimental treatments.
The first simulation, as in the SBG experiment, considered an external demand identically
distributed (iid) with fixed and known mean (100) and standard deviation (20). The lead time
was constant (one period of information and processing delay plus two periods of
transportation lead time) and known. The second simulation, as in the SLT experiment,
besides the stochastic demand, considered a stochastic transportation lead time uniformly
distributed in the interval (1, 2, 3) periods.
In both simulations, orders are filled from stock in a FIFO manner, with backordering used
when stock-outs occur. Partial replenishments are used when there is not enough stock to fill
an order completely. With stochastic lead times, the simulation model accommodates order
crossover. Supply chain nodes possess only local information and are “blind” to what is going
on outside their level. Each node’s supply chain knowledge-base is derived from the incoming
demand flow coming from the downstream partner and the outgoing flow of orders being
placed with the upstream partner.
Each node makes all assessments based on the available data and attempts to adjust its actions
to adapt to the “current” conditions.
At each stage and period, the inventory manager considers downstream demand, Di, and
upstream replenishment, Ri, as random variables. The average balance of Ri-Di is null if the
manager follows the Forrester rule and simply forwards downstream demand (Di) to the
upstream echelon. The variance of Ri-Di can be estimated as:
Ri-Di2 = Di2 + Ri2
where independency of Ri and Di is assumed either because of the stochastic replenishment
lead time (LTi) and the allowed order crossover, or because of the assumptions that the player
lacks the cognitive ability to estimate the covariance matrix.
At the end of each period, each player places replenishment order-up-to Oi to raise or lower
the inventory position to a safety stock (SS) level according to the selected service level.
Thus, the inventory policy is an order-up-to level (Ri, Ai), with the following features:
 R=1 is the review period;
 Ai is the target availability which can be calculate as:
Ai = ERi-Di + k(LS)Ri-Di;
Where ERi-Di~0 is the average value of the Ri-Bi balance;
k(LS) is the generic safety stock factor which corresponds to a desired service level;
Ri-Di = (Di2 + Ri2)0.5 is the standard deviation of the Ri-Bi balance.
 Ai- = Ii + iOi-1 - iRi + Bi is the availability at the end of period i before (-) a
replenishment order Oi is placed; where:
Ii = Ii-1 + Ri - Di is the on hand quantity at the end of period i;
iOi-1 is the sum of placed orders until the decision making moment;
iRi is the sum of received replenishments from upstream level at the end of i period;
Bi is the current backlog.
 Oi = Ai – Ai- if it is a positive value, otherwise Oi=0;
 Ai+ = Ai- + Oi is the inventory availability after the order Oi is placed (+).
To estimate (D, sD2) at each node, the virtual player uses all the historical information
available at each stage.
The virtual player can emulate different inventory management policies depending on the
designed amount of safety stocks; so an abacus of results was performed simulating several
safety stock levels, by varying k(LS) parameter (Figure 1-2).
Figure 1 - Virtual players results playing SBG and SLT (100 replications).
5. Results
a. Evidence of bullwhip effect
In Figure 1 the standard deviation of orders, averaged over all participants playing the same
role in each experimental treatment, is reported. The left hand side compares average standard
deviations in the first repetition of each treatment (SBG-; SLT-). The figure shows a marked
BWE in both cases, although it is not possible to clearly identify a differential impact of
uncertainty in lead times. The right hand side figure compares average standard deviations in
the second repetition of each treatment (SBG+; SLT+) and shows that the standard deviation
of orders is higher under stochastic lead times for each echelon. A comparison of the two
figures allows appreciating the extent of the reduction of order volatility brought about by
task experience. As in other studies, our results suggest that learning-by-doing can reduce
BWE but does not eliminate it. The right hand figure in fact shows that the standard deviation
of orders of the factory under SLT is more than twice that of the retailer.
Figure 1 – Average standard deviation of orders by role, by treatment, and repetition
Figure 2 compares BWE in each treatment by out-of-task experience and task experience. The
left hand side of the figure shows that managers participating in the experiment and playing
the SBG game for the first time outperformed students playing their first repetition, although
as already underlined one session of task experience was sufficient to dramatically decrease
BWE generated by students. The figure further reports the predicted BWE for a virtual agent
adopting an order-up-to inventory policy with a conservative service level (SL=0.90). The
behavior of experienced students appears to follow closely this predicted pattern. The right
hand side of the figure shows that managers (practitioners) participating in the experiment and
playing the SLT game as their second game outperformed students playing their second
repetition. The standard deviation of orders of managers’ chains is in fact lower and very
close to the pattern of the virtual conservative agent.
The figure also shows that managerial experience curbs BWE but does not eliminate it. In
fact, the average standard deviation of orders for the factory (53.17) is more than twice that of
the retailer (20.30).
Figure 2 – Comparison of BWE by experience level
6. Discussion
Results of our experiments have provided evidence to support out first two hypotheses. In
particular, we find that, once players have gained task experience during the first session, the
oscillation of orders under known lead times is smaller than the oscillation under stochastic
lead times, for all layers of the chain. This result confirms the extant literature on BWE under
stochastic lead times (Chatfield et al., 2004; Kim et al., 2006). We believe that the first
repetition of the game (under both treatments) performed by students is too noisy to be
considered useful for comparison. The dramatic reduction in the oscillation of orders across
repetitions further suggests that the first repetition can be considered as a sort of “warm-up”.
The third hypothesis, however, is not supported, since managers performed better than
students. This result runs contrary to the findings of Bolton et al. (2008). More disaggregated
analysis investigating the behaviour of every chain in our sample will be necessary to confirm
the patterns of orders suggested by averages, and to explore the decision making process
underlying such behaviour.
The experiment presented positions itself among the contributions that aim at studying the
relevance that SC vulnerability plays in SC management: in the experiment, lead time
uncertainty in the presence of a single supplier can be considered a proxy of the vulnerability
of the SC to stock-outs. The experiment shows that although both task and out-of-task
experience can significantly reduce the variance of orders at each echelon of the chain, further
benefits may only accrue from the reduction of uncertainty in supply.
7. References
 Ben-Zion, U., Cohen, Y., Peled, R., Shavit, T. (2008). Decision-making and the
Newsvendor Problem: An Experimental Study. The Journal of the Operational Research
Society 59(9), 1281–1287.
 Blanchard, O.J. (1983). ‘‘The production and inventory behaviour of the American
automobile industry. Journal of Political Economy 91 (3), 365–400.
 Bolton, G.E., Ockenfels, A., Thonemann, U. (2008). Managers and students as
newsvendors: How out-of-task experience matters. Working Paper No.39, University of
Cologne, Working paper series in Economics.
 Bolton, G.E., Katok, E. (2008). Learning by Doing in the Newsvendor Problem: A
Laboratory Investigation of the Role of Experience and Feedback. Manufacturing &
Service Operations Management 10(3), 519-538.
 Bostian, AJ.A., Holt, C.A., Smith, A.M. (2008). Newsverndor “Pull-to-Center” Effect:
Adaptive Learning in a Laboratory Experiment. Manufacturing & Service Operations
Management 10(4) 590-608.
 Cantor, D.E., Macdonald, J.R. (2009). Decision-making in the supply chain: examining
problem solving approaches and information availability. Journal of Operations
Management 27(3), 220-232.
 Chaharsooghi, S.K., Heydari, J. (2010). T variance or LT mean reduction in supply chain
management: which one has a higher impact on SC performance. International Journal
of Production Economics 124(2), 475-481.
 Chatfield, D.C., Kim, J.G., Harrison, T.P., Hayya, J.C. (2004). The bullwhip effect Impact of stochastic lead time, information quality, and information sharing: a simulation
study. Production and Operations Management 13(4):340–353.
 Chen F., Drezner Z., Ryan, J.K., Simchi-Levi, D. (2000). Quantifying the bullwhip effect
in a simple supply chain. Management Science 46 (3), 436–443.
 Croson R., Donohue K. (2002) Experimental economics and supply chain management.
Interfaces 32(5), 74-82.
 Croson R., Donohue K. (2006) Behavioral causes of the bullwhip effect and the observed
value of inventory information. Management Science 52 (3), 323-336.
 Croson, R., Donohue, K. (2003). Impact of POS data sharing on supply chain
management: an experimental study. Production and Operations Management 12(1), 111.
 Forrester, J. (1958). Industrial dynamics: a major breakthrough for decision makers.
Harvard Business Review 36, 37–66.
 Forrester, J. (1961). Industrial dynamics. MIT Press and John Wiley & Sons, Inc., New
York.
 Gavirneni, S., Isen, A.M. (2010). Anatomy of a Newsvendor Decision: Observations
from a Verbal Protocol Analysis. Production and Operations Management 19(4), 453–
462.
 Geary, S., Childerhouse, P., Towill, D.R. (2002). Uncertainty and the seamless supply
chain. Supply Chain Management Review July/August, 52-61.
 Geary, S., Disney, S.M., Towill, D.R. (2006). On bullwhip in supply chains—historical
review, present practice and expected future impact. International Journal of Production
Economics 101, 2–18.
 Gupta, S., Steckel, J.H., Banerjii, A. (2002). Dynamic decision making in marketing
channels. In A. Rapoport, (Ed.), Experimental Business Research (pp.4-21). Boston:
Kluwer Academic Publishers.
 Harland, C., Brenchley, R., Walker, H. (2003). Risk in supply networks. Journal of
Purchasing and Supply Management 9 (2), 51–62.
 Heydari, J., Kazemzadeh, R.B., Chaharsooghi, S.K. (2009). A study of lead time
variation impact on supply chain performance. International Journal of Advanced
Manufacturing Technology 40, 1206-1215.
 Holt, C.A. and Laury, S.K. (2002). Risk aversion and incentive effects. American
Economic Review 92(5), 1644-1655.
 Kim, J.G., Chatfield, D.C., Harrison, T.P., Hayya, J.C. (2006). Production, manufacturing
and logistics quantifying the bullwhip effect in a supply chain with stochastic lead time.
European Journal of Operational Research 173(2), 617-636.
 Lee, H.L., So, K.C., Tang, C.S., (2000). The Value of Information Sharing in a TwoLevel Supply Chain. Management Science 46(5), 626–643.
 Lee, H.L., Padmanabhan, V., Whang, S. (1997). Information distortion in a supply chain:
the bullwhip effect. Management Science 43 (4), 546–558.
 Machuca, J.A.D., Barajas, R.P. (2004). The impact of electronic data interchange on
reducing the bullwhip effect and supply chain inventory costs. Transportation Research
Part E 40(3), 209-228.
 Steckel, J.H., Gupta, S., Banerji, A. (2004). Supply chain decision making: will shorter
cycle times and shared point-of-sale information necessarily help? Management Science
50 (4), 458-464.
 Sterman, J. (1989). Modeling managerial behavior: Misperceptions of feedback in a
dynamic decision making experiment. Management Science 35(3), 321-339.
 Tang, C.S. (2006). Perspectives in supply chain risk management. International Journal of
Production Economics 103 (2), 451-88.
 Truong, T.H.D., Luong, H. T., Kim, Y. (2008). A measure of the bullwhip effect in
supply chains with stochastic lead time. International Journal of Advanced
Manufacturing Technology 38, 1201–1212.
 Wagner, S.M., Bode, C. (2006). An empirical investigation into supply chain
vulnerability. Journal of Purchasing and Supply Management 12, 301-312
 Wagner, S.M., Neshat, N. (2010). Assessing the vulnerability of supply chains using
graph theory. International Journal of Production Economics 126(1), 121-129.
 Wu, D., Katok, E. (2006). Learning, communication, and the bullwhip effect. Journal of
Operations Management 24(6), 839-850.