Behavioral Causes of the Bullwhip Effect:
“Satisficing” Policies with Limited Information Cues


Rogelio Oliva
Mays Business School
Texas A&M University
Wehner 301F – 4217 TAMU
College Station, TX 77843
Tel (979) 862-3744; Fax (979) 845-5653
roliva@tamu.edu



Paulo Gonçalves
MIT Sloan School of Management
30 Wadsworth St. E53-339
Cambridge, MA 02142
Tel (617) 253-3886; Fax (617) 253-7579
paulog@mit.edu

---

Behavioral Causes of the Bullwhip Effect:
“Satisficing” Policies with Limited Information Cues

We evaluate, in an experiment with the Beer Distribution Game, a complementary behavioral
source of the bullwhip effect that has been previously ignored in the literature: overreaction to
backlogs. By separating the estimation of the response to inventory and backlog, we find that
players treat backlog differently than inventory. Contrary to our expectations, players do not
over-order when in backlog; instead, they have a measured response, saturating order adjustment
and limiting the amount of amplification they introduce in the order stream. We also find
stronger evidence than previous studies that players underestimate the supply line, leading to a
more unstable ordering policy. Using a simulated order stream, we find that players display
bounded rationality and that their estimated decision policy is not different in form and
performance than a policy that, with the information cues available in the Beer Distribution
Game (inventory position and orders), minimizes local cost. Players’ estimated ordering policy,
however, aims to maintain higher inventory levels, leading to increased order amplification and
costs for upstream echelons. Hence, the estimated ordering policy presents strong behavioral
components: it ignores the supply line and under-reacts to backlog while aiming for higher than
necessary inventory levels. We conclude by discussing the implications of these findings for
future research and practice in supply chain management.


Keywords: supply management, experiments, heuristics, system dynamics.

---

1. Introduction
The bullwhip effect, the tendency for the variability of orders to increase as one moves from
customers to manufacturers, is a frequent and costly problem in supply chains, leading to
excessive capital investment, inventory gluts, low capacity utilization and poor service (Armony
and Plambeck, 2005; Gonçalves, 2003; Lee, Padmanabhan, and Seungjin, 1997a; Sterman,
2000). For instance, Hewlett-Packard lost millions of dollars in unnecessary capacity and excess
inventory following a post-shortage demand surge for its LaserJet printers (Lee, Padmanabhan,
and Seungjin, 1997b). Cisco Systems incurred more than US$ 2 billion inventory write-off due
to a strong inventory built up followed by a drastic decrease in retailer orders (Adelman, 2001;
Armony and Plambeck, 2005). The sources for this amplification in demand variability include
operational causes — such as batching of orders, order gaming due to shortages, forward buying
due to price discounts, and errors in demand forecasting (Lee et al., 1997a) — and behavioral
ones — such as failure to account adequately for the supply line of unfilled orders (Sterman,
1989) and the adoption of coordination stocks (Croson, Donohue, Katok, and Sterman, 2005).
Motivated by Sterman (1989; 1992), a number of experimental studies have used the Beer
Distribution Game (BDG) to explore behavioral causes for the bullwhip effect and methods for
dampening it (see Croson and Donohue, 2002, for a review.) Kaminsky and Simchi-Levi (1998)
find that reducing the ordering and shipment lags decrease overall supply chain costs even
though order amplification remains the same. Gupta, Steckel and Banerji (2001) and Steckel,
Gupta and Banerji (2004) also show that reducing lead times leads to lower costs. Their results
suggest, however, that the impact of sharing POS data on costs depends on the nature of
customer demand. Using a stationary and known demand (as proposed by Chen and
Samroengraja, 1999), Croson and Donohue (2003) find that POS data significantly reduces order
oscillation — particularly in upstream echelons — and reduces overall supply chain costs.
Croson and Donohue (2006) find a similar result when echelons shared inventory information.

1

---

Interestingly, the bullwhip effect occurs even when demand is fixed, commonly-known, and
players start at the optimal inventory level (Croson et al., 2005). The authors suggest that players
build inventory to protect against coordination risk (i.e., the risk that others will deviate from
optimal behavior.) Investigating the effect of learning and communication on the bullwhip effect,
Wu and Katok (2006) find that order variability decreases when team players are allowed to
formulate strategies collaboratively. All these studies, when estimating the ordering decision rule
for individuals, arrive at a common source of supply chain instability: players underestimate the
supply line of unfilled orders. This work contributes to this line of empirical research by
articulating and analyzing a complementary behavioral source of the bullwhip effect that has
been overlooked by previous research: overreaction in response to shortages. Overreaction
implies that subjects order more aggressively (e.g., have a stronger reaction) when they face
shortages than when they hold inventory.
As Mitchell suggests, when competing with other retailers for scarce supplies (i.e., horizontal
competition), retailers inflate their orders to manufacturers to improve their chances of obtaining
the supply they need.
[R]etailers find that there is a shortage of merchandise at their sources of supply.
Manufacturers inform them that it is with regret that they are able to fill their orders only
to the extent of 80 percent. … Next season, if [retailers] want 90 units of an article, they
order 100, so as to be sure, each, of getting the 90 in the pro rata share delivered.” (1924,
p. 645)

Since there is no horizontal competition in the BDG, we cannot justify overordering as a rational
consequence of the rationing game proposed by Lee et al. (1997a). However, we hypothesize
that players could overreact in response to backlogs motivated by Tversky and Kahneman’s
(1974) availability heuristic (i.e., the tendency to overreact to dramatic or vivid events). A
backlog is a dramatic event in the beer game because (a) is twice more costly than inventory and
(b) causes great disruption to the supply chain. Contrary to our expectations, we find that players

2

---

do not overreact when in backlog, instead their correction saturates at a maximum value; a policy
that is more stable than the linear response to backlogs suggested in previous studies. We also
find stronger evidence than previous studies that players underestimate the supply line, leading to
a more unstable ordering policy. Using a simulated order stream to test the rationale of these two
components of the ordering policy, we found that players show bounded rationality using only
the information available to them in a policy that is not significantly different in form and cost
performance from the policy that minimizes local cost. The estimated ordering policy, however,
aims to maintain a higher inventory level than the cost-minimizing rule, which leads to increased
order amplification and costs for upstream echelons. Hence, the estimated ordering policy
indicates a strong behavioral component to supply chain instability, i.e., it ignores the supply line
and underreacts to backlog while aiming for higher than necessary inventory level.
The remainder of the paper is structured as follows. In §2 we present the experimental design
and methods, in §3 our models and results. In §4 we perform sensitivity analysis of the
parameters of the estimated rule and compare the estimated rule with the local cost minimizing
rule with the available information cues. We conclude with a summary of our findings and
implications for practitioners and researchers in supply chain management.
2. Experimental Design
Our experiment utilizes a web-based version of the Beer Distribution Game (BDG) developed at
Harvard Business School that maintains the essential structure of the board game (Sterman,
1989). The game represents a serial supply chain with four echelons: retailer, wholesaler,
distributor, and factory (R, W, D, and F, respectively). Each supply chain is independent of the
other and managed by a team charged with minimizing the supply chain cost. Each echelon
incurs an inventory holding cost of $0.50 per unit/week and a backlog cost of $1.00 per
unit/week. Shipment and order delays between echelons are two weeks and factories incur a one-
week production delay with no capacity constraints. Each simulated week players face the

3

---

following sequence of events: (1) receive shipments; (2) fill customer orders, if sufficient
inventory is available, otherwise accumulate a backlog; and (3) place an order with its supplier,
where orders are constrained to be non-negative, i.e., it is not possible to cancel orders with the
supplier.
The game is initialized in flow equilibrium: order and shipment flows are 4 units/week and
each echelon starts with an initial inventory level of 12 units. Subjects are not informed about the
shape of demand. A single time increase in retailer orders (a step input) is introduced in the
second period (week), bringing orders to 8 units/week. To avoid end-of-horizon behavior the
experiment is announced to run for a simulated year, but is, in fact, terminated after 36 weeks.
The web-based version, by virtue of its automatic computation of order receipts, incoming
orders, shipments, and inventory-backlog levels, can be run with less time pressure than the
board version of the game on which a facilitator imposes the pace. The automatic recording of
transactional data avoids reporting errors, although data entry (i.e., “typing”) errors are still
possible. Because of the cascading effects to other players, we did not attempt to correct typing
errors.
Our data set consists of a sample of 116 pairs of first-year MBA students that played the game
as part of the introductory course in operations management. This student sample has similar
characteristics of previous studies using the BDG (Croson and Donohue, 2002; 2003; 2005;
2006; Sterman, 1989; Wu and Katok, 2006). Students had incentives to minimize team cost; the
game was a graded assignment with team performance as the major component of the grade. The
winning team also received a token award – similar to Sterman (1989). The students were on
average 27 years old and had about two years of work experience in diverse areas. Prior to the
game, players received a five-page document describing the structure of game and the sequence
of events they will be facing. Less than two percent of the players expressed prior knowledge of

4

---

the game. Due to the reduced number of “experts,” they were not excluded from our sample.
Players were randomly assigned, in pairs, to echelons (R, W, D, or F) and teams. Team members
interacted via a computer screen and, in contrast to the board version of the game, lacked both
visual access to the state of the supply line and knowledge of who other teammates were. We
eliminated four games from our original sample. These games included one or more players
showing anomalous ordering behavior (consistently not ordering when in backlog or placing
high orders when holding large inventory) suggesting they had misunderstood the stock
management task. Our analysis is based on the remaining 25 games.
2.1. Methods
We treated the BDG’s non-negativity constraint on orders as censored data. That is, we assumed
that an order for zero could represent situations in which a subject wished to cancel a previously
placed order (a negative order) but was restricted by the rules of the game to a minimum order of
zero. Accordingly, we estimated our model using a tobit model (Tobin, 1958). Also, to estimate a
decision rule that reflects the full range of observations available, we structured the data from the
games as a panel (cross-sectional time-series data set) with individual players the cross-sectional
unit (i) and week of decision the time index (t). In contrast to previous studies that estimate the
decision rules at the individual level, our panel data structure increases the efficiency of the
estimates and the representativeness of the resulting rule as it allows us to make estimations
across individuals and echelons. There being no reason to suspect that individual differences can
be captured by changes in the constant term, and subjects being clearly a sample from a larger
population, we assumed random effects across individuals (Greene, 1997). Estimations were
performed using Stata’s (2003) implementation of the random-effects cross-sectional time series
tobit model and we tested the significance of the model’s panel-level variance component by
comparing the regression to the results of a pooled tobit regression.

5

---

3. Estimation of ordering policies
In a setting similar to the BDG with stationary and commonly-know demand distribution Chen
(1999) demonstrated that a base-stock policy — where orders placed equal those received —
minimizes total supply chain cost and avoids demand amplification. Since the demand in our
experiment is both non-stationary and unknown to players (a step increase), it is not possible for
players to calculate an optimal strategy prior to the game. While there is no reason to expect a
base-stock policy to be optimal, it provides a starting point to test players’ ordering policies.
With the base-stock policy as a starting point, we incrementally increase the complexity of the
ordering policies to include information cues and heuristics that players might have used. This
incremental approach allows us to explore the marginal contribution of each of the information
cues available to the players.
3.1 Base-stock and adaptive base-stock policies
A model that estimates the ability of a base-stock policy to explain the variability in orders is
given by:

O = MAX (0, β L
+ u +ε ) (I)
it
L
it−1
i
it
where, to be consistent with the BDG, orders are constrained to be nonnegative; L
represents
it−1
orders received by the ith subject in the last period (t-1); u is the random disturbance
i
characterizing the ith subject, and ε is an additive disturbance term. According to Chen’s (1999)
it
base-stock policy, orders placed ( O ) must equal those received in the previous period ( L
),
it
it−1
thus we expect β to be equal to one.
L
Model I in Table 1 shows the estimated parameters for the base model together with the
model’s log-likelihood value, significance ( χ 2), R2, and root mean percent error. The model is
highly significant (p<0.001), explains 54% of the variance in orders, and differences among
players do not contribute to explain unexplained variance in orders ( ρ = σ 2 σ 2 +σ 2
(
)= 0.0). While
u
u
ε
a base-stock policy (using a lag forecast as a predictor for orders) provides a good fit for players’

6

---

ordering policy, the fact that the β coefficient is slightly greater than one (p=0.03 for H : β = 1)
L
0
L
suggests that the rule does not fully capture all the adjustments being made by the players.
For cases when demand is non-stationary, Graves (1999) proposes an adaptive policy that,
like the base-stock policy, replenishes the demand just realized, but adjusts orders to changes in
demand. He suggests that the adjustment on orders should be based on the difference between
successive demand forecasts projected over the supply lead-time:

O = L
+ LT ˆ
L
( − ˆ L ) (1)
t
t−1
t
t−1
where L is the demand just realized, ˆ
L the current demand forecast, and LT the lead-time for
t−1
t
the supply chain to replenish orders. Assuming a simple lag forecast ˆ
L
( = L ), we define G as
t
t−1
the difference between successive forecast G
= ˆ
L
( − ˆ L )= L( −L ). Adding the non-
t−1
t
t−1
t−1
t− 2
negativity constraint and the random disturbances, and expanding the panel notation, yields the
following model:

O = MAX 0,
it
( β L + β G + u +ε ) (Ia)
L
it−1
LT
it−1
i
it
Under this model, we expect β to be equal 1, i.e., full replacement of past orders, and β to
L
LT
be close to the supply lead-time in the BDG, i.e., four weeks. Model Ia in Table 1 shows the
results of the estimation of this model. The coefficient for the forecast adjustment ( β ) is not
LT
significantly different from zero, thus the results are identical to the base-stock policy. We obtain
similar results when we use, as suggested by Graves (1999), an exponential smoothing process to
forecast demand in the adaptive base-stock policy. While the coefficient for the forecast
adjustment is significant β
(
= 0.21, S.E. = 0.04), its value is considerably smaller than the expected
LT
four weeks of supply lead-time, and the additional regressor only explains an additional 1% of
2
the variance in orders R
( = 0.55). We, thus, failed to find evidence for an order adjustment based
on demand forecast.

7

---

--- Insert Table 1 about here ---
3.2 Stock management policy
We revise the base-stock policy to incorporate inventory and supply line adjustments suggested
by Sterman (1989). Due to the difficulty in finding the optimal ordering policy in the traditional
BDG, Sterman proposes a simple, self-correcting ordering heuristic that uses information locally
available to the decision maker and presumes no knowledge of the structure of the system.
Specifically, managers are assumed to size orders to (1) replace expected losses from stock, (2)
reduce the discrepancy between desired and actual stock, and (3) maintain an adequate supply
line of unfilled orders. The decision rule is formalized as:

O = ˆ
L + α (S* − S ) + α
(SL* − SL ) (2)
t
t
S
t
SL
t
where ˆ
L represents the expected loss from the stock, S and SL the inventory and supply line
t
t
t
positions at time t, S* and SL* the desired levels for stock and supply line, and the parameters α
S
and α the fractional adjustment rate for inventory and supply line, respectively.
SL
Sterman (1989) assumed adaptive expectations for the formation of the expected loss
according to an exponential smoothing process:

ˆ
L = θL
+ 1
( −θ)ˆ L (3)
t
t−1
t−1
and obtained, for each player, maximum likelihood estimates for the simultaneous equations 2
and 3, subject to the constraints 0 ≤ θ ≤ 1 and α ,α ,S*,SL* ≥ 0. The joint estimation of these
S
SL
equations, however, has the potential of shifting variance between the stock replenishment and
forecasting equations, eqs. 2 and 3 respectively. Lower values of θ make the forecast series more
stable and shift the residual variance to the replenishment decision, thus potentially biasing its
parameter estimates (Oliva, 2003).
We assume a simple lag forecast ( ˆ
L = L
) , an implied θ = 1 in the exponential smoothing
t
t−1
model in equation 3, and an intuitive and plausible model of expectation formation (Kleinmuntz,

8

---

Document Outline

•  
• ﾿
• 
• ﾿
• 
  • ﾿
  • 
  • ﾿
• • 
  • ﾿
• 
• ﾿

---