"Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment,"

Abstract

En la UE se ha estimado que los costes de la congesti�n representan el 2% de su PIB y que el coste de la poluci�n del aire y ruido supera el 0,6% del PIB, siendo alrededor del 90% de los mismos ocasionados por el transporte terrestre. Ante este hecho y el continuo aumento de la demanda del transporte privado frente al p�blico para los desplazamientos, muchos abogan por una conjunci�n de medidas tanto restrictivas como alternativas al uso del coche. Dentro de las primeras se encuentra el establecimiento de un peaje o una tarifa por el uso de las carreteras, medida que aunque desde el punto de vista de la Teor�a Econ�mica es la manera m�s eficiente para corregir el fallo de mercado que supone la congesti�n, desde la visi�n de pol�ticos y del p�blico no goza de gran aceptaci�n. En este trabajo se pretende hacer una simulaci�n de los efectos que tendr�a sobre el bienestar social de la implantaci�n de una medida de este tipo en la Bah�a de C�diz. In the European Union it has been estimated that the congestion cost are the 2% of the gross domestic product and the cost of pollution and noise is over 0,6%, olso it is known that the 90% of this cost are caused by overland transport. For this reason and for the always increasing demand of private transport, there are professionals who thinks that the solution have to be restrictive measures added to alternatives to the car. road pricing is a restrictive measures that for the economic theory is the most efficient way to solve congestion cost but for politicians and user of transport is not always accepted. In this study we are going to simulate road pricing for commuters in the Bah�a of C�diz and then it will be estimated welfare effects.

Full text

D-3919
MODELING
MANAGERIAL BEHAVIOR:
MISPERCEPTIONS
OF
FEEDBACK
IN
A
DYNAMIC
DECISIONMAKING
EXPERIMENT
by
John
D.
Sterman
WP-1933-87

D-3919
Modeling
Managerial
Behavior:
Misperceptions
of
Feedback
in
a
Dynamic
Decisionmaking
Experiment
John
D.
Sterman
Associate
Professor
Sloan
School
of
Management
Massachusetts
Institute
of
Technology
Cambridge,
MA
02139
September
1987
The comments
of
John Carroll,
James
Hines, and
Don
Kleinmuntz
are
gratefully
acknowledged.
Dan
Ryu
provided
invaluable
research
assistance.

D-3919
ABSTRACT
Studies
in
the
psychology
of
individual
choice
have
identified numerous cognitive,
informational,
temporal,
and
other
limitations which bound human
rationality,
often
producing
systematic errors
and
biases in
judgment
and
choice.
Yet for
the
most
part
models
of
aggregate
phenomena
in
management
science
and
economics
have
not
adopted postulates
of
human
behavior
consistent
with
such
micro-empirical
knowledge
of
individual
decisionmaking.
One
reason
has
been
the
difficulty
of
extending
the
experimental methods used
to
study individual
decisions
to
aggregate,
dynamic
settings.
This
paper
reports
an
experiment
on
the
generation
of
macro-
dynamics
from
microstructure
in
a
common
and
important
managerial
context.
Subjects play
the
role
of
managers
in
a
simulated
inventory management
system,
the
"Beer
Distribution
Game".
The
simulated environment contains multiple
actors,
feedbacks,
nonlinearities,
and
time delays.
The
interaction
of
individual
decisions
with
the
structure
of
the
simulated
firm
produces
aggregate
dynamics
which
systematically diverge
from
optimal
behavior.
Subjects
generate
large
amplitude
oscillations
with
stable
phase
and
gain
relationships
among
the
variables.
An
anchoring
and
adjustment heuristic
for
stock
management
is
proposed
as
a
model
of
the
subject's decision
process.
The
parameters
of
the
rule
are
estimated and
the rule
is
shown
to
explain
the
subjects'
behavior
well.
Analysis
shows
the
subjects
fall
victim
to
several
'misperceptions
of
feedback'
identified
in
prior
experimental
studies
of
dynamic
decisionmaking.
Specifically,
they
fail
to
account
for
control
actions
which have
been
initiated
but
not
yet
had
their
effect. More
subtle,
subjects
are
insensitive
to
the
presence
of
feedback
from
their decisions
to
the
environment
and
attribute the
dynamics
to
exogenous
variables,
leading
their
normative
efforts away
from
the
source
of
difficulty.
The
experimental
results
are
related
to prior
tests
of
the
proposed
heuristic
and the
generality
of
the
results is
considered.
Finally implications
for
behavioral
theories
of
aggregate
social
and
economic
dynamics
are
explored.

D-3919
Economics
and
psychology,
despite
their common focus
on
human
behavior,
have
been
locked
in battle
for
much
of
the
past
century.
The battle
centers
on
the
assumptions about
decisionmaking
behavior
upon
which theories
of
choice
are
to
be
based.
At
the
risk
of
oversimplification,
the
two
positions
can
be
characterized
as
follows.
Economists favor
theories
based
on
axioms
of
rational
choice.
Decisionmaking
behavior
is
assumed
to
be
rational
and
consistent.
Agents
maximize
utility
or
profits,
and
the
information
required
to
do
so
is
either
freely
available
or
optimally
purchased. In
the
most
extreme
form,
exemplified
today
by
rational
expectations models,
agents
have
perfect models
of
the
economy and never
systematically
err.
In
contrast,
psychologists
have
arrayed
on
the
battlefield
a
formidable
host
of
experimental
results
documenting
departures
from optimal
behavior
in
a
wide variety
of
decisionmaking
tasks.
Rationality
is
bounded
by
limitations
of
information,
time,
and
cognitive capability
(Simon
1979).
Preferences
are
frequently
intransitive
and
are
shaped
by
alternate
modes
of
elicitation and
framing
(Slovic
and
Lichtenstein
1983).
Individuals
are
inconsistent
and
can
often
be
outperformed
by
simple
models
(Kleinmuntz
1985,
Hogarth
and
Makridakis
1981a,
Goldberg
1976,
Dawes
1971,
Bowman
1963).
Experiments
have
identified
numerous heuristics
commonly
used
in prediction
and
decisionmaking
and
a
wide
array
of
systematic
errors
to
which
these
heuristics
are
prone
(Tversky
and Kahneman
1974,
Kahneman, Slovic,
&
Tversky
1982,
Hogarth
and Makridakis
1981b).
The
broad
gulf
between the
perspectives
elicits diverse
reactions.
Zeckhauser
(1986)
argues
that
the
debate
has
many
of
the
properties
of
a
Kuhnian paradigm
conflict: each
side
can
score
points
on
their own
court
at
will,
but few
on
either
side
are
convinced
to
change. Others,
notably
Leontief
(1971),
Phelps-Brown
(1972)
and
Simon
(1984)
call
for
renewed
empirical
investigation
designed
to
"secure
new
kinds
of
data
at
the
micro
level,
data
that
will
provide
direct
evidence
about
the
behavior
of
economic
agents
and
the
ways
in
which
they
go
about
making
their
decisions"
(Simon
1984,
40).
Much
of
the
empirical
work
in
experimental
economics
and
the
psychology
of
choice has
generated
just
such
microlevel data
(Einhorn
and Hogarth
1981,
Plott
1986,
Smith
1986).
But
the
1

D-3919
focus
of
much research
in
behavioral
decision
theory
on individual
behavior
in
static and
discrete
tasks has
limited
the
penetration
of
psychological
perspectives
in theories
of
aggregate
dynamics
such
as the
behavior
of
markets,
firms,
and
other
economic
systems.
In a
1981
review
Hogarth
laments
the
"insufficient
attention"
paid
"to
the
effects
of
feedback between
organism
and
environment."
By
feedback
is meant not merely
outcome
feedback
but
changes
in the
environment,
in
the
conditions
of
choice,
which
are
caused,
directly and
indirectly,
by
a
subject's
past
actions.
For
example,
a
firm's decision
to
increase
production
feeds
back through
the
market
to
influence
the price
of
goods,
profits,
and
demand; greater
output
may
tighten
the
markets
for
labor
and materials;
competitors may react
-
all
influencing future production
decisions.
Such
multiple feedbacks
are
the
norm rather than the
exception
in
real
problems
of
choice.
As
a
result
it
has
been
difficult
for behavioral
decision theory
to
make
much headway in analyzing the
dynamics
of
aggregate
organizations
such
as a
firm
or
industry.
Coleman (1986) argues
that
the greatest
progress
in
bridging
the
gulf
lies
in
understanding
the
"apparatus
for
moving
from
the
level
of
the
individu.
actor
to
the
behavior
of
the
system,"
that
is,
the
generation
of
macrobehavior from
microstructure.
This
paper
applies
the
experimental
methods
used
so
effectively
in
the study
of
individual
behavior
to the
generation
of
macrodynamics
from
microstructure
in a
common and
important
managerial context.
In the
experiment
subjects
play the role
of
managers
in
a
simulated
industrial
production
and distribution
system, the
"Beer
Distribution
Game".
The
decisionmaking
task is
straightforward:
subjects
seek
to
minimize
total costs
by managing
their
inventories
appropriately
in
the
face
of
uncertain
demand.
But
the
simulated environment
is
rich,
containing multiple
actors,
feedbacks,
nonlinearities, and
time delays.
The
interaction
of
individual
decisions with
the
structure
of
the
simulated
firm
produces
aggregate
dynamics
which
diverge
significantly
and
systematically
from optimal
behavior. Subjects generate
large
amplitude
oscillations
with
stable
phase and
gain
relationships
among
the
variables.
An
anchoring and
adjustment
heuristic
for
stock
management
is
proposed
as
a
model
of
the
subject's
decision process.
The
parameters
of
the
rule
are
estimated and
the
rule
is
shown
to
explain
the
subjects'
behavior well.
Analysis
of
the
results
2

D-3919
shows
the
subjects
of
the
experiment
fall
victim
to several
'misperceptions
of
feedback.'
Specifically,
subjects failed
to
account
for
control actions which
had
been
initiated
but
not
yet
had
their
effect.
Most
important,
subjects
were
insensitive
to
the
presence
of
feedback
from
their
decisions
to the
environment.
The majority
attribute
the
dynamics
to
external
events,
when
in
fact
the
dynamics
they
experience
are
internally
generated
by
their own
actions.
These
misperceptions
are
shown
to
be
responsible
for
the
poor
performance
of
the
subjects.
Further,
the
subjects'
open-
loop
mental
model,
in
which
dynamics
arise
from
exogenous
forces,
is
hypothesized
to
hinder
learning
and
retard evolution
towards
greater
efficiency.
The
experimental
results
are
related
to
prior
tests
of
the
proposed
heuristic
(Sterman
1987a,
1987b)
and
the
generality
of
the
results
is
considered.
It
is
shown
that the
same
regularities
evident
in
the
subjects'
behavior appear
in
real-world
production-distribution
systems.
Finally
implications
for
behavioral
theories
of
aggregate
social
and
economic
dynamics
are
explored.
The
Stock
Management
Problem
One
of
the
tm
rst
common
dynamic
decisionmaking
tasks
is
the
regulation
of
a
stock
or
system
state.
In
such
a
problem,
the
manager
seeks
to
maintain
a
quantity
at
a
particular
target
level,
or
at least within
an
acceptable
range.
Typically
the
stock cannot
be
controlled
directly
but
rather
is
influenced
by
altering
the
rates
of
flow which
accumulate
into
and
out
of
the
stock.
The
manager
must
set
the
inflow
rate
so
as
to
compensate
for
losses
from
the
stock
and
to
counteract
disturbances
which
push
the stock
away
from
its
desired
value.
Frequently
there
are
lags
between
the
initiation
of
a
control
action
and
its
effect
on
the
stock,
and/or
lags
between
a
change
in the
stock
and
the
perception
of
that
change by
the
decisionmaker.
The
duration
of
these
lags
may
vary
and
may
be
influenced by
the
manager's
own
actions.
Stock
management
problems
occur
at
many levels
of
aggregation
from
the
micro to
the
macro.
At
the
level
of
a
firm,
managers
must
order
parts and raw materials
so
as
to
maintain
inventories
sufficient
for
production
to
proceed
at
the
desired
rate,
yet prevent
costly inventories
from
piling
up.
They
must
adjust
for
variations
in the
usage and
wastage
of
these
materials
and for
changes
in
their
delivery
delays.
At
the
level
of
the
individual,
people
regulate
the
temperature
of
3

D-3919
the
water
in
their
morning
shower,
guide
their
cars
down
the
highway,
and
manage
their
checking
account balances.
At
the
macroeconomic
level,
the Federal
Reserve seeks
to manage
the
stock
of
money
so as
to
provide
sufficient credit
for
economic
growth
while avoiding
inflation,
compensating
for
variations
in
credit
demand, budget deficits,
and
international
capital
flows.
The
generic
stock
management
control
problem
may
be
divided
into two
parts:
(i)
the stock
and
flow
structure
of
the
system; and
(ii)
the
decision rule used
by
the
manager
(figure
1).
Considering
first
the
stock
and
flow
structure,
the
stock
of
interest
S
is
the
accumulation
of
the
acquisition
rate
A less
the
loss rate
L:
S
t
(At
-
L)dt
+
St
0
(1)
Losses from
the
stock
must
depend
on
the stock
itself,
and may
also
depend
on
other
endogenous
variables
X
and
exogenous variables
U:2
Lt
=
fL(St,Xt,Ut).
(2)
The
acquisition
rate
will
depend
on the
supply
line
SL
of
units
which
have
been
ordered
but
not
yet
received,
and
the
average
acquisition
lag
.
In
general,
.
may
be
a
function
of
the
supply
line
itself
and
the
other
endogenous
and
exogenous
variables:
At
=
fA(SLt,At).
(3)
The
supply
line
is
simply
the
accumulation
of
the
orders
which
have
been
placed
O
less those
which
have
been delivered:
SLt
=
( -
A)d
+
SLt
0
(4)
The
structure
represented
by
figure
1
and
eq.
(1)-(4)
is
quite
general.
There is no
presumption
that
the
functions governing
losses
and
the acquisition lag
are
linear.
There
may
be
arbitrarily
complex
feedbacks
among
the
endogenous
variables,
and
the
system
may
be
influenced
by
a
number
of
exogenous
forces,
both
systematic
and
stochastic.
Table
1
maps
common examples
into
the
generic
form.
In each
case, the
manager's task
is
to
choose the
order
rate
over
time
so
as
to
keep
the
stock close
to a
target.
3
It
is
interesting
to
note that
the characteristic
behavior
modes
of
many
of
these systems
include
oscillation
and
instability.
4

D-3919
There
are
two
extreme
approaches
to
modeling
the
decision
process used
to
determine
orders.
At
one
extreme, one
may
assume
that
the
manager
chooses
the
path
of
orders optimally
with
respect
to
some
objective function.
At
the
other
extreme, one may assume
the
decisionmaker
is
random,
i.e.
that
there
is
no
control
at
all.
The
model proposed here
is
an
intermediate
one.
It
assumes
that
managers
are
unable
to
optimize and instead
utilize
a
heuristic
which is
locally
rational.
The
proposed
heuristic thus falls
firmly
in
the
tradition
of
bounded
rationality
as
developed
by
Simon
(1982),
Cyert
and
March
(1963),
and
others.
Cognitive
limitations
are
recognized,
as
are
information
limitations
caused by
organizational structures
such
as
task
factoring
and
subgoals.
Local
rationality
in
the
context
of
simulation models
is
discussed
by Morecroft
1983,
1985
and Sterman
1985, 1987a.
The
proposed
decision rule thus
utilizes
information locally available
to
the decisionmaker,
and
does
not
presume
the
manager
has
global
knowledge
of
the
structure
of
the system.
The
generic
decision
rule
recognizes
three
motives
for
ordering:
Order enough
to
(1)
replace expected
losses from
the
stock,
(2)
reduce
the
discrepancy
between
the
desired
and
actual
stock, and
(3)
maintain
an
adequate
supply
line
of
unfilled
orders.
1.
Replacement
of
losses.
The
replacement
motive is
straightforward.
In
equilibrium,
when
the
desired
and actual
stock
are equal, the
manager
must
continue to
order
enough
to
replace
ongoing
losses. Losses
may
arise
from
usage
(as
in
a
raw
material
inventory)
or
decay
(as
in
the
depreciation
of
plant
and
equipment).
Failure to
replace
losses
would
cause
the
stock to
fall
below
the
desired level, creating
steady-state
error.
Accurate forecasts
of
losses
allow replacement
alone
to
maintain
the
stock
close
to
its
desired
value.
2.
Stock
adjustment.
The
possibility
of
forecasting
errors
or
changes
in the
desired
stock
demands
a
mechanism
to
adjust
orders
above
or
below replacement. Orders
to reduce
the
discrepancy between
the
desired and
actual
stock
form
a
negative
feedback
loop which regulates
the
stock
(shown
in
the
bottom
part
of
figure
1).
Any
rule
which
fails to
compensate
for
discrepancies
between
the
desired and
actual
stock
fails
to
control
the
stock
at
all.
Such
a
rule
5

III
D-3919
6
could
not
respond
to
a
change
in
the
desired stock,
nor
restore
the stock
to the
desired
value
if
displaced.
The
stock
would
follow
a
random
walk
as
the
system
is
bombarded
by shocks.
3.
Supply
line adjustment.
Delays between
the
initiation
and
impact
of
control
actions
give
stock
management
systems significant inertia
and
should
be
accounted
for
by
managers
to
ensure
a
stable
response
to shocks.
The importance
of
the
supply
line
adjustment
can
be
illustrated with
two simple
examples.
Consider
first
hammering
a nail
into
a
board,
the
classic
example
used
by
Miller,
Galanter,
and
Pribram
(1960)
to
illustrate
the
use
of
feedback
in
their concept
of
the
TOTE
unit
(Test-Operate-Test-Exit)
as
a
structure
for managing
systems.
"In
a
TOTE
unit,
one
Tests
to
see
if
a
goal
is
met, Operates
to
approach
the
goal,
Tests
again,
and
Exits
from
the
loop
when
the
goal
is
reached" (Richardson
1984,
292).
The
nail-hammer
system
is
a
simple stock-management
situation
in
which
the
system
state
to
be
managed
is the
distance between
the nail
head
and
the
surface
of
the
board.
The
desired
state
is
to
have
the nail
head flush
with
the
board. The
following
decision
rule
for
hammering
will
work
well:
Routine
"Hammer"
TEST:
is nail_height>O?
if
yes,
then
OPERATE: hammer!
goto
TEST
if
no,
then EXIT.
The decision
rule
implements
a
simple
negative
feedback
loop
whose
goal
is
to reduce
the
distance
between
nail
head
and
board
to
zero.
Note
the
simplicity
of
the
feedback
system: there
are no
losses
or
external
disturbances
which influence
the
state
of
affairs
(the
nail
does
not
pull
itself
out
of
the
board),
and
there
are
no significant
time
lags
between
striking
a
blow
and the
distance
remaining,
or
between
a
change
in
the
distance
remaining and
the
perception
of
that
change.
Now
apply
the
same
logic
to
the
problem
of
ordering
dinner
in
a
restaurant.
The
desired
stock
is
a
full
stomach,
the actual
stock
is
initially
an
empty
one.
Dinner
is
ordered
in
response
to
the
discrepancy between
the
desired
and
actual
stock:
Routine
"Dine
Out"
TEST:
is
hunger>desired
hunger?
if
yes, then
OPERATE: order
dinner
goto
TEST
if
no, then EXIT.

D-3919
Using
this
rule
one
would
order
another
meal
each
time
the
waiter
passed
by
(since
the
discrepancy
between
desired
and
actual
stock
would
still
exist).
You
would
only
stop
ordering
when
the
first
dinner
was
served.
Soon
your
table
would
be
piled
high
with
redundant
dinners.
A
stock
management
heuristic
which
fails
to
measure
and
respond
to
the
supply
line
of
unfilled
orders
is
predisposed
to
instability.
4
Despite
its
importance
it
is
not
obvious
a
priori
that
people
actually
do
attend
to
the
supply
line.
In
many
stock
management
situations
the
lag
between
action
and
response
so
short
that
the
supply
line
can
be
effectively
ignored,
as
in
the
case
of
the
nail.
In
others
information
about
the
supply
line
is
not
available
or
salient,
as
in
a
decentralized
market
where
each
participant
is
unaware
of
the
plans
of
the
others.
We
might
question
the
rationality
of
the
person
who
inadvertently
orders
several
dinners
in
a
restaurant,
but
consider
cooking
dinner
at
home
on
an
electric
range.
Who
among
us
has
never
overcooked
a meal
by
failing
to
account
for
the
supply
line
of
heat
in
the
coils
of
the
range
which,
even
after
the
burner
has
been
turned
off,
continues
to
heat
the
pot?
Whether
managers
account
for
the
supply
line
is an
empirical
question
in
any
particular
situation.
Formalizing
the
Heuristic
The
following
equations
formalize
the
ordering
heuristic
proposed
above.
First,
orders
in
most
real
life
situations
must
be
nonnegative,
Ot
=
MAX(0,IOt)
(5)
where
IO0
is
the
indicated
order
rate,
the
rate
indicated
by
other
pressures.
5
The
indicated
order
rate
is
based
on
the
anchoring
and
adjustment
heuristic
(Tversky
and
Kahneman
1974).
Anchoring
and
adjustment
is
a
common
strategy
in
which
an
unknown
quantity
is
estimated
by
first
recalling
a
known
reference
point
(the
anchor)
and
then
adjusting
for
the
effects
of
other
factors
which
may
be
less
salient
or
whose
effects
are
obscure,
requiring
the
subject
to
estimate
their
effects
by
what
Kahneman
and
Tversky
(1982)
call
'mental
simulation.'
Anchoring
and
adjustment
has
been
shown
to
apply
to
a
wide
variety
of
decisionmaking
tasks
(Einhorn
and
Hogarth
1985,
Davis,
Hoch,
and
Ragsdale
1986,
Johnson
and
Schkade
1987,
Hines
7

D-3919
1987,
Lopes
1981).
Here
the
anchor
is the
expected
loss
rate
Le.
Adjustments
are
then
made
to
correct discrepancies
between
the
desired
and
actual
stock
AS,
and
between
the
desired
and
actual
supply
line
ASL:
IOt
=
Let
+
ASt
+
ASLt.
(6)
The
expected
loss
rate
may
be
formed
in
various
ways.
Common
assumptions
in
economics
and
management
science
include
static
expectations
Let =
L*
(a
constant
or equilibrium
value),
regressive
expectations
Let=
yLt-1
+
(1-y)L*,
0_y•1,
adaptive
expectations
Let
=
OLt.
+ (1
e)Let-1,
0<0<1,
and
extrapolative
expectations,
ALet
=
Ici*ALt-i,
where
A
is
the
first
difference
operator
and
ci>0.
The
adjustment
for
the
stock
AS
creates
the
chief
negative
feedback
loop which
regulates
the
stock.
The
proposed
heuristic
assumes
for
simplicity
that
the adjustment
is
linear
in
the
discrepancy
between
the
desired
stock
S*
and
the
actual
stock:
ASt
=
cs(S*t
-
St),
(7)
where
the
stock
adjustment
parameter
as
is
the
fraction
of
the
discrepancy
ordered
each
period.
The
adjustment
for
the
supply
line
is
formulated
analogously
as
ASLt
=
aSL(SL*t
-
SLt),
(8)
where
SL*
is the
desired
supply line
and
oaSL
is
the
fractional
adjustment
rate
for
the
supply
line.
The
desired
supply
line
in general
is
not
constant
but
depends
on
the
desired
throughput
*
and
the
expected
lag between
ordering
and
acquisition
of
goods:
SL*t
=
ket*(*t.
(9)
The
longer
the
expected
delay
in
acquiring goods
or
the
larger
the
throughput
desired,
the
larger
the
quantity
on
order must
be.
For
example,
if
a
retailer wishes
to
receive
1,000
widgets
per
week
from
the
supplier
and
delivery
requires
6
weeks
the
retailer
must
have
6000 widgets
on
order
to
ensure
an
uninterrupted
flow
of
deliveries.
The
adjustment
for
the
supply
line
creates
a
negative
8

D-3919
feedback
loop
which
adjusts orders
so
as
to
maintain
an
acquisition
rate
consistent
with the
desired
throughput
and
the
lag
in
acquiring
orders.
The
supply
line
adjustment
thus
avoids
overordering
(as
in
the
restaurant example) and
also
compensates
for
changes
in
the
acquisition
lag.
For
example
if
the
acquisition lag
doubled
the
supply
line
adjustment
would
induce
sufficient
additional
orders
to
restore
the
desired
throughput.
As
in the
formation
of
expected
losses,
there
are
a
variety
of
possible representations
for
ke
and
)*,
ranging
from
constants through sophisticated
forecasts.
6
In
terms
of
the
anchoring
and
adjustment
heuristic,
the
expected
loss
forms
an
easily
anticipated
and
relatively
stable
starting
point
for
the
determination
of
orders. Loss
rate
information
will
typically
be
locally available
and
highly salient to
the
decisionmaker.
Replacing
losses will
keep
the
stock
constant
at
its
current
level.
Adjustments
are
then made
in
response
to
the
adequacy
of
the
stock
and
supply
line.
No
assumption
is
made that these
adjustments
are
optimal
or
that managers
actually calculate
the
order
rate
as
given
in
equations
(5)-(9).
Rather,
pressures arising from
the
discrepancies between
desired
and
actual
stock
and
desired
and
actual
supply
line
cause
managers
to
adjust
the
order
rate above
or
below the
level
which
would
maintain
the
status
quo.
The
adjustment
parameters
as
and
asL
reflect
the
manager's
response
to
disequilibrium:
large
values indicate
aggressive
efforts
to
bring
the
stock
and
supply line
in
line
with
their
desired
levels, respectively;
small
values
indicate a
cautious approach,
or
less
sensitivity
to
discrepancies
between
desired and
actual
stocks.
The
negative
feedback
loop structure
of
the
rule
reduces
the
sensitivity
of
the
results
to
the
adjustment
parameters:
if
the initial
response to
disequilibrium
is
insufficient,
additional
adjustments
will
be
made
until
balance
is
restored;
overcorrection will
likewise ultimately
itself
be
corrected.
These
self-correcting feedbacks
allow
the heuristic
to
be
used in
any
stock
management situation
without
detailed knowledge
of
its
dynamics.
Prior
Tests
of
the
Proposed
Heuristic
The
proposed
heuristic
has
a
long
history in economics
and
management
science.
Variants
9

D-3919
10
of
the
rule have
been
used
in
models
of
aggregate
capital
investment
(e.g. Samuelson
1939,
Hall
and
Jorgenson
1967)
and production
planning
at the
level
of
the
firm
(Holt,
Modigliani,
Muth,
and
Simon
1960,
Forrester
1961),
among others.
However,
these
rules
were
not
tested
experimentally
but were
postulated
ad hoc
as
'reasonable'
or
justified
as
optimal
under
certain restricted
conditions
(e.g.
quadratic
costs).
A
recent
experiment
(Sterman
1987a,
Sterman
1987b)
tested
the
proposed
rule
in
a
macroeconomic
context.
Subjects
were
responsible
for
capital
investment
decisions
in
a
simulated
multiplier-accelerator
economy.
The
results
strongly
supported
the
proposed
rule.
The
rule
explained
an
average
of
85%
of
the
variance
of
the
subject's
decisions,
and
the
estimated
parameters
were generally
highly
significant.
The
performance
of
the subjects
was
decidedly
suboptimal.
Subjects
produced
large
amplitude
cycles
in
response
to
nonoscillatory
inputs.
The
analysis revealed
several
misperceptions
of
feedback
structure
on
the
part
of
the subjects.
In
particular,
subjects
were
insensitive
to
the
presence
of
feedback
from
their
decisions
to
the
environment,
underestimated
the
time
lag
between
action
and
response,
and
failed to
account for
control
actions
which
had
been
initiated
but not
yet
had
their
effect.
While
the
macroeconomic experiment
was
suggestive
several
issues
regarding
the
generality
of
the
results
remain.
The
experiment
was
a
one-person
game.
Would
subjects
use
a
different
heuristic
in
the
presence
of
multiple
players
and
the
possibility
for
strategic
behavior
(gaming)
thus
created?
The
simulated
economy
was
quite
simple
and
the
number
of
possible
inputs
to
the
decisions
of
the subjects
was
severely
limited.
How
would
a
more
complex
feedback
environment
with
many
information
sources
influence
stock
management
behavior?
The
"cover
story"
of
the
experiment
was
an
aggregated
macroeconomic
setting.
Would
stock
management
behavior
differ
in
a
different task
environment,
specifically
a
task
at
the
level
of
an
individual
firm?
In
short,
does
the
stock
management
heuristic
apply
to
other
situations?
Do
the
misperceptions
of
feedback
structure
identified
in
the
earlier
experiment
arise
in
other
stock
management
situations,
or
were
they
artifacts
of
the experiment?
A
Stock
Management
Experiment
The
"Beer Distribution
Game"
is
a
role-playing
simulation
of
an
industrial production
and

D-3919
distribution
system
developed
at MIT
to
introduce
students
of
management
to
the
concepts
of
economic
dynamics
and
computer
simulation.
In
use
for
nearly three decades,
the
game
has
been
played
all
over
the
world
by
thousands
of
people
ranging from
high
school students
to
chief
executive officers
and
government
officials.
The
game
is
played
on
a
board
which
portrays
in
a
simplified
fashion the
production
and
distribution
of
beer
(figure
2).
Orders
for
and
cases
of
beer
are
represented
by
markers
and
pennies which
are
physically
manipulated
by
the
players
as
the
game
proceeds.
Each
brewery
consists
of
four
sectors:
retailer,
wholesaler, distributor,
and
factory
(R,
W,
D, F).
One
person
manages
each
sector.
Customer
demand
is
represented
on
a
deck
of
cards.
Customers
demand
beer
from
the
retailer, who
ships
the
beer requested
out
of
inventory.
The retailer
in
turn
orders
beer
from
the
wholesaler,
who
ships
the
beer
requested
out
of
the
wholesaler's
inventory.
Likewise
the
wholesaler
orders
and
receives
beer
from
the
distributor,
who
in
turn
orders
and
receives
beer from
the factory.
The
factory produces
the
beer.
At
each
stage
there
are
shipping
delays
and
order
receiving
delays.
These
represent
the
time
required
to
receive,
process,
ship,
and
deliver
orders, and
as
will
be
seen
play
a
crucial
role
in
the
dynamics.
The
subjects'
objective
is
to
minimize
total company costs
over
the
length
of
the
game.
Costs
are
incurred at
each
link
of
the
distribution
chain
as
follows.
Inventory
holding
costs
are
$.50
per
case
per
week,
and stockout
costs
(costs
for having
a
backlog
of
unfilled orders)
are
$1.00
per
case
per
week.
The
decision
task
of
each
subject
is
a
clear
example
of
the
stock
management
problem.
Subjects
must
keep
their
inventory
as
low
as
possible
while
avoiding backlogs
and
satisfying
customer
demand.
Inventory
cannot
be
controlled directly
but
must
be
ordered.
The
lag
in
receiving beer
is
potentially
variable:
if
the
wholesaler
has
beer
sufficient
to
cover the
retailer's
orders
the
retailer
will
receive
the beer
desired
after
three weeks.
But
if
the
wholesaler
has
run
out,
the
retailer
must
wait
until
the
wholesaler
can
receive
additional
beer
from
the
distributor.
Only
the
factory,
the
primary
producer,
faces
a
constant delay
in
acquiring
inventory
(there
is
no
limit
to
the
production
capacity
of
the
factory).
11

D-3919
Experimental
Protocol
The
game
is
initialized
in
equilibrium.
Each
inventory
contains
12
cases
(pennies).
Initial
equilibrium
throughput
is
four
cases
per
week. Each shipping
and
production
delay
thus
contains
four
cases,
and
each
order
slip
reads
four. Customer
demand
is
initially
four
cases
per
week.
To
disturb
the
system
customer
demand
increases to
eight
cases
per
week
in
week
5
and
remains
at
that
level
thereafter
(figure
3).
The
step
input
is
used rather
than,
say,
a
more
realistic pattern
with
seasonality,
trends,
or
noise
to
simplify
the
analysis. The
step
creates
a
disequilibrium
disturbance
to
which
the
subjects
must
react, while
facilitating subsequent
analysis.
A
typical
session
would involve
from
three
to
eight teams
of
four
players.
Subjects
are
randomly
assigned
roles
as
retailer,
wholesaler,
etc.
After
description
of
the
rAoduction
and
distribution
system,
each
team
briefly
confers
and
selects
a
name
for
their
brewery.
The
names
are
written
on
the
blackboard.
Each
person
is
then asked
to
place
$1
in
a
kitty
to
be
wagered
against
the
other teams.
7
The
kitty
goes
to
the
team
with
the
lowest
total
costs
at
the
end
of
the
game,
winner
take
all.
The cost
function
is
explained
and
written
on
the
blackboard,
and
the
prohibition
against
communicating
with
teammates
or
other
teams
is
announced.
The
game leader
then
explains
the
steps
of
the
game
(figure
2).
The
first
four
weeks
of
play
are
used
to
familiarize
the
subjects
with
the
mechanics
of
filling
orders,
recording
inventory,
etc.
During
this time
customer
demand
remains
constant,
and
each
player
is
directed
to
order
four
cases,
thus
keeping
the system
in
equilibrium.
Beginning
in
week four
the
players
are
allowed
to
order
any nonnegative
quantity
they
wish.
During
the
briefing
as
well
as
during
play
questions
concerning rules,
procedures,
or
interpretation
are answered;
questions concerning
strategy
or
customer
demand
are
not.
During
play
the
game
leader
calls
out
the
steps
and
writes the
current
week
on
the
blackboard
to
keep
each
player
and
team
in
step.
Occasionally
players
become
confused
and
the
facilitators
will
stop
play until
the
problem
is
corrected.
The
subjects
are
told
the
game
will
run
for
fifty
simulated
weeks,
but
play
is
actually
halted
after about 36
weeks,
thus
avoiding horizon
effects.
Typically
the game
is
introduced
and
played
in 90 minutes,
followed
by
a
debriefing
session.
12

D-3919
Information
availability
The
game
is
designed
so
that
each
subject faces
severe
information
limitations. Customer
demand
is
not known
to
any
of
the subjects
in
advance.
Each
week,
the
retailer
examines
the
top
card
on
the
customer
order
deck,
fills those
orders,
and discards
the
card,
face
down.
Thus
retailers
are
the
only
subjects with direct
knowledge
of
customer
demand. Similarly,
each
person
places
their
order
slips face
down
in
the
'orders
placed'
box.
Thus
each
knows only
the
orders
of
their
own customer, and
these only after
a
delay
of
one
week.
Subjects
have
good
local
information.
Each
maintains
a
record
sheet
which includes
their
inventory
or
backlog and orders placed
with their supplier
for
each week.
However,
subjects
are
directed not
to
communicate
with
other
players, either
across
or
within
a
game.
Even
though
the
objective
of
each
brewery
is to
minimize
total costs,
there
is no
process
for
the
players to
coordinate
their
decisions
or
jointly
plan
strategy.
As
in
many
real
situations
the
problem
of
global
optimization
is
factored into
subgoals which
are
distributed
throughout
the
organization.
The
players
are,
of
course,
sitting
next
to
one
another,
so
a
certain
amount
of
crosstalk
and
signalling
is
unavoidable. Each
can
readily look
up
and down
the
board and
see
how
large
the
inventories
of
beer
are
at
the
other
stations
thus
gleaning
information potentially
useful in ordering.
Game play
is
usually
quite lively and
the
players'
outbursts
may
also
convey information.
Thus
in contrast
to
the
earlier
experiment
there
are
numerous
sources
of
information
which
are
potentially
relevant
and
available
to
the
subjects
to
assist
them
in
making ordering
decisions.
The
sample
The
game has been
played
hundreds
of
times
with
a
wide range
of
people
in
many
nations.
The
results
reported
here
were
drawn
from
four
dozen
games
(192
subjects)
collected
over
a
period
of
four
years.
Since
the
records
are
kept
manually by
each
player
there
are
occasional
accounting
errors.
A
computer
model
of
the
game
was used
to
test
the
records
for
consistency.
Trials
in
which there
were
errors
of
more
than
a
few
cases
per
week
for
more
than
a
few
weeks
in
any
of
the
four
sectors
were
discarded
from further
analysis.
Eleven games
were
retained,
thus
providing
44
subjects.
8
That
sample
consists
of
undergraduate, MBA,
and
Ph.D.
students
at
MITs
Sloan
13

D-3919
School
of
Management,
executives
from
a
variety
of
firms
participating
in
short
courses
on
computer
simulation,
and
senior
executives
of
a
major
computer
firm.
Results
Comparison
to optimal
behavior
The complexity
of
the
system
(it
is
a
19th
order
nonlinear
difference
equation)
renders
calculation
of
the
optimal
behavior
intractable.
However,
a
benchmark
for
evaluating
the
performance
of
the
subjects
may
be
obtained
through
computer
simulation. As
implemented
below,
the
proposed
decision
rule
involves
four
parameters.
The
parameters
which produce
the
minimum
total
costs
were calculated
by
simulation
of
the
game
over
the
plausible parameter
space.
9
The
benchmark
costs
were
computed
subject
to
the
same
information
limitations
faced
by
the
subjects.
The
minimum
costs
produced
by
the
decision
rule
thus
provide
an
upper
bound
for
minimum
costs.
The
benchmark
costs
are
shown
in
table
2
compared
to
the
actual
costs
for
the
eleven
trials.
The
average
team
cost
is
ten
times greater
than
the
benchmark.
The individual
sectors
exceed
the
benchmark
costs
by
similar
ratios.
The differences
between
actual
and
benchmark
costs
are
highly
significant.
The
subjects
are
clearly
not
producing
behavior
consistent
with
optimal
management
of
the
distribution
system.
Behavioral
Regularities
More interesting
is the
character
of
the
departures
from
optimality.
Are
the
subjects
behaving
in
similar
ways?
Do
their
errors
arise from
common
sources?
Figure
4
shows
several
typical
trials;
table
3
summarizes
key
indicators
of
the
behavior
for
the
full
sample.
Examination
of
the
subjects'
pattern
of
ordering reveals
several
regularities.
1.
Oscillation:
The
trials
are
all
characterized
by
instability
and
oscillation.
The
pattern
of
orders
and
of
inventory
is
dominated
by
a large
amplitude
fluctuation
with
an
average
period
of
21
weeks.
Close
examination
of
the
behavior
shows
that
in
virtually
all
cases,
the
inventory
levels
of
the
retailer
decline,
followed
in
sequence
by
a decline
in
the
inventory
of
the
wholesaler,
distributor,
and
factory.
As
inventory
falls
subjects
tend
to increase
their
orders.
'Effective
inventory'
is
defined
as
inventory
less
any
backlog
of
unfilled orders
and
generally
become
14

D-3919
significantly
negative,
indicating
the sectors
have
backlogs.
The
maximum
backlog
for
the
full
sample
averages
35
cases,
and
generally
occurs
between weeks
20
and
25.
As additional
product
is
brewed
and
shipped
there
is
a
surge
in
inventory
levels, and
inventory in
many
cases
substantially
overshoots
its
initial levels.
The
average
peak
inventory
level
is
40
cases,
and
occurs
between
weeks
25
and
30.
Orders fall
off
rapidly
as
excess
inventory
builds
up.
Recalling
that
the
cost
function
penalizes
both
backlogs
and
excess
inventory
it
is
clear
that
the
large fluctuations
of
inventory
over the
cycle
(the
average
excursion
of
inventory
is
75
cases)
are
responsible
for
the
huge
costs
compared
to
the
benchmark
response.
2.
Amplification:
The
amplitude
of
the
excursion
in
orders increases
steadily
as
one
moves
from
customer
to
retailer
to
factory. The
peak
order
rate
at
the
factory
level
is on
average
more
than
double
the
peak
order
rate
generated
at the
retail
level.
Likewise
the
variance
of
factory
orders
averages
5.5
times
the
variance
of
retail
orders.
Customer
orders
increase from
4
to
8
cases
per
week;
by
the
time
the
disturbance
has
propagated
to
the
factory the
order
rate
averages
a
peak
of
32
cases,
an
amplification
factor
of
700%.10
Amplification
in
inventory excursions
is
also
apparent.
1
1
3.
Phase
lag:
The
peak
order
rate
tends
to
occur
later
as
one
moves
from
the
retailer
to
the
factory.
Customer
orders
increase
from
4
to
8
in
week
5.
Retailer
orders
do
not
reach
their
peak
until
week
16,
on
average.
Factory
orders
lag
behind
still
further,
peaking
at week
20 on
average.
The
phase
lag
is
not
surprising
since
the
disturbance
in
customer
orders
must
propagate
through
decisionmaking
and
order
delays
from
retailer
to
wholesaler
and
so
on.
1
2
Thus
while
the
behavior
of
the
subjects
is
plainly
far
from
optimal,
their
behavior
exhibits
significant
regularities, suggesting
the subjects
used
similar
heuristics
to
determine
their
orders.
The
pervasiveness
and
qualitative
similarity
of
the
oscillations
is
particularly
noteworthy
since
the
customer order
rate,
the
only
external
disturbance,
does
not
oscillate
and is
in
fact
virtually
constant.
The
oscillation
is
endogenously
produced
by
the
interaction
of
the
subjects' decisions
with the
feedback
structure
of
the
system.
Explaining
the
origin
of
the
cycle
and
the
determinants
15

D-3919
16
of
its
period
and
amplitude
are
major
tasks
for
any
theory
of
dynamic decisionmaking behavior.
Testing
the
Theory
To
test
the
model
the
proposed
decision
rule
must
be adapted
to
the
particular
situation
in
the
beer
game and
cast
in
a
form
suitable
for
estimation
of
the parameters.
In
the context
of
the
beer
game, the stock
S
corresponds
to
the
inventory
of
the
subject
and
the
supply line
SL
to
the
sum
of
orders
in
the
mail
delays,
the
backlog
of
the
subject's
supplier
(if
any),
and
the
beer
in
the
shipping
delays.
The
loss
rate
is
the
rate
at
which
each
subject
receives
orders.
To
test the
rule
it
is
necessary
to specify
expected
losses
Le,
the
desired
stock
S*,
and
the
desired
supply
line
SL*.
Expected
losses
from
the
stock
are
the
rate
at
which
each
subject expects
their immediate
customer
to place orders,
that
is, the
retailer's
forecast
of
the
customer
order
rate,
the
factory's
forecast
of
the
distributor's
order
rate,
etc.
Adaptive
expectations
are
postulated.
Adaptive
expectations
are
widely
used
in
simulation
modeling
of
corporate
and
economic
systems,
they
are
often
a
good
model
of
the
evolution
of
expectations
in
the
aggregate
(Sterman
1987c,
Frankel
and
Froot
1987),
and
they
are
one
of
the
simplest
formulations
for
expectations
flexible
enough
to
adapt
to
a
nonstationary
process.
Each
subject
is
free
to
determine
the
desired
level
of
inventory
S*
according
to
their
own
beliefs about
how
to
minimize
costs.
Theory
suggests
the
target
inventory
level
should
be
chosen
so
as
to
minimize
expected
costs
given
the
cost
function
and
the
expected
variability
of
deliveries
and
incoming
orders.
However,
the subjects
do
not
have
the
time
nor
information
to
determine
an
optimal
inventory
level.
The
asymmetry
of
the
cost
function
suggests
desired
inventory
should
be
nonnegative.
One
might
further
hypothesize
that
in
the
absence
of
a
procedure
to
calculate
optimal
inventory levels
the subjects'
choice
of
S*
would
be
strongly
anchored
to
the
initial
level
of
12
units.
This
hypothesis
is
tested
below.
In
general
the desired
supply
line
is
variable
and
depends
on
the
anticipated
delay
in
receiving
orders.
However,
subjects
have
no
direct
way
to
determine
the
current
lag
in
receiving
orders.
That
lag
is
never
less
than
four weeks
but may
be
longer
if
the supplier
has
insufficient
inventory
to fill
incoming
orders.
It
is
therefore
assumed
that
the
desired
supply
line
SL* is
III

D-3919
constant,
and
thus
SL*
becomes
a
parameter
to
be
estimated.
The
generic
decision
rule
of
eq.
(5-9)
then
becomes:
Ot
=
MAX(0,IOt),
(10)
IOt
=
Let
+
ASt
+
ASLt,
(11)
Let
=
OLt-1
+ (1-O)Let-1,
0<0<1,
(12)
ASt
=
as(S*
-
St),
(13)
ASLt =
asL(SL*
-
SLt),
(14)
where
S*
and SL*
are
constants.
Defining
[
=
asL/as
and
S'=
S*
+
SL*
and
collecting
terms
yields
IOt
=
Let
+
as(S'
-
St
- SLt).
(15)
Note
that
since
S*,
SL*,
aSL
and
as
are
all
20,
S
'0.
Further,
it
is
unlikely
that
subjects
will
place
more
emphasis
on
the
supply
line
than
on
the
inventory
itself:
the supply
line
does
not
directly
enter
the
cost
function
nor
is it as
salient
as
the inventory.
Therefore it
is
probable that
aSL
<
as,
meaning
0<3<1.
Thus
can
be
interpreted
as
the
fraction
of
the
supply
line
taken
into
account
by
the
subjects.
If
P
=
1,
the
subjects
fully
recognize
the
supply
line
and
do
not
double
order.
If
[
=
0,
orders
placed
are
forgotten
until
they
arrive,
encouraging
overordering
and
instability,
as in
the
restaurant
example.
The decision
rule
contains
four
parameters
to
be
estimated
(0,
as,
S',
and
)
and
is
nonlinear.
To
estimate the
parameters
an
additive
disturbance term is
assumed:
Ot
= MAX(O,IOt+et),
et-
N(0,a
2
).
(16)
The
disturbances
e
are
assumed
to
be
independent,
identical,
and normally
distributed.
In this
case,
maximum
likelihood
estimates
of
the
parameters
may be
found
by
minimizing
the
sum
of
the
17

D-3919
18
squared
errors
.et
2
.
Est.
:S
for
each
sector
of
each
trial
were
found
by
grid
search
of
the
parameter
space
subject
to
the
constraints
0<01
and
as,
S',
3
20.13
Independence
and
normality
of
the
errors
implies
the
estimated
parameters
of
such
nonlinear
models
are
consistent
and
asymptotically
efficient,
and
the
usual
measures
of
significance
such
as
the
t-test
are
asymptotically
valid
(Judge
et
al.
1980).14
Comparing
simulated
and
experimental
results
The
estimated
parameters
are
displayed
in
table
4
together
with
R
2
and
root
mean
square
errors
between
estimated
and
actual
orders.
The
mean
R
2
is
71%
(median
76%);
R
2
is
less
than
50%
for
only
6
of
44
subjects.
A
large
majority
of
the
estimated
parameters
are
significant.
Only
7
values
of
as,
4
values
of
S',
and
15
values
of
are
not
significantly
different
from
zero.
Of
course
any
of
these
parameters
could
legitimately
take
on
a
value
of
zero.
Zero
is in
fact
the
estimated
value
for
14
of
the
26
insignificant
estimates,
and
the
standard
errors
of
these
estimates
are
smaller,
on
average,
than
those
for
the
rest
of
the
sample.
However,
two-thirds
of
the
estimated
values
of
0
are
not
significant.
It
appears
that
there
is
insufficient
variation
in
incoming
orders
to
determine
if
the
expectation
formation
process
is
misspecified
for
these
subjects.
15
As
a
further
test
of
the
proposed
decision
rule
the
game
was
simulated
using
the
rule
as
specified
in
eq.
(10-15)
and
the
estimated
parameters
for
each
sector
in
each
trial.
Note
that
the
costs
incurred
by
a
sector
depend
not
only
on
the
behavior
of
that
sector
but
on
all
the
other
sectors
in
the
distribution
chain,
and
thus
on the
vectors
of
parameters
0,
as,
S',
and
3
for
the
entire
chain.
If
the
rule
were
perfect,
simulated
and
actual
costs
would
be
equal,
and
regression
of
the
simulated
costs
on
the
actual
costs
would
produce
a
slope
of
unity
(t-statistic
in
parentheses):
Costsij
=
1.11*Simulated
Costs(0j,asj,S'j,1j)i;
i=R,W,D,F;
j=l,...,11
(17)
(16.7)
III

D-3919
N=44,
R
2
=
.40.
The
slope
is
less
than
two
standard
errors
from
unity
and
highly
significant,
indicating
an excellent
correspondence between
the
actual
and
simulated costs
using
the
estimated
parameters.
There
is,
however,
a
modest
bootstrapping
effect.
Replacing
the
subjects
with
the
model
of
their behavior improves
performance. The average
improvement
is
about
5%
of
actual
costs.
The
improvement
arises
from
the
consistency
of
the
decision rule
compared
to
the
subjects,
who
often
introduced
high-frequency
noise
by
changing
orders
from week
to
week
(figure
4).
The
magnitude
of
the
bootstrapping
effect
is
comparable
to that
found in
many
prior
studies
of
bootstrapping (reviewed
in
Camerer
1981)
even
though these
studies
involved linear models
of
clinical
judgments
where
there were
in
general
no
significant
feedbacks
or
dynamics.
The
improvement
is
consistent
as
well
with
the
results
of
Bowman's
(1963)
application
of
similar rules
to
inventory
management
data for
actual
firms.
The
results
strongly
support
the
hypothesis
that
subjects
use
the
proposed
anchoring
and
adjustment
heuristic
to
manage
their inventories.
Approximately
three
quarters
of
the
variance
in
__.ual
orders
is
explained
by
the
proposed
rule,
and
the vast
majority
of
the estimated parameters
are
highly
significant. Several
issues may
now be addressed.
What
do
the
estimated
parameters
reveal
about
the
causes
of
the
severely dysfunctional
performance
of
the
subjects?
To
what
causes
do
subjects
attribute the
dynamics
they experience,
and
how
do
these
attributions affect
the
potential
for
learning?
And
finally,
if
the
rule
produces
such
poor
results,
why
is
it
used?
Misperceptions
of
Feedback
The
results
reveal
several
distinct misperceptions
of
the
feedback
structure
of
the
simulated
environment. These misperceptions
are
directly
responsible
for
the
poor
performance
of
the
subjects.
Anchoring
in
the
choice
of
the
desired
stock
The
complexity
of
the
system
and
limited
time
for
decisions
make
calculation
of
optimal
inventory
levels
infeasible.
It
was therefore
hypothesized
that
the
choice
of
the
desired
stock
S*
would
be strongly
anchored
to
the
initial
level
of
12
units.
Though
S*
is
not
estimated
directly,
the
19

D-3919
results
do
allow
S*
to
be
imputed.
Recalling
that
S'=S*+3SL*
it
is
clear that
S*
and
SL*
can
be
estimated
by
regression
of
the
estimated values
of
[3
on
S'.
The
regression
yields
the
expected
relationship:
S'=
13.9
+
*8.4,
N=40,
R2=.09.
(18)
(6.9)
(2.8)
The
low
R2
indicates,
as
one
might
expect, that
individual differences
in
S*
and
SL*
account
for
most
of
the
variance
in
S'.
The
estimated
value
of
SL*,
significant
at
the
10%
level,
is
considered
below.
The estimated
value
of
the
desired
stock
S*,
that
is
the
value
of
S'when
f3
=
0,
is
not
significantly
different
from
the
initial inventory
level
of
12
units.
As
hypothesized,
in
the absence
of
a
calculus
to
determine
optimal
inventory levels,
subjects'
choice
of
desired
inventory
levels
appears to
be
strongly
anchored
to the
initial
inventory.
Misperception
of
time
lags
To
understand
the
source and
magnitude
of
the
oscillation
it
is
necessary
to
consider
the
adjustment parameters
as
and
a
which
govern
the
response to
disequilibrium.
The
optimal
adjustment parameters
for
the
decision
rule,
as
determined
by simulation,
are
=
1
and
as
=
1:
the
supply
line
is
fully
accounted
for
and
the
discrepancy
in
the
stock
is corrected
each
period
in
full.
Intuitively,
a
full
accounting for
the
supply
line
prevents
overordering,
as
in
the
restaurant
example.
And
when
the
supply
line
is
fully
accounted
for,
the
speed
of
adjustment
can
be
increased
without
destabilizing
the
system.
Inspection
of
the
results
shows that
most
subjects
failed
to
account
adequately for
the
supply
line.
The
evidence
takes
two
forms.
First,
the
small
estimate
of
SL*
found
in
equation
(18)
indicates
that
the
subjects'
underestimated
the
lag
between
placing
and receiving
orders.
To
ensure
an
appropriate
acquisition rate
the supply
line
must
be
proportional
to
the
lag
in
acquiring
beer
(eq.
(9)).
The
acquisition
lag
is
never
less
than
4
weeks.
Even
if
subjects'
expectations
of
demand
(and
thus
desired
throughput)
remained
at the
initial
level
of
4,
the
required
supply
line
20

D-3919
would
be
16
cases,
far
greater
than the
estimated
value
of
8.4
cases.
Thus
it
appears
that
subjects
failed
to
allow
for
sufficient
beer
in
the
pipeline
to
achieve
their
desired
inventory
level.
More significant
is
the extent
to which
subjects
responded to
the
supply
line
itself,
as
indicated
by
the
estimated
values
of
1.
The
average
value
of
is
just
.34;
only
five subjects
(11%)
accounted
for
more
than
two-thirds
of
the
supply
line.
The
result
is
overordering
and
instability.
For
example,
consider
the
Grizzly
factory
(figure
4;
R2=.75).
As
in
most
of
the
trials,
the
distributor
begins
to
place
substantially
higher
orders
around
week
15.
These
orders
deplete
the
factory's inventory
and build
up
a
backlog
of
unfilled
orders,
encouraging
the factory
to
restore
inventory
by
ordering
additional units
of
beer.
However,
as
for
the
Grizzly factory
is
.65
while
3
=
0,
meaning
the
subject
ordered
two-thirds
of
any
discrepancy
between
S'and
S
each
period,
and
completely
ignored the
orders in
the
supply
line.
Since
the
factory's supply
line
is
three
weeks
long, the subject orders
two-thirds
of
the
required amount
for
three
successive
weeks
before
receiving
any
of
these
new
orders.
After
three
weeks
inventory
rises
toward
the
desired
level
and
the subject cuts
orders
back.
But
the
orders
already
in
the
pipeline
continue
to
arrive,
ultimately
swelling
inventory above
desired
levels
by
nearly
a
factor
of
three.
Thus
factory
orders
reach
a
peak
of
50
units
in
weeks
18
and
19,
coincident
with the
largest backlog.
Factory
inventory
subsequently
reaches
a
peak
of
69
units,
well
in
excess
of
reasonable coverage
of
either
equilibrium
or
actual
distributor demand.
Because
the
Grizzly
distributor also
acquired
excess
inventory
(the
distributor's
1.25),
distributor
orders
plummet
to
an
average
of
just
5
cases
per
week
after
week
25,
and
the
factory
ends
the
trial
with
high
inventory,
no
way
to
unload
it,
and
considerable
frustration.
Note
that
the
factory's
ordering policy
significantly
amplifies
the
distributor's
orders:
distributor
orders
rise
from
4
to 20 units;
the
factory
responds
by raising
orders
from
4 to
50
units,
an
amplification
factor
of
290%.
By
ignoring
the
supply
line
the
factory's ordering
policy
is
highly destabilizing.
In
contrast consider
the
Suds factory
(figure 4,
R
2
=.95).
For
this
subject
=-1.05
while
21

III
D-3919
22
-xs=.35,
indicating
the
subject
fully
accounts
for
the
supply
line
and
seeks
to
correct
35%
of
any
discrepancy
between
S'and
S
each period.
Compared
to
Grizzly
the
Suds
distributor
is
more
extreme,
increasing
orders to
a
peak
of
50
cases
in
week
20.
Nevertheless
the
response
of
the
Suds
factory
is
more
stable
than that
of
Grizzly.
Because
the Suds
factory accounted
for
the
supply
line
orders
peak
and
fall
before
the
backlog reaches
its
maximum
since
the
subject realizes
that
sufficient orders
to
correct
the
problem
are
already
in
the
pipeline.
The
Suds factory
actually
stabilizes
the
system:
the
amplification
factor
is
85%,
meaning
the
parameters
which
characterize
the
factory
attenuate
demand
shocks
rather
than
exacerbating
them.
"Open-loop"
explanations
of
dynamics
At
the
end
of
the
game
subjects
are
debriefed.
Emotions
run
high.
The
majority
express
considerable
frustration
at
their
inability
to
control
the
system.
Many
report
feelings
of
helplessness
-
they
feel themselves
to
be
at
the
mercy
of
forces
outside
their
control.
Subjects
are
then
asked
to
sketch
their best
estimate
of
the
pattern
of
customer
demand,
that
is
the
contents
of
the
customer
order
deck.
Only
the
retailers
have
direct knowledge
of
that
demand.
Figure
5
shows
a
typical
set
of
responses.
Invariably
the
majority
of
subjects
judge
that
customer
demand
was oscillatory,
first rising
from
the
initial level
of
4
cases
per
week
to
a
peak
anywhere
from
12
to
40
cases,
and then
dropping
to
the
neighborhood
of
0
to
12
cases
per
week.
Factories
and
distributors
tend
to
draw
the
largest
excursion;
wholesalers
tend
to
draw
smaller
fluctuations.
Only
a small
fraction
suggest
that
customer
demand
was
essentially
constant.
It
may
seem
obvious
that
subjects'
judgments
of
customer
demand
reflect
their
experiences
during
the
game:
after
all,
customer
demand
in
reality
does
fluctuate.
Yet
these
beliefs
are
revealing.
Most
subjects
attribute
the
cause
of
the
dynamics
they
experienced
to
external
forces.
Most
blame
their
own
poor
performance
on
what
they
see
as
a
perverse
pattern
of
customer
demand:
the customers
increased
their
demand,
encouraging
them
to order
additional
beer,
then
pulled
the
rug
out
just
when
the
tap
began
to
flow.
Many
participants
are
quite
shocked
when
the
actual
pattern
of
customer
orders
is
revealed;
some
voice
strong
disbelief.
Few
ever
suggest
that
their own
decisions
were
the
cause
of
the
behavior
they
experienced.
Fewer
still
explain
the pattern
of
oscillation
in
terms
of
the

D-3919
feedback
structure, time delays,
or
stock
and
flow
structure
of
the
game.
The subjects
exhibit
a
strong
tendency
to
attribute
behavior
to
external
variables
which
they
believe
to
be
closely
correlated
in
time and
space with
the
phenomenon
to
be
explained.
Such
explanations
reflect
an
'open-loop'
conception
of
the
origin
of
dynamics
as
opposed
to
a
mode
of
explanation
in
which
change
is
seen as arising
from
the
endogenous
interactions
of
decisionmakers
with
their
environment
Such misperception
of
the
origins
of
dynamic
behavior
has
implications
for
the
possibilities
of
learning
from
experience. When
asked
how
they
could do
better
many
argue
that
performance
would
be
improved
through
better
forecasting
of
customer
demand. The
erroneous open-loop
attribution
of
dynamics
to
exogenous events
thus draws normative efforts
away
from
the
high
leverage
point
in
the
system
(the
stock management
policy)
and
towards efforts
to
anticipate
and
react
to
external
shocks.
While
better
forecasts
are
likely to help,
the
results
show
clearly
that the
source
of
the
dynamics
and the
ability
to
improve performance
lie
within
the
policy
individual
people use
to
manage
the
system
and
not
in
the
external
environment.
Even
a
perfect
forecast will
not
prevent
a
manager who
ignores
the
supply
line
from
overordering.
Discussion
and
Conclusions
The
experiment,
despite
its
rich
feedback
structure,
is
vastly simplified
compared
to the
real
world.
To
what
extent
do
the
experimental
conditions
and
results
apply?
This
question
has
several
components:
are
the
main features
of
the
experimental
behavior
(oscillation,
amplification, phase
lag)
observed
in
real
production-distribution
systems?
If
so,
to
what
extent
are
the
proposed
heuristic
and
specifically
the
misperceptions
of
feedback identified
in the
experiment
responsible
for
that
behavior?
How
robust
is
the
proposed
heuristic
in
the face
of
the differences
in
information
availability,
time,
and
other
factors
between
the
experiment
and
reality?
These
are
empirical
questions
which
can and should
be
investigated
at
the
micro
level
of
individual firms.
Nevertheless,
the experimental results
are
suggestive.
It
has
long
been
recognized that production-distribution
networks
in
the
real
economy
exhibit
the
three
aggregate
behaviors
generated
in
the
experiment,
i.e.
oscillation,
amplification
from
retail
to
primary
production,
and
phase
lag
(T.
Mitchell
1923,
Hansen
1951,
W.
Mitchell
I__l___*I________I_
23

D-3919
24
1971,
Zarnowitz
1973).
Figure
6
shows
detrended
data
for production
of
consumer
goods,
intermediate
goods,
and
primary
materials
in
the
U.S.
from
1947
to
1987.
Production
at
all
three
stages
fluctuates
significantly
over
the
business
cycle,
cycle
amplitude
and
coherency
grow
as
one
moves
from
retail
sales
to
materials,
and
the
expected
phase
lags
are
apparent
as
well
(table
5).
How
plausible
is
it
that managers
in
the
real economy
use
the
proposed
heuristic,
and
if
they
use
it,
fall
victim
to
the
same
misperceptions
of
feedback
which
plague
subjects
of
the
experiment?
After
all,
in
reality
managers
have
access
to
more
information
than
is
available
in the
experiment.
More
time
is
available
to
gather
intelligence
and
arrive
at
a
decision.
Decision
aids
may
be
used.
On
the
other
hand
information
in
the
real
world
is
often
out
of
date,
noisy,
contradictory
and
ambiguous.
Managers
have
far
more
demands
on
their time
and
must
make
many
additional
decisions
besides
the
quantity
of
goods
to
order.
Consultants
and
models
are
subject
to
many
of
the
same
cognitive,
informational,
and
temporal
limitations,
and
there
is
no
accepted
calculus
for
integrating
numerous
and
possibly
conflicting
positions
and
information
sources.
The
hypothesis
that
managers
in
real
stock
management
contexts
use the
proposed
anchoring
and
adjustment
heuristic
rather
than
optimizing
does
not
require
equivalence
of
the
decisionmaking
tasks
but
only
the
weaker
condition
that
in
both
cases
the
determination
of
optimal
quantities
exceeds
the
abilities
of
the
decisionmakers.
The
robustness
of
the
proposed
stock
management
heuristic
is
illuminating
here.
The
decision
rule
has
been
shown
to
be
an
excellent
model
of
behavior
in
two distinct
experimental
settings.
In
the
macroeconomic
experiment
the
dynamic
structure
of
the
system
was
rather
simple.
There
were
no
other
participants
to
consider
and
therefore
no
game-theoretic
component
to
the
decision
task.
Perfect
information
was
available
to
the
subject.
The
cost
function
was
symmetric.
There
was
no
time
limit
for
each
decision.
In
contrast,
the
beer
game
is
substantially
more
complex.
The underlying
dynamic
system
is
high
order,
has
multiple
nonlinearities,
and
involves
numerous
time
lags.
There
are
multiple
decisionmakers
whose
behavior
should
be
taken
into
account.
Local
information
is
good
and
limited
information
about the
other
sectors
is
available.
The
cost
function
is
asymmetric.
Subjects
"I1

D-3919
must
make
their decisions
under
time pressure.
Yet
the
same
heuristic
explains
decisionmaking
in
both experiments with
a high degree
of
accuracy.
In
both
cases
people appear
to
be
insensitive to
the
feedback environment,
differences
in
individual performance
are
closely related
to
differences
in
the
parameters
estimated
for
each
subject,
and
the
same
misperceptions
of
feedback
are
documented
in both.
If
the
rule is
prone
to such
major
misperceptions
and produces
such
grossly dysfunctional
performance, why
is
it
used? The virtue
of
the
rule
is
its
simplicity.
It
requires no
knowledge
of
the
feedback
structure or
general
equilibrium
of
the
system.
It
is
self-correcting
-
the feedback
structure
of
the
rule
ensures
that
forecast errors,
changes
in
the
structure
of
the
environment,
and
even
self-generated overreactions
can
eventually be
corrected.
The benchmark costs
(table
2)
show
the
rule
can,
with
reasonable
parameters,
produce
excellent
results.
As
argued
in Sterman
1987a,
the
decision
rule
works
because
it captures
the
essential
attributes
of
any
minimally
sensible
stock
management
procedure.
These
are
replacement
of
expected
losses, correction
of
discrepancies
oetween the
desired
and actual stock, and
an
accounting
for
the
supply
line
of
unfilled orders.
It
does
not
follow
from
the
generality
of
the
rule,
however,
that
it
is
so
flexible
that it
can
be
made
to
work
in
any
situation.
The
rule
is
clearly
inconsistent
with
any
decisionmaking
strategy
based
on
global
optimization
or
rational
expectations.
How plausible
is
it
that
firms
in
the
real
economy fail
to
adequately
account
for
the
supply
line?
It
is
not credible
that
individual
managers
forget
that
they
have
goods
on
order.
The
problem
in
the
real
economy is
one
of
aggregation.
There
are
many
examples
of
stock
management
situations
in
which the
aggregate
supply
line
is
distributed
among individual
competitors
and
largely
unknown
to
each.
It
is
interesting to
note
that
many
of
the
markets
most
prone
to
instability
such as
agricultural
commodities,
commercial
construction,
machine tools, electronic
components,
and
other durable
goods
are
characterized by
both
significant
delays
in
bringing
investments
to
fruition
and
imperfect
knowledge
of
the
plans,
commitments,
and pending
investments
of
the
participants
(Meadows
1970,
Hoyt
1933,
Commodity
Research
Bureau,
various
years).
Verification
of
the
supply
line
hypothesis
requires
further
empirical
work
focussed
not
only
on
the
25

D-3919
26
decision
processes
of
individual
firms
but
also
on
the
availability,
timeliness,
salience, and
perceived
accuracy
of
supply line
information.
Though
the
stock-management
task
investigated
here has
wide
applicability,
there
are
many
dynamic
decisionmaking
tasks
which cannot
be
described
by that
framework
(e.g.
price-setting
behavior).
However,
the
results
suggest
the
method
used
here
may
be
helpful
in
explaining
how
unintended
and
dysfunctional results
may
be
produced
by
apparently
reasonable decision
processes
in
diverse systems
(e.g.
Hall's
account
(1976,
1984)
of
the
Saturday
Evening
Post
and other
organizations).
Morecroft
(1985)
suggests
the
use
of
simulation
to test
the
intended
rationality
of
the
decision
rules
in
simulation
models.
The experimental
approach
used
here
allows
direct
investigation
of
the
decision processes
of
real
managers,
and
provides
a
technique
to relate
these
decision rules
to
performance. Normative
use
of
the
techniques
appears
also
to
be
a
promising
avenue
for
future
work.
16
Future
work should
apply
the
experimental method
used
here to
other
dynamic
decision
tasks
and
should
consider
the
processes
by which
the
parameters
of
the
heuristics
are
modified or
the
heuristics
themselves
revised
or replaced
by
learning
and
the
selective
pressures
of
the
market.
Tversky
and
Kahneman
(1986)
and
Hogarth
(1981)
have
stressed
ways in
which
inadequate
outcome feedback
may
hinder
learning
and efficiency.
The
results
here
suggest
that
outcome
feedback
alone
may not
be
sufficient:
by
attributing
the
source
of
change
to
external
factors
people's
mental
models
lead
them
away
from
the
true
source
of
their
poor
performance. Efforts
to
improve performance
may
therefore
have
little leverage
and
additional
experience
may
not
lead
rapidly
to
improved
mental models,
allowing
dysfunctional
performance
to persist.
These results
reinforce
and
extend
prior
work
in
dynamic
decisionmaking
(Hogarth
1981,
Kleinmuntz
1985,
Mackinnon
and
Wearing
1985,
Remus
1978).
Not
only
does
the
efficacy
and
robustness
of
particular
decision
strategies
depend
crucially
on
the
availability
and
nature
of
outcome
feedback,
but
on
the
nature
of
the
action
feedback
between
decisions
and
changes
in the
environment
which
condition
future
decisions.
The
same
heuristic
may produce
stable
behavior
in
one
setting
and
oscillation in
another
solely
as
a
function
of
the
feedback
structure
in
which
that
II]

D-3919
27
heuristic
is
embedded.
That
structure
consists
of
the
stock-and
flow
structure,
information
networks,
time
delays;
and
nonlinearities
which
characterize
the
organization.
The
magnitude
of
the
oscillations
produced
by
the
actors
despite
a
virtually
constant
external
environment
suggests
the
powerful
role
of
action
feedback
in
the
genesis
of
dynamics.
Further,
the
qualitative
behavior
of
the
different
teams
is
strikingly
similar
despite
wide
variation
in
individuals'
responses
(as
represented
by the
diverse
parameters
which
characterize
the
subjects
across
positions
and
teams).
As a
result
the aggregate
dynamics
of
an
organization
may
be
relatively
insensitive
to
the decision
processes
of
the
individual
agents,
suggesting
the
importance
in
both
descriptive
and
normative
research
of
research
methods
which
integrate
individual
decisionmaking
with
theories
of
feedback
structure
and
dynamics.
In
that spirit
the
results
show
how
experimental
methods
may
be
coupled
with
simulation
to
form
a
useful
part
of
the
"apparatus
for
moving
from
the
level
of
the
individual
actor
to
the
behavior
of
the
system,"
ultimately
yielding
testable
theories
to explain
the
endogenous
generation
of
macrobehavior
fronm
e
microstructure
of
human
systems.

D-3919
Notes
1.
See
Hogarth
and Reder
(1986)
for
a
full
exposition
of
positions
on
both
sides.
2.
For
any
real
quantity
the
loss rate
must
approach
zero
as
the
stock
is
depleted.
However,
there
is
no
presumption
in
eq.
(2)
that
the
loss
process
is
linear,
nor
that
losses
are
independent
of
the
age
distribution
of
individual
units
in
the
stock.
3.
In
particular
situations
the
choice
of
the
desired
stock
and
the
meaning
of
'close'
will
be
influenced
by
the
loss
function
perceived
by
the
manager
and the
manager's priors regarding
the
variability
of
the
environment. These
choices
are
not
in
general
separable
from
the
dynamics
of
the
system.
4.
The example
is
not
intended
to
criticize
the
TOTE methodology
but
rather
serves to
illustrate
the
importance
of
accounting
for
the
supply
line.
More general
TOTEs
could
account
for
the
delay between
ordering
and
receiving
dinner.
5.
Order
cancellations
are
sometimes
possible
and
may exceed
new
orders
in
extreme
conditions
(e.g.
the
U.S.
nuclear
power
industry
in the
1970s).
Since
cancellations
are
likely
to
be
subject
to
different costs
and
administrative
procedures
than
new
orders they
should
be
represented
separately
as
a
distinct
outflow
from
the
supply
line
rather
than
as
negative
orders.
6.
A
common
specification
in
dyn
..-
ic
models
is
Xe=X
and
D*=
Le.
7.
Protocols
for
experimental
economics
(e.g.
Smith
1982)
call
for significant monetary
rewards
geared
to
performance
in
the
task.
However
a
number
of
experiments have
shown
performance
is
not
significantly
improved
and
may be
worsened
by increases
in
reward
levels
(e.g.
Grether
and
Plott
1979,
Slovic
and
Lichtenstein
1983,
Tversky and
Kahneman
1981).
Here
subjects
wager
$1
for
a
chance
to
win
about
$4
(depending
on
the
number
of
other
teams).
Though
these
are
small
rewards they
serve
to emphasize
the
goal
of
minimum
team
costs
and appear
to have
a
powerful
motivating
effect.
8.
Analysis
showed
a
slight
tendency
for
the
trials
with
the
most
extreme
amplitude
and
highest
costs
to
be
most
prone
to
accounting
errors.
Thus
the
final
sample
of
eleven
trials is
biased
slightly
towards
those
who
understood
and performed
best
in
the game.
The
effect is modest,
however,
and
reinforces
the
conclusions
drawn
below
regarding misperceptions
of
the
feedback structure
by
the subjects.
9.
To reduce the
search space
it
was
assumed
that
all
four
sectors
were
characterized
by
the same
parameters.
The optimal
parameters
are
0=0,
as=l,
=1,
and
S'=28
(20
for
the
factory).
10.
Amplification
is
a
rough measure
of
the
closed-loop gain
of
the
system
and
is
measured
as
the
excursion
in
the
output
variable relative
to
that
of
the
input, in
this
case
A(Factory
Orders)/A(Customer
Orders)
=
(32-4)/(8-4)
= 7.
28

D-3919
11.
Note
that
the
average
period
and
excursion
of
factory
inventory
are
somewhat less
than
that
of
the
distributor
and
wholesaler.
The factory,
as
primary producer,
faces
a
shorter
and
constant
delay in
acquiring
beer
and can
therefore
correct
inventory discrepancies
faster
and
more
reliably
than the
other
sectors.
This
subtlety
in the
behavior
of
the
subjects illustrates
the
extent
to which
the
feedback
structure
of
the
task shapes
the
behavior
of
the
subjects.
12.
There
is
no apparent
lag between
retailer
and
wholesaler
or
between
distributor
and
factory,
perhaps
indicating
subjects'
use
of
information
outside
of
their
own
sector.
e.g.
the
factory
may
look
at the
distributor's
inventory
when
ordering.
13.
The
parameters
(,
as,
S',
and
)
were
estimated
to
the
nearest
.1,
.05,
1,
and
.05
units,
respectively.
The
search
was
carried
out
over
a
sufficiently
large
range
to
ensure capturing
the
global
minimum
of
Iet
2
.
The
data
and
computer
programs
are
available
from
the
author
upon
request.
14.
Note,
however,
that
the
ordering
function
does
not
contain
a
regression
constant.
Therefore
the
residuals
will
not,
in general,
satisfy
let
=
(estimated
and
actual
orders
need
not
have
a
common
mean)
and
the
conventional
R2
is
not
an
appropriate
measure
of
goodness
of
fit.
The
alternative
R2
=
r
2
is
used,
where
r
is
the
coefficient
of
correlation between
estimated
and
actual
orders
(Judge
et
al. 1980).
15.
The
expectation
adjustment
parameter
0
can
only
be
identified
if
Lt
and
Let
differ.
Since
Let
always approaches
Lt,
a
tight
estimate
of
0
requires
large
variation
in
incoming
orders
from
period
to
period.
For
a
number
of
the
sectors
and
all
the
retailers
the
variation in
incoming
orders
is
slight
(recall
that
the
retailer
faces
virtually
constant
demand).
In
fact,
the six
largest
standard
errors
for
0
are
retailers.
The hypothesis
that expectations
of
customer
demand
are
formed
adaptively
from
past
orders
cannot
therefore
be
rejected,
and
for
one
third
of
the
sample
it
is
supported.
16.
In
a
study
in
progress,
a
game
similar
to
the
beer
game
was developed
for
managers
of
an
insurance company.
The
game
focuses
on
the
claims-adjusting
division.
Like
the
beer
game,
it
appears
that
significant
underperformance
comes
about
through misperception
of
the
feedback
structure
of
the
system.
To
test
the
possibility
of
improving
actual
decisionmaking,
the
parameters
of
the
managers'
decision
rules will
be
estimated,
and
the sources
of
poor
performance
fed back
to the
managers
in
training
sessions.
It
is
hoped
that such
training
will
help managers develop
more
appropriate
heuristics
by improving
their
mental models
of
the
feedback
environment.
29

II]
D-3919
30
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-.-.-·--·--·1_11II

33

D-3919
34
Figure
1.
The
generic
stock-management
system.
U

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__1__11_1_________L·--.
-.I1 ___111^1
35
D-3919
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D-3919
Figure
3.
Customer
Orders.
Compare
against
In
week
5
customer
orders
rise
from
4
to
8
cases
per
week.
the
oscillations
in
the
subjects'
orders (figure
4).
30Jo-
25
-
20-
15-
10-
0-
O
-
I
}0
5
20
25
30
35
Figure
4a.
Key
to
experimental results
(figure 4b).
In
0
3~_B- J~
Factory
Distributor
Wholesaler
Retailer
Orders
placed
by
sector.
From
bottom
to
top,
R,
W,
D, F,
each
offset
by
15
cases/week.
Major
tick-marks=
15
cases/week.
Minor
tick-marks=5
cases/week.
Initial
orders=4
cases/week
in
all
sectors.
; O I's
20
25 o
3'5
Weeks
Effective Inventory
by
sector.
Effective
InventorytInventory-Backlog.
From
bottom
to top,
R,
W,
D.,
F,
each
offset by
40
cases.
Major
tick-marks=40
cases.
Minor
tick-marks10
cases.
Initial inventory=12
cases
in
all sectors.
Retailer
.
IS 2
2
3
.
5
X
0
I
s
20
25
30
35
Weeks
37
0
c
Factory
Distributor
Wholesaler
11--1-------
----------

38
Figure
4b.
Typical
experimental
results
Effective
Inventory
i.,,,..,.
;i
. ...
.
I....Ii.iIi
Ii
'-
M
0
'
LY-
u'-
o
Z
-
0
,,
0
LA
I
0~
,4-
Li
u'-
o
U'
.w
Lfl
U'-
0
-
L-
-
WJ
Orders
Y:-
U-
-
0-
'A
No
'A
I
.
.
I
-
C
PQ
-
10
w
-
0'
LA
U-
i
Lo
.
-
U
'
O-
D-3919
"Il
·
. .
I
I
OD
(D
~kf
l
.. .
i
. . .
I
.

D-3919
39
Table
2.
Comparison
of
experimental
and benchmark
costs.
Team
Total
Mean
(N=
11)
Benchmark
Ratio
t-statistic:
Ho:
Mean cost=
Benchmark
$2028
$204
9.9
8.7
p<.000+
Retailer
$383
$46
8.3
4.9
p<.001
Wholesaler
$635
$50
12.7
5.9
p<.000+
Distributor
$630
$54
11.7
6.9
p<.000+
Factory
$380
$54
7
9.7
p<.000+
Benchmark
costs
are
the
minimum
costs
produced
by
simulation
of
the proposed
decision
rule
for
orders
and are
an
upper
bound
estimate
for
the
optimal performance
in
the
experiment.
Table
3.
Summary
of
experimental
results.
Averages
of
11
trials.
Retailer
Wholesaler
Distributor
Factory
PERIODICITY
(weeks)
Time
to
recover
initial inventory
Date
of
Minimum
Inventory
Date
of
Maximum
Inventory
N/A
N/A
N/A
AMPLIFICATION
Peak
Order
Rate (cases/week)
8
Variance
of
Order
Rate
(cases/week)
2
1.6
Peak Inventory
(cases)
Minimum
Inventory
(cases)
Range
(cases)
PHASE
LAG
Date
of
Peak
Order
Rate (week)
N/A
N/A
N/A
24
20
28
15
13
20
-25
45
23
22
27
19
23
41
-46
88
22
20
30
27
45
49
-45
94
16
22
26
32
72
50
-23
73
16
21
20
Customer
5
16

40
Table
4.
Estimated
parameters
Trial
&
Position
0
as
J
S'
R
2
RMSE
Bassbeer
R
0.90
W
0.00
D
0.15
F
1.00
Budweiser
R
0.00
W
0.00
D
0.00
F
0.25
Coors
R
0.00
W
0.00
D
0.90
F
0.25
Freebeer
R
0.40
W
0.30
D
0.05
F
0.25
Grin
&
Beer
It
R
0.10
W
0.95
D
0.20
F
0.25
Grizzly
R
0.05
W 0.30
D
0.15
F
0.55
Heineken1
R
0.95
W
0.50
D
0.20
F
0.80
Heineken2
R
0.50
W
0.40
D
1.00
F
0.55
Heineken3
R
0.05
W
0.20
D
0.30
F
0.00
Suds
R
1.00
W
0.05
D
0.15
F
0.40
Twoborg
R
0.75
W
0.00
D
0.05
F
0.95
Minimum
Maximum
Mean
0.00
1.00
0.36
a
c
a
a
b
0.10
0.25
0.05
0.65
0.40
0.40
0.30
0.25
0.20
0.15
0.30
0.30
0.35
0.05
0.35
0.25
0.35
0.15
0.20
0.35
0.30
0.20
0.05
0.65
0.15
0.00
0.30
0.00
0.05
0.10
0.15
0.80
0.30
0.00
0.10
0.30
0.00
0.30
0.60
0.35
0.35
0.25
0.50
0.30
a
a
a
b
a
a
a
a
a
a
0.00
0.80
0.26
0.65
a
0.50
a
0.35
a
0.40
a
0.10
a
0.75
a
0.10
a
0.10
a
0.00
a
0.50
a
0.20
a
0.00
a
0.45
a
0.00
a
1.00
a
0.00
a
0.65
a
0.55
a
0.30
a
0.55
a
0.65
a
0.35
0.25
a
0.00
0.00
N/D
a
0.05
N/D
0.60
a
0.30
a
0.80
a
0.00
a
0.45
N/D
a
0.90
a
0.15
N/D
a
0.20
a
0.35
a
1.05
a 0.00
a
0.05
a
0.00
b
0.20
0.00
1.05
0.34
a
20
a 27
14
a 15
a
7
a 30
a
10
9
25
a 38
a
10
18
a
15
30
a
18
19
a
13
a
14
a
19
a 24
a
31
a
27
15
9
9
N/D
a
8
N/D
6
a
16
a
14
9
a
5
N/D
a
12
c
17
N/D
a 20
a
0
a
32
4
18
15
26
0
38
17
a
0.20
a
0.86
0.74
a
0.84
a
0.67
a
0.92
a
0.88
a
0.87
a
0.57
a
0.11
a
0.61
a
0.73
a
0.43
c
0.76
a
0.86
a
0.89
a
0.60
a
0.79
a
0.94
a
0.73
a
0.58
a
0.82
0.32
a
0.75
a
0.75
0.87
a
0.98
0.60
0.10
a
0.81
a
0.73
a
0.87
a
0.89
0.23
a
0.94
a
0.87
0.76
a
0.76
0.69
a
0.95
a
0.83
a
0.72
a
0.84
a
0.66
0.10
0.98
0.71
N/D: Not Defined
Significant
at
a:
.005; b:
.01;
c:
.025
level
(1-tailed
t-test
[since
parameters
must be
>
0])
D-3919
3.13
1.99
2.76
4.56
2.60
1.32
2.09
2.52
1.60
2.84
2.84
4.07
4.29
3.57
2.72
3.82
1.79
2.24
1.75
5.02
1.88
2.32
7.47
5.93
1.92
1.25
0.96
3.70
4.08
2.18
3.26
3.08
0.97
3.17
0.83
1.46
0.85
2.23
5.19
2.06
1.53
2.65
3.80
5.42
0.85
7.47
2.86
III

D-3919
41
Figure
5.
Typical
sample
of
subjects'
post-play
judgments
of
customer
orders.
Compare against
actual
customer
orders
(Figure
3).
0n
0,
E
0
n
0
01
0
53
54
20
Weeks
I_________
_____
11____
25
30
35
40
0
5
10
15

III
Figure
6.
Three
stages
of
industrial
production.
Ratio
to
trend,
1947-1987.
Note
the
growing
oscillation,
amplification,
and
phase
lag
from
consumer
goods
to
intermediate
goods
to
materials
production.
Source:
See
Table
5.
1957
1967
1977
Table
5.
Amplification
and
phase
lag
in
three
stages
of
production.
Standard
Deviation
(/6%)
Consumer
Goods
Intermediate
Goods
Materials
Phase
Lag
(months)
6.22
6.31
10.00
Materials
-
Intermediate
Goods
Intermediate
Goods
-
Consumer
Goods
Source:
Federal
Reserve
Board,
industrial
production
index
for
Consumer
Goods,
Intermediate
Goods,
and
Materials;
monthly
data,
1947.1-1987.5.
Figure
6
and
table
above
show
detrended
data.
The
ratio
to
trend
Rt
=
Pt/Tt;
Pt=Production
and
Tt=Trend.
Trend
Tt
=
exp(a+bt)
where
a,
b
are
determined
for
each
series
by
linear
regression
on
the
log
of
the
production
index:
In(Pt)
-
a
+
b*t.
D-3919
1.2
42
o
'8
0
E
0
ao
0
U
1.1
1.0
0.9
0.8
1.2
1.1
.
1.0
0.9
0
0
U)
0
O
*1
2
0.8
1.2
-
.1
.
1.0
0.9
0.8
.
0.7
1947
1987
1987
1.5
2.1
I
-
.
·-
·
·
I·
1
-
·
· ·
_
q
_
I
.
_
_
_
_
·
· _
_
_