Paper summary by Leo Gomes Tsay, A. 1999. The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science 45(10) 1339-1358

1. March,
2015
Paper’s
summary
The
Quan7ty
Flexibility
Contract
and
Supplier-­‐Customer
Incen7ves
(Tsay
1999)
Based on the paper “Tsay, A. 1999. The Quantity Flexibility Contract and Supplier-Customer Incentives. Management Science 45(10) 1339-1358”
Leonardo
Laranjeira
Gomes
PhD
Student
MIT-­‐Zaragoza
Interna5onal
Logis5cs
Program
Zaragoza
Logis5cs
Center

2. Page - 2 -
Contents
1. Research
ques7on
2. Relevant
literature
3. Assump7ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

3. Page - 3 -
Contents
1. Research
ques7on
2. Relevant
literature
3. Assump5ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

4. Page - 4 -
The
paper
considers
an
external
manufacturer
(EM)
that
provides
a
product
to
a
retailer,
which
in
turn
serves
the
end
market…
Base
scenario:
• EM
commits
resources
to
produc5on
quan55es
based
on
forecasted
rather
than
realized
demand
• Uncertain
market
demand:
retailer
oNen
prefers
to
postpone
the
purchase
commitment
• Retailer
provides
an
ini7al
point
es7mate
of
its
intended
purchase
to
assist
the
EM’s
produc5on
quan5ty
decision
• Retailer’s
eventual
purchase
will
likely
differ
from
the
forecast:
• Demand
uncertainty
• Individual
preferences
towards
overproduc5on
and
underproduc5on
• A
careful
EM
will
adjust
for
these
incen7ves
and
will
incorporate
its
own
economic
prospects
…in
a
base
scenario
that
leads
to
an
efficient
outcome
for
the
overall
system
Source: Tsay 1999

5. Page - 5 -
Lee
et
all
(1997)
described
the
emergence
of
QF
contracts
as
a
response
to
supply
chain
inefficiencies…
…however
firms
are
unwilling
to
reveal
the
terms
of
the
trade
and
liale
formal
documenta7on
existed
describing
how
industrial
users
arrived
at
the
contracts’
parameters
Source: Tsay 1999
Author
Year
Company
using
QF
Lovejoy
1999
Nippon
Otis
Lovejoy
1999
Toyota
Ng
1997
Solectron
Faust
1996
HP
and
Compaq
Farlow
et
al.
1995
Sun
Microsystems
Connors
et
al.
1995
IBM
Magee
and
Boodman
1967
Within
departments
of
individual
Kirms
(e.g.
manufacturing
and
marketing/sales
functions)
The
QF
contract:
• The
retailer
commits
to
purchase
no
less
than
a
certain
percentage
below
the
forecast
• The
EM’s
guarantee
to
deliver
up
to
a
certain
percentage
above
the
retailer’s
forecast
• Single
transfer
price
per
unit

6. Page - 6 -
Tsay
studied
the
supplier-­‐customer
incen7ves
in
such
sebng
and
how
the
quan7ty
flexibility
(QF)
contract
can
overcome
channel
inefficiency
Main
research
ques7on:
• How
can
the
quan5ty
flexibility
(QF)
contract
be
used
to
promote
the
achievement
of
system-­‐wide
efficiency?
Addi7onal
ques7ons:
• What
are
each
party’s
behavioral
incen5ves
in
an
inefficient
seng?
• What
are
the
parameters
of
the
QF
contract?
• What
are
the
impacts
of
the
QF
contract’s
parameters
on
the
economic
outcomes
for
each
party
involved?
• How
does
the
QF
contract
performs
under
demand’s
informa5on
asymmetry?
• What
are
the
condi5ons
for
a
coordina5ng
QF
contract?
Source: Tsay 1999

7. Page - 7 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

8. Page - 8 -
Channel
miscoordina7on
and
its
addressing
approaches
have
been
exposed
by
several
authors,
in
different
fields…
…and
Tsay
described
Iyer
and
Berger’s
(1997)
model
of
quick
response
(QR)
as
the
most
relevant
for
this
par7cular
study
Source: Tsay 1999
Author(s)
Year(s)
Topic/:ield
General
Idea
Spengler
Tirole
1950
1988
Double
marginalization
In
most
cases,
a
SC
composed
of
independent
agents
acting
in
their
own
best
interests
will
be
inneKicient
Tsay
et
al.
1999
SC
contracts
Reconsider
the
nature
of
the
supply
contracts
along
the
chain
Whang
1995
The
goal
in
SC
contracts
Install
rules
for
materials
accountability
and/or
pricing
that
will
lead
to
the
desired
outcome
Methewson
and
Winter
Katz
1984
1989
Economic
literature
“Vertical
restraints”
Jeuland
and
Shugan
Moorthy
1983
1987
Marketing
literature
“Channel
coordination”
Bergen
Van
Ackere
1992
1993
Pol.
Sci.
/
economics
Agency
theory
Lee
and
Whang
Chen
Iyer
and
Berger
1997
1997
1997
Operations
literature
Multiechelon
inventory

9. Page - 9 -
Iyer
and
Berger
(1997)
modeled
the
delay
of
the
SC’s
commitment
to
quan7ty
in
a
manufacturer-­‐retailer
sebng
on
a
QR
effort..
Source: Tsay 1999
• The
retailer
benefits
from
procuring
under
improved
informa5on,
yet
the
manufacturer
can
be
made
worse
off
• Manufacturer
produces
to
order
and
its
payoff
is
determined
once
the
retailer
orders,
regardless
of
how
the
uncertain
market
demand
resolves
• The
manufacturer
naturally
prefers
a
large
retailer
order,
even
if
this
includes
excess
amounts
of
safety
stock
that
never
get
sold
• Higher
service
to
the
end
customer
• Wholesale
price
increase
• Volume
commitments
• Manufacturer
forces
the
retailer
to
buy
or
pay
more
than
it
would
with
the
QR
alone
• Focus
on
Pareto
improvement
at
the
cost
of
system-­‐wide
or
local
op5mality
Manufacturer’s
incen.ves:
overproduc.on
Side-­‐agreements
to
preserve
manufacturer’s
profit
…showcasing
the
importance
of
individual
incen7ves
in
implemen7ng
SC
reform

10. Page - 10 -
“Rela7onal
contracts”
(Masten
and
Crocker
1985,
1991)
arises
a
class
of
mechanisms
to
coordinate
the
disparity
of
the
order
and
the
es7mate…
Source: Tsay 1999
• Described
in
the
contrac5ng
literature
of
law
and
economics
• Acknowledges
that
informa5on
changes
over
5me
• A
control
structure
that
preserves
the
ability
to
act
on
new
informa5on
can
be
advantageous
• Formally
establishes
the
rela5onship
• Defers
precise
decisions
on
price,
quan5ty,
and
other
aspects
of
the
exchange
Background
Characteris.cs
…examples
of
papers
that
model
variants
of
this
rela7onship
can
be
segmented
into
two
general
categories:
those
focused
on
the
buyer’s
decision
and
those
focused
on
both
par7es

11. Page - 11 -
Examples
of
papers
describing
single-­‐node
models
for
“rela7onal
contracts”
Source: Tsay 1999
Author(s)
Year(s)
General
Idea
Bassok
and
Anupidini
1995
Buyer
forecasts
month-­‐by-­‐month
for
a
year
then
revises
within
speciKied
percentage
bounds
Anupidini
1997a
When
cumulative
multi-­‐period
purchases
must
exceed
an
speciKied
quantity
(a
form
of
minimum-­‐purchase
agreement)
Bassok
and
Anupidini
1997b
Rolling-­‐horizon
:lexibility
contract,
similar
to
the
QF
structure,
for
a
retailer
facing
independent
and
stationary
market
demand
Eppen
and
Iyer
1997
Backup
agreements:
buyer
is
allowed
a
quantity
in
excess
of
its
forecast
at
no
premium,
but
pays
a
penalty
for
any
of
these
units
not
purchased
Fisher
and
Raman
1996
Two-­‐stage
production:
initial
run
covers
20%
of
the
selling
season,
whose
sales
inform
a
second
run
that
covers
the
rest
of
the
season.
An
exogenous
constraint
on
second-­‐run
capacity
forces
some
production
to
the
riskier
early
commitment.
These
allow
considera7ons
of
complex
sebngs
by
focus
on
only
one
party,
but
ignores
the
supplier’s
preferences

12. Page - 12 -
Examples
of
papers
describing
two-­‐party
models
for
“rela7onal
contracts”
(most
are
variants
of
the
newsvendor
model)
Source: Tsay 1999
Author(s)
Year(s)
General
Idea
Pasternack
1985
Determines
that
coordination
can
be
achieved
full
return
at
partial
refund.
The
manufacturer
can
determine
the
efKicient
prices
without
knowing
the
market
demand
distribution
.
However,
requires
common
information.
Kandel
Ha
Emmons
and
Gilbert
1996
1997
1998
Full
return
at
partial
refund
with
price-­‐sensitive
demand
Donohue
1998
EfKiciency
with
three-­‐prices
in
a
two-­‐stage
decision
model:
(1)
Kirst
commitment
on
price
and
quantity;
(2)
Bayesian
update
with
observed
demand
before
additional
order
(for
a
different
price).
Buyback
at
a
third
price.
QF
contracts
differ
from
these
as
it
provides
flexibility
with
no
explicit
penalty
for
exercise,
but
uses
constraints
as
a
way
to
mo7vate
appropriate
behavior.

13. Page - 13 -
The
author
also
evaluate
a
number
of
other
papers
describing
buyer-­‐
suppliers
rela7onships
in
which
flexibility
plays
some
role…
Source: Tsay 1999
…and
Tsay
posi7ons
the
study
on
the
mechanism
of
incen7ves
and
parameters
that
drive
the
QF
contract,
enabling
comparison
with
other
SC
coordina7on
methods
Other
examples:
• Parlar
and
Weng
(1997)
model
independent
supply
and
manufacturing
departments
under
a
nonlinear
internal
transfer
pricing
arrangement.
However,
no
specific
coordina5on
mechanism
is
proposed
or
evaluated
• Barnes-­‐Schuster
et
al.
(1998)
discuss
op7ons
for
supplier
capacity
as
a
means
of
affec5ng
flexibility
for
the
buyer
• Tsay
and
Lovejoy
(1999)
examine
the
QF
contract
in
a
mul7-­‐period,
rolling
horizon
context.
But
no
op5mal
benchmark
is
available
• Weng
(1997)
considers
a
manufacturer-­‐distributor
supply
chain
facing
price-­‐sensi7ve
stochas7c
demand.
Excess
demand
is
sa5sfied
via
a
second,
more
costly
produc5on
run

14. Page - 14 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump7ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

15. Page - 15 -
Cost’s
structure
and
assump7ons
are
common
knowledge,
in
a
modified
newsvendor
model
Source: Tsay 1999
• Cost
parameter
values
are
common
knowledge
and
all
are
exogenous
to
the
model,
except
c
• Salvage
value
is
the
same
to
both
par5es
Cost
structure,
per
unit
Assump.ons
lossgoodwills
valuesalvageu
tproductionm
pricetransferwholesalec
priceretailp
cos
/
=
=
=
=
=
p > c > m > 0
u < m
s ≥ 0

16. Page - 16 -
Chronology
of
events,
nota7on,
and
informa7on
structure
are
as
follows
Source: Tsay 1999
1. The
terms
of
the
supply
contract
are
nego5ated
2. The
retailer
states
qj
3. The
EM
builds
Qj,
thus
determining
πEM,j
and
πR,j
Note:
all
decisions
up
to
this
point
are
based
on
the
prior
X
4. μ
is
observed
5. The
retailer
places
rj,
based
on
the
updated
informa5on
X|μ.
This
is
the
amount
of
material
available
to
meet
market
demand.
Any
EM
surplus
is
salvaged
6. Market
demand
X
is
revealed,
and
is
filled
to
the
extent
possible
by
the
retailer’s
stock.
Any
retailer
surplus
is
salvaged
Decision
flow
Nota.on
qj = initial purchase order forecast
Qj = quantity produced by the EM
πEM, j and πR, j = expected profits
X = distribution of market demand
µ = signal about market demand
rj = retailer's firm order
Note:
Subscripting
identiKies
the
control
scheme
being
considered:
j
takes
values
CC,
NC,
and
QF,
to
denote
control
by
a
central
planner,
a
no-­‐commitment
arrangement,
and
the
QF
contract,
respectively

17. Page - 17 -
Ra7onality
assump7on:
both
par7es
are
ra7onal,
risk
neutral,
and
an7cipates
the
op7mal
counterpart’s
behavior,
by
backward
induc7on…
Source: Tsay 1999
1. Retailer’s
actual
purchase
is
made
aher
q
has
been
stated,
Q
has
been
produced,
and
μ
has
been
observed.
qj
has
no
impact
here.
G(r|μ)
represents
retailer’s
expected
profits
at
this
point
2. The
EM
commits
to
produc7on
prior
to
the
forecast
update.
πEM,j
an7cipates
the
possible
outcomes
of
μ
and
the
retailer’s
adjustment
3. The
retailer
states
qj
with
knowledge
of
the
EM’s
subsequent
produc7on
response
(from
2)
and
its
own
purchasing
policy
(from
1)
rj
*
(qj,Qj,µ) ≡
argmaxr
s.t.
G(r | µ)
r ≤ Qj
r due to the arrangement
tarrangementhetodueQ
QqrqQ
ts
qQ
j
jjjjjEMQ
jj
)),,(,,;(
..
argmax
)(
*
,*
µπ
≡
qj
*
≡ argmaxq {πR, j (rj
*
(qj,Qj
*
(q),µ))}
…so
the
retailer
(the
first-­‐mover)
an7cipates
the
game
outcomes
and
manipulates
its
ini7al
forecast

18. Page - 18 -
Demand
assump7on:
EM
must
commit
at
a
par7cular
7me,
no
maaer
when
the
retailer’s
order
becomes
firm
Source: Tsay 1999

19. Page - 19 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa7on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan7ty
flexibility
(QF)
contract
• The
efficient
quan7ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

20. Page - 20 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa5on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan5ty
flexibility
(QF)
contract
• The
efficient
quan5ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

21. Page - 21 -
A
centrally-­‐controlled
SC
provides
an
efficiency
benchmark
by
applying
the
standard
newsvendor
problem…
Source: Tsay 1999
…
and
since
there
is
no
intermediate
transfer,
q,
rj
,and
c
play
no
role
here
Central
control
• Manufacture
and
retail
are
coordinated
by
a
single
firm
• Delivers
the
greatest
possible
expected
system
profit
• Unique
op5mal
produc5on
quan5ty
• Standard
newsvendor
problem:
Underage
cost
(p+s-­‐m)
Overage
cost
(m-­‐u)

22. Page - 22 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa7on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan5ty
flexibility
(QF)
contract
• The
efficient
quan5ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

23. Page - 23 -
NC,
with
asymmetric
informa7on,
leads
to
a
game
of
specula7ons
in
which
the
outcome
is
subop7mal
Source: Tsay 1999
• EM
does
not
share
the
retailer’s
visibility
of
the
market
demand
• Retailer
provides
a
forecast
of
intended
purchase
• EM
is
leh
with
its
own
beliefs
about
the
retailer’s
purchasing
behavior
Λq(
),
influenced
by
the
forecast
• Retailer
buys
in
order
to:
• EM
produces:
• A
retailer
devoid
of
economic
consequences
will
state
large
forecasts
to
induce
overproduc5on
and
postpone
decisions
• A
careful
EM
will
an5cipate
this,
but
must
s5ll
ascertain
how
to
best
deflate
the
exaggerated
numbers
• Retailer
has
incen5ves
to
bias
Λq(
)
by
exaggera5ng
qNC
• Λq(
)
is
low
quality,
since
EM
is
not
privy
to
retailer’s
informa5on
• EM
posi7ons
to
retailer’s
behavior,
based
on
its
cri7cal
frac7le,
as
opposed
to
the
system
as
a
whole
• Different
cri7cal
frac7les
to
the
EM,
retailes,
and
the
system
as
a
whole
leads
to
different
op7mal
quan77es
NC,
asymmetric
informa.on
Causes
of
inefficiency

24. Page - 24 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa5on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan5ty
flexibility
(QF)
contract
• The
efficient
quan5ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

25. Page - 25 -
NC,
with
common
knowledge,
leads
to
subop7mal
expected
profits
as
well,
due
to
asymmetric
incen7ves
(i.e.
cri7cal
frac7les)
Source: Tsay 1999
NC,
common
knowledge
• Common
beliefs
on
market
demand
• Retailer
provides
a
forecast
of
intended
purchase
• Since
the
forecast
does
not
imply
firm
commitment,
it
does
not
affect
demands
to
EM
• EM
solves
a
newsvendor,
as
before,
only
improving
the
demand
parameter
• Profit
alloca5on
can
be
determined
by
c
• Cri7cal
are
s7ll
divergent
among
EM,
retailer,
and
the
system
as
a
whole
Proposition
1.
If
the
forecast
of
the
retailer’s
purchase
represent
no
commitment
for
either
party,
then
for
any
c,
underproduction
occurs
relative
to
the
optimal
centralized
solution
(i.e.
Q*
NC
<
Q*
CC
).
Therefore,
expected
total
system
proKit
is
strictly
suboptimal

26. Page - 26 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa5on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan7ty
flexibility
(QF)
contract
• The
efficient
quan5ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

27. Page - 27 -
QF
contract
{c,(α,
ω)}:
retailer,
for
a
price
c,
has
purchase
flexibility
of
a
certain
percentage
above
and
below
a
previously
established
forecast
Source: Tsay 1999
The
quan7ty
flexibility
(QF)
contract
• Retailer
must
purchase
at
least
qQF(1+
ω),
ω
ϵ
[0,
1]
• EM
guarantees
product
availability
of
up
to
qQF(1+
α),
α
ϵ
[-­‐ω,
∞]
• Retailer’s
purchase:
• EM’s
produc5on:
• Equilibrium:
Proposition
2.
Under
the
terms
of
a
QF
contract,
when
qQF
>
0,
the
EM
produces
exactly
qQF(1
+α
).
If
qQF
=
0,
for
any
given
c
the
EM
will
prefer
the
NC
arrangement.

28. Page - 28 -
The
equilibrium
solu7on
for
the
retailer’s
forecast
considers
equality
of
expected
cost
and
benefit
for
increasing
the
forecast
Source: Tsay 1999
Proposition
3.
Properties
of
the
equilibrium
solution
when
ω
<
1:
(a)
q*
QF
is
strictly
positive
and
Kinite,
and
may
be
obtained
as
the
unique
solution
to:
• Retailer’s
expected
marginal
benefit
for
increasing
the
forecast
• G’(q(1+α)|μ))
Retailer’s
marginal
benefit
on
product
availability
• Integral
takes
the
expecta5on
for
all
scenarios
in
which
add.
unit
is
desired
but
not
obtained
• (1+α)
mul7plier:
unit
increase
in
q
affects
addi5onal
product
availability
• Retailer’s
expected
marginal
cost
for
increasing
the
forecast
• Cost
is
imposed
by
the
minimum
purchase
implica5on
LHS
RHS

29. Page - 29 -
For
the
system
as
a
whole,
the
flexibility
parameters
(α,
ω)
can
be
simplified
by
a
net
amount
of
flexibility
(ψ)
Source: Tsay 1999
Proposition
3.
Properties
of
the
equilibrium
solution
when
ω
<
1:

30. Page - 30 -
Tsay
also
describes
the
dynamics
of
the
supply
rela7onship
for
the
retailer
and
the
EM
with
respect
to
the
parameters
of
the
QF
contract...
Source: Tsay 1999
Proposition
3.
Properties
of
the
equilibrium
solution
when
ω
<
1:
(c)
Comparative
statics
q*
QF
Q*
QF
π*
R,QF
π*
EM,QF
↑c
-­‐
-­‐
-­‐
+
or
-­‐
↑ω
+
+
+
+
or
-­‐
↑α
+
or
-­‐
+
+
+
or
-­‐
Dynamics
of
the
supply
rela7onship
• Higher
c
means
retailer’s
higher
overage
and
lower
underage
cost,
decreasing
op5mal
forecast
• Higher
ω
means
relaxa7on
of
the
minimum
purchase,
so
increasing
the
forecast
makes
retailer
worse-­‐off
when
demand
are
low,
but
beuer-­‐off
when
demand
is
high
(upside
availability)
• Increase
in
α
is
undetermined
as
retailer
has
incen5ves
to
decrease
forecast
(lower
minimum
purchase)
and
also
to
increase
(mul5plica5ve
effect)
• EM’s
profits
are
undetermined
because
its
demand
is
sen55ve
to
both
price
and
flexibility,
since
both
influence
the
retailer’s
purchase

31. Page - 31 -
...and
provides
two
scenarios
as
examples
that
the
QF
contracts
are
not
necessarily
efficient
Source: Tsay 1999
Proposition
4.
Properties
of
extreme
forms
of
the
QF
contract,
for
any
transfer
price
c:
(a) If
the
retailer
is
not
bound
to
any
minimum
purchase
commitment
(ω=1,
or
ψ=∞),
overproduction
occurs
relative
to
the
central-­‐control
case
(b) If
the
retailer
must
purchase
the
full
amout
forecast
((α,ω)=(0,0),
or
ψ=1),
underproduction
occurs
relative
to
the
central-­‐control
case
In
both
cased,
total
system
proKit
is
strictly
suboptimal
• An
upside
promise
with
no
minimum
purchase
commitment
• Presumably
the
retailer
would
prefer
this
arrangement
• Without
the
upside
commitment
this
would
revert
to
the
NC
case
• Problem:
lack
or
retailer’s
accountability
for
the
forecast
• Requires
the
retailer
to
accept
exactly
what
it
forecasts
• Likely
to
be
preferable
to
the
EM
• Problem:
double
marginaliza7on
Proposi.on
4.a
Proposi.on
4.b

32. Page - 32 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
• Central
control
(CC)
• Decentralized
control
with
no
commitment
(NC)
and
asymmetric
informa5on
• Decentralized
control
with
no
commitment
(NC)
and
common
knowledge
• The
quan5ty
flexibility
(QF)
contract
• The
efficient
quan7ty
flexibility
(QF)
contract
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

33. Page - 33 -
As
retailers
pay
more
for
flexibility,
there
exists
an
unique
net
flexibility
solu7on
that
coordinates
the
supply
rela7onship
in
a
QF
contract
...
Source: Tsay 1999
Assumed
condi7ons
for
system
efficiency:
i. Q*
CC
must
be
resident
in
the
model,
and
ii. It
must
be
fully
accessible
to
the
end
customer
when
market
demand
occurs
Proposition
5.
for
any
c
ϵ
(m,
p
+
s):
(a) There
exists
and
unique
ψ
such
that
Q*
QF(c,
ψ)
=
Q*
CC
(b) Among
such
combinations,
greater
Klexibility
(ψ)
is
associated
with
a
higher
transfer
price
…
however,
there
is
not
a
closed-­‐form
general
characteriza7on
for
the
op7mal
c,
ψ...

34. Page - 34 -
...Yet,
under
a
simplifying
assump7on,
the
solu7on
for
(c,
ψ)
can
be
established
Source: Tsay 1999
• To
preserve
efficiency,
any
increase
in
α,
which
encourages
lower
q*
EF,
must
be
couteracted
by
reducing
ω,
which
commits
the
retailer
to
a
larger
por5on
of
the
q*
EF
• When
transfer
price
is
simultaneously
adjusted
to
restore
the
system’s
efficiency,
it
turns
out
that
the
EM
ends
up
claiming
more
of
the
system
profits
Proposition
6.
for
the
demand
model
in
which
σϵ=0:
(a) System
efKiciency
will
result
from
a
QF
contract
with
total
Klexibility
ψ
≣(1+α)/(1-­‐ω)
when
the
transfer
price
is
(b) Any
split
of
the
expected
profits
can
be
achieved
with
some
efficient
QF
contract
(c) Among
these
contracts,
increasing
the
flexibility
shiNs
profit
to
the
EM
Reitera7on
note:
even
with
the
necessary
condi7on
demand’s
common
beliefs,
inefficiencies
can
result
if
the
individual
incen7ves
are
not
aligned!

35. Page - 35 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

36. Page - 36 -
Numerical
analysis
setup
Source: Tsay 1999
• Simplified
model
σϵ=0
• Market
demand
X
is
uniform
• Unless
stated
otherwise
{p=15,
c=10,
m=6,
u=3,
s=0}
• Demand
parameters
{m=100
δ=100)
and
α=0
in
all
QF
contracts

37. Page - 37 -
Juxtaposi7on
of
control
methods
depicts
the
alloca7on
of
expected
profit
and
how
the
total
compares
to
what
central
control
could
achieve
Source: Tsay 1999
• NC
is
inefficient
because
of
underproduc5on
• Allowing
complete
cancela5on
results
in
overforecas5ng
• QF
with
no
flexibility
is
not
the
solu5on,
although
is
good
for
the
EM
Comparison
of
control
methods
Comments
In
the
efficient
contract,
the
retailer
accepts
a
55%
purchase
commitment
in
exchange
of
a
price
reduc7on
of
~7%

38. Page - 38 -
Sensi7vity
of
the
flexibility
parameter
indicates
that
retailer
profit
increases
with
ω
Source: Tsay 1999
Expected
profit
and
produc.on
vs
flexibility
(c=10)
Comments
• Since α=0, this is only
specified by ω
• LeN-­‐to-­‐right
progression
provides
the
transi5on
from
full
purchase
commitment
to
full
cancela5on
privileges
This
makes
concrete
the
value
of
the
flexibility
to
a
buyer
and
therefore
the
willingness
to
pay
for
it

39. Page - 39 -
Sensi7vity
of
the
transfer
price
parameter
confirms
that
while
retail
profit
is
always
decreasing
in
c,
EM’s
profit
increases,
then
decreases...
Source: Tsay 1999
Expected
profit
and
produc.on
vs
transfer
price
((α,ω)=(0,
0.2))
Comments
• The
leN
extreme
has
EM
pricing
at
cost
(c=m).
This
imparts
on
the
retailer
the
cost
structure
of
the
whole
channel
• For
the
given
flexibility
parameters,
efficiency
occurs
at
p=7.1
…corrobora7ng
to
the
illustra7on
of
the
general
tension
in
the
contract
nego7a7on
due
to
the
duality
between
pricing
and
constraints

40. Page - 40 -
An
illustra7on
on
how
profits
are
allocated
when
the
set
of
efficient
contracts
is
arrayed
by
ω
Source: Tsay 1999
Expected
profit
and
flexibility
in
an
efficient
QF
contract
Comments
• Whenever
the
retailer
receives
more
flexibility,
the
efficient
c
also
increases
to
offset
any
profit
gains
Any
profit
alloca7on
is
possible

41. Page - 41 -
Along
the
QF
efficient
fron7er,
there
is
a
Pareto
improvement
region,
where
no
party
can
be
worse-­‐off,
compared
to
NC
Source: Tsay 1999
The
QF
efficient
fron.er
and
Pareto
improvement
Comments
• At
L,
which
is
the
lowest
efficient
c,
the
retailer
reaps
all
gains
and
the
EM
is
indifferent;
the
reverse
is
true
at
H
• All
these
combina5ons
represent
the
retailer’s
willingness
to
accept
greater
inventory
for
a
price
reduc5on

42. Page - 42 -
Efficient
QF
contracts
are
dependent
on
the
distribu7on
of
the
demand
Source: Tsay 1999
Expected
profit
and
efficient
transfer
price
vs.
demand
variability
(ω=0.2)
Comments
• As
σX
increases
the
efficient
c
decreases.
This
is
because
the
retailer
finds
the
installed
flexibility
to
be
decreasingly
meaningful
in
the
task
of
matching
the
market
demand
• A
reduc5on
in
transfer
price
counteracts
this
effect,
while
shiNing
profit
to
the
retailer
(since
the
flexibility
is
unaltered)
Contracts
needs
to
be
renego7ated
whenever
beliefs
about
demand
change

43. Page - 43 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

44. Page - 44 -
QF
contract
takes
its
place
among
solu7ons
for
divergences
on
inventory
ownership
and
the
commitment
implied
by
a
forecast
Source: Tsay 1999
Key
insights
• In
a
decentralized
supply
rela5onship
in
which
the
customer’s
forecast
does
not
imply
commitment,
inefficiency
will
result
in
the
absence
of
addi5onal
structure
• Behaviors
such
as
overforecas5ng
and
decisions
based
on
the
local
perspec5ve
are
natural
consequences
of
decentralized
control
• These
problems
can
be
at
least
par5ally
remedied
by
the
QF
contract,
in
which
the
retailer
commits
to
a
minimum
purchase
and
the
EM
guarantees
a
maximum
coverage
• QF,
by
itself,
does
not
guarantee
efficiency.
The
correct
parameters
must
be
stablished
• Trade-­‐off
between
flexibility
and
price:
customer
commits
to
minimum
purchase
in
exchange
of
price
reduc5on
and
supplier
offers
that
price
break
in
exchange
for
more
predictable
sales
• Naturally,
the
retailer
pushes
for
lower
price
and
greater
flexibility
• The
economics
of
the
model
indicates
that
some5mes
the
EM
can
concede
a
more
aarac7ve
price,
when
demand
is
price-­‐sensi7ve

45. Page - 45 -
However,
the
QF
contract
relies
on
common
beliefs
about
the
demand,
which
are
difficult
to
achieve
Source: Tsay 1999
Most
significant
limita7ons
• The
results
of
the
research
can
only
demonstrate
efficiency
under
shared
beliefs
about
the
demand
• These
common
beliefs
are
difficult
to
achieve,
even
with
informa5on
sharing
systems
• The
issues
of
coordina5on
under
informa5on
asymmetry
remains
unresolved

46. Page - 46 -
The
concept
of
QF
contracts
is
simple
and
has
a
qualita7ve
appeal
with
coopera7ve
flavor
Source: Tsay 1999
Managerial
implica7ons
• QF
may
be
useful
when
the
EM
relies
heavily
on
the
retailer
for
guidance
about
market
condi5ons
• The
concept
is
simple
and
has
a
coopera7ve
flavor
in
that
each
party
accepts
some
of
the
inventory
and
stock
out
burden
• QF
has
a
qualita7ve
appeal
in
the
sense
that
a
single-­‐price
structure
is
more
poli5cally
palatable
• The
single-­‐rate
pricing
reflects
a
philosophical
view
of
many
companies
in
turbulent
demand
environments

47. Page - 47 -
The
concept
of
QF
contracts
is
a
candidate
to
extension
to
supply
chains
with
many
players
Source: Tsay 1999
Possible
extensions
• As
QF
contracts
may
be
effec5ve
at
mi5ga5ng
the
retailer’s
gaming
by
auaching
economic
accountability
to
the
forecasts,
it
seems
to
extend
naturally
to
supply
chains
with
more
than
two
players
deep,
as
each
link
represents
another
opportunity
for
informa5on
distor5on
• Coordina5on
under
informa5on
asymmetry

48. Page - 48 -
Contents
1. Research
ques5on
2. Relevant
literature
3. Assump5ons
4. Model
5. Numerical
analysis
6. Conclusions
and
discussion
7. Personal
opinion

49. Page - 49 -
Personal
opinion
Source: personal opinion
• Nice
concept,
simple,
and
can
be
useful
• Paper
explains
the
dynamics
of
the
QF
contract
parameters
• Incen5ves
and
behavior
are
elegantly
clarified
• Condi5ons
for
efficiency
are
described
• Mo5vates
further
inves5ga5on
• A
very
influen5al
paper
on
QF
contracts
(the
most
relevant
according
to
Google
Scholar,
with
897
cita5ons)
However…
• Relies
on
strong
assump5ons:
• Common
beliefs
about
market
demand
(difficult
to
achieve)
• Closed-­‐form
solu5on
with
σϵ=0
(not
generally
observed
in
the
real
world)
• Does
not
fully
explains
how
to
translate
it
into
prac5cal
terms