TELKOM
NIKA
, Vol. 11, No. 12, Decem
ber 20
13, pp.
7640
~76
4
8
e-ISSN: 2087
-278X
7640
Re
cei
v
ed
Jun
e
30, 2013; Revi
sed Aug
u
st
19, 2013; Accepted Sept
em
ber 4, 201
3
Optimal Pricing Strategies and Computer Simulation of
DCSC with Fairness P
r
eference and Risk-Aversion
Members
Guang
x
ing Wei*,
Qiang Lin
Schoo
l of Man
agem
ent, Cho
ngq
ing Ji
aoto
n
g
Univ
ersit
y
, C
hon
gqi
ng, Ch
in
a
*Corres
p
o
ndi
n
g
aauth
o
r, e-mail:
w
g
x777
@1
26.com*, lqg
o
od_
70
24@s
o
h
u
.com
A
b
st
r
a
ct
F
i
rstly, this pa
per d
e
vel
op
a
basic tw
o-ech
e
l
on
D
C
SC
mo
del
as the c
o
mparativ
e be
nch
m
ark
in
the g
e
n
e
ral
c
a
se
of the st
o
c
hastic
de
ma
n
d
effected
by
the serv
ice
le
vel
of the r
e
tailer, w
h
ere th
e
ma
nufactur
e
r'
s opti
m
a
l
dir
e
ct price,
w
hol
esal
e pric
e an
d th
e retai
l
er'
s
opti
m
a
l
retai
l
pric
e
w
e
re achi
eve
d
und
er Stackel
berg g
a
m
e.
T
hen, throu
g
h
incorp
or
ate
the fairn
e
ss prefere
n
ce a
n
d
risk-avers
i
o
n
character
i
stics into
the bas
ic DCSC
mo
de
l, the man
u
factur
er'
s
opti
m
a
l
dir
e
ct price, w
hol
esal
e pric
e a
n
d
the retail
er'
s
o
p
timal reta
il p
r
ice w
e
re obt
ain
ed u
nder S
t
ackelb
erg g
a
m
e. At last, b
y
the nu
mer
i
c
a
l
simulati
on, th
e
effect of fair
n
e
ss pr
eferenc
e
an
d risk
avers
i
on
lev
e
l
on t
h
e o
p
ti
mal
pric
i
ng strate
gies
a
nd
utility of DCS
C
w
a
s examin
e
d
resp
ectively.
The resu
lts s
how
that for a
DCSC w
i
th fair
ness pr
eferenc
e
and risk av
ersi
on
me
mb
ers, the
man
u
factur
er and th
e reta
i
l
er w
ill cho
o
se
a reduc
ed pr
ic
e to avoi
d inc
o
me
risk eve
n
if t
h
e
market d
e
m
a
nd is
stab
le. Al
thoug
h th
e d
e
c
i
sion
mak
e
rs c
an r
eal
i
z
e
th
e i
m
pr
ove
m
ent of
their ow
n utility
in some circu
m
stanc
es, the utility of the w
hole su
pply
c
hai
n alw
a
ys prese
n
ts decreas
in
g.
Ke
y
w
ords
:
d
u
a
l-ch
ann
el su
p
p
ly ch
ain (
D
C
S
C), pricin
g st
rategi
es, fairn
e
ss prefer
enc
e, risk-aversi
o
n
,
service l
e
vel, c
o
mputer Si
mul
a
tion
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In real life,
the theo
ry
of behavio
r
sci
en
ce a
n
d
a serie
s
of game te
st
s alway
s
empha
si
zed t
hat be
side
s p
eople'
s
selfi
s
h pr
efere
n
ce
, people
also
have a fai
r
ne
ss
prefere
n
ce
,
and p
eople
not only con
c
ern thei
r o
w
n mate
rial
incom
e
, but
also fo
cu
s o
n
wh
ether th
e
distrib
u
tion
re
sult of th
eir m
a
terial i
n
com
e
is
fair or no
t [1-2]. Th
ere
has be
en
ma
ny do
cume
nts
inco
rpo
r
ate t
he co
ncept
of fairness into
the behavioral de
cisi
on gam
e
and incenti
v
e
mech
ani
sm o
f
princip
a
l-ag
ent probl
em
at pre
s
ent
[3-5]. On the other ha
nd, the
risk attitude of
different de
ci
sion
subje
c
ts to market in
come
ri
sk is
different. For example, the sup
p
ly chai
n
membe
r
who
ha
s
a risk aversi
on attitude will cho
o
se
con
s
erv
a
tive
de
cisio
n
,
but
the ri
sk
prefe
r
en
ce m
e
mbe
r
s a
r
e u
s
ually pu
rsuin
g
the highe
r-risk a
nd hig
h
e
r-yieldi
ng.
Ho
wever, the
documente
d
literatures
o
n
DCSC
at h
o
me an
d ab
road mai
n
ly focu
s on
the hypothe
sis
of “ratio
nal econo
mi
c man
”
an
d
without consi
der peo
ple's beh
avior
psycholo
g
ical
factors, su
ch as fai
r
ne
ss pref
eren
ce
, risk
aversi
on atti
tude. Therefore,
th
e
previou
s
re
se
arch
results do
not real re
flect
the realit
y of supply
chain ma
nag
e
m
ent beh
avio
r
and
ca
n not
guid
e
ma
na
gement
pract
i
ce
effectivel
y. So the re
sea
r
ch of
DCSC
ba
sed
on
behavio
r p
s
ychol
ogi
cal fa
ctors be
co
m
e
s a
n
impo
rtant theoretical and p
r
a
c
ti
cal p
r
obl
em
and
need
s furthe
r developme
n
t [6].
Given the re
al pre
s
e
n
t an
d impo
rtan
ce
of
behavio
r
psycholo
g
ical
factors in
de
cisi
on-
makin
g
process of busi
ness
contex
ts (in
c
ludin
g
chan
nel re
lationship), theori
s
ts
and
pra
c
titione
rs
have called
attention to the fairn
e
ss prefe
r
en
ce a
nd
ri
sk attitude
of
de
ci
sio
n
-
mak
e
rs
. Increas
i
ng interes
t, more
an
d m
o
re
re
se
arch
ers,
center
o
n
the
pri
c
in
g
strategi
es a
n
d
contractin
g m
e
ch
ani
sms b
a
se
d on
the
behavio
r fa
ct
ors an
d exte
nd p
r
eviou
s
a
nalytical m
o
d
e
ls
in the t
r
aditi
onal
sin
g
le
retail chan
nel
su
pply
chai
n ma
nage
me
nt field. Fo
r
instant,
Cui [
7
]
pointed
out t
hat no
matte
r o
n
ly the
ret
a
iler
co
nc
ern
s
fai
r
ne
ss, or both
sid
e
s p
a
y attention t
o
fairne
ss,
a
co
ordin
a
ting
wh
olesale
pri
c
e
contract
can
be d
e
si
gne
d
with the
line
a
r
d
e
man
d
. Th
at
is to say, th
e “do
uble m
a
rgin
alization
probl
em”
ca
n be elimin
ated, even tho
ugh the
sup
p
ly
chai
n memb
ers
have fairness p
r
efere
n
ce. Demira
g [8] extend the results
of Cui [7]. They
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Optim
a
l Pricing Strategie
s
and Com
put
er Sim
u
lation of DCSC
with
… (Gu
ang
xin
g
Wei)
7641
pointed o
u
t that comp
ari
n
g to linear d
e
mand fun
c
ti
on, the coo
r
d
i
nation condit
i
ons of a line
a
r
whol
esale p
r
i
c
e
unde
r in
d
e
x dema
nd f
unctio
n
a
r
e
relatively loo
s
e
whe
n
o
n
l
y
the retaile
r
con
c
e
r
n
s
fairness. Ho an
d Zhang [9] con
d
u
c
ted
a laboratory experim
ent to test wheth
e
r t
h
e
laboratory
re
sults con
s
iste
nt with the
a
nalytical
p
r
e
d
iction
s when
the
fixed fee
wa
s introdu
ced
to incentive
chann
el effici
e
n
cy. Surpri
si
ngly, t
he int
r
odu
ction
of the fixed fe
e f
a
ils to
in
cre
a
s
e
cha
nnel effici
ency be
ca
use of the lo
ss
aversi
on of d
e
ci
sion
-ma
k
e
r
s.
In the context of DCSC, th
e behavio
r psycholo
g
ical factors of de
cision-m
a
kers m
a
y be
appe
ar mo
re
obviou
s
. However, the literature
s
co
nsi
d
ering the b
e
h
a
vior psy
c
hol
ogical factors
of de
cisio
n
-m
ake
r
s in
DCS
C a
r
e ve
ry fe
w. Fo
r a
su
pp
ly chain
with
a ri
sk averse
sup
p
lier an
d
a
risk ave
r
se
re
tailer, Wang
and Z
hou
[10
]
discu
s
sed t
he o
p
timal di
rect p
r
ice, ret
a
il pri
c
e
and th
e
adde
d value
unde
r centralized
de
cisi
on.
They pointe
d
out that the risk
aver
sion
of sup
p
ly ch
a
i
n
membe
r
s l
e
sseni
ng thei
r o
p
timal pri
c
e.
Li [11]
co
nstructed
a two
-
l
e
vel DCSC m
odel
con
s
ide
r
ed
the memb
ers’ risk attitude
and fou
nd t
hat the
optim
al dire
ct
cha
nnel p
r
ice a
n
d
optimal
ret
a
il
price i
s
influe
nce
d
by
risk
aversi
on
of two
partie
s
. B
u
t their m
odel
did n
o
t con
s
i
der th
e effe
ct of
the retaile
r'
s
servi
c
e level
on ma
rket de
mand. Th
e st
udie
s
of Xing
[12] sho
w
ed
that when th
e
retaile
r's
market share is l
e
sser, the
m
anufa
c
ture
r
will not pay attention to whe
t
her the
retail
er
fells fair or n
o
t; Whe
n
the
retaile
r'
s ma
rket
sh
are is larg
er, the
manufa
c
turer will fo
cu
s o
n
cha
nnel fai
r
n
e
ss to avoid
the puni
shm
ent from the
retailer
by setting highe
r retail pri
c
e.
In
addition, the cha
nnel fairn
e
ss ca
n improve the “do
u
b
l
e margin
alization pro
b
lem
”
effectively.
But
the model th
ey establi
s
he
d is very sim
p
le and di
d
n
o
t con
s
ide
r
th
e effect of the retaile
r'
s effort
factor o
n
market dema
nd.
It is clear th
at the existin
g
literatures
co
n
s
id
erin
g the fairn
e
ss
prefe
r
en
ce a
nd ri
sk
aversi
on
are
very few. So t
he theo
ry research th
at the
effect of
p
e
o
p
le's be
havio
r p
s
ych
o
logi
cal
factors on
de
cisi
on-markin
g in bu
sine
ss relation
shi
p
s and chan
nel
relation
shi
p
s need
s to be
stren
g
then
ed.
In this p
ape
r, we i
n
corporate the
co
ncept of fai
r
ne
ss a
nd
ri
sk av
ersi
on i
n
to th
e
two-e
c
h
e
lon
DCS
C to
inv
e
stigate
ho
w
fairne
ss p
r
ef
e
r
en
ce
and
ri
sk ave
r
sion
affect the
p
r
ici
n
g
strategi
es
of both pa
rties u
nder Sta
c
kelb
erg ma
ste
r
-sl
a
ve game mo
del. We a
s
su
me the marke
t
deman
d is st
och
a
sti
c
and
effected by the se
rvic
e l
e
vel of the retailer. As a
first step, the
manufa
c
turer'
s optimal di
re
ct pri
c
e, whol
esal
e pr
i
c
e a
nd the retail
e
r
's
optimal retail pri
c
e were
achi
eved un
d
e
r ba
sic
DCS
C model. Th
en, throug
h introdu
ce the
fairne
ss p
r
ef
eren
ce a
nd ri
sk
aversi
on
ch
a
r
acte
ri
stics in
to the b
a
si
c
DCS
C m
odel
, the man
u
fa
cture
r
'
s
o
p
tim
a
l direct
pri
c
e,
whol
esale pri
c
e an
d the retailer'
s opti
m
al retail
p
r
i
c
e were anal
yzed. At last
, the effect of
fairne
ss preferen
ce and ri
sk aversion
l
e
vel
on
o
p
ti
mal pri
c
in
g strategie
s
an
d
utility of DCSC
wa
s examine
d
throug
h the
numeri
c
al ex
ample.
2. The Basic
Model of DCSC
2.1. The Mod
e
l Descrip
tio
n
In the
DCSC,
the m
anufa
c
turer (he)
sell
ing p
r
od
uct
s
t
o
custo
m
er n
o
t only th
rou
gh the
retaile
r (she
) but also the d
i
rect
chan
nel
(onlin
e
sal
e
s
by himself). A
s
sume that th
e total market
deman
d fun
c
tion of the
p
r
odu
ct i
s
Aa
,
2
~(
0
,
)
N
,
a
r
e
pr
es
en
ts
th
e
ba
s
i
c
mar
k
e
t
deman
d scal
e(Wang
and
Zhou, 20
09
). Let
w
be the m
anufa
c
ture
r'
s
whol
esale p
r
i
c
e,
s
c
be the
per unit
prod
uction co
st,
r
p
be the retail p
r
i
c
e of th
e retailer,
e
p
be the di
rect p
r
ice. If the market
deman
d scal
e is fixed, then the ad
dition of di
re
ct
cha
nnel by
manufa
c
turer will red
u
ce the
retaile
r's m
a
rket sh
are. In addition, the
market dem
a
nd of both bo
dies i
s
clo
s
el
y related to their
sale
s p
r
i
c
e a
nd the
retaile
r's
se
rvice l
e
vel. Ther
efore, sup
p
o
s
ing
th
e market
dem
and fun
c
tion
of
dire
ct cha
nne
l is given as f
o
llows:
11
1
(1
)
ee
r
dA
b
p
p
v
(1)
The ma
rket d
e
mand fun
c
ti
on of retail ch
annel i
s
given
by:
22
2
rr
e
dA
b
p
p
v
(2)
In Equation (1) an
d Equat
ion (2
),
rep
r
ese
n
ts the al
locatio
n
prop
ortion of p
r
o
duct
market agg
re
gate dem
and
in retail ch
a
nnel,
01
. Let
i
b
be
the price ela
s
ticity of dem
and,
j
be
the cro
s
s price
sen
s
itivity,
v
be the retailer's
servi
c
e level,
j
be the se
rvice
ela
s
ticity o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 764
0 – 7648
7642
deman
d. In addition, with
out loss of generality, we assume
i
b
,
j
, and
j
are grea
ter tha
n
zer
o
,
ij
b
and
ij
b
,
1,
2
i
,
1,
2
j
. The total
servi
c
e cost
of the retaile
r unde
r given
s
e
r
v
ic
e
le
ve
l
i
s
2
()
/
2
Cv
v
. Differ to literatu
r
e [
13], we
pre
s
ume
v
is exog
enetic fo
r t
h
e
derivation
of
the n
e
cessary an
alytic
expre
ssi
on.
In ad
dition,
for e
a
se of
cal
c
ul
ation
and
analysi
s
, su
p
posi
ng
12
bb
b
,
12
,
12
.
Acco
rdi
ng to Equation (1
),
Equation (2
)
and above h
y
pothesi
s
, we have the re
tailer'
s
expecte
d prof
it function as
follows,
[]
[
(
)
(
)
]
rr
r
E
E
pw
dC
v
2
()
(
)
/
2
rr
e
pw
a
b
p
p
v
v
(3)
The man
u
fact
ure
r
's exp
e
ct
ed profit funct
i
on is:
[]
[
(
)
(
)
]
mm
r
e
m
e
EE
w
c
d
p
c
d
()
(
)
mr
e
wc
a
b
p
p
v
(4)
The expe
cted
profit functio
n
of whole
su
pply chai
n is:
[]
[
(
)
(
)
(
)
]
sc
r
m
r
e
m
e
EE
p
c
d
p
c
d
C
v
()
(
)
rm
r
e
pc
a
b
p
p
v
(
5
)
2.2. Stackelb
e
rg Game Decision-M
aki
ng
We ta
ke the
assumptio
n
that the ma
nu
factur
e
r
i
s
do
minant in the
sup
p
ly ch
ain
.
Th
e
seq
uen
ce
of
Stackel
b
e
r
g
game
as foll
o
w
s: th
e man
u
f
acture
r first t
o
dete
r
mine
the di
re
ct pri
c
e
and whole
s
al
e price, then the retaile
r according to
the
obse
r
ved inf
o
rmatio
n to identify the retail
price. Usin
g
the reve
rse-derivation
m
e
thod, t
he retailer determines
the re
tail
pri
c
e at
the
assumptio
n
o
f
the known d
e
ci
sion info
rmation of
the
manufactu
re
r in the se
co
nd stag
e. In the
first
stage, th
e ma
nufa
c
turer fully
kn
ows the
reta
ile
r'
s
deci
s
io
n info
rmation
and
b
a
se
d o
n
whi
c
h,
the optimal di
rect p
r
i
c
e an
d
whole
s
al
e p
r
ice
were
dete
r
mined. In the
followin
g
anal
ysis, in o
r
de
r
to simplify th
e analy
s
is,
we think th
at th
ere i
s
o
n
ly on
e optimal
sol
u
tion a
s
lon
g
as the
se
co
n
d
-
orde
r of obje
c
tive function is neg
ative.
2.2.1. The Re
tailer's O
p
ti
mal Decisio
n
Und
e
r Sta
ckelberg m
a
ste
r
-slave
game
,
the firs
t-o
r
d
e
r of th
e
reta
iler'
s exp
e
cte
d
profit
function in
r
p
is:
[]
2
r
re
r
E
ab
p
p
v
b
w
p
(6)
It is
eas
ily to k
n
ow that
22
[]
/
2
0
rr
Ep
b
, therefo
r
e, the
retailer exi
s
ts a uniq
u
e
optimal retail price
oo
r
p
. Orderi
ng Equatio
n (6) is
equ
al to
zero, the opti
m
al retail p
r
i
c
e in
e
p
and
w
is given by:
(,
)
2
oo
e
re
ap
v
b
w
pp
w
b
(7)
Theorem 1
0
2
oo
r
e
p
pb
,
1
0
2
oo
r
p
w
Theo
rem 1
shows that the
optimal retail
pric
e
appe
ars increa
sin
g
with the incre
a
se of
the direct p
r
i
c
e a
nd the
whole
s
ale
pri
c
e. If t
he
man
u
facturer'
s
whole
s
ale pri
c
e
increa
se
s one
(
)[(
1
)
]
em
e
r
p
ca
b
p
p
v
2
()
[
(
1
)
]
/
2
em
e
r
pc
a
b
p
p
v
v
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unit, the optimal retail p
r
i
c
e will in
cre
a
se one
-half u
n
i
t; if the direct
price in
cre
a
se one u
n
it, the
optimal retail price will i
n
crease
less than one-half uni
t. Therefor
e, when the manufacturer in
a
leade
rship
po
sition, h
e
ca
n mani
pulate
the reta
il p
r
i
c
e th
rou
gh
a
d
justin
g the
whol
esale p
r
i
c
e
and direct p
r
i
c
e, whi
c
h aff
e
cting the retailer'
s in
com
e
and ma
ke
himself o
w
n
gain the bigg
est
sha
r
e of the supply ch
ain b
enefits.
2.2.2. The Manufacturer's Optimal De
cision
Und
e
r Sta
ckelberg ma
ste
r
-slave g
a
me
, the first
-
ord
e
r of th
e ma
nufactu
re
r's e
x
pected
profit function
in
e
p
and
w
are gi
ven belo
w
:
[]
()
[
(
)
m
me
m
e
E
wb
c
p
c
p
(
8
)
[]
oo
m
re
E
ab
p
p
v
w
(
9
)
From th
e
above a
s
su
mptions,
we
have
22
2
2
[]
/
(
4
)
/
2
0
me
Ep
b
b
and
22
[]
/
/
2
0
m
Ew
b
. So, there i
s
only a group of
optimal equilibrium
sol
u
tion of
the
manufa
c
turer. Substituting
Equation
(7
) t
o
Equatio
n (8
), Equatio
n (9
) an
d o
r
de
rin
g
Equatio
n (8
)
and Equatio
n
(9) a
r
e equ
al
to zero, we can get the
opt
imal dire
ct pri
c
e an
d wh
ole
s
ale p
r
ice are
:
22
22
(
2
2
)
(2
)
(
2
)
(2
)
()
2(2
)
oo
mm
e
ab
b
b
w
c
v
b
c
b
pw
b
(10)
2(
)
()
2
o
em
e
ap
v
c
b
wp
b
(11)
Acco
rdi
ng
to Equation (7
), Equation (10
)
and
E
quatio
n (1
1), the
eq
uilibriu
m
solu
tion of
Stackel
b
e
r
g maste
r
-slave game
a
s
follo
ws:
22
22
22
22
()
(
)
(
)
2(
)
()
(
)
(
)
2(
)
33
(
)
4
oo
m
e
o
m
oo
oo
em
r
ab
b
v
b
c
b
p
b
ab
v
b
c
b
w
b
pa
v
c
b
p
bb
(
1
2
)
Theorem 2
(i
)
0
oo
r
p
,
0
oo
r
p
v
;
(ii)
0
oo
e
p
,
0
oo
e
p
v
;
(iii)
0
o
w
,
0
o
w
v
.
Theo
rem 2
shows that th
e optimal retail pri
c
e i
s
in
cre
a
si
ng
with
the increa
se
of the
retaile
r's ma
rket sh
are a
n
d
service level, howeve
r
, the optimal dire
ct price ap
pea
rs de
cre
a
si
ng.
Clea
rly, the optimal whol
esale pri
c
e is al
so incr
e
a
si
ng
with the increase
of the retailer'
s market
sha
r
e
and
se
rvice l
e
vel. T
h
is i
s
be
cau
s
e when
the
market
sha
r
e
and
service l
e
vel of the
re
tail
cha
nnel in
creasi
ng g
r
ad
ually, the retailer
will improve the
retail pri
c
e
,
howeve
r
, th
e
()
]
(
1
)
2
2
oo
me
r
bw
c
a
b
p
p
v
b
()
(
)
2
em
m
pc
b
w
c
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manufa
c
turer co
mplete
knowl
edge
th
e retailer's
deci
s
io
n info
rmation.
The
r
efore, whe
n
observing
th
e retail
er'
s
m
a
rkup
beh
avior, the
man
u
f
acture
r also will
e
nhan
ce
the
whole
s
al
e
price
acco
rdi
ngly so that
sharin
g the
retailer'
s
i
n
crea
sed in
co
me fo
r marku
p
.
Ho
wever,
there i
s
a competition
relatio
n
b
e
twee
n the
direct
ch
a
nnel
and th
e retail
ch
annel, th
e
r
efore, when
the
dire
ct chan
n
e
l's
ma
rket sha
r
e
and
servi
c
e
level
are at
a
disa
dvantag
e
po
sition, th
e
manufa
c
turer will ch
oo
se the low
dire
ct
price in o
r
de
r to improve th
e sale
s of the
dire
ct cha
n
n
e
l
and get a ma
ximum expected earni
ng
s.
3. The Dcs
c
Model of Fai
r
ness Pre
f
er
ence an
d Ri
sk Av
ersion
3.1. The Mod
e
l Descrip
tio
n
The
retaile
r
who
ha
s
distinguishing
fairne
ss p
r
efe
r
en
ce
p
s
ych
o
logy in
the
selli
n
g
terminal
of the entire
su
ppl
y chain a
nd
close
r
to
custo
m
ers, is a
nat
ural p
e
rson i
n
many ca
se
s;
the manufa
c
t
u
re
r a
s
a
co
mpany o
r
ga
n
i
zation
wh
ose fairne
ss p
r
eferen
ce
psy
c
hol
ogy is
n
o
t
obviou
s
. Th
erefo
r
e, taki
ng the a
s
su
mption t
hat the
retaile
r con
c
e
r
n
s
fai
r
ne
ss and
t
he
manufa
c
turer is fairne
ss
neutral. T
h
e
retaile
r al
ways takes th
e man
u
factu
r
er'
s
profit f
o
r
referen
c
e an
d weigh
s
up
whethe
r she
obtains fair
outcom
e
. Base
d on this,
we adopt th
e
fairness preference
utility f
unction
Du [14] has used. Let
0
be the fairn
e
ss
p
r
eferen
ce
level. Algebra
i
cally, we hav
e then:
(
)
[
]
[(
)]
f
rm
r
UE
E
(13)
Equation
(1
3
)
Sho
w
s that
only
whe
n
t
he
retaile
r's
material
in
co
me i
s
le
ss th
an the
manufa
c
turer'
s, the
retail
e
r
will o
c
cur t
he utilit
y-lo
si
ng, an
d th
e
utility-increa
si
ng
conve
r
sel
y
.
Divide Equati
on (13
)
by (
1
), then the fairn
e
ss prefe
r
e
n
ce utility function is given by
:
ˆ
(
)
[]
[
]
[]
[
]
1
f
rr
m
r
m
UE
E
E
E
(
1
4
)
ˆ
also m
ean
s the fairne
ss preferen
ce
par
a
m
eter,
is the si
m
p
lified form
of the
expre
ssi
on i
n
.
ˆ
[0
,1
)
is in
crea
sing i
n
for
0
. When
0
, then
ˆ
0
,
i.e., the
retaile
r is
fai
r
ne
ss
ne
utral
;
Whe
n
, then
ˆ
1
, i.e., the retailer
c
o
nc
erns fairness
extremely.
As is
kn
own to all, both in
the ente
r
pri
s
e
ope
ration
a
nd individ
ual'
s
be
havior de
cisi
on-
makin
g
, the deci
s
io
n-m
a
ker also cho
o
s
e to avoid ri
sk for the fea
r
of loss. The
r
efore, we al
so
take the
hy
pothe
sis th
at the man
u
fa
cture
r
a
nd t
he retailer
a
r
e b
o
th the
risk-averte
r
s.
Con
s
id
erin
g the ri
sk-ave
rsi
on beh
avior
of the
deci
s
i
on-m
a
ker, we taking th
e
mean
-varia
nce
method La
u [15] and Wa
n
g
[10] have used to me
a
s
ure the de
cision-m
a
ker'
s e
x
pected utility.
As sho
w
n in
Equation (15):
()
[]
[
]
a
UE
k
V
a
r
(15)
In Equation
(15),
k
is the
ri
sk-ave
rsi
on l
e
vel of the
d
e
ci
sion
-ma
k
e
r
.
0
k
means the
deci
s
io
n-m
a
ker con
c
e
r
n
s
risk-ave
rsi
on,
and
0
k
mean
s the de
ci
sion
-make
r
i
s
ri
sk-neutral, at
this time, the deci
s
io
n-m
a
ker'
s expe
cted
utility is equal to the expected profit.
The retaile
r's and th
e ma
n
u
facturer'
s
expecte
d utility function f
r
om
the ab
ove a
nalysi
s
is given by:
ˆ
()
[
]
[
]
[
]
rr
m
r
r
UE
E
k
V
a
r
(16)
()
[]
[]
mm
m
m
m
UE
k
V
a
r
(17)
3.2. Stackelb
e
rg Game Decision-M
aki
ng
The a
nalysi
s
method
and
step
s of thi
s
sub
s
e
c
tion
is
same
wit
h
su
bsectio
n
(2.2),
therefo
r
e, we
only list the final re
sults fo
r simplify.
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Optim
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u
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ang
xin
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Wei)
7645
3.2.1. The Re
tailer's O
p
ti
mal decision
The
retailer's utility function based on t
he fa
irness preference
and
ri
sk-aversi
o
n level
is:
ˆ
()
[
]
[
]
[
]
rr
m
r
r
UE
E
k
V
a
r
2
()
(
)
/
2
rr
e
pw
a
b
p
p
v
v
()
(
)
]
em
e
r
p
ca
a
b
p
p
v
(18)
Let the first-o
r
de
r of
()
r
U
in
r
p
is
equal to
zero, the optim
al retail pri
c
e
in
e
p
and
w
is
given by:
*
ˆ
[(
)
(
)
]
(,
)
2
re
m
e
m
re
ak
v
p
b
w
c
p
c
w
b
pp
w
b
(19)
3.2.2. The Manufacturer's Optimal De
cision
The manufact
urer's utility function
based
on the risk-av
ersi
on level is:
()
[]
[]
mm
m
m
m
UE
k
V
a
r
*
()
[
(
,
)
]
mr
e
e
wc
a
b
p
p
w
p
v
[(
)
(
)(
1
)
]
mm
e
m
kw
c
p
c
(20)
Let the first-o
r
de
r of
()
mm
U
in
e
p
an
d
w
are e
qual
to zero, we
can get the o
p
timal
dire
ct pri
c
e a
nd wh
ole
s
ale
price are:
2
*
22
2
ˆ
ˆ
2(
1
)
(
2
2
)
(
2
)
2
(
1
)
(
2
)
2
(
)
()
ˆ
2(
2
)
rm
m
m
m
e
bw
a
b
b
v
b
k
k
b
b
c
b
c
b
c
pw
b
(21
)
*
ˆ
22
(
)
2
[
(
)
]
()
ˆ
2(
1
)
rm
e
m
e
m
e
ak
k
p
v
c
b
p
c
b
wp
b
(22)
Acco
rdi
ng to
Equation
(19
)
, Equation
(2
1) a
nd Eq
uati
on (22
)
, the
equilib
rium
solution
of Stackelb
erg maste
r
-slav
e
game a
s
follows:
22
*
22
*
*
*
*
()
(
)
(
)
()
2(
)
ˆ
2(
)
2
(
)
ˆ
2(
1
)
ˆ
32
3
(
)
2
4
mm
e
er
m
m
m
er
m
m
m
r
ab
b
v
b
c
b
k
b
b
p
b
pa
k
k
v
c
b
c
b
w
bb
pa
k
k
v
c
b
b
c
p
bb
(23)
Theorem 3
(i
)
*
0
ˆ
r
p
,
*
0
r
r
p
k
,
*
0
r
m
p
k
;
(ii)
*
0
ˆ
e
p
,
*
0
e
r
p
k
,
*
0
e
m
p
k
;
(iii)
*
0
r
w
k
,
*
0
r
w
k
, and if
ˆ
[(
)
(
)
mr
e
wc
a
b
p
p
v
()
rr
kp
w
*
()
[
(
1
)
(
,
)
]
em
e
r
e
pc
a
b
p
p
p
w
v
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7646
(2
)
(
)
0
rm
m
ak
k
v
c
b
, then
*
0
ˆ
w
.
Theo
rem 3 (i
) shows that the optimal re
tail pr
ice is in
cre
a
si
ng with
the incre
a
se
of the
retaile
r's fairn
e
ss p
r
eferen
ce level, but d
e
crea
sing
wit
h
the in
crea
se of the
risk-a
versio
n level
of
the both
sid
e
s. Th
eo
rem
3 (ii
)
sho
w
s that the
op
tima
l d
i
re
c
t
pr
ic
e is d
e
c
r
ea
s
i
ng
w
i
th the
increa
se of the manufa
c
t
u
re
r's
risk-aversi
on
level, however, ha
s nothing
with the retailer's
fairne
ss p
r
efe
r
en
ce
and
ri
sk-ave
rsion.
T
heorem
3
(iii) sh
ows th
at t
he o
p
timal
whole
s
ale
pri
c
e is
decrea
s
in
g with the increa
se of the ma
nufactu
re
r's
ri
sk-ave
rsi
on l
e
vel and in
creasi
ng with t
he
increa
se of the retaile
r'
s risk-a
ve
rsi
on level. In addition, if
(2
)
(
)
0
rm
m
ak
k
v
c
b
,
the optimal
whole
s
ale p
r
i
c
e is de
crea
si
ng with t
he i
n
cre
a
se of the
retailer's fai
r
ness p
r
efe
r
e
n
ce
level. As a matter of fact, when
co
nfronting
a retailer
with stron
g
e
r
fairness p
r
efere
n
ce
psychology, the manufacturer
will
offer
a lower wholesale pri
c
e
so
as to maintai
n
the stability o
f
the ch
ann
el relation
ship, n
o
matter from
the mathem
a
t
ical sen
s
e (t
he ba
si
c ma
rket de
mand
a
is
a larg
e num
b
e
r, the value
of the other
e
x
ogeneti
c
pa
rameters i
s
ve
ry small
)
o
r
in
tuitive though
t.
The theo
rem
4 also sho
w
s that all the m
anufa
c
tu
re
r a
nd the
retaile
r wh
o with
th
e risk-aversio
n
cha
r
a
c
teri
stic will
ch
oo
se
mark-d
own to
deal
with
the
un
ce
rtain m
a
rket
dem
and
and
re
duce t
h
e
risk of
incom
e
. Beca
use t
he retaile
r al
so
co
nc
ern
s
fairne
ss, th
erefore,
she
wi
ll improve th
e
retail pri
c
e to
get what
she
thinks more fair
in
come. S
o
, the retaile
r need
s to bal
ance the effe
ct
of her fairn
e
ss prefe
r
e
n
ce and ri
sk-ave
rsion
level o
n
her sale
s pri
c
e and expe
ct
ed utility.
4. Computer Simulation
In order to
discu
s
s the
model
and
il
lustrate
the
con
c
lu
sio
n
m
o
re
sp
ecifi
c
al
ly, this
se
ction throu
gh num
eri
c
al
example a
n
a
lysis th
e effect of the su
pply chai
n m
e
mbe
r
s' fai
r
n
e
ss
preference and ri
sk-ave
rsi
on on thei
r optimal pri
c
ing strat
egi
es and utility. Su
ppose a
cert
ai
n
prod
uct h
a
s t
he follo
wing
market chara
c
teri
stics:
100
a
,
1
b
,
0.5
,
0.6
,
5
v
,
2
,
0.4
,
10
m
c
,
20
.
We p
u
t this
para
m
eters i
n
the ab
ove
model
a
nd m
a
ke
use of
Matlab software, the
optimal de
cision re
sults of
deci
s
ion
-
ma
kers in the b
a
si
c model u
nder Sta
c
kel
berg g
a
me
were
obtaine
d, a
s
follo
ws:
*
62
.1
7
r
p
,
*
57.33
e
p
,
*
52
.6
7
w
,
*
65
.20
r
,
*
18
60
.7
9
m
,
*
1
925.99
sc
.
Whe
n
the
fai
r
ne
ss p
r
efere
n
ce
an
d ri
sk-aversi
on
ch
a
r
acte
ri
stics
were
co
nsi
d
e
r
ed, in
orde
r to analy
s
is
The effe
ct of
the supply
ch
ain me
mbe
r
s'
fairne
ss p
r
ef
eren
ce
an
d ri
sk-ave
rsi
on
o
n
their
optimal pri
c
in
g strate
gie
s
and utility, we assu
m
e
th
at the marke
t
demand i
s
stable, n
a
mel
y
,
20
. In Stackelbe
r
g gam
e, given the differ value of
ˆ
,
r
k
and
m
k
, res
p
ec
tively, we have:
(i) Whe
n
ˆ
0
,
0
r
k
a
nd
0
m
k
, the retailer is fai
r
n
e
ss
neutral
and
ri
sk
neutral, the
manufa
c
turer is also
risk n
eutra
l. In this
ca
se, there e
x
ists
*
oo
ee
pp
,
*
o
ww
and
*
oo
rr
pp
.
(ii) When
ˆ
0
,
0
r
k
an
d
0
m
k
, the manufacturer an
d the retaile
r are both the risk-
averter, th
e retailer
also
concern
s
fai
r
n
e
ss. We di
scuss the
follo
wing
thre
e
ca
se
s, a
s
sho
w
n in
Table 1
-
3.
Table 1
sh
ows that when t
he fairn
e
ss p
r
eferen
ce
and
risk-aversion
level of the retaile
r
are fixed, all
the optimal
whole
s
ale
pri
c
e, dire
ct p
r
ice and
retail
p
r
ice
are d
e
creasi
ng
with t
h
e
increa
se of t
he man
u
fact
ure
r
's ri
sk-av
e
rsi
on le
vel.
Ho
wever, the
pri
c
e de
crea
sing
rate
of the
retail ch
ann
el
is less tha
n
the dire
ct ch
annel
an
d whole
s
ale p
r
ice. This may be the positi
v
e
influen
ce of the retaile
r'
s fairne
ss prefe
r
en
ce on
h
e
r
prici
ng st
rate
gy so as to m
i
tigate the pri
c
e
redu
ction.
Th
erefo
r
e, the
u
t
ility of the manufa
c
ture
r i
s
de
cre
a
si
ng
with the
in
cre
a
se
of hi
s
risk-
aversi
on leve
l, the retailer'
s utility is increa
sing
with the increa
se of
the manufacturer'
s ri
sk-
aversi
on level, however, the growin
g rat
e
of the retail
er's utility is smaller than t
he dam
ping
of
the manufa
c
ture
r's utility. So, the whole
suppl
y chain'
s utility is a decrea
s
ing fun
c
tion.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Optim
a
l Pricing Strategie
s
and Com
put
er Sim
u
lation of DCSC
with
… (Gu
ang
xin
g
Wei)
7647
Table
1.
The Optional De
ci
sion Re
sults
of DCSC u
n
d
e
r Different
m
k
ˆ
r
k
m
k
*
r
p
*
e
p
*
w
*
r
U
*
m
U
*
s
c
U
0.5
0.5
0.2
61.80
55.20
45.53
-842.26
1625.38
783.12
0.5
0.5
0.4
59.94
53.07
43.40
-822.73
1466.93
644.20
0.5
0.5
0.6
58.07
50.93
41.27
-798.51
1317.11
518.60
0.5
0.5
0.8
56.20
48.80
39.13
-769.44
1175.78
406.34
Table
2.
The Optional De
ci
sion Re
sults
of DCSC u
n
d
e
r Different
ˆ
ˆ
r
k
m
k
*
r
p
*
e
p
*
w
*
r
U
*
m
U
*
s
c
U
0.1
0.5
0.5
57.00
52.00
46.45
-125.04
1446.60
1321.56
0.3
0.5
0.5
58.00
52.00
44.08
-468.42
1414.56
946.14
0.5
0.5
0.5
59.00
52.00
42.33
-811.13
1390.98
579.85
0.7
0.5
0.5
60.00
52.00
41.00
-1154.30
1373.00
218.70
0.9
0.5
0.5
61.00
52.00
39.95
-1498.34
1358.80
-139.54
From th
e Ta
b
l
e 2 we
can
see that when
bot
h
the sup
p
l
y
chain mem
bers' risk-ave
rsio
n
level are fixed, the
opti
m
al whole
s
al
e pri
c
e
is
d
e
crea
sing
an
d the
optima
l
retail
pri
c
e
is
increa
sing
wit
h
the in
crea
se of the
retail
er'
s
fa
irne
ss
prefe
r
en
ce l
e
vel. The di
re
ct price remain
s
unchan
ged d
ue to it has nothing
with the retaile
r'
s
fairne
ss prefe
r
en
ce level. Therefore, bo
th
the supply chain mem
b
ers' and
the
whol
e supply
chain's
utilit
y are decreasing with t
h
e
increa
se of the retaile
r's fai
r
ne
ss p
r
efe
r
e
n
ce level.
Table
3.
The Optional De
ci
sion Re
sults
of DCSC u
n
d
e
r Different
r
k
ˆ
r
k
m
k
*
r
p
*
e
p
*
w
*
r
U
*
m
U
*
s
c
U
0.5
0.2
0.5
59.60
52.00
41.53
-763.05
1379.86
616.81
0.5
0.4
0.5
59.20
52.00
42.07
-795.69
1387.49
591.80
0.5
0.6
0.5
58.80
52.00
42.60
-826.18
1394.92
568.74
0.5
0.8
0.5
58.40
52.00
43.13
-854.66
1403.06
548.40
Table
3
sho
w
s that if the
fairne
ss p
r
efe
r
en
ce
of the
retaile
r an
d ri
sk-ave
rsi
on l
e
vel of
the manufa
c
ture
r are fixe
d, the optimal whol
es
al
e
price i
s
increasi
ng and t
he optimal re
tail
price is de
cre
a
sin
g
with th
e retaile
r's
risk-ave
rsion le
vel. The dire
ct price rem
a
ins un
ch
ange
d
due to it
ha
s
nothing
with t
he retailer's
ri
sk-ave
rs
i
on l
e
vel. Therefo
r
e, the m
anuf
acturer'
s
utility
is increa
sin
g
and the ret
a
iler'
s utility is de
crea
si
ng
with the increa
se of the
retailer's ri
sk-
aversi
on leve
l, and the
da
mping
of the
retaile
r'
s ut
ili
ty is larg
er t
han the
growing rate of th
e
manufa
c
turer'
s utility. So,
the wh
ole su
p
p
ly chain'
s uti
lity is decre
asing.
We
ca
n o
b
tai
n
the
com
p
re
hen
sive viewpoints combi
ned
with th
e
Table
2, Ta
bl
e 3
and
Table
4: In th
e given
value
of the
fairn
e
ss p
r
efe
r
en
ce
and
ri
sk-aversion
level,
we
have
*
oo
ee
pp
,
*
o
ww
and
*
oo
rr
pp
. The
retailer's utilit
y is
decreasi
ng
with the i
n
crease
of her fai
r
ness
prefe
r
en
ce
a
nd ri
sk-aversi
on level, i
s
i
n
cre
a
si
ng
with
the in
crea
se
of the
manu
facture
r
'
s
risk-
aversi
on leve
l; The manuf
acturer'
s utility is decre
a
s
i
ng with the i
n
crea
se of hi
s ri
sk-aversio
n
level and the
retaile
r's fai
r
n
e
ss prefere
n
ce level, is
increa
se of the retailer'
s ri
sk-aversi
on leve
l.
Ho
wever, the
growi
ng rate
of one's utility is alwa
ys le
ss tha
n
the damping of ot
her'
s
utility. So,
there is al
way
s
decreasi
ng
of t
he whole
supply chai
n's utility.
5. Conclusio
n
This p
ape
r d
e
velop
s
a two-e
c
hel
on
DCSC mo
del
with a man
u
facturer a
nd a
retailer.
The beh
avior psych
o
logi
cal cha
r
a
c
teri
stics, like
fairness prefere
n
ce a
nd ri
sk-aversi
on, we
re
con
s
id
ere
d
. The re
sult
s unde
r Stackelberg gam
e
sho
w
that for a DCSC with fairne
ss
prefe
r
en
ce a
nd risk aversi
on membe
r
s, the m
anufa
c
ture
r and the retailer will ch
oose a red
u
ced
price to
avoid
income
risk
even if the
m
a
rket
de
man
d
is
stabl
e, al
though
the d
e
ci
sion
ma
ke
rs
can
reali
z
e the improvement of their own utility in
some ci
rcumstances,
howev
e
r, the utility of
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
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Vol. 11, No
. 12, Dece
mb
er 201
3: 764
0 – 7648
7648
the wh
ole
su
pply ch
ain al
ways
pre
s
e
n
ts de
crea
sing
. That is to
say, wh
en
consi
deri
ng th
e
sup
p
ly mem
ber'
s
fairne
ss prefe
r
en
ce
and ri
sk-a
ve
rsion
cha
r
a
c
t
e
risti
c
sim
u
ltaneo
usly in t
he
prici
ng de
ci
si
ons of DCS
C
, the "double
margi
nal ut
ility" of the supply chain di
d
n't get mitigation
effec
t
ively.
The ma
rket d
e
mand
fun
c
tion in o
u
r
mo
del is
rel
a
ted
to the retail
er'
s
ma
rket sha
r
e a
n
d
servi
c
e level, therefo
r
e, the
e
ffect of the retailer'
s ma
rket s
hare and
servi
c
e level
on the optima
l
cha
nnel p
r
ice
under diffe
rent deci
s
io
n-makin
g
mod
e
s
wa
s furth
e
r examined a
nd the intuitive
explanation
wa
s given i
n
the co
rresp
ondin
g
theo
rems.
Ho
wever, this
pap
e
r
al
so h
a
s t
h
e
followin
g
limit
ations:
Firstly, we
do
not
con
s
id
er t
he
manufa
c
turer'
s fai
r
ne
ss p
r
eferen
ce
an
d
effort factor.
The manufact
urer w
ill al
so
concerns fairness and exerts
effort activities to improve
the sale
s of
dire
ct chan
n
e
l in the
real
com
m
er
cial
activity. The
se
con
d
i
s
th
at it doe
s n
o
t
con
s
id
er the
sub
s
titutes
o
n
the ma
rket and ig
nore th
e co
mpetition
betwe
en the
own
e
rs of th
e
sub
s
titute. Th
erefo
r
e, we
will engage to t
h
is work in the later.
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