Home appliance closed-loop supply chain super-network based on returns and replacement was established in this paper, by analyzing the equilibrium conditions of various d[r]
Trang 1* College of Management and Economics, Tianjin University, Tianjin, China
■2012 JSPS Asian CORE Program, Nagoya University and VNU University of Economics and Business
Research on the Equilibrium of Home Appliance Closed-Loop Supply
Chain Super-network Based on Returns and Replacement
Tianjin University Ju-hong GAO1, Yan-sha MENG2, Feng-juan WU2
ABSTRACT: Through the analysis of returning and replacing process and status against home appliance supply chain, a
closed-loop supply chain super-network was established which consisted of raw material suppliers, manufacturers,
retailers and consumers And variation inequality formulation was used to model the optimizing behavior of the various
decision-makers and derive the equilibrium conditions and the optimal solution of the whole supply chain, then got the
rational volume and price for transaction Finally, the model was verified by a simulation example
KEYWORDS: Home appliance industry; Returns and replacement; Super-network; variation inequality formulation
1 INTRODUCTION
With the increasing of consumption levels,
people’s demand also increased Due to the production
and the difference of personal preferences, the return
and replace rate of goods also increased, especially in
the field of e-commerce According to the statistics, the
average return rate of companies that implemented
e-commerce was 30%, in which the return of seasonal
products was as high as 70%-80% [1] The returning
also caused high processing costs; the annual
processing cost of returned goods was up to $37 billion
in America
Among home appliance, consumers give goods
that they want to return or replace back to the retailer,
and the retailer give the defective products back to the
manufacture, thus a reverse supply chain was formed
The combine of forward supply chain and reverse
supply chain among home appliance constitute a
super-network
Most scholars focused [3-9] their study about returning and replacing goods on return game and contract research, by which they could decide the behavior and strategies of supply chain participants
Padmanabhana and Png [5] explained how to adopt different returning strategies in different circumstances and analyzed their benefits and costs Tsay [6]
described how the risk influences the manufacture and distributer’s returning Donohue [7] explored how to achieve coordination in the supply chain contract of two productions and ordering prices
Super-network is composed by inferior networks, which exists in a complex system and contains logistics networks, information networks and funding
The home appliance industry closed-loop supply chain
is a complex super-network
The super-network center led by Anna Nagurney [11-12] had focused on the research of super-network that applied to supply chain They studied the
Trang 2independent behavior and interaction of the various
decision-makers in the supply chain by using
equilibrium theory and inequality formulation, and got
the equilibrium conditions of the whole supply chain
system Yang Guangfen [13] established a supply chain
super-network which consisted of manufactures,
retailers (in charge of take-back) and consumers With
the equilibrium theory and inequality formulation, he
analyzed the independent behavior and interaction of
various decision makers, and also got the equilibrium
conditions of the supply chain system Wang
Haichao[14] established a super-network which
consisted of manufacturers, distributors, demand
markets and collectors through applying super-network
theory to recovery supply chain of green logistics He
analyzed the optimal behavior of decision-makers and
got the equilibrium conditions by using inequality
formulation Zhou Ruohong and Wang Zhiping[15]
considered the closed-loop super-network supply chain
under e-commerce environment They established a
super-network which consisted of manufactures,
retailers, consumers and collectors in e-commerce
With the inequality formulation, they analyzed the
independent behavior and interaction of various
decision makers in online transactions Zhang Tiezhu
and Zhou Qian considered the online and offline
transaction as well as the multi-cycle transaction and
established a super-network which consisted of
manufactures, retailers, and demand markets They not
only studied the independent behavior and interaction
of various decision makers, also considered the impact
of the stock and online transaction to the whole supply
chain Eventually, the rational trading volume and price
is gotten
In summary, it is easy to get the equilibrium
conditions of complex problems by using inequality
formulation to super-network It was beneficial for
decision-makers to make decisions from independent
to interactive So far, many researchers have focused
on supply chains concluding recovery behavior or closed-loop supply chain There was less research involves the replacing process, though there were some researches concentrated on returning problems This paper established a super-network which consisted of suppliers, manufactures, retailers and consumers based
on the returning and replacing of home appliance and studied the closed-loop supply chain of home appliance With the inequality formulation, the author got the rational trading volume and price by analyzing the independent behavior and interaction of the decision-makers, which could offer some reference for home appliance industry to develop returning and replacing strategy
The basis of this study is that the defective products will be dealt with by retailers according to the requirements of consumers, and will be delivered to the manufactures by retailers The products which are defect-free will be managed by retailers, and the returns could continue to be sale The closed-loop supply chain of home appliance was shown as Fig 1
Fig.1 Closed-loop supply chain of home appliance
A complex super-network model established by supplier, manufacture, retailer and consumer was shown in Fig 2
Supplier Manufacture Retailer Consumer
Returns and replacement;
Returns of defective products;
Defective materials or parts;
Sales of returned products
Sales of defectiveness products that replaced
Trang 31 2 S
…
…
…
…
供应商
制造商
零售商
消费者
…
…
…
Fig.2 Closed-loop supply chain super-network of home
appliance based on returns and replacement
2.1 Model assumption
For the purpose of our argument, the following
assumptions were set which have no influence on the
accuracy of the conclusions
(1) The same kind of home appliance is of same quality
And after disposal, the returns and replaces could be
treated as totally news
(2) It was the manufactures that shoulder the returning
and replacing expenditure
(3) The returns and replacement only occurs between
the retailers and consumers
(4) The locations of decision-makers were not
considered in
(5) The consumers are permitted to return and replace
goods for only one time
(6) The cost functions between all the decision-makers
were convex functions
2.2 Parameter description
s = 1,2 ， ， ，m S = 1,2 ， ， M ，n = 1,2 ， ， N ，i = 1,2 ， ， I
The suppliers, manufactures, retailers and consumers;
sm
， ， ， : Trade volume between supplier
and manufacture, manufacture and retailer, retailer and
consumer, and the quantity that retailers got from
consumers for returning and replacing
: The ratio of returned goods Then is the ratio of
replaced goods;
: The ratio of detective products in all returns and
replacement goods
: Transaction price between supplier and manufacture, manufacture and retailer, retailer and consumer
: Repurchase price between manufacturer and retailer
m
: The lost of manufacture for returning of per unit
goods
: The lost of retailer for returning of per unit goods.
In the super-network model of this paper, each node pursues to maximize its objective function
3.1 The behavior and equilibrium condition of supplier
Assume that f Q s( s)is the production cost of supplier, in which Q s is column vectors consisted by And assume that the transaction cost between supplier and manufacture is , then the objective function of supplier is as following:
M
M
(1)
Eq (1) indicates that the profit of supplier is the sales revenue minus the production and transaction costs with manufacture Eq (1) is continuous convex function judged by model assumptions, so the optimal value of it is the variation inequality’s optional solution when It must apply to the following inequality:
1 1
0
S M
f Q c q
(2)
3.2 The behavior and equilibrium condition of manufacture
The production cost of manufacture is related to the ordering and returning of retailer
as , in which is column vectors consisted by stand for the transaction cost between the manufacture and supplier, manufacture and retailer And the repurchase price between manufacturer and retailer is ;
Supplier
Manufacture
Retailer
Consumer
1-
sm , mn , ni
mn
r
n
sm q
sm sm sm
0
s
Q
mn
q c sm(q sm),c mn(q mn)
1
N
mn mn n
r q
Trang 4, m
m
c c
represent the cost of returning and replacing
respectively Thus, c mc q m(mn),cm (1 )cm(qmn)
The objective function of manufacture is as following:
N
S
sm
m
p q f Q q c q c q r q
(3)
.
mn
mn
s t q q
(4)
Eq (4) expresses that home appliance that
returned are less than the amount that returned and
replaced And by the assumptions we know that Eq (3)
is convex function Then, the optimal solution is
seeking (q sm,q mn,qmn,m)0 to meet
1 1
1 1
( , ) (1 ) ( ) ( )
( )
M N
n
m n
M N
m m mn mn mn
mn m mn mn
sm sm
f Q q c q c q
f Q q c q
c q
q
0
p q q q q
(5)
is a lagrange multiplier
3.3 The behavior and equilibrium condition of
retailer
The behavior of retailer is related to manufacture
and consumer Similarly, the objective function of
retailer is:
ni ni mn mn n n
mn mn ni ni mn mn n mn
p q r q f Q
c q c q p q q
(6)
(7)
The optimal solution of retailer is seeking
to meet:
(8)
is a lagrange multiplier
3.4 The behavior and equilibrium condition of consumer
Assume that is the transaction cost between retailer and consumer; is the demand price of consumer, then and is a column vector of all demand prices; is the demand of consumer Then the equilibrium condition of consumer
is for any , there is
3 3
( )
ni
if q
f q
(9)
The supply and demand balance condition of consumer is for any , there is
3 1 3
3 1
N
n
n
q if d
q if
(10)
Eq (9) expresses that under equilibrium conditions, if transaction is greater than zero, a transaction took place, and the cost of retailer must be equal to the demand price of the products Otherwise, there won’t be a transaction Eq (10) indicates that under equilibrium conditions, if the demand price is more than zero, then the demand of products is equal to the trading volume of them Otherwise, the former will
be less than the latter
For all the consumers, i1, 2,,I , the equilibrium point could be got by variation inequalities:
3
1 1
1 1
( )
N I
ni
n i
i n
q d
(11)
4 EQUILIBRIUM OF THE MODEL
By the theory of variation inequality, equilibrium conditions can be obtained by summing the
3
(q sm ,q mn ,qmn,q ni , i , m , n ) 0 to meet
m
.
s t q q
(q mn ,qmn,q ni ,n ) 0
( )
ni ni
c q f Q
c q
q
0
n
3i
I
3 3 1 =
i i
3 ( )
i i
d
1, 2, ,
n N
Trang 5
(12)
There is optimal solution for Eq (12) on the basis
that the cost function of various decision-makers is
continuously differentiable convex function Fixed
projection algorithm (Fenglian Li, 2009) was used in
this paper And finally the followings could be
obtained:
sm
f Q c q
p
( )
ni ni
ni
c q p
q
;
;
5 NUMERICAL EXAMPLE
Assume that a closed-loop supply chain network
of one home appliance was consists of two suppliers,
one manufacturer, one retailer, two consumers and one
recycler The super-network of it was shown as Fig 3
1
供应商
制造商
零售商
消费者
Fig.3 Home Appliance Closed-Loop Supply Chain
Super-network Functions in the model were set as follows
Production cost functions of suppliers:
1 ( 1 ) ( ) 1 0.5 1 2 ( ) 2
f Q q q q q
2 ( 2 ) ( 2 ) 0.8 1 2 ( 1 )
f Q q q q q
In which q1 q11 q12 , q2 q21 q22 and the followings are similar
Transaction cost functions between suppliers and the manufacture were set as:
Production cost functions of manufactures:
2 2 2
2 2 2
( ) 2.5( ) 0.005 ( ), ( ) 2.5( ) 0.005 ( )
f Q q q q q q
f Q q q q q q
Transaction cost functions between manufactures and suppliers:
Transaction cost functions between manufactures and retailers:
The cost that manufactures pay for goods that returned:
; The cost that manufactures pay for goods that replaced:
The lost of manufactures for the returns from retailers:
, ,
The operating cost functions of retailers:
2 2 2 1 2 1
f Q q q q q
Transaction cost functions between retailers and manufactures:
11 ( )11 11 2, 12 (12) 12 2, 21 (21) 21 2, 22 (22) 22 2
c q q c q q c q q c q q
Transaction cost functions between retailers and consumer:
Supplier
Manufacture
Retailer
Consumer
1 1
1 1
S M
sm
s s sm sm sm
sm sm mn mn
M N
mn
m m mn mn mn mn n n
m n
m m mn
mn
f Q c q c q
q q q q
f Q q c q c q f Q
f Q q
q
1 1
3
1 1
1 1 1
( ) ( )
M N
m
m n m
m n
N I
ni ni
ni ni n i ni ni
mn mn
n i ni
c q c q
c q
q
1 1 1
3 3 3
1 1
3
( , , , , , , ) 0
N M I
ni n n
n m i
I N
i n
sm mn mn ni i m n
q d
q q q q
r
p
12 12
) (1 )(0.5 1), ( ) (1 )(0.5 1), ( ) (1 )(0.5 1), ( ) (1 )(0.5 1)
Trang 6The lost retailer for the returns from consumer:
Consumer’s demanded function of
consumer:d1 (3 ) 231 1.532 500
The step size was set to be 0.01, the cycle
validation criteria were 10-4, and the initial values were:
By MATLAB simulation, the trade volumes were
different when the values of 、were changed
When 0.5 , 0 : 0.1:1, how the trade
volume changes with was shown in Fig 4
Fig 4 How the trade volume changes with
s m n
replacement volume between supplier and manufacture,
manufacture and retailer, retailer and consumer
respectively (the followings were the same)
From Fig 4 When increases, the trade
volumes between the nodes decreases, but the amount
of returning and replacing increases, too Thus, the
returning of goods should be strengthened while the
replacing should be encouraged to increase the revenue
of all the nodes
When 0.5 , 0 : 0.1:1 how the trade
volumes changes with was shown in Fig 5
Fig 5 How the trade volume changes with Similarly, the suppliers need to pay attention to the quality of the products to decrease the defect rate and increase the trade volume
When =0.5，0.5, all the trade volume were shown in table 1 to table 5
Table 1: The trade volume between suppliers and
manufactures Manufacture 1 Manufacture 2
Table 2: The trade volume between manufactures and
retailers Retailer 1 Retailer 2
Table 3: The trade volume between retailers and the
consumer
Table 4: The amount of returning and replacing between
the consumer and retailers
Consumer 1
Consumer 1
11 ( 11 ) 0.5 11 1, 21 ( 21 ) 0.5 21 1,
31 32 1, q11 q12 q21 q22 , 0.5, 0.5
Trang 7Table 5: The amount of replacing product between the
consumer and retailers
Consumer 1
By the numerical results, the trade volumes
between different layers were the same, which verifies
the correctness of the model
6 CONCLUSION
Home appliance closed-loop supply chain
super-network based on returns and replacement was
established in this paper, by analyzing the equilibrium
conditions of various decision-makers, the transaction
price and the trade volume of various decision-makers
were got Also, by setting different returning and
defective returning ratio, instructive conclusions which
said the returning of goods should be strengthened
while the replacing should be encouraged and the
quality of the products should be improved were
gained
The later study will consider the punishment
mechanism of returns and replacement due to raw
materials or parts defectiveness to make the model
better
ACKNOWLEDGMENTS
This research was supported by the Grant-in-Aid for
Asian CORE Program "Manufacturing and
Environmental Management in East Asia" of Japan
Society for the Promotion of Science (JSPS)
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