2010 International Conference on Management Science & Engineering (17th)
November 24-26, 2010
Melbourne, Australia
The Study of Supply Chain Competition Model
and Cooperative Innovation between Supply Chains
TENG Chun-xian，HU Yin-xia，ZHOU Yan-shan
School of Management, Harbin University of Science and Technology, P.R.China, 150080
Abstract: Through providing the new definitions of
supply chain economy, market pertinent chain, operation
link and interface link, we establish the supply chain
economy model with electronic commerce based on
variational inequality theory and spatial price theory.
Furthermore, we have analyzed the characteristics and
feasible conditions of cooperative innovation between
supply chains, and added the cooperative innovation into
the supply chain competition model. The results indicate
that, through the cooperative innovation between supply
chains, the large enterprise will inevitably promote the
development of small enterprise, so every one wants to
cooperative with a stronger enterprise. In other words,
the cooperative innovation just can be in agreement
between two enterprises with similar size.
Keywords: supply chain competition, cooperative
innovation, cooperation between supply chains,
variational inequality
1 Introduction
The essence of competition between enterprises is
core competitiveness. In order to win the fierce
competition, enterprises form strategic alliances to
increase their strength[1]. Along with the development
and application of supply chain management, the
enterprises strategic alliances reengineer business
process according to supply chain management idea.
Strategic alliances gradually transform into supply chain,
and competition between enterprises gradually transform
into competition between supply chains[2].
In the respect of supply chain competition, scholars
and experts have made some study. For example, Boyaci
(2004) consider a market with two competing supply
chains, each consisting of one wholesaler and one retailer.
They find that coordination is a dominant strategy for
both supply chains, but as in the prisoner's dilemma, both
supply chains are often worse off under the coordinated
scenario relative to the uncoordinated scenario. The
consumers are the only guaranteed beneficiaries of
coordination[3]. Pranab Majumder (2007) study network
Supported by the National Natural Science Foundation of
China (70471067); Heilongjiang Provincial Overseas
Academics Foundation ( 1055HZ029)
supply chains with price dependent demand by
modelling them as large acyclic networks. Such large
networks are common in the automobile and apparel
industries. The results show that contract leadership, as
well as leader position in the network, affect the
performance of the entire supply chain[4]. Albert(2008)
investigate contracting and information sharing in two
competing supply chains, each consisting of one
manufacturer and one retailer. Their results highlight the
importance of contract type as a driver of the value of
information sharing and the role of information sharing
capability as a source of competitive advantage under
supply chain competition[5]. Tiaojun Xiao(2008) develop
a price-service competition model of two supply chains
to investigate the optimal decisions of players under
demand uncertainty. Each supply chain consists of one
risk-neutral supplier and one risk-averse retailer. They
find that the higher the service investment efficiency of
one retailer, the lower the optimal retail price and service
level of his rival will be[6]. Biying Shou (2009) study the
competition of two supply chains which are subject to
supply uncertainty. They show that supply chain
coordination is a dominant strategy, and customers are
always better off. If supply risk is low, coordination
actually could decrease supply chain profit, which results
in a prisoner’s dilemma; If supply risk is high,
coordination always increases supply chain profit[7].
The former researches of this field emphasize
competition, and highlight how the coordination within
supply chain influences the competitive results. However,
almost all researchers ignore the “win-win” cooperation
between supply chains.
The cooperative innovation in this paper, which is
different from the traditional innovation in the trinity of
enterprises, campuses and research institutes[8], means
“win-win” cooperation between supply chains. The
cooperative innovation in this paper is a cooperative
activity which is pay out together by two same type
enterprises (both are retailers or manufacturers), whose
goal is to increase the profit of both enterprises, and help
them win in the fierce competition. Generally, this kind
of innovative activity cost so prodigious that it can not be
bear by a single enterprise[9]. Therefore, cooperative
innovation can be beneficial to both enterprises. If the
extra profit brought by cooperative innovation was not
- 363 978-1-4244-8119-4/10/$26.00 ©2010 IEEE
justly distributed, then the cooperative activity can not be
well afoot. In this paper, we mainly study the application
and “win-win” effect of cooperative innovation based on
supply chain competition model.
2 Supply chain economy concepts and
mathematical representation
In order to establish supply chain competition
model under B2C circumstance, we introduce several
new concepts, which will be mathematically formulated
into a network model in subsequent sections.
2.1 Supply chain economy (SCE)[10]
A SCE is a network of interrelated activities of
procurement, production, distribution, and consumption
of one or many related products or services, conducted
by several coalitions of business entities who act
collectively within a coalition. Take as granted the
definition of supply chain, we can state that a SCE is a
network of interrelated supply chains.
2.2 Market pertinent chain (M-chain)
Traditional market pertinent chain pertaining to an
end product (or service) market, is a network of
coordinated business activities involved in procurement,
production, distribution and vendition, that are associated
with the delivery of the pertinent product (or service) to
the pertinent market. Under B2C trading environment,
market pertinent chain consists of web construction,
advertisement, order on the internet, electronic payment,
transportation, consumer evaluations and so on[11][12].
Through the Fig.1 we can gain a better interpretation of
SCE and M-chain.
consists of M-chains. The supply chain competition in
this paper is implemented by M-chains.
Denote G = [ N , L] as a connected network in
which N represents the collection of nodes, and L
represents the collection of directed links. A link in our
model can be either an operation link or interface link,
with the orientation indicating the direction of flow of
material or information. An operation link represents a
substantial business function performed by a firm in a
supply chain network and, as such, can be a
manufacturing operation, a transportation operation, a
storage operation, or a service operation. In general, our
model allows an operation link to participate in multiple
supply chains. An interface link represents a coordination
function between two successive operation links in a
supply. In our model, an interface link is defined to be
supply chain specific and thus, every interface link only
belongs to one supply chain. Denote A as the set of all
operation links, and B as the set of interface links. Thus,
we have L = A ∪ B .
An M-chain in our model will be denoted by a
connected sub graph of G . In the sub graph, there are
several origin nodes and one destination node, which
corresponds to the pertinent market. Thus, a SC, as a
family of coordinated M-chains, is a connected sub graph
with at least one origin and one destination. The entire
G represents the SCE under study which is usually
comprised of several SCs. Let i = 1, , m represents a
specific supply chain, j = 1,
, n represents a specific
product (or service), and k = 1, , l represents a
specific market. We suppose that the l markets are
different in locations or on Internet.
We use Sijk to represent a potential M-chain which
B 2C
is in traditional trading mode, and Sijk
SCE system
Family Car
Ford SC
China
M-chain which is in electronic commence trading mode.
The electronic commence in this paper is mainly B2C.
Sport Car
B 2C
S B 2C as the set of Sijk ,
and S as the set of all M-chains, that is S = S ∪ S B 2C .
Denote S as the set of Sijk ,
Family Car
America
GM SC
to represent a
The flow of a M-chain is defined to be the quantity of
products or service delivered to its specific destination
market. The flow is called the output of M-chain. Let
X s be the chain flow (or output) of M-chain s , and
Sport Car
Fig.1 SCE of ford and GM
Fig.1 shows a SCE consisting of Ford supply chain
and GM supply chain, both of whom produce family car
and sport car, and sell their product to China market or
America market[13]. Ford supply chain and GM supply
chain are related to each other. For example, they may
have the same row material supplier or the same 3PL.
Ford family car from production to consumption in
China market form a market pertinent chain of Ford. In
Fig.1, the broken line means B2C trade, and for clarity,
we have not marked all possible B2C trade. Over all, a
SCE consists of supply chains, and a supply chain
X = ( X s , s ∈ S ) be the vector of all the chain flows
of M-chains in SCE.
2.3 Process rate
Process rate λas represents the product quantity
on operation link a with respect to one unit product on
M-chain s . Process rate unifies the unit of product from
raw material to end product on the M-chain[14]. For
example, each car requires 4 tires, considering defective
rate, work time, machine time and storage, the process
- 364 -
rate of tire manufacturer with respect to original
equipment manufacturer, is more than 4. Based on the
analysis, we assume λas ≥ 1 .
2.4 Link flow, chain flow
For any link a ∈ L , we use
xa to denote the flow
on link a . For an operation link a ∈ A , xa is the total
amount of work processed on this link in the network of
the SCE. For example, the link flow of a transportation
operation represented by a trucking company should be
the total shipments it is handling for all the M-chains in
which it participates.
We define the operational link chain incidence
matrix Δ = (δ as )a∈A, s∈S to be |
A | × | S | zero-one matrix,
where
⎧1 if link a participates in M-chain s
otherwise
⎩0
δ as = ⎨
(1)
X s be the chain flow of chain s , then the
chain s induced link flow on link a is λas X s , if a is a
participant of s . Mathematically, one has flow the
Let
following conservation equation for operation link flow
variables and chain flow variables:
xa = ∑ s∈S δ as λas X S , ∀a ∈ A
(2)
For an interface link b ∈ B , the link flow xb
indicates the amount of integration work, coordination
effort or information processed on this link. Since
interface links are chain specific, the family of all
interface links, B , can be partitioned into sub families,
operation links that it bridges. The geographic distance,
past cooperation experience, level of information
integration, and the compatibility between the two
operation links, etc., could be the factors that account for
the cost of an interface link. Since the effective
coordination of two successive operation links may
depend on other joints of the chain as well, we assume
that the cost of an interface link may, in general, depend
on the flows of all the interface links belonging to the
same M-chain. As interface links are chain specific,
however, flows on all interface links are determined by
the chain flow of the governing M-chain. Therefore, we
define cb = cb ( X s ) , and cb = ∂cb ( X b ) ∂X b , where
b ∈ Bs , s ∈ S .
As a general rule, one operation link can participate
in more than one M-chains simultaneously, so the cost of
the operation link should also be imputed to its
participating M-chains. The operation link cost
imputation can be performed under flow weighted
average principle, or performed according to different
contracts designed before trading. In order to simplify
research, we use flow weighted average principle to
imputable the operation link cost. For an M-chain s
and its participant operation link a , the chain-imputable
link cost of link a with respect to M-chain s , denoted by
Cas , is the cost accountable for M-chain s , attributed to
the work processed for s on operation link a . The
chain-imputable link cost Cas , may depend on the total
link flow on link
link a , λas X S , which is the amount of work contributed
by M-chain s to link a . Therefore, the chain-imputable
link cost Cas can be expressed as
Cas = ca ( xa )
Bs , according to their governing M-chain s ∈ S .
Therefore, the link flow of an interface link is uniquely
determined by the chain flow of its governing M-chain.
2.5 Link cost, chain cost
We define the link cost ca , by a genetic cost
ca = ca ( xa ) , ∀a ∈ A . Define
ca = ∂ca ( xa ) ∂xa as marginal cost of link a cost
function ca , measures an appropriate combination of
function of its flow xa ,
monetary cost and other relative cost (time, quality, etc.).
In a modeling effort, ca can take a weighted majority
form, with the monetary cost being assigned a weight of
one, and other factors of ineffectiveness being assigned
relative weights that can convert to an equivalent dollar
amount. The cost of an interface link reflects the
effectiveness of coordination and integration of the two
xa , and chain s induced flow on
λas X s
xa
, ∀a ∈ A
(3)
The cost of an M-chain s is the aggregated
generalized cost incurred in all the operation and
interface links of this M-chain in delivering the final
product to the pertinent market. The cost of an M-chain
s is the sum of s -imputable link costs of all the links it
employs, which can be mathematically expressed as
Cs = ∑a∈A δ asCas + ∑b∈B cb
s
Define Cs
s∈S
(4)
= ∂Cs ( X s ) ∂X s as the chain marginal
cost. In equation (4), the cost of M-chain do not only
depend on its own flow (output), but also depend on
other M-chains’ flow of the entire SCE. The equation (4)
reflects cooperation and competition relationship among
M-chains in SCE.
- 365 -
2.6 Demand
For the sake of simplicity, we restrict our
presentation to a fixed demand model in this paper.
Nevertheless, the model can be extended directly to
incorporate market elasticity, in form of a demand
function or a price function. Suppose that the market for
product j in marketplace k has a fixed demand d jk , for
every
j = 1,
, n, k = 1,
, l . Therefore, d jk can be
expressed as
∑
X +∑i =1 X S B 2C = d jk
i =1 Sijk
m
m
ijk
j = 1, , n; k = 1, , l
(5)
M-chains, that is S j ′k ′ = {Sij ′k ′ , Sij ′k ′ , i = 1,
B 2C
, m} .
In our model, the operation link cost and interface
link cost represent generic costs that measures not only
the monetary but also other effectiveness such as
delivery time, service and quality issues. Therefore, the
winning M-chains defined by the equilibrium conditions
are also strongest in the actual market competition. In
addition, the above definition of SCE equilibrium is in
accordance with the spatial price equilibrium theory
economically. According to the equivalence relationship
of the spatial price equilibrium theory and the variational
inequality problem[18], we can use the variational
inequality problem to characterize the SCE equilibrium.
Theorem 1 (VIP in chain variables) If and only if
∗ solves the following variational inequality problem
X
An end consumer market is a destination of a
commodity, which pulls the flow of materials through its
pertinent M-chain. Therefore, the M-chains, as
alternative “paths” to the destination, are competing
against each other in delivering the commodity to the
destination. Covinato (1992) argued that the firms’
cooperation quest in SC management is to make the final
product at overall lower total cost than competing sets of
SC firms. Following this philosophy, the winning
M-chain in this competition must be the “shortest paths”,
who can deliver the commodity at the lowest marginal
total cost[15]. There is an interesting analogue between
this competition and that in a traffic network problem[16]
in which the travelers seek to determine the shortest
paths to travel from their destinations. This analogue
inspires us to use variational inequality to solve supply
chain competition problem.
(7), then X ∗ is a SC network equilibrium, that is, find
3 Supply chain competition model based on
B2C environment
4 The study of cooperative innovation
between supply chains
According to the above basic introduction of supply
chain economic network, we can draw some conclusions.
In a SCE system, for the same kind of products or
services in the same market, all the potential M-chains
that have higher marginal total cost that their competing
M-chain should have no market share. In other words, all
the less cost-effective potential M-chains will be inactive
in equilibrium[17]. Mathematically, a feasible SCE X ∗
constitutes a supply chain network equilibrium if and
only if the follow system of equalities and inequalities
holds true:
In this section, we take manufacturing technology
innovation for example to analyze the coordination
process and influence of cooperative innovation between
supply chains. In order to illustrate distinctly, we assume
that there are two M-chains, s1 and s2 in the supply chain
economy, who produce the same product and compete
with each other in the same market, as depicted in Fig.2.
The M-chain s1 consists of a1b1a2b2 a3 , and s2 consists
⎧= min Cs ( X ) if X > 0,
⎪ s∈S jk
Cs ( X ) ⎨
∀s ∈ S jk
∗
∗
min
C
(
X
)
if
X
0,
≥
=
⎪ s∈S jk s
s
⎩
∗
∗
[19]
X ∗ ∈Ω such that
n
l
∑∑ ∑ C ( X
j =1 k =1 s∈S jk
s
∗
)( X s − X s∗ ) ≥ 0, ∀ X ∈ Ω
Where Ω = { X s ≥ 0, s ∈ S :
∑
s∈S jk
(7)
X s = d jk , ∀j , k} is
the feasible set of M-chain variables for the supply chain
network.
VIP(7) can be seen as a general framework for the
formulation of SCE equilibrium, which represents link
marginal cost function. This model does not include the
operation cost imputation contracts. Just as above
mentioned, in this paper we use the chain flow weighted
average principle to impute the operation cost.
of a4b3 a5b4 a6 . The same to the above, a means
operation link, and b means interface link.
The operation link a1 , a4 denote that suppliers
∗
s
(6)
provide row material, a2 , a5 denote manufacturers’
production, and a3 , a6 denote retailers sell their goods
We will use S jk to denote the set of all M-chains
pertaining to the end consumer market ( j , k ) , including
traditional trading M-chains and e-commerce trading
to consumer. The interface link b1 , b2 , b3 and b4 denote a
coordination function between two successive operation
links.
- 366 -
b1
a1
b1′
a9
b3′
a4
b3
Cs′ ( X ) = Cs ( X ) − 0.9θγ X s
a2
b2
b8
a2′
b9
a5′
a5
b4
Xs
1
+ ρθ 2 ⋅
2
∑ s∈S coop X s
a
b2′ 3
market
b4′ a6
Fig.2 Cooperative innovation between supply chains
After adding the cooperative innovation between
supply chains, we assume operation link a9 denotes the
innovation
process,
interface
In equation (8), S coop denotes the set of
cooperative innovation M-chains, which include two
elements.
Let C saving denote the total cost saved by
cooperative innovation. When the technological
innovations intensity is θ , the C saving can be expressed
as equation (9).
C saving = ∑ s∈S coop ( Cs ( X ) − Cs′ ( X ) )
link b8 , b9 denote
coordination of covert behavior, patent ownership,
cryptology of technique and so on, operation link
a2′ , a5′ respectively denotes production activity of
M-chain s1 , s2 after innovation, and interface link b1′ ,
b2′ , b3′ , b4′ denote the corresponding coordination after
innovation. If the two supply chains have agreed upon
the major points of the cooperative innovation, then the
M-chain s1 turn to s1′ = a1b1′a9b8 a2′ b2′ a3 , and s2 turn
to s2′ = a4b3′a9b9 a5′b4′ a6 .
After the innovation completed together by
M-chain s1 and s2 , production technology of both
M-chains will improve simultaneity. In other words,
production cost of operation link a2′ and a5′ will reduce.
We assume that γ denotes the highest degree of unit cost
saving which caused by two manufacturers cooperative
innovation, and then θγ denotes unit cost saving which
caused by two manufacturers cooperative innovation,
where 0 ≤ θ ≤ 1 denotes technological innovations
intensity. In this paper, technological innovation needs
ρθ 2 represents capital
M-chain, where ρ is a great
much capital, we assume that 12
invested together by the
positive constant[20]. In other words, if the two M-chain
ρθ 2 together，then their unit production cost will
cut by θγ . Therefore, the cost of the innovation
2
operation link a9 is 12 ρθ . Interface link b8 and b9 have
According to the first order condition of equation
(9), θ = 0.9γ
*
(∑
s∈S coop
Xs
)
ρ maximizes
the saving
cost C saving . Substituting θ * into the expression of
C saving , we gain the equation (10).
C saving =
0.405
ρ
γ 2 ( ∑ s∈S
coop
Xs
)
2
(10)
As mentioned above, ρ is a great positive constant,
so we can draw two conclusions. (1) the total saving cost
is positive, that is C saving > 0 ; (2) the total saving cost
increases as the total chain flow (the sum of the two
cooperative M-chains chain flow) increases; (3) the
saving cost, in turn, will enhance the core
competitiveness of the two cooperative M-chains. We
suppose that there are only two M-chain performed the
cooperative innovation with each other of all the
M-chains in the SCE, and let the difference set
S = S \ S coop be the set of M-chains which have done
nothing with cooperation in the supply chain competition
model. Then, the supply chain competition model with
cooperative innovation can be expressed as variational
inequality problem (11).
∑
Cs ( X ∗ )( X s − X s∗ ) +
∑
Cs′ ( X ∗ )( X s − X s∗ ) ≥ 0
s∈S
s∈S coop
∀X ∈ Ω
(11)
In inequation (11), the feasible set Ω can be express
as Ω = { X s ≥ 0, s ∈ S :
operation link a9 is a part of both M-chain s1 and s2 , if
the two M-chains distribute a9 cost according to flow
weighted average principle, then M-chain s cost
function can be expressed as (8).
(9)
= 0.9θγ ∑ s∈S coop X s − 0.5ρθ 2
invest 12
the same function, coordinating problems caused by
innovation. The higher the innovation intensity is, the
more the coordination cost, so we assume that the unit
cost of link b8 and b9 is 0.1θγ . Due to that innovation
(8)
s ∈ S coop
∑
s∈S jk
X s = d jk , ∀j , k} .
Through the analysis of saving cost function
—equation (9), we know that
∑
s∈S coop
C saving increases with
X s . In other words, the larger the total output
of the two cooperative M-chains is, the more the total
saving cost is. Therefore, we can gain
- 367 -
Conclusion through the cooperative innovation
between supply chains, the large enterprise will
inevitably promote the development of small enterprise,
so every one wants to cooperative with a stronger
enterprise. In other words, the cooperative innovation
just can be in agreement between two enterprises with
similar size.
In the view of the above conclusion, if a small
enterprise wants to cooperate with a large enterprise,
with the aim to improve manufacture technology,
increase awareness, expanding the market or others, it
must design a reasonable contract to impute the
cooperative cost and share the extra profit.
5 Conclusion
Through the analysis of supply chain cooperation
and competition, we redefine the concepts of supply
chain economy, market pertinent chain, operation link
and interface link, and establish the supply chain
competition model with B2C trade environment and
cooperative innovation based on variational inequality
theory and spatial price theory. Cooperation between
supply chains is a new research field, so we have not
found interrelated academic achievements. Our research
about cooperative innovation between supply chains is
just an attempt of this field, but we find some interesting
results: (1) cooperative innovation between supply
chains can achieve a “win-win” effect; (2) through
cooperation, the large enterprise can inevitably promote
the development of small enterprise. Future research may
consider other problem in cooperation between supply
chains.
References
[1] C Martin. Logistics and supply chain management:
Strategies for reducing cost and improving service[M].
The Financial Times Press, 1999: 5-25.
[2] M Christopher, D R Towill. Supply chain migration
from lean and functional to agile and customized[J].
Supply Chain Management: An international Journal,
2000, 5 (4): 206-213.
[3]T Boyaci, G Gallego. Supply chain coordination in a
market with customer service competition[J]. Production
and Operations Management, 2004, 13(1): 3-22.
[4]P Majumder, A Srinivasan. Leadership and
competition in network supply chains [J]. Management
Science, 2007, 11: 1-16.
[5]Y H Albert, S L Tong. Contracting and information
sharing under supply chains competition[J]. Management
Science, 2008, 54(4): 701-715.
[6]T Xiao, D Yang. Price and service competition of
supply chains with risk-averse retailers under demand
uncertainty[J]. Int. J. Production Economics, 2008, 114:
187-200.
[7]Biying Shou, Jianwei Huang, Zhaolin Li. Managing
supply uncertainty under chain to chain competition[R].
Working Paper, 2009.
[8]W Zhang, J Li. The analysis about stability of the
cooperation of cooperation of enterprises, colleges and
institutes which based on the evolution game[J].
Technoecomomics & Management Research, 2009,5:
25-27.
[9]H Sigvald, K sandra, D Rafal. Making innovative use
of academic knowledge to enhance corporate technology
innovation impact[J]. International Journal of
Technology Management, 2007, 39: 131-157.
[10]D Zhang. A network economic model for supply
chain versus supply chain competition[J]. Omega, 2006
34: 283-295.
[11] M N Hung, J Norma. Electronic supply chain
orientation and its competitive dimensions[J]. Production
Planning &Control, 2004, 15(9): 596-607.
[12] L Chen, J Long, T Yan. E-supply chain
implementation strategies in a transitional economy[J].
International Journal of Information Technology &
Decision Making, 2004, 3: 563-574.
[13]R Bordin, K Susumu, J L Larry. EDI performance in
the automotive supply chain [J]. International Journal of
Technology Management, 2000,20:287-303.
[14]S Lakhal, A Martel, O Kettani, M Oral. On the
optimization of supply chain networking Decisions[J].
European Journal of Operational Research, 2001,
129:259-270.
[15]J. A Cavinato. Total cost/value for supply chain
competitiveness[J]. Journal of Business Logistics, 1991,
27: 10-15.
[16]A Nagurney, L Zhao. Networks and variational
inequalities in the formulation and computation of
market disequilibria: The case of direct demand
functions[J]. Transportation Science, 1993, 27: 4-15.
[17] Q Wu，H Chen．Chain-chain competition under
demand uncertainty[R]．Vancouver: The University of
British Columbia, 2003: 27-29.
[18]S Dafermos, A Nagurney. Oligopolistic and
competitive behavior of spatially separated markets[J].
Regional Science and Urban Economics, 1987,17:
245-254.
[19]P Harker, J S Pang. Finite-dimension variational
inequality and nonlinear complementarity problems: A
survey of theory, algorithms and applications[J].
Mathematical programming, 1990, 40: 161-220.
[20]F Ye, Y Li, X Hu. Supply chain technology
innovation revenue sharing contract under random
demand[J]. Science and Technology Management
Research, 2005(3): 81-83.
- 368 -