Quality Control in Food Supply Chain Incorporating Government ...

2012 2nd International Conference on Materials, Mechatronics and Automation
Lecture Notes in Information Technology, Vol.15
Quality Control in Food Supply Chain Incorporating Government
Inspecting
JuanjuanTan a , Di Xiao b , Yunhong Hao c
School of Business Administration , Zhejiang Gongshang University, China
a wodemingzijiaotjj@163.com, b xiao_di1980@163.com c haoyh@mail.zjgsu.edu.cn
Keywords: the food supply chain, quality, government supervision
Abstract. In recent years, food security events had happened frequently in the Chinese food market,
which causes a high degree of public concern. This research is on the basis of the supply chain
between direct participants and indirect participants in the supply chain game, and studies further to
discover the effective way to achieve quality management of the chain. This article, using the
Stackelberg game model, separately analyzes how the suppliers and government make the optimal
decisions and behaviors. The research shows that, whatever positions the firms are, quality
improvement and profit increase are available as long as they obey the government regulations on
quality.
1. Introduction
With economic globalization, the degree of integration of the market development continues to
deepen, and competition between enterprises is more and more intense, so it is with the food
industry. Food supply chain has inter-departmental, inter-regional and cross-border characteristics,
expanding the operational range of the food industry and, to a certain extent, improving the profit of
the chain members through operating costs reduction by smooth procurement, production and
distribution operations. But the most important feature of the food supply chain is the difficult
product quality management resulting from cross-regional feature while which brings the big profit.
Franca(2010) [1] ,Karipidis and Xie etal(2011) [8] point out that quality management practices and
interactions of chain members are closely related, and that interactions directly affect the
transactions on the market and customer satisfaction. Then Hsieh and Liu(2010) [3] have researched
quality investment and regulatory policies of suppliers and manufacturers in the non - cooperation
game, impact of regulation information on equilibrium strategies and profits of both sides.
However, in the actual market, chain members behave to maximize own benefits instead of
interest of the chain as a whole, resulting in low quality investment inputs, quality deceit and
different quality standards. On the other hand, the food supply chain, due to its own characteristics,
is very different form the traditional supply chain.
Firstly, customers are difficult to assess the quality of the food industry products and potential
quality dangers are hard to identify. Once safety events occur, buyers will bear huge losses, not only
economically, but more physically and psychologically. What’s more, track and confirmation source
of the virus take a longer time, not only because of long supply chains, but also because of
separation of the source of crisis and food producing area, therefore, firms especially the leading
enterprises dare to adopt low-quality production. Secondly, as people research deeper, Kan, Wang,
Tao, Wang (2005), Li and Liu (2007) [4] and Zhou (2010) successively put forward that the
formation of quality in the food supply chain should not only consider the direct role of supply
chain members, but also consider the members play an indirect role such as the government. For
example, the government has given some large food companies, as Yurun, a lot of economic
978-1-61275-015-6/10/$25.00 ©2012 IERI ICMMA2012
352

incentives in order to promote their productions. Then enterprises like this don’t have to fear the
consequences of their poor quality.
Besides, more other literatures have talked about the effect of government supervision of
products. Since the government's safety supervision system reform of developed countries in 1990,
China has undergone a series of food safety issues in recent years, causing customers in the market
paying more and more attention to food quality. Zhan and Kong (2004), Yu and Zhou (2005) and
Wang (2011) [9] , from the perspective of game theory, point out that the quality of the products in
the food industry is the result of coordination jointly by the enterprise and government.
2. Dynamic game model of Government and Enterprise
2.1 Basic assumptions and models
In order to facilitate the analysis, this paper makes the following basic assumptions under the
premise of no affecting the results: 1) In a oligopoly market of the food industry,customers choose
products considering the price of the products p e
and the quality of all products i . 2) The
participants have the same information about the behavioral characteristics,strategies and revenue
functions of other actors. The game has only two participants: government and food production
enterprises. They make decisions respectively on the degree of probability and quality efforts. 3)
Food sales is D . The cost of government supervision using administrative means is θ Dm
. The
probability of government detection isθ . Government inspection cost for each product is m . If the
government finds out the quality of the product is lower than the requirements, penalty on producer
is d . 4) Orders of government’s and enterprises’ behaviors are not consistent. Both sides decide
their actions based on self-interest maximization .
The Demand Curve
Market demand producers face is uncertain, so the article sets the demand function on the basis
of the one Lu (2008) putted forward:
The demand function is De () = l+ αe
(1)
i
Inside: α represents the entire needs of customers in the whole market, which reflects the
development level of the product in the market as a whole (Banker R D, 1998).
2.2 Government decides first. The enterprise undertakes strategic analysis.
This article establishes a two-stage game model according to the relationship between government
and the leading enterprises in the supply chain. The first stage is government decision making on
detection, and the second stage is enterprise’s choice of quality efforts strategy under the estimation
of the probability of governmental detection.
kG
First, government's utility function is U ( θ ) = ln
G 1- θ
, ( ) '
0, ( )
'
U θ > U θ < 0
G
G , and kG
is the
government utility parameters , θ ∈(0,1) .
So the government's benefits is
⎧ k
G
⎪ln -θDm + γ ( ei-e L)
+ d , e
ieH
⎩ 1-θ
After the government determines his own strategy, producing company will determine the
quality strategy based on the strategy of the government. Company’s demand function is (1). The
government will give each industry the corresponding quality requirements in the beginning of the
industry production. Assuming the quality requirements are set from e L
to e H ,
and producer’s cost
353

of quality effort under the given requirement is
K M , and
KM
is an increasing convex function,
2
kei
e
which means i , KM '( ei) > 0, KM ''( ei) > 0 . The function of quality effort is
K
M
=
2 (3),
and the
quality effort cost parameter k>0. Similar cost function of quality effort is also used by Gurnani and
Erkoc(2008),Kaya and Ozer (2009).
e
H
The company’s profit is
2
⎧ kei
⎪ DM − − [ θϕd + θ (1 − ϕ)0 ],
ei
< e
⎪
2
2
⎪ kei
Π
M
= ⎨ DM − , eL ≤ ei
≤ eH
⎪ 2
2
⎪ kei
⎪ DM − +R
G,
ei
> eH
2
⎩ (4)
α
As can be seen from above in either case, company face reflected function is ( p-c)
ei
=
k
Here, on
e ∗ i
case discussion,we know that
⎧ M + kR M + M −k Me − R −ke
⎪ e < e < < e e < e <
⎪ k k k k k
∗ ⎪αM αM αM+ 2kRG
αM
αM+
2kθϕd
αM+ 2 k( θϕd+
RG
)
ei = ⎨ , 当 < eH且 eH > ; 若 < eL, eL > , eH
>
⎪ k k k k k k
⎪ αM+ α M − (2kR + 2 kαMe − k e ) αM+
2kθϕd
⎪ < < <
k k k
2 2 2
αM
α 2
G αM
αM+
2kθϕd
α α (2α
L
2
G L
)
H, 当
H
; 若
L, H
,
H
2 2 2 2
αM
G H H
eL 当 eL , eL
⎪⎩ , ,
α M
eL
k
<
( 一 )If the
(A)The government quality level line is in the range
2 2 2
αM + 2kθϕ d αM + α M −k(2αMeL −2 RG −keL
)
< , eH
<
k
k
Enterprise will choose eH
as the quality level
kG
∏
G
= ln − θ( l+ αeH) m+ r( eH −eL)
At this time 1−
θ
The government in order to achieve maximum profits, θ on both sides to be derivative
1
θ = 1 − ( l + αe ) m
H
2
keH
∏
M
= ( l+ αeH)
M − + RG
∏
G
= ln kG( l+ αeH) m− ( l+ αeH) m+ 1 + r( eH −eL)
2
,
(7)
αM + 2kθϕ d αM + 2 k( θϕd + RG
)
eL
> , eH
>
(B) From the condition, we can get
k
k
M
e
∗ = α
Enterprise will choose i
k
kG
αM αM
∏
G
= ln − θ( l+ α ) m+ r( − eL)
+ d
1− θ k k
(8)
The government in order to achieve maximum profits, θ on both sides to be derivative
1 k
θ = − ( 2
kl + α M ) m
Put (7) and (9) in (8)
2 2
α M ( kl+
α M)
m αM
G G L
∏ = ln k ( l+ ) m− + r( − e ) + d
k k k ,
2 2 2
α M ( kl+ α M) m−1
∏
M
= lM + −
ϕd
2
2 k ( kl+
α M)
m
L
(5)
(6)
(9)
(10)
354

(C)if
e
< L, αM + α M − (2kR + 2 kαMe −k e )
Enterprise will choose ei
2 2 2 2
G H H
∗ =
k
e
L
,
αM + 2kθϕd
eL
<
k
, We can get 1
θ = 1 − ( l + αe ) m
2
∏
G
= ln kG( l+ αeL) m− ( l+ αeL) m+ 1
keL
, ∏
M
= ( l+ αeL)
M −
2
(11)
α M
e < < e
( 二 )When L k
H
,
(D)At this time α M + 2kR
e
G
H
>
Enterprise will choose
M
e
∗ i
= α
2
k ,
k ,
1 k
θ = − ( lk + α M ) m
2 2
2 2 2
α M ( lk+ α M)
m−k αM
α M α M
∏
G
= ln kG( l+ ) m− + r( −eL)
∏
M
= ( l+ ) M −
k k k ,
k 2 (12)
(E)
If α M + 2kR
e
G
H
<
k
Enterprise will choose e
∗ i
= eH
.
The condition is the same to the (A)
2
∏
G
= ln kG( l+ αeH) m− ( l+ αeH) m+ 1 + r( eH −eL)
keH
, ∏
M
= ( l+ αeH)
M − + R
(13)
G
( 三 )If
αM
> e
H
k
(F)Enterprise will choose
2.3 Simulation analysis
M
e
∗ i
= α
k
2
,
1 k
θ = − ( lk + α M ) m
2 2
α M ( lk+ α M)
m−k αM
G
ln kG( l ) m r( eL)
RG
∏ = + − + − −
k k k
,
L
2 2 2
α M α M
∏
M
= ( l+ ) M − + R
k 2
In the context of enterprise determining his own level of quality efforts considering the
e
government’s strategy, we set
L
= 1.5
,
e
H
= 2 ,the product’s profit per unit is M=8
From the diagram we can see that enterprise profit increases as the promotion of quality level.
3. Summary
From the above chart, we can see enterprises’ profits will increase if they strictly implement the
policy after the government working out specific provisions. And as the product quality is
constantly improved, firm’s profit will undergo a large degree of promotion.
Table 1 Based on Government - led supply chain quality management
e ∗ θ ∏
i
M
∏
G
0.9000
1.2000
1.5000
1.8000
2.1000
2.4000
2.7000
3.0000
3.3000
3.6000
0.2683
0.5652
0.7143
0.7987
0.8507
0.8851
0.9088
0.9259
0.9387
0.9484
-11.9672
-13.6750
-16.2449
-19.7241
-24.1235
-29.4445
-35.6852
-42.8434
-50.9169
-59.9036
22.7750
29.6000
38.3750
49.1000
61.7750
76.4000
92.9750
111.5000
131.9750
154.4000
2
G
(14)
355

4
3.5
企 企 利 利
政 政 利 利
3
质 质 质 质
2.5
2
1.5
1
0.5
-100 -50 0 50 100 150 200
利 利
Figure 1 Government first, the enterprise underwent
In this process, the government itself through reward incentives to raise the level of quality of
enterprise, in the run continued decline in themselves’ profits, but we know, the Government's profit
is the sum of the profits of the community as a whole, profit enterprises get far more than the
Government in part of the losses by the corresponding quality levels.
Of course, this discussion is only considered a production enterprises in the supply chain, and
does not involve other members of the supply chain, and in the reality of supply chain always exist
in horizontal or vertical competition, those competition in the supply chain have a great effect on
enterprise profits.Therefore, the study about this two aspect will become supply chain quality
strategy directions for further research in this article.
Acknowledgement
The authors are very grateful to Xiao Di for his permission and help in the National Natural Science
Foundation of China (No.70902072), Social Sciences Foundation of Ministry of Education of China
(No. 09YJC630201,10YJC630004) and China Postdoctoral Science Foundation (No. 20110491823).
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