mathematical model for the sustainable ... - industrial cluster.

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A Systematic Analysis on the Sustainable Development of Tourism Industry
Cluster
-------Take Hainan Province as an Example
Xiao-mei Qi1, Li-jun Hu2
1
College of Business Administration, Zhejiang Gongshang University, Hangzhou, China
1
School of Economics and Administration, Hainan University, Haikou, China
2
College of Foreign Languages, Quzhou University, Quzhou, Zhejiang, China
(164228345@qq.com1, lovonne78@hotmail.com2)
Abstract - This article mainly analyzes the composition
and structure of tourism industry cluster and makes a
quantitative judgment of the formation of Hainan's tourism
industry cluster. Firstly, it explores the connotation of
sustainable development of tourism industry cluster both
from the harmonious management theory and selforganization theory. Secondly, it puts forward the system
framework to study the sustainable development of tourism
industry cluster. Thirdly, it carries out a systematic analysis
on Hainan tourism industry cluster's sustainable
development.
Keywords - Hainan, tourism industry cluster,
sustainable development, system framework, systematic
analysis
I. INTRODUCTION
Under the background of constructing Hainan into an
international tourism island, we, as the scholars in
tourism, should undertake the responsibility for the
research of Hainan tourism. Hainan tourism can be
regarded as a system from the angle of system theory, or
it can be considered as an industry from the perspective of
economics and management. It also can be thought as the
combination of a system and an industry which are not
contrary to each other. The paper will discuss Hainan
tourism from the latter point.
The early study of industrial cluster mainly focused
on the manufacturing and new hi-tech industry, but few
cases were applied to the tourism industry. There has been
a large quantity of literature on this field in the late 20th
century and the early 21st century. Since the end of 2003,
the domestic scholars with the representative of Professor
Wang Jici from Beijing University begin to pay close
attention to tourism industrial cluster. After fierce debates,
they reached unanimous agreement that the tourism
industrial cluster is theoretically possible [1], [2].
This article mainly analyzes the composition and
structure of tourism industry cluster and makes a
quantitative judgment of the formation of Hainan's
tourism industry cluster. It explores the connotation of
sustainable development of tourism industry cluster both
from the harmonious management theory and selforganization theory. It also gives some research on the
macro and micro mechanism of industrial cluster's
sustainable development, on which it provides a
mathematical model for the sustainable development of
industrial cluster.
II. THE CLUSTER JUDGEMENT
The cluster judgment should be based on its
definition as well as its characteristics. Take Michael
Potter and Wang Jici as representatives from broad and
home, many scholars have brilliant exposition on the
definition and characteristics of industrial cluster
respectively from different point of view. And the method
to judge the industrial cluster is quantitative and
qualitative. The method of Location Quotient is only used
in this article to judge whether Hainan tourism industry
cluster is formed or not.
Location quotient (referred to as LQ) is a ratio
between the share of a specific sector's output value in the
regional total and the share of the whole sector's output
value in the national industrial total. In area economics,
location quotient is often used to determine whether an
industry constitutes a regional specialized department. A
LQ of more than 1.0 indicates the industry is the
specialized department in this area. A higher LQ means
more professional. Otherwise, a LQ equal to or less than
1.0 indicates this industry is self-sufficient department.
LQ is also a tool to analyze the industry efficiency and
benefits, which is a common method to identify clusters
and measure a certain aspect of an industry and the
relative concentration of a particular region.
The formula used to compute a LQ follows:
LQ = (Lij/Li)/(Lkj/Lk)
Lij refers to the output value of j industry in i region,
Li the total production value in i region, Lkj the production
value of j industry in country k, Lk the national total
production in country k. A LQ of more than 1 means the
specialization of an industry. With over 1.12, it is a rather
higher specialization. In the process of identify the
industrial cluster; if LQ is greater than 1, it is considered
the industrial cluster has been formed [3]. The data of
Hainan's tourist industry from 2001 to 2009 have been
calculated to find out the LQ of Hainan tourism in the
following Table I.
Table I shows that the LQ of Hainan tourism were
above 3.0 from 2001 to 2010, with an increase year by
year especially from 2004 to 2009, which fully illustrates
the formation of Hainan's tourism industry cluster as well
as a strong development tendency compared to other
provinces in China.
TABLE I
LQ OF HAINAN TOURISM
Items
Years
Total GDP
(trillion RMB)
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
109655.2
120332.7
135822.8
159878.3
183217.4
211923.5
257305.6
300670.0
340506.9
397983.0
National
Tourism
revenues
(trillion
RMB)
4995.00
5565.63
4882.96
6841.13
7685.79
8936.15
10958.14
11585.85
12894.72
15680.43
Hainan
Share of
tourism in
GDP (%)
Total GDP
(trillion
RMB)
4.56
4.63
3.60
4.28
4.19
4.22
4.26
3.85
3.79
3.94
579.17
642.74
713.97
819.67
905.03
1031.90
1223.28
1459.23
1646.60
2052.12
Tourism
revenues
(trillion
RMB)
87.91
95.37
93.58
111.05
125.07
141.45
176.36
192.33
211.72
257.63
Share of
tourism in
GDP (%)
LQ of
tourism
15.18
14.84
13.11
13.55
13.82
13.71
14.42
13.18
12.86
12.55
3.33
3.21
3.65
3.17
3.29
3.25
3.39
3.42
3.40
3.19
Data from National Statistics Yearbook, National Economy and Social Development Statistics Bulletin, Hainan Statistics Yearbook
and the Economic and Social Development of Hainan province.
III. THE COMPOSITION AND STRUCTURE OF
HAINAN TOURISM INDUSTRY CLUSTER
The article holds the opinion that Hainan tourism
industry cluster consists of the following three parts [2], [4-6]:
Firstly, the core of industry includes tourist
attractions (core attraction), hotels, travel agencies, tour
companies, tourist goods and souvenirs, and so on.
Secondly, tourism leading industry includes food
and food processing industry, tourism real estate, tourism
transports, tourism supply and repair business, tourism
planning and consulting business, producing and
processing of tourism products, landscaping and cleaning.
Thirdly, the corresponding supporting mechanism
and service mechanism include the providers and related
organizations in the fields of finance, insurance,
telecommunications, training institutions, government
management departments and associations which are
helpful to the cluster infrastructure, tourist activities, the
production and operation of cluster enterprises.
The structure of Hainan tourism industrial cluster
can be divided into three levels:
The first level is tourist attraction (core attractions)
and related business.
The second level is food, housing, traffic, travel,
shopping, and entertainment.
The third level are the providers and related
organizations in the fields of finance, insurance,
telecommunications, training institutions, government
management departments and associations which are
helpful to the cluster infrastructure, tourist activities, the
production and operation of cluster enterprises.
IV.THE IMPLICATION OF SUSTAINABLE
DEVELOPMENT OF TOURISM INDUSTRY
CLUSTER
Since the birth of tourism industry, tourism industry
cluster's sustainable development has been worthy of
attention. The previous literature focused on the
coordination of tourism cluster development from the
static angle and its main index is a reasonable ratio among
the essential factor investment, which is the foundation of
sustainable development. The sustainability discussed in
this paper has a wider perspective, not only including the
"sources" harmony based on various elements reasonable
input, but the "human" harmony of social relations and
humanistic spirit [7]. The following is to be illustrated both
from the perspectives of harmonious management theory
and the theory of self-organization.
A. Perspective of Harmonious Management Theory
It is thought that industry clusters' sustainable
development consists of the sustainability of cluster
system's development and the coordination development
between the cluster system and the external social and
economic
environmental
system.
Harmonious
development can be divided into "being together " and
"harmony" according to the theory of harmonious
management the former is persons' or people's ideas and
behaviors desirable embedded. And harmony refers to all
physical elements input reasonably in the organization. It
carries out analysis in accordance with the principle of
"being together "and "harmony". The principle "being
together" is used to adjust the interpersonal relationship.
There are various social relations of the inside and outside
of cluster system, such as organizational culture and
humanistic spirit, which are important to cluster
development. These soft factors were often ignored in the
previous studies, together with the material elements, also
known as the hard elements coordination and matching.
"Harmony" refers to the rational investment of material
elements. It is a process of pursuing optimization for
material elements under the determined condition with the
constraints of existing objectives and circumstances. Only
both of them play their own roles, can the whole cluster
system develop coordinately [8].
B. Perspective of Theory of Self-organization
Tourism industry cluster is characterized with
openness, far from equilibrium, nonlinear effect and
fluctuation, which are in accordance with self
organization. Based on the analysis of self-organization
mechanism of tourism industry cluster, we found that the
synergy of competition and cooperation is the drive for
the self-organization evolution of the tourism industry
cluster and its order parameter is the tourism culture. It
also reflects that the culture plays an important role in the
tourism industrial cluster. The theory of self-organization
gives an explanation the sustainable development is the
system spontaneous evolution from a disorderly state to
orderly and even to a higher one. This kind of evolution is
necessarily to ensure its own compatibility, clear away
outside interference and keep sustainable development.
V.SYSTEM ANALYSIS ON TOURISM INDUSTRIAL
CLUSTER SUSTAINABLE DEVELOPMENT
According to the theory of system science, the
system development is closely related to the elements
within the system, the links and interactions between the
system itself and its external surroundings. Not only the
internal dissonance of the system but the external will
affect the system's overall development [10], [11]. This part
begins with analyzing the systematization of tourism
industry cluster, namely, the macro mechanism of the
sustainable development, followed by its micro
mechanism. Finally, it provides a mathematical model for
the sustainable development of industrial cluster.
A. Systematization of tourism industry cluster---macro
mechanism of sustainable development
Tourism industrial cluster is a phenomenon of
tourism industry aggregation. The internal of each
subsystem within the cluster system, the subsystem
themselves, the cluster system itself and its external
surroundings form a complex open system through a
variety of interactions. Its macro mechanism for operating
is to be discussed in the following, which is characterized
with entirety, hierarchy, correlation, openness, selfadaption and environmental adaptability.
1)
Entirety: Its unified entirety leads to the
existence of tourism industry cluster. Integrity is the basic
attribute of the system, which is demonstrated that only
within the entirety, can each subsystem's purpose, nature,
motion and function be performed, and they have to
subordinate to the need of overall development. The
subsystem is not the best one if it is pursuing the best
results without considering the overall interests.
Otherwise, even if each subsystem is not the perfect, they
still can make the entire system function well through
complementation, comprehension and coordination. This
is the entirety of the cluster system. Entirety determines
the overall functions of cluster system much greater than
the linear summation of all subsystems'.
2) Hierarchy: Tourism industry cluster has at least
three levels. The core level is tourist attractions and
related enterprises. The auxiliary level includes some
subsystem such as food, accommodation, travel,
shopping, entertainment, transportation. The supporting
level refers to the suppliers of the cluster infrastructure,
relevant organizations, institutions and organizations.
Cluster system's hierarchy is reflected on the relative
independence and effectiveness of each hierarch's
function. Destroying their independence and effectiveness
will eventually reduce the whole system's efficiency.
3) Correlation: Tourism industry cluster correlation
refers that each subsystem with the system restricts to
each other, influence each other and interdependent on
each other. They have mutual connections and
dependence in the process of operation, including the
structure, function and causal relations. Each subsystem's
function and their reasonable and correct coordination
will reach the system's goal. These links determines the
whole system's operation mechanism. While, analyzing
these links is the basis of constructing clusters[12].
4) Openness: The tourism system is an open system.
It exists in a certain environment and constantly
exchanges its material, information and energy with the
external environment. The main function of tourism
industrial cluster is to provide tourists with tourism
products and services, which determine its higher
openness. Clusters take tourism resources as its core, the
subsystem of food, accommodation, transportation, travel,
shopping, and entertainment as its auxiliary layer, and
infrastructure providers, related organizations, institutions
and groups as the supporting layer. Each part of each
layer is an open system, which does not only constantly
exchange material, energy and information with the
external environment, but the internal expanded
cooperation and exchanges widens its openness.
5) Self-adaption: Enterprises are the basic elements
of tourism industrial cluster, and they have their own
purposes, initiative and adaptability. Each enterprise is in
the pursuit of their benefit maximization. With this goal,
they have to be active and take the initiative to achieve it.
In addition, enterprises and elements within the cluster as
well as without the cluster, and the internal and external
environment interact with each other. This interaction and
impact constantly changes the cluster itself, and also
changes the surroundings. It is called the cluster's self
adaption, which is basic power for tourism industry
cluster development.
6) Environmental adaptability: Tourism industrial
cluster is operating in a certain environment, and
changing its material, energy and information with the
external environment. The system which can not adapt to
the change of environment is no vitality. The boundary of
cluster system is the dividing line between cluster system
and its external environment (see Figure 2). Objectively,
there is no obvious line between them. Only for the
convenience of research, the system scope, scale,
structure and the problems to be solved should be limited.
B. Micro mechanism for sustainable development of
tourism industrial cluster
From above, tourism industrial cluster, as a system,
has various characteristics which a system has. These
characteristics are rather macroscopic. In order to conduct
an in-depth research of the cluster system's sustainable
development, it is necessary to analyze its microscopic
structure and environment because the microscopic
behavior determines its macroscopic properties [13]. The
system's boundary should be firstly defined for the need
of the study. The boundary of tourism industrial cluster in
this paper is set between the system's core, auxiliary layer
and supporting layer so as to clearly distinguish the inside
and outside of the system. The fundamental object of the
study concerns tourist attractions in which there are six
subsystems
related
to
food,
accommodation,
transportation, travel, shopping and entertainment. These
subsystems are made up of enterprises. The model of
energy standard, also known as the mathematical formula
to test its function, is to be constructed according to the
three layers. Energy standard here not only takes both the
role of material elements and non-material one into
consideration, but the linear and non-linear function. In
the end, it offers the mathematical expressions to calculate
the cluster system's overall energy level.
1) Internal energy levels of six subsystems composed
of tourism industry cluster system
Enterprises are the basic unit of the six subsystem
concerning food, accommodation, transportation, travel,
shopping and entertainment. The enterprise itself can be
regarded as an independent system, whose energy level is
determined by its elements. Enterprises' subsystems are
composed of all kinds of productive elements and nonproductive ones which can be classified into material and
non-material according to their existing forms, marked
respectively as m and k. The energy level of each
subsystem depends on the enterprise's energy level
(linear), marked as q (m, k), within the system and the
interaction (nonlinear) marked as ∆q among enterprises.
Suppose that there are j enterprises in each subsystem and
there are i subsystem, then the energy level of each
subsystem marked as E is:
E =∑f i(q( m j, k j), ∆q),
(i= 1, 2 , ..., 6, j=1, 2, ...,
n)
(1)
This is the energy level of a linear function, but the
energy level of enterprises within each subsystem is
nonlinear.
2) Energy levels produced by the interaction of six
subsystems
The cluster system produces competition and
cooperation among each subsystem because of their nonlinear interaction. The energy level (marked as C)
produced by this kind of competition and cooperation is:
C = c (q (m j, k j), ∆q)
(2)
It is necessary to point out that the coordination
among the six subsystems relies on the culture which is
the soul of tourism.
3) Energy levels produced by the exchanges and
cooperation between tourism cluster and its external
environment
Tourism cluster, as an open system, has to
continuously exchange with the external environment to
maintain its sustainable development. The energy levels
(marked as H) produced by the exchanges between
tourism cluster and its external environment can be
expressed as:
H = a (q (m j, k j), ∆q)
(3)
4) Overall energy levels of tourism industrial cluster
system
The overall energy level of tourism industrial
cluster system (marked as N) is the function of these three
kinds of energy levels. Its mathematical formula can be:
N = f (E, C, H)
(4)
C. A mathematical model for sustainable development of
tourism industry cluster system
From formula (4), it can be seen that the energy
levels of tourism industrial cluster system are closely
related to f, E, C and H. They should be improved in order
to increase the overall energy levels N. At present, it is
still hard to theoretically prove it continuously
differentiable because the specific F function form can not
be determined. However, it should be continuously
differentiable according to the meaning of f.
It can be concluded that the tourism industry cluster
is featured with systematization. Suppose that there is a
good state among the inside of each subsystem within the
cluster, each subsystem, the cluster and its external
environment, a whole system has been constituted, in
which each can integrate with others and promote others.
Only then, can the industry cluster system achieve its
maximum energy level.
Therefore, the sustainable development of tourism
industry cluster system can be defined as the following.
There is an overall coordination for the internal of the
system and each subsystem concerning tourism core
layers such as food, accommodation, transportation,
travel, shopping and entertainment. And the cluster
system can adapt itself to the external surroundings. Using
K to represent the cluster's sustainable development, its
mathematical expression can be:
K=k (k1 (E), k2 (C), k3 (H))
(5)
k1 (E) refers to the internal sustainable development
of six subsystems, k2 (C) means the sustainable
development of competition and cooperation among six
subsystems, and k3(H) represents the sustainable
development of exchanges between six subsystems as a
whole and external environment which also means the
overall sustainable development of tourism industrial
cluster system.
VI.SYSTEMATIC DESCRIPTION OF HAINAN
TOURISM INDUSTIAL CLUSTER’S SUSTAINABLE
DEVELOPMENT
On the basis of the above analysis, Hainan's tourism
industrial cluster's sustainable development can be
described like this: with the core of natural attractions and
tourist attractions, it should focus on the sustainable
development of six subsystems of food, accommodation,
transportation, travel, shopping and entertainment. The
energy levels of each subsystem and between them can
reach its optimum. And the energy levels of the
exchanges between the industry cluster system composed
of six subsystems and the external environment also can
be optimal so as to make the whole cluster energy level
maximum. The higher the whole energy level is, the more
its sustainable development is.
Taking the current situation of Hainan's tourism
industry cluster into account, how to maximize its value is
the significance of the paper since Hainan boasts its rich
tourism resources. However, there are some issues to be
solved. How to coordinate the six subsystems under the
guidance of culture? How do Hainan administration,
tourism infrastructure providers, relevant organizations,
institutions and groups provide six subsystems support? In
more detail, Hainan has good natural landscape and
tourist attractions. The issue is how to make it coordinate
and match with the subsystem of diet. It not only needs a
hard material matching, but also a soft culture and
organization. Whether the diet can match with tourist
attractions in terms of specialty, price, location,
environment and atmosphere?How do the tourists feel
while eating? This paper stresses more on the
coordination of charming natural environment,
geographical resources and humanistic spirit, which is a
special perspective in this paper to study the sustainable
development of tourism industry cluster from system
theory. It should be paid enough attention to in the
research of cluster at all levels.
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