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Production, Manufacturing and Logistics

A hybrid fuzzy integral decision-making model for locating manufacturing

centers in China: A case study

Cheng-Min Feng

a,*

, Pei-Ju Wu

a,1

, Kai-Chieh Chia

b,2 a

Institute of Traffic and Transportation, National Chiao Tung University, 4F, 118, Sec. 1, Chung Hsiao W. Rd., Taipei 10012, Taiwan, ROC

b

Department of Business Administration, Soo Chow University, 56, Sec. 1, Kuei-Yang Street, Taipei 10012, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 24 February 2006 Accepted 6 December 2008 Available online 16 December 2008 Keywords:

Location

Manufacturing center Hybrid decision model Fuzzy integral Multiple criteria

a b s t r a c t

This study presents a hybrid fuzzy integral decision-making model that integrates factor analysis, inter-pretive structural modeling, Markov chain, fuzzy integral and the simple additive weighted method for selecting locations of high-tech manufacturing centers in China. The analytical results of this case study demonstrate the feasibility of the proposed model for solving fuzzy multiple attribute decision-making problems, especially when criteria are interdependent. Further, the empirical study brings out some properties that are crucial for high-tech manufacturing centers to invest in China.

Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction

Over the past decade, many Taiwanese manufacturing enter-prises have modified the processes and activities of their supply chains to enhance competitiveness in an increasingly globalized economy. Global competition has also imposed tremendous pres-sure on manufacturing enterprises to transform and adjust their supply chain operations. Meanwhile, countries with considerably low worker salaries have attracted enterprises to relocate manu-facturing activities (Bock, 2008). Based on this trend, many Tai-wanese enterprises have relocated their supply chain activities and have advanced into Mainland China to capture comparative advantages in production costs.

When configuring global supply chains, the manufacturing pro-cesses of a product are often distributed across multinational bor-ders. Complicating factors therefore arise, such as duties, trade blocks, exchange rates, transfer prices, taxes and production im-port/export quotas (Vidal and Goetschalckx, 2001; Goetschalckx et al., 2002; Lakhal et al., 2005; Leung et al., 2007). Moreover, agglomerated economies usually drive the location decisions of enterprises.Figueiredo et al. (2002)indicated that overseas loca-tion choices are strongly governed by agglomeraloca-tion economies and proximity to major urban centers, possibly replicating prior location decisions to economize on search costs. Blonigen et al.

(2005)also demonstrated that the location decisions of enterprises are affected by membership in either vertical or horizontal keire-tsu. Other important location factors include labor climate, land costs and utilities, proximity to markets and customers, industrial development incentives and quality of life (Sarkis and Sundarraj, 2002; Coyle et al., 2003).

Aside from the above factors, it should be noted that, in China, most logistics activities are administered or controlled by the gov-ernment (Luk, 1998).Sheu (2003)further pointed out several crit-ical issues of the facility location problem in China such as the diversity of local governmental regulations in logistics, cultural dif-ferences, etc.

Additionally, model formulations and solution algorithms for the location problem have been proposed and extensively devel-oped over the past several decades. Herein, some studies synthe-size an extensive array of past research concerning the evolution of location literature. For example,ReVelle and Eiselt (2005) re-viewed many facets of location analysis by referencing both semi-nal works and current reviews. Further details can be found elsewhere (Vidal and Goetschalckx, 1997; Min et al., 1998; Owen and Daskin, 1998; Goetschalckx et al., 2002; Díaz-Báñez et al., 2004; Klose and Drexl, 2005; Alumur and Kara, 2008). However, the above methods are hard to deal with some qualitative factors regarding this problem.

In real-world systems, manufacturing center location decisions may involve conflicts between the above factors. However, most criteria are interdependent or interactive, so they cannot be evalu-ated by conventional additive measures. Further, the values of the qualitative criteria are often imprecisely defined by decision 0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.ejor.2008.12.004

* Corresponding author. Tel.: +886 2 2349 4956; fax: +886 2 2349 4965. E-mail address:cmfeng@mail.nctu.edu.tw(C.-M. Feng).

1

Tel.: +886 2 2349 4956; fax: +886 2 2349 4965.

2 Tel.: +886 2 2311 1531; fax: +886 2 2371 7990.

Contents lists available atScienceDirect

European Journal of Operational Research

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makers under many situations. Considering many different criteria to evaluate facility location candidates may yield a vast body of data that are often inaccurate or uncertain.Doukas et al. (2007) indicated that using crisp values in the decision-making problem may oversimplify the imprecision and subjectivity of related

infor-mation. Sheu (2008)also mentioned that most decision-making

approaches, e.g., analytic hierarchy process (AHP), appear inade-quate for imprecise and vague comparisons of qualitative criteria. The purpose of this research is therefore to develop a hybrid fuzzy integral decision-making model for locating manufacturing centers in China which combines factor analysis, interpretive structural modeling (ISM), Markov chain, fuzzy integral and the simple additive weighted (SAW) method. Real-world case studies show that the proposed model is a suitable method for solving the location decision problem, particularly when the criteria are not independent. Moreover, the empirical data reveal some prop-erties that are critical for high-tech manufacturing centers invest-ing in China.

The rest of this paper is organized as follows. Section2presents the architecture of the proposed hybrid fuzzy integral decision-making model and its primary procedures. Section3 describes a case study to demonstrate the feasibility of the proposed method and to further analyze the case study findings. Finally, Section4 summarizes the conclusions of the study.

2. Methodology

Appropriate locations were identified using a hybrid fuzzy inte-gral decision-making method. The proposed approach involves five procedures. Fuzzy set theory is also applied to weight criteria as well as the performance values of alternatives.Fig. 1presents the framework of the proposed hybrid fuzzy integral decision-making model, and the main details are presented in the following subsections.

2.1. Extracting common factors by factor analysis

Since the decision criteria are not completely independent, fac-tor analysis can be introduced to extract common facfac-tors where the factors are mutually independent.

Hence, factor analysis can reveal latent structures (dimensions) of a set of variables and reduce attribute space from a larger num-ber of variables to a smaller numnum-ber of factors. For example, from

Fig. 1 the set of fxF

1;xF2g is in the same aspect and the set of

fxF

3;xF4;xF5;xF6g is in the other aspect through factor analysis, where

superscript F is termed a form of factor analysis. 2.2. Structuring the criteria relationship by ISM

Traditional pairwise comparison matrices assumed that the relationship of the criterion xF

i affected by the criterion xFj is

analo-gous to how criterion xF

j is affected by the criterion xFi. However,

the relationship between xF

i and xFj may have different effects.

Therefore, ISM technology was used to cope with the above problem.

ISM (Warfield, 1974a,b, 1976; Huang et al., 2005) is a computer-assisted methodology to construct and understand the fundamen-tal of the relationships of the criteria in complicated situations or systems. The theory of ISM is based on discrete mathematics, group decision-making, graph theory, computer assistance, and so-cial sciences (Huang et al., 2005). The ISM procedures were imple-mented through individual or group mental models to calculate binary matrices, also called relation matrices, to present the rela-tions of the criteria (Huang et al., 2005). A relation matrix can be formed by asking a question (Huang et al., 2005) such as ‘‘Does cri-terion xF

i affect criterion xFj? ‘‘If the answer is ‘‘Yes” then

p

ij= 1;

otherwise,

p

ij= 0. FromFig. 1, the first aspect of the relation matrix

can be presented as follows:

,

ð1Þ

where xF

1is the 1th criterion,

p

12denotes the relation between 1th

and 2th criteria, R is the relation matrix.

After constructing the relation matrix, the reachability matrix can be calculated using the following equations:

E ¼ R þ I; ð2Þ

E

¼ Ek¼ Ekþ1; k > 1; ð3Þ

where I is the unit matrix, k denotes the powers, and E*is the

reach-ability matrix. Thereafter, the original pairwise comparison matrix is transferred to ISM pairwise comparison matrix based on the reachability matrix E*. Restated, ISM pairwise comparison matrix

creates zeros according to the corresponding position in the

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ability matrix instead of numbers in the same position of the origi-nal pairwise comparison matrix. Consequently, the criteria relation-ship can be structured by ISM, e.g. xFI

1;xFI2; . . . ;xFIn fromFig. 1, where

superscript I is termed a form of ISM. Notable, the reachability ma-trix is under the operators of the Boolean multiplication and addi-tion (i.e., 1  1 = 1 and 1 + 1 = 1). For example,

E ¼ 1 0 1 1   ; E2 ¼ 1 0 1 1   :

2.3. Finding the steady-status criteria relationship with the Markov chain

Since locating manufacturing centers is a long-term investment problem, the Markov chain method was applied to find steady-sta-tus criteria relationships. The Markov chain has been frequently used to find reliability models in many real-world problems (Zhang and Yin, 1997; Prowell and Poore, 2004). The analytic network

process (ANP) proposed by Saaty (1996)uses the Markov chain

Fig. 2. The basic concept for fuzzy integral.

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concept to find stable weights. Nevertheless,Sarkis (2003)noted that a major limitation of the ANP approach is that additional interdependency relationships increase geometrically the number of pairwise comparison matrices and pairwise comparison ques-tions required for an evaluation. Furthermore, logically assessing how other clusters impact a cluster is another problematic issue that respondents must face. Supporting arguments can also be found elsewhere (Wolfslehner et al., 2005). Therefore, based on the above reasons, Markov chain is incorporated into our proposed model instead of directly using ANP.

The Markov chain method (Lay, 2003) is the key to understand-ing the steady-status behavior, or evolution, of a dynamic system. A vector with non-negative entries that add up to 1 is termed a probability vector (Lay, 2003). A stochastic matrix is a square ma-trix in which columns are probability vectors (Lay, 2003). More-over, the sum of these probabilities for all states must equal 1 before performing step 3 of the proposed method. Accordingly, ISM pairwise comparison matrix must be transformed into a nor-malization matrix.

The steady-status criteria relationship can be determined by the following theorem (Lay, 2003): If P is an n  n regular stochastic matrix, then P has a unique steady-state vector q. Further, if P0is

any initial state, then the Markov chain Pk converges to q as k ? 1. Restated, the stochastic matrix is raised to limiting powers such as Eq.(4)to obtain the steady-status criteria relationship, e.g. xFIM

1 ;xFIM2 ; . . . ;xFIMn fromFig. 1, where superscript M is termed a form

of Markov chain:

lim k!1p

k¼ q: ð4Þ

2.4. Solving the criteria interdependencies by fuzzy integral

Fourthly, the non-additive fuzzy integral was used to solve the criteria interdependencies within each common factor. The con-cept of fuzzy measure and fuzzy integral are briefly narrated as fol-lows (Sugeno, 1974, 1977; Grabisch, 1995; Narukawa et al., 2000; Chen and Tzeng, 2001; Chen and Wang, 2001; Chen et al., 2002; Angilella et al., 2004; Tzeng et al., 2005; Chiou et al., 2005; Grab-isch et al., 2008).

2.4.1. Fuzzy measure

A fuzzy measure is a measure for representing the membership degree of an object in candidate sets. It assigns a value to each crisp set of the universal set and signifies the degree of evidence or belief of the membership of the element in the set (Banon, 1981; Tseng and Yu, 2005). Let X = {x1, x2, . . ., xn} be the set of criteria, and let

P(X) denote the power set of X or set of all subsets of X.

Definition 1. A fuzzy measure on the set X of criteria is a set function g: p(x) ? [0, 1] satisfying the following equation: Fig. 4. The relationships of the criteria of operation climate.

Fig. 5. The fuzzy integral of operation climate of Jiangsu. Table 1

Score and fuzzy integral with respect to criteria of operation climate of Jiangsu.

Criteria Performance score Fuzzy integral

A3 73.46 61.76a A1 72.70 A4 59.90 A5 59.40 A2 53.66 a Global evaluation = (73.46  72.70)  0 + (72.70  59.90)  0.29 + (59.90  59.40)  0.51 + (59.40  53.66)  0.72 + (53.66  0)  1 = 61.76. Table 2

The final synthetic score of Jiangsu.

Aspects Fuzzy integral Final synthetic score

Operation climate 61.76 63.74a

Logistics support system 63.24

Labor resource 62.30

Government influence 60.31

Industry clustering effect 66.40

Quality of life 68.44

aGlobal evaluation = 61.76  1/6 + 63.24  1/6 + 62.30  1/6 + 60.31  1/6 +

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gð/Þ ¼ 0; gðXÞ ¼ 1 ðboundary conditionsÞ;

A  B  X implies gðAÞ 6 gðBÞ ðmonotonicityÞ: ð5Þ

A k fuzzy measure, gk, is a special kind of fuzzy measure defined on

P(X) of a finite set X and satisfying the finite k-rule (Sugeno, 1974). If the universal set is infinite, the extra equation of continuity is re-quired (Klir and Folger, 1988).Sugeno (1977)introduced the k fuzzy measure satisfying Eq.(6). Thus, the k fuzzy measure is also called a Sugeno measure:

8

A; B 2 PðXÞ; A \ B ¼ /;

gkðA [ BÞ ¼ gkðAÞ þ gkðBÞ þ kgkðAÞgkðBÞ; where k 2 ð1; 1Þ: ð6Þ

Let X be a finite criterion set, X = {x1, x2, . . ., xn}, and P(X) be a class of

all the subsets of X. It should be noted that gk({xi}) for a subset with

a single element xiis called a fuzzy density, and can be denoted as

gi= gk({xi}). The fuzzy measure gk(X) = gk({x1, x2, . . ., xn}) can be

for-mulated as the following equation (Leszczynski et al., 1985):

gkðfx1;x2; . . . ;xngÞ ¼ Xn i¼1 giþ k Xn1 i1¼1 Xn i2¼i1þ1 gi1 gi2þ    þ k n1g 1  g2   gn ¼1 k Yn i¼1 ð1 þ k  giÞ  1           for  1 < k < 1: ð7Þ

Based on Eq. (7), since the boundary conditions, gk(X) = 1, the

parameter k can be uniquely determined by the following equation:

kþ 1 ¼Y n

i¼1

ð1 þ k  giÞ: ð8Þ

2.4.2. Fuzzy integrals

Two definitions of fuzzy integrals are explained as follows ( Su-geno, 1974; SuSu-geno, 1977; Ishii and SuSu-geno, 1985; Grabisch, 1996):

Definition 2. Let g be a fuzzy measure on X. The Sugeno integral of a function h: X ? [0, 1] with respect to g is defined by

Suðhðx1Þ; . . . ; hðxnÞÞ :¼ _ni¼1ðhðxðiÞÞ ^ gðAðiÞÞÞ; ð9Þ

where suffix (i)indicates that the indices have been permuted so

that 0 6 h(x(1)) 6    6 h(x(n)) 6 1 and A(i): = {x(i), . . ., x(n)}.

Definition 3. Let h be a measurable function from X to [0, 1] and g

be a fuzzy measure on X. Assuming that h(x1) P

h(x2) P    P h(xn), then the fuzzy integral is defined as following

equation: ðcÞ Z h dg ¼ hðxnÞgðHnÞ þ ½hðxn1Þ  hðxnÞgðHn1Þ þ    þ ½hðx1Þ  hðx2ÞgðH1Þ ¼ hðxnÞ½gðHnÞ  gðHn1Þ þ hðxn1Þ½gðHn1Þ  gðHn2Þ þ    þ hðx1ÞgðH1Þ ð10Þ

where H1= {x1}, H2= {x1, x2}, . . ., Hn= {x1, x2, . . ., xn} = X. The fuzzy

integral defined by ðcÞRh dg is termed a Choquet integral. The Cho-quet integral can be used instead of the max–min integral (Wang and Klir, 1992; Ishii and Sugeno, 1985; Murofushi and Sugeno, 1989). In practice, h can be considered the performance of a partic-Table 3

Compare the results of the proposed model with fuzzy AHP.

Candidates The proposed model Fuzzy AHP Current investment locationa

Synthetic scores Ranking Synthetic scores Ranking Ranking

Jiangsu 63.74 1 61.95 2 1 Zhejiang 61.68 2 62.88 1 2 Guangdoing 59.71 3 55.54 5 3 Fujian 57.30 4 58.84 3 4 Hubei 52.69 5 56.06 4 5 a

Current investment location represents the statistical analysis of our questionnaire for current major investment locations in China.

Satisfactory very satisfactory Unsatisfactory Very unsatisfactory 0 1 20 30 40 50 60 70 80 90

x

µ

10 100 Ordinary

x

Fig. A.2. Interval of each triangular fuzzy number for degree of satisfaction.

1

µ

2 3 4 5 6 7

1

~

2

~

3

~

4

~

5

~

6

~

7

~

x

x

0 1

Fig. A.1. Interval of each triangular fuzzy number for degree of importance. Table 4

The comparison of the various type of enterprise. Candidates Large enterprise Small/medium enterprise Domestic sale Export sale The whole samples Jiangsu 1 2 1 1 1 Zhejiang 2 1 2 2 2 Guangdoing 3 4 3 3 3 Fujian 4 3 4 4 4 Hubei 5 5 5 5 5

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ular attribute for the alternatives while g stands for the grade of subjective importance of each attribute. A fuzzy integral of h with respect to g gives the overall evaluation for each alternative. The application of fuzzy integrals in multiple attribute decision-making (MADM) have been studied extensively in the literature,

see for example, Grabisch (1996), Chen and Chiou (1999), Wang

and Keller (1999), Chen and Tzeng (2001), Chen et al. (2002), Tseng and Yu (2005), Tzeng et al. (2005), and Chiou et al. (2005). Relying on Eq. (10), the basic idea of fuzzy integral can be illustrated in Fig. 2.

2.5. Establishing a synthetic alternative score with the simple additive weighted method

Finally, the simple additive weighted method is used to aggre-gate the final synthetic score with respect to each alternative. Deci-sion makers can then determine the appropriate facility locations based on the final score.

Apart from the five primary procedures of the hybrid fuzzy integral decision-making model, the defuzzification procedure has been found to derive the best non-fuzzy performance (BNP) value as fuzziness in the data. Since utilizing the Centroid method (COA, center of area) to determine the BNP is a practical measure and introducing the preferences of evaluators is unnec-essary (Yager and Filev, 1994; Tsaur et al., 1997; Tang et al., 1999), this method is adopted herein and should be used before step 2 of the proposed method. The BNP value of the triangular fuzzy number (li, mi, ui) can be obtained by Eq. (11). Each

candi-date of the facility location can then be evaluated. The order of importance of each criterion can also be ranked according to the value of the derived BNP:

BNPi¼ ½ðui liÞ þ ðmi liÞ=3 þ li

8

i: ð11Þ

3. Applications

This section describes an empirical study which demonstrates the feasibility of the proposed model in determining the appropri-ate locations for high-tech manufacturing centers in China. This section is divided into two subsections: (1) assessing the impact of location on key factors; (2) discussion.

3.1. Assessing the impact of location on key factors

Besides two experienced professors, five senior managers coming from different manufacturing enterprises participated in this project. Bi-weekly meetings were held regularly during the first 2 months of this project. Initially, five managers were asked to describe their experience in making location decisions for the high-tech manufacturing centers in China. Then, critical location factors were discussed, along with their definitions through ref-erence to both experiences and literature reviews. Finally, each member needed to fill out the questionnaire regarding which factors should be taken into account when locating manufactur-ing centers in China (Appendix A). A series of meetings was sub-sequently held to ensure all factors deemed necessary were certainly included. Furthermore, when a consensus could not be reached, members shared their experiences to reflect personal concerns. Based on information mutually received members made inferences about the others’ opinions and adjusted their perspectives accordingly. Several iterations were necessary to reach satisfaction-compromised solutions across all members in the group. Subsequently, five primary procedures of a hybrid fuzzy integral decision-making model are employed as follows:

Step 1: Factor analysis

First of all, since the evaluated criteria are not quite mutually independent in actual MADM problems, factor analysis was ap-plied to extract the criteria in six mutually unrelated aspects (oper-ation climate, logistics support system, labor resource, government influence, industry clustering effect and quality of life). Herein, the 25 criteria were regrouped into the above six aspects through fac-tor analysis. The top five facility location candidates (Jiangsu, Zhe-jiang, Guangdoing, Fujian and Hubei) were also determined according to statistical data for trans-border investment locations of high-tech Taiwan enterprises investing in China in 2004 (MOEA, 2004), as shown inFig. 3.

Based on the above hierarchy framework, 1000 questionnaires were fully administered via mail in the beginning. Nevertheless, only seven questionnaires were returned, while two of these questionnaires could not be adopted. Therefore, our sampling strategy had to be adjusted accordingly. We consulted with the Global Logistics Council of Taiwan for their assistance in the questionnaire survey. First, the Council targets the enterprises that were both locating their manufacturing centers to China over 3 years and also willing to answer survey questions involv-ing the 30 large enterprises and 30 small/medium enterprises (capital 6NT$80 million) from their members. Six well-trained postgraduates then held face-to-face surveys. Therefore, a total of 65 questionnaires were returned; such a response rate is rather valuable with respect to expert questionnaire. Besides, the above sampling process also reveals that mailed question-naires achieve a lower response rate than face-to-face surveys do. Additionally, except for the parts of ISM, the questionnaire in our project is similar to the conventionally adopted fuzzy AHP questionnaire.Appendix A provides illustrative patterns of the questionnaire attempting to determine the high-tech manu-facturing centers in China.

Thereafter, Eq.(11)was used to derive the final fuzzy weights and non-fuzzy BNP values, including the criteria weights for eval-uating suitable manufacturing centers, the fuzzy performance scores of suitable manufacturing centers and the BNP values of the fuzzy performance scores with respect to the criteria, as shown inAppendices B–D, respectively.

Step 2: ISM

Secondly, ISM was performed to further clarify the relationships between criteria in each aspect. The analysis of operation climate illustrates the ISM procedure. This aspect consists of taxes and industrial development incentives (A1), availability and expense

of utilities (A2), IT development (A3), cost of leasing land and

fac-tory buildings (A4) and availability and cost of raw materials (A5).

The relationships of the criteria of operation climate can be ex-pressed inFig. 4.

The relation matrix, R, was then converted into Eq.(12)through Eq.(2): E ¼ R þ I ¼ 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 : ð12Þ

Further, the reachability matrix are obtained by powering the ma-trix, E, to satisfy Eq.(3):

E¼ 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 2 6 6 6 6 6 6 4 3 7 7 7 7 7 7 5 ; ð13Þ

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where the star (*) indicates the derivative relation which does not emerge in the original relation matrix.

The reachability matrix, Eq. (13), was then used to transform the original matrix, Eq.(14), into the ISM matrix, Eq.(15):

,

ð14Þ

.

ð15Þ

Step 3: Markov chain

Thirdly, the operation climate aspect was continually analyzed as an example to show the steps of Markov chain. First, the sum of probabilities in each column must equal 1. Therefore, ISM pair-wise comparison matrix must be transformed into a normalization matrix as follows:

.

ð16Þ

The normalization matrix was then raised to limiting powers such as Eq.(4)to obtain the steady-state matrix as follows:

.

ð17Þ

Step 4: Fuzzy integral

Fourthly, fuzzy integral was used to solve the criteria interde-pendencies within each aspect. Considering the aspect of operation climate of Jiangsu, the k fuzzy measure was calculated using Eq. (8), and then gaining the fuzzy measures of criteria: g({A3}) = 0,

g({A3, A1}) = 0.29, g({A3, A1, A4}) = 0.51, g({A3, A1, A4, A5}) = 0.72 and

g({A3, A1, A4, A5, A2}) = 1. Thereafter, asFig. 5shows, the fuzzy

inte-gral was obtained through Eq.(10).Table 1shows the performance score and fuzzy integral with respect to criteria of operation cli-mate of Jiangsu.

Step 5: Simple additive weighted method.

Finally, the simple additive weighted method was used to aggregate the final synthetic score with respect to each candidate

facility location.Table 2shows the final synthetic score obtained for Jiangsu.

3.2. Results and discussions

FromAppendix B, the five most important criteria in determin-ing the appropriate locations for the high-tech manufacturdetermin-ing cen-ters in China are vertical industry agglomeration (E1), efficiency in

government (D3), taxes and industrial development incentives (A1),

government restrictions (D2) and availability and expense of

utili-ties (A2). If decision makers want to make this kind of location

deci-sion, they should pay much attention to the above key criteria. Based on the procedure of the proposed method mentioned above, the final synthetic score with respect to each candidate of facility location are summarized inTable 3. The synthetic scores for facility location candidates were also ranked as follows:

Jiangsu  Zhejiang  Guangdoing  Fujian  Hubei, in which

Jiangsu  Zhejiang indicating that Jiangsu is preferred to Zhejiang.

However, the ranking order is Zhejiang  Jiangsu 

Fuj-ian  Hubei  Guangdoing as the fuzzy AHP method was further employed. Notably, ranking order differed when the two methods were used to obtain overall scores. The ranking derived by using the proposed model appears reasonable since the ranking corre-lated with the statistical analysis of our questionnaire for current major investment locations in China. The main reason for these statistical results may be that the fuzzy AHP method assumes that criteria are mutually independent while the proposed method does not.

After verifying the proposed method, the ranking effects of large enterprise, small/medium enterprise, domestic sales and export sales were further investigated. Table 4 indicates that the location rankings of large enterprise, domestic sale and ex-port sale are equivalent to the whole samples. Nevertheless, the ranking of small/medium enterprises clearly differed from the others. Moreover, Spearman’s test (Zuwaylif, 1979) was con-ducted to analyze the ranking results of both large and small/ medium enterprises. According to results of Spearman’s test, low correlation could be found between large enterprises and small/medium enterprises (P > 0.05). Restated, the rankings of the facilities differ with respect to industry-level differences. To explain this finding, managers of Taiwan manufacturing enter-prises (including large and small/medium enterenter-prises) operating in Mainland China were interviewed. Most interviewed manag-ers agreed that small/medium enterprises often lack sufficient capital to locate in the best sites, such as Jiangsu, and tend to choose the second best location adjacent to the best (main) loca-tion. For example, because Jiangsu is close to Zhejiang, small/ medium enterprises may choose Zhejiang instead of Jiangsu. The same reason could be applied to the location of Guangdoing and Fujian. Additionally, domestic and export sales have similar effects when selecting locations for manufacturing centers.

The key findings of the extended analysis can be summarized as follows. First, the traditional method (i.e., fuzzy AHP) ignores the problem of preference independence and cannot perform rational decision-making in practice. To address this problem, the hybrid fuzzy integral decision-making model is proposed to overcome the non-additive problem among criteria. Applying the proposed approach to an actual case study indicates that the method is both operational and rational. Second, vertical industry agglomeration is the crucial factor when selecting locations for high-tech manu-facturing centers in China, which indicates that enterprises invest-ing in China should take into account the effects of agglomeration economics. Third, government of China has a powerful influence on the location of manufacturing centers. The formation and development of good social networks in government is essential for success. Finally, small/medium enterprises should carefully

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observe how large enterprises are deployed prior to investing in China.

4. Conclusion

This study presents a hybrid fuzzy integral decision-making model for locating manufacturing centers, especially when most criteria have interdependent or interactive characteristics and a vast body of data that are often inaccurate or uncertain. The pro-posed method involves five major components: (1) factor analysis, (2) ISM, (3) Markov Chain, (4) fuzzy integral and (5) simple addi-tive weighted method. A case study of a series of methods provides academics and managers a macro view of the strategies for imple-menting location decisions.

To demonstrate the applicability of the proposed methodology, this research designed and conducted a questionnaire survey as well as in-depth interviews to examine the location problem of Taiwan enterprises in China. The results from the empirical study revealed some crucial properties as follows. First, enterprises investing in China should consider the effect of agglomeration eco-nomics. Second, the formation and development of good social net-works in China government can help foreign enterprises operate in the unique business environment in China. Finally, small/medium

enterprises should carefully observe the activities of large enter-prises before investing in China. Further, managers conferred that these findings would be useful when selecting locations for manu-facturing centers in China. This survey is significant in practice due to the growing trend among enterprises to locate manufacturing centers in Mainland China.

Our study differs from previous MADM problems in several re-spects. First, since the evaluated criteria are not quite mutually independent in actual MADM problems, factor analysis was used to extract the criteria in several mutually unrelated aspects. Sec-Table A.1

An example of the relative importance degree and the relationships of the criteria. Former criterion affects latter

criterion

Former Relative importance of the criteria with respect to operation climate Latter Latter criterion affects former criterion 7:1 6:1 5:1 4:1 3:1 2:1 1:1 1:2 1:3 1:4 1:5 1:6 1:7 s A1 U A2   A1 U A3 s s A1 U A4 s  A1 U A5 s  A2 U A3   A2 U A4 s s A2 U A5   A3 U A4   A3 U A5   A4 U A5 

Note: A1– taxes and industrial development incentives; A2– availability and expense of utilities; A3– IT development; A4– cost of leasing land and factory buildings; A5–

availability and cost of raw materials.

Table A.2

Example of the degree of satisfaction of the candidates of facility location. Criteria Degree of

satisfaction

Candidates

Jiangsu Zhejiang Guangdoing Fujian Hubei Availability and cost of raw materials Very satisfactory U Satisfactory U U Ordinary U Unsatisfactory Very unsatisfactory U Table A.3

Example of the degree of importance of the factor. Factors Degree of importance

Very unimportant

Unimportant Ordinary Important Very important Availability and cost of raw materials U Table B.1

The criteria weights for evaluating suitable manufacturing centers. Aspects and

criteria

Local weights Overall weights BNP Ranking

Operation climate (0.183, 0.286, 0.892) A1 (0.206, 0.379, 0.829) (0.038, 0.109, 0.740) 0.295 3 A2 (0.210, 0.342, 0.796) (0.039, 0.098, 0.710) 0.282 5 A3 (0.187, 0.290, 0.511) (0.034, 0.083, 0.456) 0.191 15 A4 (0.212, 0.334, 0.608) (0.039, 0.096, 0.543) 0.225 10 A5 (0.170, 0.316, 0.580) (0.031, 0.091, 0.518) 0.213 12 Logistics support system (0.169, 0.270, 0.781) B1 (0.129, 0.130, 0.632) (0.022, 0.035, 0.493) 0.183 16 B2 (0.128, 0.129, 0.630) (0.022, 0.035, 0.491) 0.182 17 B3 (0.124, 0.125, 0.525) (0.021, 0.034, 0.410) 0.154 22 B4 (0.128, 0.129, 0.530) (0.022, 0.035, 0.413) 0.156 20 B5 (0.129, 0.129, 0.530) (0.022, 0.035, 0.414) 0.157 19 B6 (0.126, 0.127, 0.527) (0.021, 0.034, 0.411) 0.155 21 B7 (0.114, 0.116, 0.518) (0.019, 0.031, 0.405) 0.152 23 B8 (0.113, 0.115, 0.517) (0.019, 0.031, 0.403) 0.151 24 Labor resource (0.171, 0.272, 0.872) C1 (0.258, 0.359, 0.761) (0.044, 0.098, 0.664) 0.268 6 C2 (0.231, 0.335, 0.737) (0.040, 0.091, 0.643) 0.258 8 C3 (0.155, 0.256, 0.557) (0.027, 0.070, 0.486) 0.194 14 C4 (0.250, 0.350, 0.750) (0.043, 0.095, 0.654) 0.264 7 Government influence (0.173, 0.275, 0.876) D1 (0.276, 0.280, 0.589) (0.048, 0.077, 0.516) 0.214 11 D2 (0.251, 0.351, 0.851) (0.043, 0.096, 0.746) 0.295 4 D3 (0.251, 0.371, 0.851) (0.043, 0.102, 0.746) 0.297 2 D4 (0.209, 0.317, 0.722) (0.036, 0.087, 0.633) 0.252 9 Industry clustering effect (0.159, 0.297, 0.992) E1 (0.288, 0.564, 0.879) (0.046, 0.168, 0.873) 0.362 1 E2 (0.221, 0.436, 0.445) (0.035, 0.130, 0.442) 0.202 13 Quality of life (0.129, 0.136, 0.640) F1 (0.232, 0.437, 0.646) (0.030, 0.059, 0.414) 0.167 18 F2 (0.214, 0.363, 0.468) (0.028, 0.049, 0.299) 0.125 25

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ond, ISM was employed to clarify the relationships of the criteria in each aspect. Third, Markov chain was used to find stable weights. Fourth, the non-additive fuzzy integral was used to cope with interdependencies existing among criteria. Finally, the sim-ple additive weighted method was used to establish the final syn-thetic score of each alternative regarding the independence among aspects. The methodology presented in this research may stimulate research in the related fields of decision-making and may help address issues regarding the non-independent criteria case.

Acknowledgements

This study was supported by grant NSC 93-2415-H-009-011 from the National Science Council of Taiwan. The valuable sugges-tions of Prof. Jih-Jeng Huang to improve this study are gratefully acknowledged. The authors would like to thank the Global Logis-tics Council of Taiwan for assistance in performing the question-naire survey, as well as six postgraduate students for assistance in data collection and the application of the proposed model. Any errors or omissions remain the sole responsibility of the authors.

Appendix A. Illustrative patterns of the questionnaire for selecting important factors, identifying critical factors and selecting a suitable location

Part 1: Interval of each triangular fuzzy number

Fig. A.1illustrates the interval of each triangular fuzzy number for degree of importance. The meaning of each fuzzy number is ex-pressed as follows:

~

1: equally important; ~

3:weakly more important; ~

5:strongly more important; ~

7:absolutely more important; ~

2; ~4; ~6:intermediate value.

A triangular fuzzy number is denoted simply as (l, m, u). The parameters l, m, and u indicate the smallest possible value, the most promising value, and the largest possible value, respectively. Please fill in the blanks with subjective determinations of each tri-angular fuzzy number for degree of importance. For example, ~

1 ¼ ð1; 1; 2Þ; ~2 ¼ ð1; 2; 3Þ; ~3 ¼ ð2; 3; 4Þ; ~4 ¼ ð3; 4; 5Þ; ~5 ¼ ð4; 5; 6Þ; ~

6 ¼ ð5; 6; 7Þ; ~7 ¼ ð6; 7; 7Þ.

Fig. A.2illustrates the interval of each triangular fuzzy number for degree of satisfaction. Please fill in the blanks with subjective determinations of each triangular fuzzy number for degree of sat-isfaction. For example, Very unsatisfactory = (0, 0, 20);

Unsatisfac-tory = (10, 30, 40); Ordinary = (36, 50, 65); Satisfactory =

(60, 72, 91); Very satisfactory = (85, 100, 100). Moreover, the ques-tionnaire items regarding the interval of each triangular fuzzy number for degree of importance for selecting important factors was similar to degree of satisfaction.

Part 2: Relative importance degree and the relationships of the criteria

Please place a check ‘‘U”on the pairwise comparison matrix for the degree of importance of the criteria. Also, answer ‘‘s” (denot-ing ‘‘Yes”) or ‘‘” (denot(denot-ing ‘‘No”) on the first and last column for the relationships of the criteria.Table A.1displays an example of the relative importance degree and the relationships of the criteria. Herein, for the relationship between A1and A2, placing ‘‘s”on the

first column means that A1affects A2and placing ‘‘”on the last

column means that A2does not affect A1.

Table C.1

The fuzzy performance scores of suitable manufacturing centers.

Candidates Criteria A1 A2 A3 A4 A5 Jiangsu (61.35, 72.56, 84.18) (38.86, 54.16, 67.97) (62.19, 73.28, 84.91) (46.77, 59.92, 73.00) (46.39, 59.30, 72.51) Zhejiang (56.98, 68.48, 80.62) (39.05, 52.63, 66.27) (55.20, 67.06, 79.48) (47.79, 60.53, 73.62) (49.39, 61.73, 74.79) Guangdoing (52.14, 65.49, 78.39) (42.76, 56.59, 70.13) (57.23, 68.92, 81.10) (40.41, 54.68, 68.35) (47.22, 60.01, 73.28) Fujian (50.14, 62.19, 75.07) (43.24, 56.40, 69.81) (46.54, 59.12, 72.31) (51.71, 64.31, 77.28) (49.18, 61.66, 74.75) Hubei (43.50, 56.41, 69.77) (35.14, 49.46, 63.32) (39.79, 53.77, 67.47) (54.71, 67.10, 79.75) (48.28, 61.01, 74.14) B1 B2 B3 B4 B5 Jiangsu (59.72, 71.29, 83.27) (51.74, 64.14, 76.94) (61.52, 73.03, 85.04) (53.85, 66.11, 78.69) (58.58, 70.41, 82.67) Zhejiang (51.67, 63.93, 76.72) (52.15, 64.15, 76.92) (55.87, 67.47, 79.85) (50.19, 62.70, 75.46) (51.47, 63.73, 76.53) Guangdoing (58.33, 69.86, 81.98) (56.52, 68.44, 80.73) (57.30, 70.26, 82.54) (48.71, 62.66, 75.76) (54.42, 69.08, 81.91) Fujian (43.82, 56.62, 69.95) (47.02, 59.64, 72.75) (40.22, 54.31, 68.02) (44.07, 58.14, 71.59) (43.07, 56.79, 70.30) Hubei (36.81, 49.98, 63.57) (41.40, 54.49, 67.95) (35.47, 50.42, 64.48) (40.56, 54.68, 68.38) (35.48, 49.87, 63.78) B6 B7 B8 C1 C2 Jiangsu (51.81, 64.15, 76.91) (43.58, 57.04, 70.45) (46.32, 59.19, 72.47) (45.48, 58.79, 72.04) (51.65, 55.48, 66.42) Zhejiang (47.02, 59.80, 72.96) (42.21, 55.21, 68.57) (46.14, 58.61, 71.84) (44.34, 62.98, 71.32) (49.27, 65.92, 75.95) Guangdoing (50.95, 64.60, 77.60) (43.94, 58.04, 71.58) (45.52, 58.39, 71.70) (45.65, 58.79, 72.07) (51.94, 59.18, 77.34) Fujian (41.68, 55.45, 69.03) (36.64, 50.73, 64.60) (42.94, 55.67, 69.10) (53.92, 66.12, 78.77) (55.88, 67.52, 79.94) Hubei (40.09, 54.14, 67.81) (33.47, 47.72, 61.64) (42.74, 55.30, 68.67) (59.52, 71.03, 83.11) (50.26, 68.01, 75.57) C3 C4 D1 D2 D3 Jiangsu (49.68, 63.70, 76.94) (53.36, 66.97, 79.94) (50.32, 53.52, 72.01) (43.78, 57.75, 71.23) (51.04, 56.93, 62.51) Zhejiang (67.70, 70.84, 75.16) (50.42, 63.94, 77.10) (49.23, 61.02, 70.20) (45.87, 59.54, 71.08) (51.84, 63.22, 71.65) Guangdoing (40.32, 48.42, 53.49) (48.93, 62.48, 75.66) (44.73, 50.86, 59.84) (40.42, 51.63, 56.61) (39.80, 42.02, 51.57) Fujian (37.01, 52.72, 66.93) (40.34, 55.09, 68.97) (41.92, 55.99, 69.64) (40.56, 54.51, 68.22) (32.64, 48.41, 62.76) Hubei (46.61, 58.72, 59.71) (45.98, 53.71, 58.59) (46.71, 55.96, 63.76) (56.12, 59.39, 62.17) (40.19, 51.61, 59.30) D4 E1 E2 F1 F2 Jiangsu (48.13, 51.24, 57.01) (45.48, 58.38, 75.63) (50.49, 63.75, 76.77) (50.42, 56.75, 65.13) (58.84, 70.45, 82.52) Zhejiang (40.66, 63.48, 68.38) (53.89, 65.90, 78.49) (48.31, 68.25, 76.41) (48.61, 67.14, 69.48) (54.27, 66.12, 78.67) Guangdoing (34.12, 34.92, 60.12) (41.06, 44.51, 64.23) (41.03, 45.63, 70.06) (39.14, 48.45, 62.01) (48.82, 51.20, 55.39) Fujian (35.30, 50.56, 64.69) (47.56, 69.22, 70.21) (45.26, 67.84, 71.31) (47.73, 63.17, 69.84) (50.74, 62.87, 75.69) Hubei (37.32, 51.61, 65.40) (41.23, 55.04, 63.45) (47.69, 58.29, 66.09) (50.64, 59.47, 65.74) (48.27, 53.75, 62.10)

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Part 3: Degree of satisfaction of the candidates of facility location Please place a check ‘‘U”on the degree of satisfaction table for each candidates of the facility location. Table A.2 describes an example of the degree of satisfaction of the candidates of the facil-ity location. Similarly,Table A.3displays an example of the degree of importance of the factor for selecting important factors. Appendix B. The criteria weights for evaluating suitable manufacturing centers

SeeTable B.1.

Appendix C. The fuzzy performance scores of suitable manufacturing centers

SeeTable C.1.

Appendix D. The BNP values of the fuzzy performance scores with respect to the criteria

SeeTable D.1. References

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Table D.1

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數據

Fig. 1 the set of fx F
Fig. 2. The basic concept for fuzzy integral.
Fig. 5. The fuzzy integral of operation climate of Jiangsu.Table 1
Fig. A.2. Interval of each triangular fuzzy number for degree of satisfaction.
+2

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