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Selection of optimal supplier in supply chain management strategy

with analytic network process and choquet integral

Tseng Ming-Lang a,*, Jui Hsiang Chiang b, Lawrence W. Lan c

a Department of Business Administration, Ming-Dao University, #369 Wenhua Road, Peetou Township, Changhwa County, Taiwan, ROC b Department of International Business, Toko University, Taiwan, ROC c Department of global marketing and logistics, MingDao University, Taiwan, ROC

a r t i c l e i n f o

Article history:

Received 14 April 2007

Received in revised form 8 December 2008

Accepted 8 December 2008

Available online xxxx

Keywords:

Supply chain management strategy

Analytical network process

Choquet integral

a b s t r a c t

Selection of appropriate suppliers in supply chain management strategy (SCMS) is a challenging issue

because it requires battery of evaluation criteria/attributes, which are characterized with complexity,

elusiveness, and uncertainty in nature. This paper proposes a novel hierarchical evaluation framework

to assist the expert group to select the optimal supplier in SCMS. The rationales for the evaluation frame-

work are based upon (i) multi-criteria decision making (MCDM) analysis that can select the most appro-

priate alternative from a finite set of alternatives with reference to multiple conflicting criteria, (ii)

analytic network process (ANP) technique that can simultaneously take into account the relationships

of feedback and dependence of criteria, and (iii) choquet integral—a non-additive fuzzy integral that

can eliminate the interactivity of expert subjective judgment problems. A case PCB manufacturing firm

is studied and the results indicated that the proposed evaluation framework is simple and reasonable

to identify the primary criteria influencing the SCMS, and it is effective to determine the optimal supplier

even with the interactive and interdependent criteria/attributes. This hierarchical evaluation framework

provides a complete picture in SCMS contexts to both researchers and practitioners.

Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In facing an ever-increasingly competitive and changeable envi-

ronment, firms require constantly managing their organizational

resources as well as tightening their industrial relationships so as

to maintain competitive advantages. More specifically, firms re-

quire reorganizing their supply chain management strategy

(SCMS) to harmonize with the external environments by integrat-

ing the organizational resources, information, and activities. How-

ever, SCMS may encounter multi-dimensional difficulties as it

involves numerous organizational functions and resources integra-

tion among various departments. In practice, the contexts of SCMS

are uncertain, unpredictable, and difficult to assess accurately withqualitative information. As a consequence, selection of appropriate

suppliers in SCMS is a complicated, challenging process.

Davis (1993) indicated that there are three different sources of

uncertainties in SCMS: (i) Supplier uncertainty, arising from on-

time performance, average lateness, degree of inconsistency. (ii)

Manufacturing uncertainty, arising from process performance, ma-

chine breakdown, supply chain performance, etc. (iii) Demand

uncertainty, arising from forecasting errors, irregular orders, and

among others. Some researchers argued that uncertainty is strate-

gic vital for firms to test their management systems (Chen & Paul-

raj, 2004; Hahn, Watts, & Kim, 1990; Krause & Ellram, 1997; Van

Hoek, 1998; Webster, 1995). Organizational SCMS is made when

it is strategic, usually rather complex with external and internal

implications (Fuentes-Fuents, Albacete-Sae, & Llorens-Montes,

2004; Ward, Duray, Leong, & Sum, 1995). Relevant literature

showed that increased competition in the marketplace and greater

pace of technological innovation than before are two primary fac-

tors driving firms’ needs for world-class suppliers and for supplier

development; hence, the SCMS alignment must be synchronized

with uncertainty in a competitive and changeable environment

(Flint, 2004; Hahn et al., 1990).

Selection of appropriate suppliers in SCMS requires battery of evaluation criteria, which include such information as customer fo-

cus, competitive priority, strategic purchasing, information tech-

nology, and top management support of a firm (Carr and

Pearson, 1999; Johnston, McCutcheon, Stuart, & Kerwood, 2004;

Li, Ganesan, & Sivakumar, 2006a; Li, Ragu-Nathan, Ragu-Nathan,

& Rao, 2006b; Tan, Lyman, & Wisner, 2002). A firm must have out-

standing competitive priority in order to perform well manage-

ment in production, such as producing high quality products

with excellent logistics arrangement. The competitive priority is

closely related to top management support that requires strategic

purchasing. Although Chen and Paulraj (2004) asserted that

customer focus, competitive priority, information technology,

0360-8352/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.cie.2008.12.001

* Corresponding author. Tel.: +886 910 309 400.

E-mail address: [email protected] (M.-L. Tseng).

Computers & Industrial Engineering xxx (2009) xxx–xxx

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Please cite this article in press as: Tseng, M.-L., et al. Selection of optimal supplier in supply chain management strategy ... Computers &

Industrial Engineering (2009), doi:10.1016/j.cie.2008.12.001

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strategic purchasing, and top management support are indepen-

dently related, it is hard to justify the independency, and this

assertion has invited many disputable arguments among the social

science studies. As such, the present study will view SCMS a com-

plex, interactive process of many different resources with multi-

dimensional, interdependent criteria/attributes. Hence, conven-

tional multi-criteria approaches and weight average method

assuming independence of attributes are not suitable for evaluat-ing SCMS because only when information sources are non-interac-

tive can their weighted effects be viewed as additive (Wang, Leung,

& Wang, 1999). To overcome these shortcomings, non-additive set

functions must be used, and choquet integral (a nonlinear integral

or so-called ‘‘non-additive fuzzy integral”) with respect to non-

additive set functions can be employed to replace the weighted

average (Kahraman, Çevik, Ates, & Gülbay, 2007; Murofushi & Su-

geno, 1989; Wang & Klir, 1992; Wang et al., 1999). By using non-

additive fuzzy integral, one can eliminate experts’ subjective judg-

ment problems involving the complex SCMS.

To date, few studies have adopted a rigorous methodology

while selecting the suppliers in SCMS. Many suppliers have built

up their capabilities to support some other services, such as SCM,

just-in-time, service quality, etc. These suppliers normally have

long-term contracts providing their customers with multiple-func-

tion services (Choi & Hartley, 1996). There are different supplier

selection criteria in different status. Chan and Kumar (2007) iden-

tified some important and critical decision criteria including risk

factors for the development of an efficient system for global sup-

plier selection. Wang and Che (2007) presented a model, based

on the concepts of parts change requirements, fuzzy performance

indicators, and integration of different attributes, to allow the parts

supplier selection of a specific commercial product to be explored.

Xia and Wu (2007) proposed an integrated analytic hierarchy pro-

cess (AHP), which is improved by rough sets theory and multi-

objective mixed integer programming, to simultaneously deter-

mine the number of suppliers and the order quantity allocated to

each supplier, under the contexts of multiple sources, multiple

products, multiple criteria, and with suppliers capacity constraints.Saaty (1996) developed analytic network process (ANP), a new

analysis method that simultaneously takes into account both the

relationships of feedback and dependence. This paper attempts to

develop a novel hierarchical evaluation framework to assess the

SCMS, wherein the interdependency among various criteria/attri-

butes can be effectively captured by a combination of ANP with

choquet integral. The major advantages of combining ANP with

choquet integral are that the evaluation can account for the inter-

dependency of criteria/attributes, the nonlinear relationship

among criteria/attributes, and the environmental uncertainties.

Such a combination was rarely seen in literature before. This pro-

posed hierarchical analytical approach is not only novel but suffi-

ciently general to be applied under various settings, thus can

help firms to measure and select the optimal suppliers in SCMS.The remainder of this paper is organized as follows. Section 2

addresses the background of SCMS with relevant literature re-

viewed. Section 3 presents the hierarchical structure of SCMS with

criteria and attributes involved in the supplier evaluation. Section

4 proposes the hierarchical analytical approach for evaluating

SCMS. A PCB manufacturing case firm’s SCMS is evaluated in Sec-

tion 5. Managerial implications are discussed in Section 6, followed

by concluding remarks.

2. Background of SCMS

A well-integrated supply chain management (SCM) involves

coordinating the flows of materials and information between sup-pliers, manufacturers and customers, and implementing product

postponement and mass customization in the supply chain. Higher

level of integration with suppliers and customers in the chain is ex-

pected to result in more effective competitive advantages (Ander-

son & Katz, 1998; White, Pearson, & Wilson, 1999). Supply chain

management strategy (SCMS) is used to explain the planning and

control of materials/information flows and logistics activities, not

only internally within a firm but also externally between firms

(Cooper, Ellram, Gradner, & Hanks, 1997; Fisher, 1997; Seo,2006). The key concept is that the channel is viewed as an inte-

grated whole, with the goal of understanding the channel as an

application system. Each firm in the channel affects, directly or

indirectly, all the other channel members, as well as the ultimate,

overall channel performance (Beamon, 1999; Carr & Pearson, 2002;

Handfield & Nichols, 1999; Tan, Kannan, & Handfield, 1998).

Increased global competition pressures have been forcing firms

to continuously adopt, develop and enhance customer focus, com-

petitive priority, information technology, strategic purchasing and

top management support. For these reasons, a firm must enhance

its SCMS for developing the optimal suppliers more suitable than

other competitive firms, and must facilitate the criteria and attri-

butes of SCMS within its organization to strengthen its competitive

advantages. The goal of integrated SCMS is to create manufacturing

processes and logistics functions seamlessly across the supply

chain as an effective competitive weapon that cannot be easily

duplicated by competitors. Tan et al. (2002) explored the relation-

ships between supplier management practices, customer relations

practices, and organizational performance with the usage of pur-

chasing, quality and customer relations to represent SCMS. Yao,

Palmer, and Dresner (2007) studied the electronically-enabled sup-

ply chains, which offer the potential for reduced costs and higher

sales. They found top management support and external influences

are both important determinants. Besides, perceived benefits to

customers, perceived benefits to suppliers, and perceived inter-

nally focused benefits are all positively influencing electronically-

enabled supply chains use. The indicators of this construct are pre-

sented to denote the presence of electronic transactions, supplier

management and competitive priorities in various forms betweenthe supply chain partners. Based on these findings, the SCMS is

presented with interactive relationships among their proposed

dimensions (Li et al., 2006a; Li et al., 2006b; Chou & Chang,

2008). Even if a firm merely focuses on the customer criteria, it still

needs top management support and adjusts its competitive prior-

ity accordingly.

Numerous criteria and attributes must be considered when

evaluating the SCMS. In this study, we emphasize the following

five criteria: customer focus, competitive priority, information

technology, strategic purchasing, and top management support.

First of all, customer focus practices involve the establishment of

links between customer needs and satisfaction and internal pro-

cesses (Sousa, 2003; Stuart, 1997). Mendoza, María Pérez, and

Grimán (2007) forecasted that for various reasons and with moreor less clarity concerning the subject, the firms have a new trend

to implement customer relationship management as a factor

allowing them to survive in the new market conditions and favor-

ing the relationship with their customers. Tan et al. (1998) consid-

ers customer relationship management as an important

component of SCMS. Closer customer relationship allows an orga-

nization to differentiate its products from competitors, sustain cus-

tomer loyalty, and dramatically extend the value it provides to its

customers (Magretta, 1998). Closer customer relationship also re-

quires improving the customer satisfaction (Hwang, 1998; John-

ston et al., 2004). Day (2000) pointed out that committed

relationships are the most sustainable advantage because of their

inherent barriers to competition. The growth of mass customiza-

tion and personalized service has led to an era where relationshipmanagement with customers is becoming crucial for corporate

2 M.-L. Tseng et al. / Computers & Industrial Engineering xxx (2009) xxx–xxx

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survival. Good relationships with supply chain members, including

customers, are needed for successful implementation of SCMS.

Secondly, for competitive priority, Cox and Blackstone (1998)

stated that ‘‘To be most effective, the manufacturing should act

in support of the overall strategic directions of the business and

provide for its competitive priorities.” It guides the choice and

development of competitive priorities and specifies how the oper-

ational function provides a firm with competitive priority in themarketplace or tactical goal of the operational function (Chenhall

& Langfield-Smith, 1998). SCMS has to be involved in top-down

operation decisions; therefore, once competitive priority is evalu-

ated it becomes the basis for making operational decision as the

goal of operational function in marketplace (Margaret, 1996).

Establishing close relationships with a limited number of suppliers,

when properly and selectively used, has been directly linked to

customer focus (Stanley & Wisner, 2001) and competitive priority.

Thirdly, for information technology (IT) in SCMS, Dehning,

Richardsonand, and Zmud (2007) examined the financial benefits

of newly adopted IT-based SCMS and found a positive relation be-

tween firms’ investment in IT-based SCM systems and firms’ per-

formance. IT enhanced supply chain efficiency by providing real-

time information about product availability, inventory level, ship-

ment status, and production requirements. In particular, the com-

mon goal of these systems is to transform all the management

systems into perfect information.

Fourthly, the importance of purchasing function that a company

needs to optimize its entire SCM, rather than individual elements

within the supply chain, suggests that purchasing is indeed strate-

gic. For purchasing, operations and other elements of a supply

chain should work together and their functional strategies should

be aligned in support of the firm’s SCMS (Watts, Kim, & Hahn,

1992). Carr and Smeltzer (1999) explored how firms with strategic

purchasing are able to foster long-term, cooperative relationships

and communication, and achieve greater responsiveness to the

needs of their suppliers. Strategic purchasing can foster greater

commitment and trust to promote long-term relationships be-

tween the focal firm and its suppliers. Moreover, purchasinginvolvement earlier in the new product development process has

provided many companies with advantages in bringing new de-

signs to market faster, with fewer quality defects, and at lower

costs (Dyer, 1996). The present study presumes that strategic pur-

chasing contributes to effective SCM when it fosters a long-term

strategic orientation between the firm and its supplier selection.

Finally, for top management support in SCMS, Wilson and

McDonald (1996) regarded it as an important factor in the success-

ful implementation of decision support systems. SCMS may create

sustained competitive advantage directly should the top manage-

ment support be able to exploit unique SCM competencies. One of

the major functions for top management executives is to influence

the setting of organizational values and to develop suitable man-

agement styles to ensure the SCMS on track. Although top manage-ment support of SCMS has generally been regarded as a key success

parameter, yet the nature of its impact and the phenomenon it

brings into being are still not very clear to us, thus it requires an

in-depth analysis to enhance our understanding to draw useful

implications for research and practice (Chen & Paulraj, 2004).

Optimal supplier evaluation depends on SCMS requirements,

including as customer focus, competitive priority, information

technology, strategic purchasing, and top management support

(Hoque, 2004; Li, Ganesan, et al., 2006; Li, Ragu-Nathan, et al.,

2006; Tan, 2001). Thus, the SCMS models on supplier evaluation

are in essence multi-dimensional, complex, and interdependency

activities (Yao et al., 2007). The SCMS models on supplier evalua-

tion permitting intuitive judgment have garnered acceptance by

various experts, including scholars and SCM professionals. To assistthe expert group to select the optimal suppliers in SCMS contexts,

this study proposes an effective hierarchical evaluation framework

by explicitly describing the decision structure of SCMS upon which

pair comparison subjective judgments of experts can base.

3. Hierarchical structure of SCMS

Generally, literature on SCM addressed the purchasing and sup-ply perspective(Morgan & Monczka, 1996). This perspectiveof SCM

is synonymous with supplier base integration that evolves fromthe

traditional purchasing and SCM functions. It emphasizes that pur-

chasingand materials management represent a basic strategic busi-

ness process, rather than a narrow specialized supporting function,

to overall business strategy. This is a management philosophy that

extends traditional internal activities by embracing an inter-enter-

prise scope, bringing trading partners together with the common

goal of optimization and efficiency (Carr & Pearson, 2002).

Literature suggested that five rules must be obeyed when devel-

oping criteria: (i) completeness, criteria must cover all primary

SCMS of the decision making problem; (ii) operational, criteria

must be meaningful for the analysis; (iii) decomposable, criteria

can be decomposed from a hierarchy to a lower hierarchy to sim-

plify the evaluation process; (iv) non-redundant , criteria must not

be counted twice; and (v) minimum size, the number of criteria

should be kept as small as possible. As aforementioned, many cri-

teria must be considered in evaluating the suppliers for SCMS and

these criteria are normally interdependent and interactive with

each other. Information of SCMS contexts can be collected by liter-

ature review as well as interviews with expert SCMS staff and re-

lated senior managers. Particularly, interviews should obtain data

regarding what changes and attributes have led the firm to sustain

success of SCMS. This creates typical MCDM problem with varying

criteria and attributes on related activities. In addition, this study

considers uncertainty as determinants for further practices of

SCMS. As discussed earlier, the uncertain determinants are in the

forms of supply, demand and technology. Supply uncertainty in-

cludes indicators that represent quality, timeliness and the inspec-tion requirements of the suppliers. Demand uncertainty is

measured in terms of fluctuations and variations in demand. Tech-

nology uncertainty measures the extent of technological changes

evident within the industry. These constructs are operationalized

based on prior research (e.g., Chen & Paulraj, 2004; Davis, 1993;

Krause, 1999; Van Hoek, 1998).

Past research has offered valuable structures for SCMS, the ma-

jor references for this study are from Lado, Boyd, and Wright

(1992), Palmer and Griffith (1998), Carr and Pearson (1999), Tan

et al. (2002), Chen and Paulraj (2004), Johnston et al. (2004), Li,

Ganesan, et al. (2006) and Li, Ragu-Nathan, et al. (2006). An in-

depth discussion and literature review have led this study to de-

cide five criteria with eighteen attributes and to select four suppli-

ers. The five criteria used are customer focus (Hwang, 1998; Johnston et al., 2004; Mendoza et al., 2007; Sousa, 2003), compet-

itive priority (Chenhall & Langfield-Smith, 1998; Cox & Blackstone,

1998; Dreyer & Gronhaug, 2004; Kathuria, 2000; Margaret, 1996),

strategic purchasing (Carr & Smeltzer, 1999; Cousins, 1999; Dyer,

1996; Watts et al., 1992), top management support (Chen & Paul-

raj, 2004; Krause, 1999; Wilson & McDonald, 1996), and informa-

tion technology (King, 1996; Carr and Pearson, 1999; Dehning

et al., 2007; Yao et al., 2007). Our SCMS model will integrate the

most relevant activities, components, and characteristics found in

SCMS literature, which are put forward as criteria. The criteria

and their associated attributes are discussed as follows.

First, the customer focus (C1) is the goal of businesses, which is

to ‘‘create and maintain customers” (Levitt, 1985). The attributes

for customer focus construct contain the responses to customersevolving needs and wants (A11), evaluation of customer complains

M.-L. Tseng et al. / Computers & Industrial Engineering xxx (2009) xxx–xxx 3

ARTICLE IN PRESS





(A12), products satisfying customer expectation (A13) and satisfy-

ing customer needs—the central purpose of business plan (A14)

(Hwang, 1998; Johnston et al., 2004; Mendoza et al., 2007; Sousa,

2003).

Secondly, the competitive priority (C2) is a common success

theme of operations strategy, which picks up the manufacturers’

choices of emphasis among key capabilities. The attributes in this

construct contain offering products with lowest price (A21), great-er emphasis on innovation (A22), launching new product quickly

(A23), and quality performance (A24) (Chenhall & Langfield-Smith,

1998; Margaret, 1996; Stanley & Wisner, 2001).

Thirdly, the strategic purchasing (C3) is critical to facilitate close

interactions with a limited number of suppliers and making effec-

tive use of the firm’s supply base (Cousins, 1999). Three attributes

in this construct are considered: purchasing function with a for-

mally written long-range plan (A31), purchasing focus on longer

term issues that involve risk and uncertainty (A32), and purchasing

performance measured (A33) (Carr & Smeltzer, 1999; Dyer, 1996;

Watts et al., 1992).

Fourthly, all the SCMS activities are involved with the top man-

agement support (C4), which is a sustained competitive advantage

directly, should it be able to exploit unique SCM competencies

(Lado et al., 1992). This construct emphasizes such attributes as

purchasing function strategic role (A41), supporting the competi-

tive priority with company mission (A42), supporting the need

for inter-organizational information system (A43), and accounting

for customer needs a vital part of corporate strategy (A44) (Chen &

Paulraj, 2004; Krause & Ellram, 1997; Wilson & McDonald, 1996).

Lastly, the information integration needs the information tech-

nology (C5) to be applied in SCMS. The complete integration into

SCMS with electronic commerce component also aids in the evolu-

tion of SCMS. Sharing information with supply chain partners

through electronic data interchange (EDI), for instance, is also a crit-icalcomponent of SCMS (King, 1996). Theattributes in thisconstruct

include a direct link of computers to computers with key suppliers

(A51), inter-organizational coordination achieved by electronic

links (A52), and using IT-enabled transaction processing (A53) (Carr

and Pearson, 1999; Dehning et al., 2007; Yao et al., 2007).

Fig. 1 presents the hierarchical structure of evaluation frame-

work for SCMS, a MCDM analysis combining ANP with choquet

integral to select the optimal suppliers for case PCB manufacturing

firm. Basically, MCDM analysis is to assist the evaluators in select-

ing one or few most appropriate alternatives from a finite set of

alternatives with reference to multiple, usually conflicting, criteria

(Yeh, Deng, & Pan, 1999); ANP is to simultaneously account for the

relationships of feedback and dependence (Saaty, 1996); while

choquet integral (non-additive fuzzy integral) is to eliminate the

interactivity of expert subjective judgment problems (Kahraman

et al., 2007; Murofushi & Sugeno, 1989; Wang & Klir, 1992; Wang

et al., 1999).

Fig. 1. SCMS hierarchical structure.


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4. Methodologies

To determine the overall performance of SCMS, evaluation crite-

ria are multiple and frequently structured into multi-level hierar-

chies. Decision-making is the process of defining the decision

objectives, gathering relevant information, and selecting the opti-

mal alternatives. Hence, the first phase is to define the decision

objectives—here is to select the suppliers in SCMS under uncer-tainty. After defining the decision objectives, it is required to gen-

erate and establish evaluation objectives in current business

scenario, which is similar to a chain of the determinants—criteria

(purposes), attributes (evaluation factors) and alternatives (deci-

sions). As discussed in the previous section, five criteria of SCMS

are to be considered: customer focus, competitive priority, strate-

gic purchasing, top management support and information technol-

ogy. Moreover, the criteria cluster has to interact with supply,

demand, and technology determinants in order to precisely find

out the best supplier among the four suppliers of case firm. Overall

SCMS performance of the case firm (Suppliers A, B, C, and D) can be

obtained by (i) assigning weights to five criteria (C1, C2, C3, C4, and

C5) and their associated Aj attributes (Cij, i = 1,2,3,4,5; j = 1,2, . . .,

Aj) and (ii) assessing the performance rating of each aspect and

its associated criteria. We will first introduce the ANP technique

and then discuss the choquet integral approach, followed by the

proposed application procedures.

4.1. ANP

Analytic hierarchy process (AHP) was first proposed by Saaty

(1980a) and Saaty (1980b). It has been widely applied in areas such

as MCDM and has become a popular application for performance

evaluation. AHP must satisfy the characteristic of independence

among the criteria before it can proceed to decision making. How-

ever, given the problems encountered in reality, a dependent and

feedback relationship will usually be generated among the evalua-

tion criteria and such an interdependent relationship usually

becomes more complex with the change in scope and depth of thedecision-making problems. Therefore, Saaty (1996) developed a

newanalysismethod—analyticnetwork process(ANP)thatsimulta-

neously takes into account both the relationships of feedback and

dependence, and developed the ANP. Tseng, Lin, Chiu, and Liao

(2008) applied ANP to selecting of competitive priority in cleaner

production implementation. The merits of AHP in group decision-

making are as follows (Dyer & Forman, 1992): (i) both tangibles

andintangibles,individualvalues, andshared valuescanbe included

in the decisionprocess; (ii) the discussion in a group canbe focused

on objectives rather than on alternatives; (iii) the discussion can be

structured so that every factor relevant to thedecision is considered;

and (iv) in a structured analysis, the discussion continues until rele-

vant information from each individual member in the group is con-

sidered and a consensus is achieved.In addition to these merits of AHP, the ANP provides a more

generalized model in decision-making without making assump-

tions about the independency of the higher-level elements from

lower-level ones and also of the elements within their own level.

A two-way arrow among different levels of attributes may graph-

ically represent the interdependencies in an ANP model. If interde-

pendencies are present within the same level of analysis, a looped

arc may be used to represent such interdependencies.

1. Saaty randomly generated reciprocal matrix using scale 1/9,1/

8,1/7, . . ., 1,. . .,8,9. The scales are described as 1: equal impor-

tance, 3 moderate importance, 5 strong importance, 7 very

strong or demonstrated importance, and 9 extreme importance.

Even numbered values will fall in between importance levels.

Reciprocal values (e.g. 1/3, 1/5, etc.) mean less importance,

strongly less importance, etc. Only the upper triangle of the

matrix needs to be completed. The lower triangle of the pair-

wise comparison matrix is composed of reciprocal values.

2. Assuming there are n number of criteria, denoted as (C 1, . . ., Cn),

its pairwise comparison matrix would be A = (aij), in which aij

represents the relative significance of C i to C j. Then, by using

the row vector average normalization proposed by Saaty(1996), the approximate weight Wi of Ci is calculated as

follows:

Wi ¼

Pn j¼1 aij=

Pni¼1aij

À Án

; 8i; j ¼ 1;2; . . . ; n ð1Þ

3. The consistency test of ANP is designed to ensure the consis-

tency of judgments by decision makers throughout the decision

making process. When inconsistencies exist in the pairwise

comparison matrix A, Saaty (1980a) and Saaty (1980b) proved

that for consistent reciprocal matrix, the kmax value is equal to

the number of comparisons, or kmax = n. Then Saaty gave a mea-

sure of consistency, called consistency index (CI), as deviation

or degree of consistency using the following formula:

CI ¼kmax À n

n À 1ð2Þ

5. The consistency ratio (CR) is then defined as the ratio of CI to

the mean random consistency index (RI) as follows:

CR ¼CI

RIð3Þ

The CR should be less than 0.1. It indicates that the consistency level

of the pairwise comparison matrix is acceptable. When CR is greater

than 0.1, it indicates that the results of the decision process are not

consistent, suggesting that the decision maker needs to perform the

pairwise comparison again.

5. Limiting the weight supermatrix for the weights.

ANP uses supermatrix to deal with the relationship of feedback

and interdependence among the criteria. If no interdependent rela-

tionship exists among the criteria, the pairwise comparison value

would be 0. In contrast, if an interdependent and feedback rela-

tionship exists among the criteria, then such value would no longer

be 0 and an unweighted supermatrix M will be obtained. If the

matrix does not conform to the principle of column stochastic,

the decision maker can provide the weights to adjust it into a

supermatrix that conforms to the principle of column stochastic,

and it will become a weighted supermatrix M . We thengetthe lim-

ited weighted supermatrix M Ã based on Eq. (4) and allow for grad-ual convergence of the interdependent relationship to obtain the

accurate relative weights among the criteria

M Ã ¼ limk!1

M k: ð4Þ

4.2. Choquet integral

The choquet integral (a non-additive fuzzy integral), is a

numeric-based approach which has been used for both pattern

recognition and image segmentation (Grabisch & Nicolas, 1994;

Keller, Gader, Tahani, Chiang, & Mohamed, 1994). Adoption of

a fuzzy integral in membership aggregation, rather than a tradi-

tional aggregation operator, leads to an important distinction as


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to how processes of fuzzy integration are utilized. The success of

a choquet integral depends on an appropriate representation of

fuzzy measures, which captures the importance of individual

criterion or their combination (Chiang, 2000; Klir, Wang, &

Harmanec, 1997). This holistic utilization of fuzzy integral is an

important component in many related works to provide informa-

tion integration capability. For instance, Chiang (2000) demon-

strated a good classification result using the proposedaggregator to integrate the memberships of several cluster in a

complex, unconstrained, handwritten digit recognition domain.

Chen and Tzeng (2001) presented a good traffic assignment

model with fuzzy integral to describe the characteristics of traf-

fic behavior in a road network, and their results have explained

more interactivity and uncertainty of traffic among links, com-

pared to traditional models. Since the fuzzy integral is not differ-

entiable with respect to fuzzy measures, an identification

scheme based on the conventional optimization technique can-

not be applied to solving k-fuzzy measures. The basic properties

and definitions of the choquet integral with respect to fuzzy

measures applied in this study are introduced as follows.

Sugeno (1974) introduced monotonic and non-additive fuzzy

integrals to express the grades of importance for attributes, which

is useful to model the preference structure. Fuzzy measure can be

explicated as the subjective importance of a criterion during the

evaluation process. Sugeno and Terano (1977) incorporated the k-

additive axiom to reduce the difficulty of collecting information. In

fuzzy measure space ( X ,b, g ), let k 2 ðÀ1;1Þ. If A 2 b; B 2 b;

A \ B ¼ /, thenthefuzzy measureg isk-additive. This particular fuz-

zy measure is termed as k-fuzzy measure because it has to satisfy k-

additively, named Sugeno measure.

Assume that X = { x1, x2, x3, . . .,xn} and P ( X ) is the power set of X ,

the set function g: P ( X )?[0,1] is called a fuzzy measure, which is

non-additive and preserves the following properties:

1. g (u) = 0 ;

2. g ( X ) = 1 ;

3. if A,BeP ( X ) and A&B then g ð AÞ 6 g ðBÞ (monotonicity);4. In P ( X ), if A1& A2& A3& A4, . . ., and U 1i¼1 Ai 2 P ð X Þ, then limi!1 g

ð AiÞ ¼ g ðU 1i¼1 AiÞ (continuity from below);

5. In P ( X ), if A1 ' A2 ' A3 ' A4 . . ., and \1i¼1 Ai 2 P ð X Þ, then limi!1 g

ð AiÞ ¼ g ð\1i¼1 AiÞ (continuity from above).

In addition, k-fuzzy measure has the following additional

properties:

g ð A [ BÞ ¼ g ð AÞ þ g ðBÞ þ k g ð AÞ g ðBÞ ð5Þ

where k > 0 for all A; B 2 P ð X Þ and A \ B ¼ /. If X is a finite set,

then U ni¼1 Ai ¼ X . The k-fuzzy measure g satisfies the following:

g ð X Þ ¼ g U

n

i¼1 Ai

¼

1k Q

n

i¼1

½1 þ k g ð AiÞ� À 1

& 'if k–0;

Pn

i¼1

g ð AiÞ if k ¼ 0;

8>>><>>>: ð6Þ

where Ai \ A j ¼ / for all i, j = 1,2,3,. . .,n and i– j. In Eq. (1), k– 0

indicates that the k-fuzzy measure g is non-additive; otherwise,

the k-fuzzy measure g is additive and there is no interaction

between Ai and A j for i – j. The interaction means there is informa-

tion fusion between criteria (Klir et al., 1997). k > 0 implies that

g ð A [ BÞ ¼ g ð AÞ þ g ðBÞ and the set { A,B} has multiplicative effect;

whereas k < 0 indicates the substitutive effect of the set { A,B} (Chen

& Tzeng, 2001). In fuzzy measure space ( X,b, g ), let h be a measurable

function from X to [0,1], the definition of the fuzzy integral of h over

A with respect to g is

Z A hð xÞd g ¼ supa2½0;1�½a ^ g ð A \ F aÞ� ð7Þ

where F a = { x|h( x)P a} (Wang & Klir, 1992). A is a domain of fuzzy

integral. When A = X , the fuzzy integral can be denoted byR

h d g .

Consider a fuzzy measure g of ( X,P ( X )) and X is a finite set here.

Let h: X ?[0,1] and assume without loss of generality that the func-

tion h(xi) is monotonically decreasing with respect to i, for instance

h(x1)P h( x2)P Á Á ÁP h( xn). To assure that the elements in X be

renumbered, we get the following equation:

Z hð xÞ g ¼ _n

i¼1½hð xiÞ ^ g ðH iÞ ð8Þ

where H = ( x1, x2 ,. . ., xi), i = 1,2, . . ., n. In practice, h can be regarded

as the performance on a particular attribute for the criteria; g pre-

sents thegrade of subjective importance of each attribute. The fuzzy

integral of h(x) with respect to g gives the overall assessment of the

attribute. To simply the calculation, the same fuzzy measure of cho-

quet integral is expressed as follow:

ðc Þ

Z hdg ¼ hð xnÞ g ðH nÞ þ ½hð xnÀ1Þ À hð xnÞ� g ðH nÀ1Þ þ Á Á Á

þ ½hð x1Þ À hð x2Þ� g ðH iÞ ð9Þ

where 0 6 hð x1Þ 6 hð x2Þ 6 . . .:hð xnÞ 6 1; hð x0Þ ¼ 0 and H i ¼ xðiÞ; . . . ;

xðnÞ. In literature, the fuzzy integral defined by

R hd

g is called ‘‘cho-quet integral.” The basic concept can be illustrated in Fig. 2. The fuz-

zy integral measurement model needs not assume independency

among alternatives; it can, therefore, be used in nonlinear

situations.

4.3. Proposed procedures

The expert group should follow the following five-step proce-

dures to the evaluation of favorable supplier in SCMS with

uncertainties.

Step 1: building up a network framework. As the subjective pref-

erence of every decision maker is different and the judgments

made will not be completely identical, Saaty (1996) suggested an

integration of decision makers’ preferences with the geometric

mean by establishing a pairwise comparison matrix for each com-

ponent, which needs to conform to the characteristic of positive

reciprocal matrix.

Step 2: calculating the relative weight for criteria and attributes.

This study calculates the relative weights of the criteria with

dependent relationships. The pairwise comparison matrices for

evaluation criteria are established. Then the maximum eigenvalues

and the corresponding eigenvectors of the pairwise comparison

matrices are calculated to generate the supermatrix.

Step 3: limiting the weighted supermatrix for the weigh. The un-

weighted supermatrix contains the priorities derived from the

Fig. 2. The basic concept of choquet integral.


ARTICLE IN PRESS





pairwise comparisons of the elements. In an unweighted superm-

atrix, its columns may not be column stochastic. To obtain a sto-

chastic matrix (i.e., each column sums to one), multiply the

blocks of the unweighted supermatrix by the corresponding cluster

priority. The supermatrix must satisfy the principle of column sto-

chastic, which means every column should add up to 1. Based on

the rule of ANP (Saaty, 1996), the decision makers believe that if

the column stochastic is not conformed, then the matrix weightsof the shadow area are 0.5 and the remaining matrix weights

would add up to 0.5.

Step 4: calculating the weights of all attributes. After obtaining

the relative weights of all criteria, integrating the evaluation by

multiplying the score of each criterion with the relative attributes

weight. Eventually, the attributes weight of hierarchical structure

can be generated based on the scores.

Step 5: calculating the final weights of each supplier. Using Eqs.

()(5)–(9) to solve the proposed SCMS model with non-additive fuz-

zy integral needs not assume mutual independence of criteria. It

can be applied to nonlinear cases. Even if any two criteria are

objectively and mutually independent, they are not considered

independent of subjective evaluators.

5. Empirical evaluation of case firm

This section aims to operationalize the proposed hierarchical

evaluation framework to evaluate an optimal alternative supplier

for the case firm. There are some reasons. First, the case firm has

to constantly improve its manufacturing processes while facing

challenges as to how they manage the SCMS in the competitive

and changeable environments. Second, the case firm has to keep

reforming the SCMS in the industrial sector to cope with market

competition and customer requirements. The expert opinions are

obtained from the expert group, composed of five professors and

six senior management staff, with extensive experience consulting

in this study.

5.1. Case firm

Under the prosperous and booming electronic consumption

products and network markets, Taiwan plants of COM Co. Ltd. were

built for IC substrates and entering IC packing field to meet the cus-

tomer demand in related products in 1998. Today, COM is the larg-

est professional PCB manufacturer in Taiwan; it is also ranked as

number six worldwide. To offer the best services for electronic

manufacturers, COM has been constantly developing new genera-

tion technology, enhancing competitiveness, fully satisfying the

market and customer demands, and building up closer relation-

ships with its suppliers and customers. COM, insisting on the prin-

ciple of ‘‘Highest Quality, Customer First,” has continually spent a

lot of effort on improving processes, developing the SCMS and set-ting up full quality system to meet customer requirements. Due to

the quick replacement of electronic products and rapid exploration

of new technologies, the R&D for COM is leading its competitors so

as to meet product demands from customers and explore new

products in markets. COM’s operational principles are focused on

prompting technology development, developing closer relation-

ships with upper- and down-stream of industry, and committing

the customer-demand satisfaction. The SCMS is relatively impor-

tant for COM to sustain in facing an ever-increasingly competitive

and changeable environment.

The expert group with eleven members strived to recommend

the SCMS criteria and attributes, which are expected to remain

long-term competition in intensively competitive markets. The

group members reviewed the SCMS criteria and attributes becauseSCMS is one of the most prioritized issues of the management

team. They have the same need to find a suitable supplier in SCMS

for COM; namely, to evaluate and select the most proper supplier

in SCMS, and to make this selection more logically and persua-

sively. For better handling of this MCDM problem, the eleven

experts’ management group should adopt possible solutions and

criteria and attributes of SCMS which cover the five criteria men-

tioned above.

5.2. The results

The objective of this empirical study is to demonstrate how ANP

and choquet integral can be used to determine the best supplier

selection prior to SCMS criteria and attributes. The expert group

followed the five-step procedures.

Step 1: building up a network framework. An expert committee

for group knowledge is formed. Relevant information from the case

firm is collected to evaluate the advantages and disadvantages and

to monitor the results to ensure the objectives canbe achieved. The

relevant information consists of five criteria and eighteen attri-

butes, most of which are determined from extensive literature

review.

Step 2: calculating the relative weight for criteria and attributes. In

the formation of a pairwise comparison matrix, group decision-

making is used to avoid the biased attitude of the decision maker

towards a particular supplier. A series of pairwise comparisons

are made to the importance of determinants in achieving objec-

tives. Table 1 shows the pairwise comparison of criteria under

determinant (U1) along with the eigenvector (local priority vector),

also known as e-vector. Decomposing k by Eqs. (1)–(3), one obtains

k1 =À7.778, k2 = À3.395, k3 =À0.981, k4 = 0.386, and k5 = 8.245.

The evaluation matrices are also reported. The kmax is equal to

8.245. The consistency of the pairwise judgment of each compari-

son matrix is also checked by consistency index and consistency

ratio, both should be less than 0.1. Table 1 presents CI = 0.035

and CR = 0.024, therefore the results are acceptable and consistent.

This computational results for e-vector are U1(0.53, 0.22, 0.70,

0.41, 0.11) and the normalized results are U1(0.27, 0.11, 0.35,0.21, 0.006). Repeat all the process of pair comparisons, the nor-

malized results under determinants U2 and U3 are, respectively,

U2 (0.26, 0.01, 0.16, 0.24, 0.32) and U3 (0.08, 0.22, 0.11, 0.14,

0.45). These computational results are for the composition of

unweighted supermatrix as shown in Table 3.

Table 2 reports the pairwise comparison of determinants under

criteria (C1). By decomposing k one would obtain k1 =À3.78,

k2 =À1.25and k3 = 8.049. The kmax is equal to 8.049. As shown in Ta-

ble2, CI = 0.007 and CR = 0.005 suggestingthe resultsare acceptable

Table 1

Pairwise comparison matrix for criteria in determinant (U1).

U1 C1 C2 C3 C4 C5 e-Vector WeightU1

C1 1 2 5/6 5 1/2 1 3/8 3 0.53 0.27

C2 2 5/6 1 2 3/5 3 4/5 2 0.22 0.11

C3 5 1/2 2 3/5 1 4 2/7 4 4/5 0.70 0.35

C4 1 3/8 3 4/5 4 2/7 1 3 1/3 0.41 0.21

C5 3 2 4 4/5 3 1/3 1 0.11 0.06

kmax = 8.245; CI = 0.035; CR= 0.024

Table 2

Pairwise comparison matrix for determinants in criteria (C1).

C1 U1 U2 U3 e-Vector WeightC1

U1 1 3 4/7 4 1/2 0.76 0.47

U2 3 4/7 1 2 1/3 0.29 0.18

U3 4 ½ 2 1/3 1 0.58 0.36

kmax = 0.007; CI = 0.007; CR = 0.005


ARTICLE IN PRESS





and consistent. The computational results for e-vector are C1(0.76,

0.29, 0.58) and the normalized results are C1(0.47, 0.18, 0.36). Re-

peated all the process of pair comparisons, the normalized results

for the remaining criteria are C2 (0.45, 0.26, 0.29), C3 (0.47, 0.15,

0.38), C4 (0.47, 0.11, 0.41) and C5 (0.47, 0.16, 0.36), respectively.Again, these computational results are for the composition of un-

weighted supermatrix as shown in Table 3.

Step 3: limiting the weighted supermatrix for the weigh. The out-

comes of the process in Table 3 form the unweighted supermatrix,

which is for interdependency among determinants and SCMS. Its

columns contain the priorities derived from pairwise comparisons

resulted from Tables 1 and 2. In an unweighted supermatrix, its

columns may not be column stochastic. To obtain a stochastic ma-

trix, i.e., each column sums to one, one can multiply the blocks of

the unweighted supermatrix by the corresponding cluster priority.

Raise the supermatrix to a large power to capture first-, second-,

and third-degree influences. If the differences between corre-

sponding elements of a column are less than a very small number,

for successive powers of the supermatrix using Eq. (4), the process

has converged. To derive the overall priorities of elements, we need

to multiply submatrices numerous times, in turn, until the col-umns stabilize and become identical in each block of submatrices.

Because our model involves inner dependences between determi-

nants and criteria, it requires adjusting the unweighted superma-

trix to make it column stochastic. Then, the weighted

supermatrix (Table 4) can be raised to limiting powers to calculate

the priority weights.

The supermatrix is made to converge to obtain a long-term sta-

ble set of weights, shown in Table 4. For convergence to occur, the

supermatrix needs to be column stochastic. In other words, the

sum of each column of the supermatrix needs to be one. The con-

verged supermatrix presents the results of the relative importance

measures for determinants and SCMS.

The elements of the supermatrix have been imported from the

pairwise comparison matrices of interdependencies, shown in

Table 5. As there are still five such pairwise comparison matrices,

one for each interdependent attribute in the criteria, therefore,

there will be non-zero columns in this supermatrix. Each of the

non-zero values in a column is the relative importance weight

associated with the interdependent pairwise comparison matrices.

The supermatrix is made to converge to obtain a stable set of

weights. The converged supermatrix is shown in Table 6.

Step 4: calculating the weights of all attributes. The local priority

weights of criteria can be obtained from the integration of determi-

nants and criteria, and the priority weights of attribute are from

the converged supermatrix. The integration weight results are

through normalization process. The resulted global priority

weights are shown in Table 7.

Step 5: calculating the final weights of each supplier. The choquet

integral provides with functionality and reliability for determiningbest alternatives by solving k-fuzzy measure, where the k values

are limited to [0,1]. The choquet integral (c )R

h d g in Eqs. (1), (3)–

(9) is employed to obtain the aggregated value for each criteria

based on attributes. The aggregated values of R

h d g for the four

alternatives are then used for case firm to select its suppliers in

SCMS and determinants. The ranking order of aggregated value

when k % 1 for these four alternative suppliers is that supplier B

(8.648) is suitable for its present requirements. Note that there is

Table 5

Supermatrix of attributes in interdependency relationships before convergence.

A11 A12 A13 A14 A21 A22 A23 A24 A31 A32 A33 A41 A42 A43 A44 A51 A52 A53

A11 0.00 0.49 0.31 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A12 0.41 0.00 0.21 0.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A13 0.40 0.21 0.00 0.39 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A14 0.47 0.13 0.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A21 0.00 0.00 0.00 0.00 0.00 0.57 0.23 0.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A22 0.00 0.00 0.00 0.00 0.53 0.00 0.26 0.21 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A23 0.00 0.00 0.00 0.00 0.52 0.29 0.00 0.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A24 0.00 0.00 0.00 0.00 0.56 0.26 0.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A31 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.78 0.22 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.81 0.00 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.83 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A41 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.30 0.16 0.00 0.00 0.00

A42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.41 0.00 0.43 0.16 0.00 0.00 0.00

A43 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.55 0.25 0.00 0.20 0.00 0.00 0.00

A44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.28 0.18 0.00 0.00 0.00 0.00

A51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.80 0.20

A52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.75 0.00 0.25

A53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.86 0.14 0.00

Table 4

Converged supermatrix for interdependency among uncertainty and SCMS.

Determinants SCM strategy

U1 U2 U3 C1 C2 C3 C4 C5

Determinants

U1 0.47 0.47 0.47 0.00 0.00 0.00 0.00 0.00U2 0.17 0.17 0.17 0.00 0.00 0.00 0.00 0.00

U3 0.36 0.36 0.36 0.00 0.00 0.00 0.00 0.00

SCMS

C1 0.00 0.00 0.00 0.20 0.20 0.20 0.20 0.20

C2 0.00 0.00 0.00 0.14 0.14 0.14 0.14 0.14

C3 0.00 0.00 0.00 0.23 0.23 0.23 0.23 0.23

C4 0.00 0.00 0.00 0.19 0.19 0.19 0.19 0.19

C5 0.00 0.00 0.00 0.24 0.24 0.24 0.24 0.24

Table 3

The unweighted supermatrix for interdependency among determinants and SCM

strategy.

Determinants SCM strategy

U1 U2 U3 C1 C2 C3 C4 C5

Determinants

U1 0.00 0.00 0.00 0.47 (Table 2) 0.45 0.47 0.47 0.47

U2 0.00 0.00 0.00 0.18 0.26 0.15 0.11 0.16

U3 0.00 0.00 0.00 0.36 0.29 0.38 0.41 0.36

SCMS

C1 0.27 (Table 1) 0.26 0.08 0.00 0.00 0.00 0.00 0.00

C2 0.11 0.01 0.22 0.00 0.00 0.00 0.00 0.00

C3 0.35 0.16 0.11 0.00 0.00 0.00 0.00 0.00

C4 0.21 0.24 0.14 0.00 0.00 0.00 0.00 0.00

C5 0.06 0.32 0.45 0.00 0.00 0.00 0.00 0.00


ARTICLE IN PRESS





unchanged ranking order of aggregated value when k % 0. The final

results are showed in Table 8.

6. Managerial implications

The proposed hierarchical evaluation framework has been

effectively applied to select the optimal supplier in SCMS for the

case PCB manufacturing firm. Especially, it has provided managers

and researchers with better understanding of the differences in

SCMS activity needs and specific management interventions by

examining the eighteen attributes. These attributes serve as a

bridging mechanism, which is very helpful in SCMS. It can also pro-

vide other PCB manufacturing firms with a mechanism to monitor

and establish measurement platform of SCMS.

In order to examine if the evaluation of suppliers is effective in

SCMS, this study further conducted a post-survey discussion with

the SCM expert group. The discussion results are summarized as

follows. First, it is a common understanding that the purposes of

SCMS often emphasize the expectation of improving performance.The expert group chose an optimal supplier with determinants of

supply uncertainty containing quality, timeliness, and inspection

requirements of the suppliers, which are most concerned by the

case firm.

Secondly, the expert group chose the satisfying customer needs

that contain purchasing function formally written with long-range

plan (A31) and direct linking computers to computers with key

suppliers (A51) to be the most important attributes. This choice

Table 6

Supermatrix of attributes in interdependency relationships after convergence.

A11 A12 A13 A14 A21 A22 A23 A24 A31 A32 A33 A41 A42 A43 A44 A51 A52 A53

A11 0.30 0.23 0.24 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A12 0.30 0.23 0.24 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A13 0.30 0.23 0.24 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A14 0.30 0.23 0.24 0.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A21 0.00 0.00 0.00 0.00 0.35 0.30 0.19 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A22 0.00 0.00 0.00 0.00 0.35 0.30 0.19 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00A23 0.00 0.00 0.00 0.00 0.35 0.30 0.19 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A24 0.00 0.00 0.00 0.00 0.35 0.30 0.19 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A31 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.45 0.38 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.45 0.38 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.45 0.38 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00

A41 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.28 0.25 0.14 0.00 0.00 0.00

A42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.28 0.25 0.14 0.00 0.00 0.00

A43 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.28 0.25 0.14 0.00 0.00 0.00

A44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.28 0.25 0.14 0.00 0.00 0.00

A51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.44 0.38 0.18

A52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.44 0.38 0.18

A53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.44 0.38 0.18

Table 7

Integrated the priority weights of criteria and attributes for Choquet integral.

Criteria Attributes Incumbent

weights

Local

priority

Global

priority

C1 0.200 A11 0.30 0.06 0.30 0.06

A12 0.23 0.05 0.23 0.05

A13 0.24 0.05 0.24 0.05

A14 0.24 0.05 0.24 0.05

C2 0.136 A21 0.35 0.05 0.35 0.07

A22 0.30 0.04 0.30 0.06

A23 0.19 0.03 0.19 0.04

A24 0.17 0.02 0.17 0.03

C3 0.233 A31 0.45 0.11 0.45 0.09

A32 0.38 0.09 0.38 0.08

A33 0.17 0.04 0.17 0.03

C4 0.187 A41 0.33 0.06 0.33 0.07

A42 0.28 0.05 0.28 0.06

A43 0.25 0.05 0.25 0.05A44 0.14 0.03 0.14 0.03

C5 0.244 A51 0.44 0.11 0.44 0.09

A52 0.38 0.09 0.38 0.08

A53 0.18 0.04 0.18 0.04

Table 8

Choquet integral computation of overall weight index for alternatives.

Attributes Global priority S1 S2** S3 S4

Value (c)R

h d g (k-value) Value (c)R

hd g (k-value) Value (c)R

h d g (k-value) Value (c)R

h d g (k-value)

A11 0.06 – 8.552 (1.00)

8.549 (0.00)

– 8.684** (1.00)

8.682** (0.00)

– 8.216 (1.00)

8.213 (0.00)

– 8.315 (1.00)

8.312 (0.00)A12 0.05 0.108 0.095 0.108 0.108

A13 0.05 0.175 0.140 0.153 0.153

A14 0.05 0.235 0.210 0.200 0.200

A21 0.07 0.272 0.298 0.237 0.266

A22 0.06 0.348 0.374 0.271 0.322

A23 0.04 0.436 0.410 0.361 0.371

A24 0.03 0.472 0.469 0.437 0.407

A31 0.09 0.521 0.507 0.471 0.495

A32 0.08 0.577 0.567 0.537 0.571

A33 0.03 0.606 0.600 0.612 0.600

A41 0.07 0.672 0.690 0.648 0.670

A42 0.06 0.720 0.766 0.737 0.729

A43 0.05 0.767 0.800 0.793 0.767

A44 0.03 0.800 0.866 0.842 0.800

A51 0.09 0.876 0.922 0.871 0.890

A52 0.08 0.966 0.971 0.940 0.966

A53 0.04 1.000 1.000 1.000 1.000


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is sensible because satisfied IT is important in central point of

SCMS activities, which should aim primarily to take good care of

their IT ability.

Thirdly, many works on SCM suggested that a sound SCMS

should be a broader consideration in many criteria, which should

integrate all attributes as the ideal form of SCMS, rather than an

attribute along. However, the expert group remarked on the merits

of the proposed solutions. Unlike a traditional hierarchical modelbased on the linear and piecemeal approach, the Modified Feedback

System model of the proposed evaluation framework is novel since

it is based on a complex interrelationship and intertwining among

criteria and attributes. It is favorable to use ANP to handle the prob-

lem of inner dependences since it can provide more valuable infor-

mation for decision-making (Wu, 2008; Tseng et al., 2008).

In broader sense, the proposed hierarchical evaluation frame-

work in SCMS can also be used as an analytical monitoring tool

to further developing or constructing an overall supplier evalua-

tion. For the practice of management, SCMS is sufficient for organi-

zational managers to better understand the relevant criteria and

attributes. Moreover, the managers are able to capture a fairly

complete picture of SCMS while assessing the relative performance

of the components developed, validated, and operationalized by

this approach.

7. Conclusions

This study has contributed to, in particular, the SCM literature

by: (i) proposing a research framework that relates determinants

to SCMS under uncertainty, (ii) developing valid and reliable mea-

sures for the dimensions based on expert’s qualitative opinion, and

(iii) developing a SCMS hierarchical analytical structure to evalu-

ate the optimal supplier using ANP and fuzzy integral. In practical

SCMS problems, vast amounts of criteria and attributes are typi-

cally interactive and interdependent and with elusive qualitative

information. This study developed an effective evaluation frame-

work to select the most appropriate supplier in SCMS. The pro-posed framework incorporated a hierarchical MCDM structure,

ANP and choquet integral, wherein MCDM is to select the most

appropriate alternative from a finite set of alternatives with refer-

ence to multiple conflicting criteria, ANP is to simultaneously con-

sider the relationships of feedback and dependence of criteria, and

choquet integral is to eliminate the interactivity of expert subjec-

tive judgment problems. The proposed evaluation framework has

been validated with its effectiveness and simplicity in selecting

the optimal supplier in SCMS for the case firm. The ANP is a rela-

tively new MCDM method which can deal with many interactions

systematically, particularly the SCMS evaluation problems. More-

over, the ANP can be used not only as a way to handle the inner

dependences within a set of criteria/ attributes, but also as a

way of producing more valuable information for decision-making.The whole supply chain members can apply the proposed frame-

work to evaluate and determine firms’ optimal suppliers in

uncertainty.

Some directions for future study are proposed here. Develop-

ment of a richer, multi-hierarchical structure that incorporates

other criteria/attributes with quantitative measurement, not only

the qualitative measurement in this study, deserves further explo-

ration. To prevent the information bias, future study might involve

the fuzzy set theory in when, especially, qualitative measures are

involving imprecision, constraints, and possible actions that are

not precisely in description (Bellman & Zadeh, 1970). Furthermore,

the uncertain environment is highly affected by subjective judg-

ments, which is vague and imprecise in nature (Al-Najjar & Als-

youf, 2003). Modeling the imprecise and uncertain problemswith proper mathematical tools, such as fuzzy logic (Zadeh,

1975), also deserves attempting to account for the vagueness in

the SCMS evaluation process.

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