A novel hybrid MCDM approach for outsourcing vendor selection: A case study for a semiconductor company in Taiwan

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A novel hybrid MCDM approach for outsourcing vendor selection: A case study

for a semiconductor company in Taiwan

Ya-Ti Lin

a,1

_{, Chia-Li Lin}

_b,*

_{, Hsiao-Cheng Yu}

a,2

_{, Gwo-Hshiung Tzeng}

c,3 a

Institute of Management of Technology, National Chiao Tung University, No. 1001 University Road, Hsinchu 300, Taiwan b

Graduate Institute of Human Resource and Knowledge Management, Department of Business Management, National Kaohsiung Normal University, Kaohsiung, No. 116, Heping 1st Road, Lingya District, Kaohsiung City 802, Taiwan

c

Department of Business and Entrepreneurial Administration, Kainan University, Taiwan, Institute of Management of Technology National Chiao Tung University, No. 1 Kainan Road, Luzhu Shiang, Taoyuan 338, Taiwan

a r t i c l e

i n f o

Keywords: Outsourcing Vendor selection

Multiple criteria decision making (MCDM) Analytic Network Process (ANP)

a b s t r a c t

Outsourcing manufacturing is a trend in today’s global business operations. Vendor selection is an essen-tial factor affecting outsourcing operations performance and has been determined as a multiple criteria decision making (MCDM) problem. The purpose of this paper is to propose a novel hybrid MCDM tech-nique to cope with the complex and interactive vendor evaluation and selection problem which can determine the structural relationships and the interrelationships amongst all the evaluation’s dimensions and support the Analytic Network Process (ANP) method to arrange appropriate weightings to each dimension and criterion in the evaluation model by summarizing the opinions of the experts. Finally, the overall performance ranking of all alternatives can be obtained to assist the decision making. Taiwan semiconductor industry is the largest provider in worldwide market. It is vertically disintegrated and out-sourcing is a main stream practice. Wafer-testing is a critical manufacturing step in the semiconductor supply chain that distinguishes whether the IC can meet the speciﬁcations. Consequently, it’s crucial to establish a thorough model for selecting the wafer-testing vendors in order to achieve the success of the outsourcing operation. A case study of a Taiwan semiconductor company in selecting its wafer-testing outsourcing vendor by using the proposed MCDM technique is demonstrated to enhance the deci-sion making quality. The results and proposed solution can be referred to by not only the semiconductor companies, but also other industries so that they can improve the vendor selection process in order to achieve a higher performance and satisfaction level.

1. Introduction

In the severe business competitiveness of today, outsourcing has become a main stream practice in global business operations (Bailey, Masson, & Raeside, 2002). Traditionally, outsourcing is an abbreviation for ‘‘outside resource using” (Arnold, 2000; Bühner & Tuschke, 1997; Quinn & Hilmer, 1994). By this means, companies release non-core business or processes to outside vendors, then the enterprise can focus on the most value-added and professional activities in the whole value chain (Lei & Hitt, 1995; Loh & Venkatr-aman, 1992; Quinn, 1999). The outsourcing items covered a wide range, including: R&D, design, manufacture, facility set up,

market-ing, and etc. The major beneﬁts that enterprises outsource business to vendors are cost reduction, quality and service performance improvement (Bailey et al., 2002; Barthélemy, 2001; Sharpe, 1997). In the outsourcing operation model, vendor selection is one of the critical factors affecting the ﬁnal success. Therefore, the vendor selection issues has been widely studied and determined as a mul-tiple criteria decision making (MCDM) issue. The papers also pro-posed some MCDM methods to cope with this topic including the Analytic Hierarchy Process (AHP), Data Envelopment Analysis (DEA), Analytic Network Process (ANP) and extended fuzzy ap-proaches (Chen, Lin, & Huang, 2006; Degraeve, Labro, & Roodhooft, 2000; Ha & Krishnan, 2008; Lee, 2009; Onut, Kara, & Isik, 2009; Shyur & Shih, 2006; Wu & Lee, 2007; Wu, Sukoco, Li, & Chen, 2009; Yang, Chiu, & Tzeng, 2008). The AHP is widely utilized in vendor selection problem, but has been recognized that is not suit-able to solve the case that contains complex interacting evaluation criteria and dimensions due to each individual criterion is not al-ways completely independent in the complicated evaluation mod-el (Leung, Hui, & Zheng, 2003; Shee, Tzeng, & Tang, 2003; Wu &

*Corresponding author. Tel.: +886 961 123747; fax: +886 3 5726749. E-mail addresses: eddylin@pchome.com.tw (Y.-T. Lin),eddy_yd_lin@hotmail.

com,linchiali0704@yahoo.com.tw(C.-L. Lin),chengyu@cc.nctu.edu.tw(H.-C. Yu),

ghtzeng@mail.knu.edu.tw(G.-H. Tzeng). 1 Tel.: +886 961 123747; fax: +886 3 5726749. 2 Tel.: +886 3 5712121x57508; fax: +886 3 5726749. 3 _{Tel.: +886 936 516698; fax: +886 3 5165185.}

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Lee, 2007). In order to better solve the above-mentioned problems, this paper proposes a hybrid novel MCDM technique that can pro-vide a better decision making quality. There are two major differ-ences of this paper. First, Warﬁeld’s Interpretive Structural Modeling (ISM) method is utilized to construct a relation map which can help to clarify the interrelations amongst the criteria and to apply this relation map to the ANP method for deriving the weighting of each criterion of the complex vendor selection problem. Second, ANP is employed to obtain the weightings which is able to overcome the problem of interdependence and feedback amongst criteria. Thus, the overall scores for each vendor in each criterion can be obtained and the selection decision can be made accordingly. This paper also conducted an empirical case study as an illustration to demonstrate how a Taiwan semiconductor com-pany can implement this solution.

The Semiconductor industry has evolved along with the world-wide outsourcing trend and thereby transformed their manufac-turing strategy, releasing many of the manufacmanufac-turing steps to outsourced subcontractors (Frederix, 1996; OhUallachain, 1997). The semiconductor industry is now composed of independent IC design houses, wafer foundry fabrication, wafer-testing, and IC packaging. The wafer-testing step tests the function and perfor-mance of the ICs. If wafer-testing companies fail to distinguish be-tween good and defective ICs, good ICs might be scrapped and cause money loss. An even worse scenario is when wafer-testing companies fail to detect defective ICs, then erroneously sending them for packaging and ultimately, delivery to customers. When this occurs, not only is packaging cost wasted, but even more importantly, the potential loss in reputation and then business is quite hazardous. Since Integrated Device Manufacturing (IDM) companies and IC design houses concentrate on their core business functions, wafer-testing outsourcing demand to professional wa-fer-testing houses is a mainstream and the market is increasing (Lee, 2006). Consequently, how to evaluate and select the most suitable wafer-testing subcontractor is crucial. Then reason to use Taiwan’s semiconductor industry as an empirical case study is because Taiwan’s semiconductor industry is considered a global paragon (Chu, Teng, Huang, & Lin, 2005). And Taiwan’s professional wafer-testing houses, ASE, SPIL, KYEC, Ardentech and etc., have 60% of the worldwide market share (IDB, 2007). Through interviews with experts in the Taiwanese semiconductor industry we ob-served that the semiconductor companies tend to use the existing subjective experience for wafer-testing outsourcing vendor evalu-ation and selection. Therefore, setting up a thorough evaluevalu-ation model, criteria and method for evaluating and selecting wafer-test-ing outsourcwafer-test-ing vendors is a critical topic and we will demonstrate the proposed solution to better solve this problem.

The remainder of this paper is organized as follows: In Section

2, the related researches of vendor selection criteria are reviewed. Additionally, the evaluation dimensions and criteria are estab-lished from our conclusions. Section3 is the research methods’ introduction of ISM and ANP. Section4is the empirical case study taking a Taiwan wafer foundry fabrication company as an example for demonstrating the wafer-testing vendor evaluation and selec-tion from the proposed model, procedure and method. The results of the empirical research are also analyzed. Section5is the conclu-sion of this research.

2. Vendor evaluation and selection issues

In this section, our research brieﬂy introduces the study of ven-dor evaluation and selection through review of relevant academic papers in Section2.1. In Section2.2, we introduce the process of selecting the dimensions and criteria for semiconductor companies to evaluate and select their wafer testing outsourcing vendors.

2.1. Introduction of vendor evaluation and selection

Since outsourcing is main stream worldwide, vendor evaluation and selection are essential for the purchaser in achieving the final result at their aspired level in their service or product. If any one of the outsourcing vendors in the supply chain cannot fulfill the pur-chaser’s requirements, it will impact the final operations’ efficiency of the purchaser, and potentially even cause business loss. In order to ensure the performance of outsourcing vendors, the purchaser needs to establish a suitable framework to evaluate and select and its vendors. The suitable framework must embrace not only the highly relative criteria with the purchaser’s satisfaction (Lee & Billington, 1992), but also the appropriate mathematical meth-odology.Degraeve, Roodhooft, and Doveren (2005)made a review of the vendor selection issues and they indicated that in the pur-chasing related literature and practice, the simple, subjective and incomplete approaches for vendor selection have been commonly used. The same phenomenon happens in the semiconductor indus-try.Degraeve et al. (2000)commented that in order to have better results with vendor evaluation and selection, a weighted scoring method has been applied in some cases.Weber, Current, and Ben-ton (1991)had reviewed 74 articles on supplier selection criteria and methods over the last 30 years. It appears the linear weighting model was the most commonly utilized quantitative approach for this issue. In this approach, a weight is given subjectively for each criterion; and ultimately, the total score of a vendor is calculated by summing up all of its weighted scores. However, the shortcom-ing of the above methods is the personal bias due to the weightshortcom-ings being given subjectively. Some researches noticed the phenomena, and therefore, have suggested some mathematical approaches, such as AHP, ANP, DEA, PROMETHEE and extended fuzzy methods. Some selections were made by using the AHP method (Sarkis& Talluri, 2002; Ting & Cho, 2008; Weber & Current, 1993; Wu & Chien, 2008; Yahya & Kingsman, 1999). The AHP method has some fallible premises that the criterion of each layer is assumed to be independent of the other layers. However, in real business practice, it is common that problems are mutually, or recursively, related. The more problems and elements that exist, the more complicated the relationships will be in the evaluation model. Therefore, the AHP model is not very suitable in the complex vendor selection case (Leung et al., 2003; Shee et al., 2003; Wu & Lee, 2007). For in-stance, delivery is correlated with quality and service priority, therefore if a supplier has a poor in-line manufacturing quality, its delivery performance may be affected. Additionally, the AHP model cannot explain the interrelationships amongst the various dimensions or the criteria inside an evaluation model. However, the experts in the industry commented that causal interrelation-ships are the key of an evaluation model, since the users can utilize the interrelationships’ results to have a clear understanding of how the different dimensions or criteria affect each other. The ANP method has been recognized as a more suitable solution to cope with complex and interacting problems (Meade & Presley, 2002;

Sarkis & Talluri, 2002; Wu et al., 2009). Besides, the understanding of the interrelationships can also help the buyer to evaluate a ven-dor, as well as to build up improvement strategies to enhance the outsourcing performance effectively.Yang et al. (2008)conducted a research in order to establish a vendor selection model that em-braces the analysis of causal relations inside the model.

2.2. Establishing an evaluation’s dimensions and criteria

This section explains the procedures to establish the wafer-test-ing outsourcwafer-test-ing vendor evaluation’s dimensions and criteria through the literature review and interviews with experts in Tai-wan semiconductor industry. In the past, companies tended to use a single index as their target for manufacturing performance,

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such as: output quantity, delivery achievement, abnormal rate, etc. However, a single index cannot represent the company’s overall performance, nor can it be used to evaluate the performance of outsourcing. The research ofYahya and Kingsman (1999)reviewed the developmental history of vendor evaluation and selection cri-teria. Their research shows thatDickson (1966)was the pioneer to validate 23 criteria for assessing a vendor’s performance. Skin-ner (1969)was the first to use the four dimensions of cost, quality, delivery and flexibility. This was done in order to evaluate the manufacturing performance of a company.Weber et al. (1991) re-viewed 74 academic papers, analyzing the criteria used for vendor selection. They found that net price was the most discussed crite-rion, followed by delivery and quality based on Dickson’s well known study. Many researchers afterwards also utilized these four dimensions, cost (price), quality, delivery and flexibility (service) in the research on outsourcing and vendor selection (Ha & Krishnan, 2008; Krajewski& Ritzman, 1998; Leong, Snyder, & Ward, 1990; Lin & Lee, 2005; Wu et al., 2009).

From the literature review, we collected usable dimensions and criteria to be used when evaluating and selecting an outsourcing vendor. In order to better determine the suitable dimensions and criteria of each dimension, this research further interviewed ex-perts in the semiconductor industry to screen for the suitable dimensions and criteria, based on our literature review. Finally, by integrating them, this research then summarized and con-structed an evaluation model with four dimensions and fourteen criteria that are most suitable. The four dimensions include: Deliv-ery Management Capability, quality management capability, inte-grated service capability, and price. Regarding financial capability, experts in this industry stated that almost all companies set vendor financial capability as a must before vendor selection. Consequently, we won’t put this criterion in the evaluation model. Under the four dimensions, there are 14 criteria. The dimension of Delivery Management Capability (D) includes three criteria: (1) accuracy of delivered contents; (2) on-time delivery; and (3) deliv-ery adjustment flexibility. The dimension of Quality Management Capability (Q) includes four criteria: (1) correctness of testing data;

(2) quality abnormal rate; (3) capability to prevent repeated error; and (4) error judgment rate. The dimension of Integrated Service Capability (S) includes four criteria: (1) response-time for custom-ers’ request; (2) efﬁciency of engineering support; (3) fulﬁlling cus-tomers’ special requests; and (4) customer service for information platform. The dimension of Price (P) includes three criteria: (1) testing price; (2) compensation rate for broken wafers; and (3) acceptance criteria. These dimensions and criteria are listed below inTable 1. We utilized these dimensions and criteria to set up a vigilant evaluation model for evaluating and selecting the most suitable outsourcing vendor, which can then ensure the desired re-sults, while preventing potential risks.

3. Research method

3.1. Interpretive structural modeling (ISM)

Interpretive structural modeling was proposed by Warfield (1974a, 1974b, 1976)as a computer assisted methodology ( Agar-wal, Shankar, & Tiwari, 2007; Huang, Tzeng, & Ong, 2005;Sharma, Gupta, & Sushil, 1995). It is used to derive an understanding of the interrelationships amongst complex elements, and allows a set of different and directly related elements to be structured into a com-prehensive systemic model (Fontela, 2003).Mandal and Deshmukh (1994)utilized ISM to identify the interrelationships amongst cri-teria in a vendor selection problem. Therefore, this paper applies ISM to build a relation map to identify the independence or depen-dence of all criteria. The theory of ISM is based on discrete mathe-matics, graph theory, social sciences, group decision-making, and computer assistance (Warfield, 1974a, 1974b, 1976). The first step of ISM is to identify the variables relevant to the problems or is-sues. It then extends with a group problem-solving technique. A structural self-interaction matrix (SSIM) is then developed based on a pair-wise comparison of variables. The SSIM is formed by ask-ing questions such as, ‘‘Will element eiaffect element ej?” If the

an-swer is yes, then

p

ij¼ 1. If the answer is no, then

p

ij¼ 0. SSIM can

be described as below:

Table 1

The criteria for wafer test vendor selection.

Dimensions Criteria Explanation of the criterion

Delivery management capability (D)

1. Accuracy of delivered contents Wafer-test vendors need to deliver correct quantity and part number to the customer 2. On time delivery Wafer-test vendors need to deliver tested wafers on time

3. Delivery adjustment ﬂexibility Wafer-test vendors can have the ﬂexibility to adjust the production priority and schedule according to customers’ adjustment

Quality management capability (Q)

1. Correctness of testing data Wafer-test vendors need to provide correct testing information and results to the customers

2. Quality abnormal rate The abnormal rate, including broken, scratched, data error, etc. wafers, during the wafer-test at vendor sites

3. Capability to prevent repeated error Wafer-test vendors need to have the capability to prevent repeated quality abnormal issue and improve their quality

4. Error judgment rate Wafer-test vendors should reduce their error judgment rate Integrated service capability (S) 1. Response time for customers’

request

Response time for vendors’ response to customers’ requests

2. Efficiency of engineering support Wafer-test vendors need to fulfill customers’ engineering support demand, including testing program development, tester adjustment, and related engineering processes 3. Fulfilling customers’ special

requests

Except the normal request from customers, wafer-test vendors should fulﬁll other special demands from them, such as manufacturing process priority change, special price request, change in the original delivery plan, extra engineering service or extra engineering resource to support a critical issue.

4. Customer information service platform

The customer information system is an interface between the vendor and customer which can provide manufacturing status, delivery, and some related information immediately. This system should be very stable and easy to use.

Price (P) 1. Testing price Testing price per wafer or per hour, and other related expense 2. Compensation rate for broken

wafers

The compensation rate for abnormal case or wafer damage 3. Acceptance criteria Reasonable acceptance criteria based on customers’ requirements

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The eimeans the ith element. The

p

ijmeans the interrelationship

between the ith and the jth elements. D is an SSIM. After establish-ing the SSIM, we can then convert it into a reachability matrix. Its transitivity is then checked with Eqs. (1) and (2) (Huang et al., 2005):

M ¼ D þ I ð1Þ

M_{¼ M}k

¼ Mkþ1; k > 1 ð2Þ

where I is the unit matrix, k denotes the powers, and M _{is the}

reachability matrix. Note that the reachability matrix is under the operations of the Boolean multiplication and addition (i.e. 1 1 = 1, 1 + 1 = 1, 1 0 = 0, 1 + 0 = 0 + 1 = 1, 1 0 = 0 1 = 0). For example: M ¼ 1 0 1 1 ; M2¼ 1 0 1 1 ð3Þ

3.2. The Analytic Network Process (ANP)

The ANP is the general form of the AHP (Saaty, 1980, 1996; Saaty & Vargas, 1998; Yu & Tzeng, 2006). The ANP was designed to overcome the problem of dependence and feedback amongst criteria (Yu & Tzeng, 2006). Therefore, the evaluation’s results through the ANP will be closer to the real practice. The ANP has been used for MCDM to release the restrictions of the hierarchical structure. It has been applied to project selection (Lee & Kim, 2000; Meade & Presley, 2002), product planning, strategic decision mak-ing (Karsak, Sozer, & Alptekin, 2002; Sarkis, 2003), and optimal scheduling (Momoh & Zhu, 2003). The ANP is robust and is hence, a more suitable method for this kind of complex MCDM issue (Leung, Lam, & Cao, 2005). The advantages of the ANP are that it is not only appropriate for both quantitative and qualitative data types, but also, it can overcome the problem of interdependence and feedback amongst criteria. The following three steps are undertaken to evaluate the decision making problem with the ANP method (Saaty, 2006; Shyur, 2006; Shyur & Shih, 2006): (1) building the network hierarchical structure; (2) calculating the weighing of factors in each hierarchy; and (3) calculating the weighting of the whole hierarchical structure.

4. Empirical case study of the vendor evaluation and selection for wafer-testing outsourcing

In this section, we illustrate this novel hybrid evaluation and selection process by using an empirical case study in Taiwan’s semiconductor industry as an example. There are four steps needed for this study. The first step is to construct the evaluation model from Section2by a literature review and interviews with the experts in Taiwan’s semiconductor industry. Through this pro-cess, we obtained four dimensions and fourteen criteria which are suitable to evaluate a wafer-testing vendor. The second step is to distinguish the interrelationships amongst dimensions in the eval-uation model by applying the ISM method, so that then a structural network relationship map (NRM) can be constructed accordingly. The third step is finding the weightings of each dimension in the evaluation model. The ANP is then utilized to derive the weigh-tings, based on these interrelationships and the NRM, from the ISM step. The final step is to discuss and analyze the results of this

case study. The research methods that were applied in this empir-ical case study are illustrated in the sub-sections below.

4.1. Background of the empirical study

The semiconductor industry is composed of independent IC de-sign houses, wafer foundry fabrication, wafer-testing, and IC pack-aging. In this industry, Fabless IC design houses focus on circuit design, and then release wafers to wafer-testing companies for wa-fer sorting/testing (also rewa-ferred to as circuit probing, or CP). More and more IDMs, IC design houses, and wafer foundry fabrication companies have been releasing their wafer-testing demand to pro-fessional wafer-testing houses to reduce their cost and investment in testing (Lee, 2006). Taiwan semiconductor industry has the important position in worldwide market and the wafer-testing outsourcing is a key operation in the manufacturing chain. The semiconductor companies need to outsource most of their wafer-testing operation to subcontractors and therefore the vendor evaluation and selection is crucial. So, this paper takes a case from Taiwan semiconductor industry to demonstrate the proposed ven-dor selection model and method. Due to the restrictions of the Non Disclosure Agreement (NDA), the real company names in this paper are replaced by codes. The company that needed to select the most suitable wafer-testing outsourcing vendor in this case study is a global, first tier wafer foundry fabrication company lo-cated in Taiwan, hereby referred to as ‘‘company X.” Company X had five available and qualified wafer-testing vendors, hereafter referred to as companies A, B, C, D and E. These five wafer-testing vendors are all public open companies and dedicated for profes-sional wafer-testing service. Company X had a new wafer testing outsourcing project and needed to select the most suitable out-sourcing vendor amongst all the current five qualified vendors. In the past, company X had made their vendor selection based on existing personal experience. This research establishes a thorough model and procedure that enables the industry experts to enhance their decisions’ quality and obtain the best performance from their outsourcing operations.

The interviews were conducted with 12 experts in company X, who were all to have more than 10 years experience in the wa-fer-testing ﬁeld. They not only replied to the questionnaires for constructing this evaluation and selection model, but they also provided their professional knowledge and experience in wafer-testing and subcontractor management, along with an industrial perspective.

4.2. Distinguishing the interrelationships of the evaluation models by using the ISM technique

The four evaluation dimensions of wafer-testing outsourcing in this research include: (1) Delivery Management Capability (D); (2) Quality Management Capability (Q); (3) Integrated Service Capabil-ity (S); and (4) Price (P). The original interrelationships data amongst all the dimensions are listed inTable 2.

Setting the threshold value = 0.50 which represents that more than 50% of the experts determine the interrelationship is existent. If the value of the element inside the matrix is P 0:50, the value is

Table 2

Original interrelation matrix.

Dimensions D Q P S

Delivery management capability (D) 0.00 0.35 0.14 0.50 Quality management capability (Q) 0.82 0.00 0.44 0.74

Price (P) 0.79 0.38 0.00 0.76

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counted as 1. If the value of the element is < 0.50, the value is counted as 0. Then the interrelationships matrix (D) could be gained, and the matrix (M) could be gained, by using Eq.(1), as shown inTables 3 and 4.

Finally, the reachability matrix can be obtained by using Eq.(2). The star (*) indicates the derivative relationship, which did not emerge in the original relation matrix. The correlations of every as-pect are shown asTable 5andFig. 1.

From the empirical survey,Table 5andFig. 1, we discovered the interrelationships amongst all the dimensions in the evaluation model. From the Delivery Management Capability (D)’s viewpoint, it has a two-way inter-affection with the dimension of the Quality Management Capability (Q), and the Integrated Service Capability (S). Additionally, D is affected by the Price dimension (P). From the Quality Management Capability (Q)’s viewpoint, it has a two-way inter-affection with the dimensions of the Delivery Manage-ment Capability (D), and the Integrated Service Capability (S). In addition, Q is affected by the Price dimension (P). From the Inte-grated Service Capability (S)’s viewpoint, it has a two-way inter-affection with the dimensions of the Delivery Management Capa-bility (D) and the Quality Management CapaCapa-bility (Q). Moreover, S is affected by the Price dimension (P). From Price P’s viewpoint, this ﬁnding is interesting in that Price affects three other dimen-sions in the evaluation model. In fact, it has a causal relationship with the other three dimensions.

4.3. Identifying the weighting by the ANP method

The ANP method was applied in this empirical research to gen-erate a suitable weighting for each dimension within the evalua-tion. The ANP steps in this research are: (1) apply to the established framework the results from Section2and the ISM step; (2) design the questionnaires and survey; (3) establish the weigh-tings by pair-wise comparison, establish the weighweigh-tings of calcu-lating factors, and establish the logical judgment consistency; (4) calculate the supermatrix; and, (5) determine the appropriate weighting decision (Shyur, 2006; Shyur & Shih, 2006).

Step 1: Establish the framework from Section2Based on the lit-erature review and the interviews with the experts in Taiwan’s semiconductor industry, this research con-structs an evaluation model for evaluating wafer-testing outsourcing vendors. The subordinate relationships, or the feedback from the dimensions themselves, are man-ifested as a one-way or two-way arrow, as shown in

Fig. 1.

Step 2: Design the questionnaire and survey According to the evaluation framework, the experts judge the degree of the relative importance between dimensions and criteria. The evaluation results were obtained by collecting and analyzing questionnaires.

Step 3: Pair-wise comparison to determine relative importance of criteria The pair-wise comparison matrix shown in

Table 6can be derived from the questionnaires. The con-sistency index (C.I.) and concon-sistency ratio (C.R.) were used to check the consistency of the experts’ judgment. The C.I.’s value is deﬁned as C:I: ¼ ðkmax nÞ=ðn 1Þ,

and the kmax is the largest eigenvalue of the pair-wise

comparison matrix. The C.R.’s value is deﬁned as C.R. = C.I./R.I.(R.I.: random index). The R.I.’s value is decided by the value of n. As shown inTable 7, the C.I.’s andC.R.’s val-ues are all less than 0.1, which means it matches the con-sistency test. Then, we calculated the eigenvalues and eigenvectors of each comparison matrix, and used the normalized eigenvector of the largest eigenvalue ðkmaxÞ

as the weights of evaluation dimensions, as shown in

Table 8.

Step 4: Calculate the super matrix In order to cope with the dependence relationship amongst dimensions and the feedback relationship within the dimension itself, the ANP method calculates factor weights by the super matrix, based on the NRM from the ISM step. The super matrix is composed by many sub-matrices, which are obtained from the pair-wise comparison matrix in Step 3. If no relative inﬂuence exists in the factors, the pair-wise comparison value of the sub-matrices is equal to zero. Taking Table 11and Fig. 1 as an example, Price (P) and the Delivery Management Capability (D) have

Table 3

Interrelation matrix (D).

Dimensions D Q P S

Price (P) 1.00 0.00 0.00 1.00

Service (S) 0.00 1.00 0.00 0.00

Table 4

Matrix (M) of all dimensions.

Dimensions D Q P S

Price (P) 1.00 0.00 1.00 1.00 Service (S) 0.00 1.00 0.00 1.00 Table 5 Reachability matrix ðM Þ of all dimensions. Dimensions D Q P S

Delivery management capability (D) 1 1 ₀ ₁

Quality management capability (Q) 1 1 0 1

Price (P) 1 1 ₁ ₁ Service (S) 1 ₁ ₀ ₁ Delivery management capability (D) Quality management capability (Q) Integrated service capability (S) Price (P) Delivery management capability (D) Quality management capability (Q) Integrated service capability (S) Price (P)

Fig. 1. Dimension interrelation structure.

Table 6

Pair-wise element comparison table.

Criteria Q1 Q2 Q3 Q4

Correctness of testing data ðQ1Þ 1.00 [1] 0.80 [2] 1.16 0.99 Quality abnormal rate ðQ2Þ 1.26 [3] 1.00 1.46 1.24 Capability to prevent repeated error ðQ3ÞÞ 0.86 0.69 1.00 0.85 Error judgment rate ðQ4Þ 1.01 0.81 1.18 1.00 Note 1: the parenthetic value 1.000 means Q1and Q1are equally important. Note 2: the parenthetic value 0.800 means Q1has 0.8 times the degree of impor-tance than Q2.

Note 3: the parenthetic value 1.260 means Q2 has 1.26 times the degree of importance than Q1.

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no interrelationship, therefore the pair-wise comparison matrix results in zero matrices. The dimension of the Delivery Management Capability (D) has a recursive rela-tionship itself, which is illustrated as a unit matrix. Tak-ing the relationship from the Quality Management Capability dimension (Q) to the Delivery Management Capability dimension (D), as shown inTable 11, we put them into each individual pair-wise comparison matri-ces. After considering the weighting of each dimension, as shown inTable 9, the relative weightings of dimen-sions can then be calculated, as shown inTable 10. Then, by multiplying the relative weighting to the pre-weighted super matrix (Table 11), we could then derive the weighted super matrix, as shown in Table 12. By the transformation process, the dependence relationship can be converged through the procedures of limitation. The relative weights of factors can be obtained by ðM MÞ2kþ1, where k is determined by assumption (as shown inTable 13).

Step 5: Determine the optimal solution The optimal solution can be judged by using the expectation index. The possible plan indexes are deﬁned as DIi, where i ¼ 1; 2; . . . ; m, as

deﬁned by the Eq.(4).

DIi¼

Xn j¼1

wjrij ð4Þ

where wjis the relative weight of criteria j; rijis the ﬁtness degree

of the satisfaction of the ith possible plan under the jth evaluation dimension. The most desired level is A

; A

¼ fr

jjrj ¼ max i¼1;2;...;mrij;j ¼

1; 2; . . . ; ng; the optimal plan is ABest

; ABest

¼ f max

i¼1;2;...;nDIiji ¼

1; 2; . . . ; ng. The gap between ABest _{and A} _{is what needs to be}

improved.

Saaty (1996)assumed the weightings of the main level is equal in the ANP, but this paper uses the pair-wise comparison method to obtain the weightings, which can accurately reﬂect the real sit-uation more authentically. From the interrelationship structure as shown inFig. 1, we discovered that the Price dimension (P) was independent, there was not any interrelation between the Price dimension (P) and others. The whole evaluation model could thus be divided into two main portions consequently; one was the ‘‘va-lue related dimensions (D, Q and S)” (we set it as ‘‘V”) and the other was the ‘‘price dimension (P)”. From the surveyed interrelation-ships, the Price dimension (P) was a driver to the value related dimensions. Through the super matrix calculation, we obtained the weighting of each dimension of the value related dimensions, and the weighting of the Price dimension (P) was zero, as shown inTable 13. The weightings of the criteria in the Price dimension (P) were also obtained by the pair-wise comparison. All weightings in this evaluation model were combined by these two results, as shown in Table 14. In the value related dimensions, the Quality Management Capability (Q) has the highest weighting, 0.375. In the Price dimension (P), the criterion of testing price has the high-est weighting, 0.422. From the weights, we also make a ranking for each criterion in each dimension which indicates the degree of importance from the questionnaire collection. After calculated all the weightings in the evaluation model through the ANP method, the completed wafer-testing outsourcing vendor evaluation and selection model can be fully established.

The final ranking of all alternatives (the 5 qualified vendors) are calculated by synthesizing the scores of each alternative under the 4 (D, Q, S, P) dimensions and 14 criteria. Because the ‘‘value related dimensions (D, Q and S)(V)” and the Price dimension (P) are deter-mined as independent, we set an index, Overall Performance (O.P.), to measure the overall scores of all alternatives by combining the ‘‘value related dimensions (D, Q and S)(V)” and the Price dimension (P). The final ranking summary of all alternatives is listed in the Ta-ble 15.

4.4. Discussion and analysis

From the interrelation map from ISM (Fig. 1) and ANP calcula-tion (Tables 14 and 15) of the ‘‘value related dimensions (D, Q and S) (V)”, it implies that the Quality Management Capability (Q) is the major concern for company X in wafer-test outsourcing vendor selection which the weight is 0.346, followed by the Deliv-ery Management Capability (D) (0.346) and the Integrated Service Capability (S) (0.279). In the Quality Management Capability (Q) dimension, the most concerned criterion is Quality Abnormal Rate ðQ2Þ (0.115). This indicates that the outsourcing quality is the

ma-jor concern of the semiconductor company. It’s also an important message to the wafer-test companies that if they want to win the business, the quality related operations need to be enhanced. The ﬁrst priority of quality enhancement is to reduce the Quality Abnormal Rate ðQ2Þ since this is determined as the most critical

criterion in this vendor selection case. The second important eval-uation and selection dimension is the Delivery Management Capa-bility (D) (0.346). The interesting ﬁnding is that the most concerned criterion in this dimension is the Accuracy of Delivered Contents ðD1Þ in stead of On Time Delivery ðD2Þ. We interviewed Table 7

The testing of consistency (C.I. and C.R. testing).

C:I: ¼ ðkmax nÞ=ðn 1Þ 0.0017 C:R: ¼ C:I:=R:I: 0.0019

Threshold value 0.1 Threshold value 0.1

Table 8

The weights (pre and post normalization) in dimension Q.

Criteria

Pre-normalization

Post- normalization (%)

Correctness of testing data ðQ1Þ 0.480 0.242 Quality abnormal rate ðQ2Þ 0.602 0.304 Capability to prevent repeated

error ðQ3Þ

0.413 0.208

Error judgment rate ðQ4Þ 0.486 0.245

SUM 1.981 1.000

Note: Pre- normalization means that the largest eigen values are used as the factor weights; Post- normalization means that the factor weights are used as the factor weights and the sum of factor weights is equal to 1.

Table 9

Relationship between aspect and weights.

Aspect Weight

Delivery management capability (D) 0.261

Quality management capability (Q) 0.283

Price (P) 0.244

Integrated service capability (S) 0.211

SUM 1.000

Table 10

Relative weighted relationship.

Aspect Proportion rate Relative weighted coefﬁcient (%)

D D/(D+Q+S) 0.346

Q Q/(D+Q+S) 0.375

S S/(D+Q+S) 0.279

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the experts of company X for exploring the inner meaning of this phenomenon. After the discussion, we discovered that if the wa-fer-testing vendor shipped the wrong contents to the buyer, there would be some critical side effects and they also need to spend numerous efforts to solve the problem. The possible critical side ef-fects include wrong shipment to the end customer which may lead to the critical intelligent property (IP) and product conﬁdential information leakage issue, and also the further delivery delay since the logistic operation needs to be re-arranged. The mixed packing with wrong items also require speciﬁc and extra human and

sys-tem efforts to verify the contents and all related documents. There-fore, the Accuracy of Delivered Contents ðD1Þ is critical to affect the

efﬁciency of logistic related operations. In the Integrated Service Capability dimension (S), the most concerned criterion is Fulﬁlling Customers’ Special Requests ðS3Þ (0.093). In order to better

under-stand the inner meaning, we consulted the experts of company X for their comments. The reason we analyzed was that due to the wafer foundry companies are all pure manufacturing for custom-ers’ products, therefore they need to be very ﬂexible to fulﬁll var-ious requests from different customers. Consequently, as an

Table 11

Original super matrix.

D Q P S D1 D2 D3 Q1 Q2 Q3 Q4 P1 P2 P3 S1 S2 S3 S4 D D1 1.000 0.000 0.000 0.383 0.451 0.381 0.477 0.256 0.313 0.329 0.280 0.267 0.243 0.411 D2 0.000 1.000 0.000 0.287 0.292 0.324 0.297 0.390 0.469 0.430 0.328 0.336 0.348 0.322 D3 0.000 0.000 1.000 0.330 0.257 0.295 0.225 0.354 0.219 0.241 0.392 0.397 0.409 0.267 Q Q1 0.242 0.214 0.198 1.000 0.000 0.000 0.000 0.223 0.166 0.253 0.275 0.235 0.232 0.294 Q2 0.304 0.309 0.315 0.000 1.000 0.000 0.000 0.318 0.444 0.316 0.293 0.305 0.310 0.284 Q3 0.208 0.214 0.227 0.000 0.000 1.000 0.000 0.176 0.235 0.152 0.191 0.209 0.201 0.194 Q4 0.245 0.263 0.259 0.000 0.000 0.000 1.000 0.283 0.155 0.279 0.241 0.250 0.257 0.229 P P1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 P2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 P3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 S S1 0.235 0.247 0.208 0.159 0.174 0.200 0.193 0.229 0.175 0.210 1.000 0.000 0.000 0.000 S2 0.299 0.302 0.323 0.324 0.338 0.362 0.373 0.298 0.336 0.304 0.000 1.000 0.000 0.000 S3 0.292 0.333 0.361 0.341 0.354 0.324 0.325 0.322 0.372 0.376 0.000 0.000 1.000 0.000 S4 0.174 0.117 0.108 0.176 0.133 0.114 0.108 0.151 0.117 0.110 0.000 0.000 0.000 1.000 Table 12

Weighted super matrix.

D Q P S D1 D2 D3 Q1 Q2 Q3 Q4 P1 P2 P3 S1 S2 S3 S4 D D1 0.346 0.000 0.000 0.132 0.156 0.132 0.165 0.067 0.082 0.086 0.097 0.092 0.084 0.142 D2 0.000 0.346 0.000 0.099 0.101 0.112 0.103 0.102 0.122 0.112 0.113 0.116 0.120 0.111 D3 0.000 0.000 0.346 0.114 0.089 0.102 0.078 0.092 0.057 0.063 0.136 0.137 0.141 0.092 Q Q1 0.091 0.080 0.074 0.375 0.000 0.000 0.000 0.063 0.047 0.072 0.103 0.088 0.087 0.110 Q2 0.114 0.116 0.118 0.000 0.375 0.000 0.000 0.090 0.126 0.090 0.110 0.114 0.116 0.106 Q3 0.078 0.080 0.085 0.000 0.000 0.375 0.000 0.050 0.067 0.043 0.072 0.078 0.075 0.073 Q4 0.092 0.099 0.097 0.000 0.000 0.000 0.375 0.080 0.044 0.079 0.090 0.094 0.096 0.086 P P1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.244 0.000 0.000 0.000 0.000 0.000 0.000 P2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.244 0.000 0.000 0.000 0.000 0.000 P3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.244 0.000 0.000 0.000 0.000 S S1 0.066 0.069 0.058 0.045 0.049 0.056 0.054 0.048 0.037 0.044 0.279 0.000 0.000 0.000 S2 0.084 0.084 0.090 0.091 0.095 0.101 0.104 0.063 0.071 0.064 0.000 0.279 0.000 0.000 S3 0.081 0.093 0.101 0.095 0.099 0.090 0.091 0.068 0.079 0.079 0.000 0.000 0.279 0.000 S4 0.049 0.033 0.030 0.049 0.037 0.032 0.030 0.032 0.025 0.023 0.000 0.000 0.000 0.279 Table 13

Limited super matrix.

D Q P S D1 D2 D3 Q1 Q2 Q3 Q4 P1 P2 P3 S1 S2 S3 S4 D D1 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 D2 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 0.109 D3 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 Q Q1 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 0.087 Q2 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 Q3 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 Q4 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 P P1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 P2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 P3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 S S1 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 S2 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 0.092 S3 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 S4 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.037

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outsourcing vendor of the wafer foundry company, she needs to be ﬂexible as well to fulﬁll the various and numerous requirements from the wafer foundry company. In the Price dimension (P), the most concerned criterion is Testing Price ðP1Þ (0.422) which

im-plies that the cost is still a critical concern in the wafer-test out-sourcing vendor selection topic.

The ﬁnal rank of the 5 qualiﬁed vendors shows that vendor A is the most preferred one for the wafer-test outsourcing demand of company X. It’s interesting that vendor A has the highest score in both the ‘‘value related dimensions (D, Q and S) (V)” and the Price dimension (P) which is different from the traditional understand-ing of price and other dimensions. The Price dimension (P) contains the Testing Price ðP1Þ, Compensation Rate for Broken Wafers ðP2Þ

and Acceptance Criteria ðP3Þ. We asked for the comments for the

experts of company X, they explained that because vendor A had better engineering, technology and manufacturing capabilities, its overall production, operation efficiency and quality were better than its competitors. And as a result, vendor A could follow the tighter criteria in the Price dimension, including acceptance crite-ria and the compensation rate of broken wafers specifically re-quested by company X. Vendor A could accept and follow these two tighter price related criteria, which made the customer more satisfied with and more confident in the outsourcing vendor. In addition, company X was concerned more about the total cost of ownership (TCO), rather than the pure testing price. This process revealed that due to the higher production and operation perfor-mance of vendor A, company X could save extra and potential costs

for dealing with abnormal quality issues, inputting engineering re-sources for failure analysis and conducting prevention activities, building inventory to avoid delivery delay, or even compensate for defected parts rejected and claimed by its end customers. Therefore, vendor A has the highest score in the rank in terms of ‘‘value related dimensions (D, Q and S) (V)”, the Price dimension (P) and the Overall Performance (O.P.).

5. Conclusion

This paper proposes a novel hybrid method to cope with the problem of the different dimensions’ interdependence and feed-back in vendor selection problem. Although there are numerous supplier selection solutions available, but this proposed hybrid method can provide a better understanding of the interrelationship amongst evaluation and selection dimensions and solve a complex interacting vendor selection issue which can enhance the quality of decision making.

A case study of a Taiwan semiconductor company in selecting the most suitable wafer-test outsourcing vendor is implemented to demonstrate the procedure of the proposed hybrid method. It can provide informative and practical suggestions to semiconduc-tor companies for evaluating and selecting their outsourcing part-ners. The decision maker can obtain a better understanding of not only the interrelationship in the selection model but also the importance ranking of each evaluation dimension and criterion. Therefore, the decision maker can obtain the ranking of all alterna-tives which can provide a better decision quality in vendor selec-tion. This hybrid MCDM technique is valuable for not only the vendor selection in the wafer-testing ﬁeld, but also other vendor selection issues of the semiconductor industry and, further, other industries and territories. Through this comprehensive, thorough and conscientious model and procedure, the buyers can thus achieve their aspired and desired level with their outsourcing operations.

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Table 14

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