A performance evaluation model by integrating fuzzy AHP and fuzzy
TOPSIS methods
Chia-Chi Sun
*Institute of Technology Management, National Chiao Tung University, No. 1001, Ta-Hsuch Rd., Hsinchu 300, Taiwan
a r t i c l e
i n f o
Keywords: Fuzzy set
Performance evaluation Fuzzy analytic hierarchy process Fuzzy TOPSIS
Multiple criteria decision-making (MCDM)
a b s t r a c t
Multiple criteria decision-making (MCDM) research has developed rapidly and has become a main area of research for dealing with complex decision problems. The purpose of the paper is to explore the perfor-mance evaluation model. This paper develops an evaluation model based on the fuzzy analytic hierarchy process and the technique for order performance by similarity to ideal solution, fuzzy TOPSIS, to help the industrial practitioners for the performance evaluation in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The proposed method enables decision analysts to better understand the complete evaluation process and provide a more accurate, effective, and systematic decision support tool.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
In order to compete in today’s competitive environment, many organizations have recognized benchmarking as being of strategic important in the drive for better performance and commitment to achieve a competitive advantage (Gleich, Motwani, & Wald, 2008; Neely, Gregory, & Platts, 1995). There are many studies that inves-tigated the method about performance evaluation (Chalasani & Sounderpandian, 2004; Gleich et al., 2008; Maiga & Jacobs, 2004;
Wynn-Williams, 2005). Some literatures identified the different
key performance indicators, including tangible and intangible as-pect (Chin, Pun, Lau, & Lau, 2001; Himes, 2007; Jones & Kaluarach-chi, 2008; Mukherjee, Nath, & Pal, 2002; Robson & Prabhu, 2001; Wainwright, Green, Mitchell, & Yarrow, 2005; Welch & Mann, 2001). It is essential for the application of performance measure-ment that a company’s tangible and intangible targets are defined in a way that is more appropriate to the requirements and objects of this targets and that its strategy is more extensively operation-alized, quantified, and linked in a mutually supplementing way.
In the literature, there is few fuzzy logic methods aimed at evaluating the relative performance by multidimensions. The main purpose of this paper is to provide practitioners with a fuzzy point of view to traditional performance research for dealing with imprecision and at obtaining the prioritization and the best perfor-mance of measurement dimensions. Moreover, we attempt to as-sist government representatives or industrial analyst in accessing the relative performance. We take the global top four notebook
computer ODM companies for pursuing our case purposes. This re-search invites 10 experts that evaluate the performance of global top four notebook computer ODM companies via the proposed fuzzy AHP and fuzzy TOPSIS techniques with MCDM. The fuzzy AHP is used to determine the preference weights of evaluation. Then, this research adopts the fuzzy TOPSIS to improve the gaps of alternatives between real performance values and pursuing aspired levels in each dimension and criterion and find out the best alternatives for achieving the aspired/desired levels based on four proposed companies. This research looks forward to pro-vide Taiwan industries and government with some strategic recommendations.
The reminder of this paper is organized as follows. Sections2
and 3present how we adopt the methodology, fuzzy AHP and
fuz-zy TOPSIS in real world. Section 4displays our empirical results along with some discussions relating to managerial implications. Finally, conclusions and remarks are then given in Section5.
2. Fuzzy analytic hierarchy process method
Analytic hierarchy process (AHP) is a powerful method to solve complex decision problems. Any complex problem can be decom-posed into several sub-problems using AHP in terms of hierarchical levels where each level represents a set of criteria or attributes rel-ative to each sub-problem. The AHP method is a multicriteria method of analysis based on an additive weighting process, in which several relevant attributes are represented through their rel-ative importance. AHP has been extensively applied by academics and professionals, mainly in engineering applications involving financial decisions associated to non-financial attributes (Saaty, 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2010.04.066
* Tel.: +886 35712121x57520; fax: +886 35726749.
E-mail addresses: samsun0712@yahoo.com.tw, samsun0712.mt95g@nctu. edu.tw.
Contents lists available atScienceDirect
Expert Systems with Applications
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a1996). Through AHP, the importance of several attributes is obtained from a process of paired comparison, in which the rele-vance of the attributes or categories of drivers of intangible assets are matched two-on-two in a hierarchic structure.
However, the pure AHP model has some shortcomings (Yang & Chen, 2004). They pointed out that the AHP method is mainly used in nearly crisp-information decision applications; the AHP method creates and deals with a very unbalanced scale of judgment; the AHP method does not take into account the uncertainty associated with the mapping of human judgment to a number by natural lan-guage; the ranking of the AHP method is rather imprecise; and the subjective judgment by perception, evaluation, improvement and selection based on preference of decision-makers have great influ-ence on the AHP results. To overcome these problems, several researchers integrate fuzzy theory with AHP to improve the uncer-tainty. Hence,Buckley (1985)used the evolutionary algorithm to calculate the weights with the trapezoidal fuzzy numbers. The fuz-zy AHP based on the fuzfuz-zy interval arithmetic with triangular fuzfuz-zy numbers and confidence index
a
with interval mean approach to determine the weights for evaluative elements.2.1. Building the evaluation hierarchy systems for evaluating the performance of global top four notebook computer companies
This research tries to evaluate the performance of global top four notebook computer ODM companies. After reviewing the re-lated literature, we set criteria that building the evaluation hierar-chy systems. Based on the evaluation criteria, this research lists the four notebook companies for improving the competitive advantage.
2.2. Determining the evaluation dimensions weights
This research employs fuzzy AHP to fuzzify hierarchical analysis by allowing fuzzy numbers for the pairwise comparisons and find the fuzzy preference weights. In this section, we briefly review concepts for fuzzy hierarchical evaluation. Then, the following sec-tions will introduce the computational process about fuzzy AHP in detail.
2.2.1. Establishing fuzzy number
Fuzzy sets are sets whose elements have degrees of member-ship. Fuzzy sets have been introduced byZadeh (1965)as an exten-sion of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition – an element either belongs or does not belong to the set (Liou, Yen, & Tzeng, 2007; Wu & Lee, 2007). The mathematics concept borrowed from Hsieh, Lu, and Tzeng (2004) and Liou et al. (2007).
A fuzzy number eA on R to be a TFN if its membership function
l
eAðxÞ : R ! ½0; 1 is equal to following Eq.(1):
l
e AðxÞ ¼ ðx lÞ=ðm lÞ; l 6 x 6 m ðu xÞ=ðu mÞ; m 6 x 6 u 0; otherwise 8 > < > : ð1ÞFrom Eq.(1), l and u mean the lower and upper bounds of the fuzzy number eA, and m is the modal value for eA (asFig. 1). The TFN can be denoted by eA ¼ ðl; m; uÞ. The operational laws of TFN eA1¼ ðl1;m1;u1Þ and eA2¼ ðl2;m2;u2Þ are displayed as following Eqs.(2)–(6).
Addition of the fuzzy number
eA1 eA2¼ ðl1;m1;u1Þ ðl2;m2;u2Þ
¼ ðl1þ l2;m1þ m2;u1þ u2Þ ð2Þ
Multiplication of the fuzzy number
eA1 eA2¼ ðl1;m1;u1Þ ðl2;m2;u2Þ
¼ ðl1l2;m1m2;u1u2Þ for l1;l2>0; m1;m2>0;
u1;u2>0 ð3Þ
Subtraction of the fuzzy number
eA1 eA2¼ ðl1;m1;u1Þ ðl2;m2;u2Þ
¼ ðl1 u2;m1 m2;u1 l2Þ ð4Þ
Division of a fuzzy number ø
eA1ø eA2¼ ðl1;m1;u1Þ ø ðl2;m2;u2Þ
¼ ðl1=u2;m1=m2;u1=l2Þ for l1;l2>0; m1;m2>0;
u1;u2>0 ð5Þ
Reciprocal of the fuzzy number
eA1¼ ðl
1;m1;u1Þ1¼ ð1=u1;1=m1;1=l1Þ
for l1;l2>0; m1;m2>0; u1;u2>0 ð6Þ
2.2.2. Determining the linguistic variables
Linguistic variables take on values defined in its term set: its set of linguistic terms. Linguistic terms are subjective categories for the linguistic variable. A linguistic variable is a variable whose val-ues are words or sentences in a natural or artificial language. Here, we use this kind of expression to compare two building Notebook Computer Companies evaluation dimension by nine basic linguis-tic terms, as ‘‘Perfect,” ‘‘Absolute,” ‘‘Very good,” ‘‘Fairly good,” ‘‘Good,” ‘‘Preferable,” ‘‘Not Bad,” ‘‘Weak advantage” and ‘‘Equal” with respect to a fuzzy nine level scale. In this paper, the computa-tional technique is based on the following fuzzy numbers defined
by Gumus (2009) in Table 1. Here, each membership function
(scale of fuzzy number) is defined by three parameters of the sym-metric triangular fuzzy number, the left point, middle point, and right point of the range over which the function is defined.
( )
x
µ
x
0 1.0 l m u ~ AFig. 1. The membership functions of the triangular fuzzy number.
Table 1
Membership function of linguistic scale (example).
Fuzzy number Linguistic Scale of fuzzy number
9 Perfect (8, 9, 10) 8 Absolute (7, 8, 9) 7 Very good (6, 7, 8) 6 Fairly good (5, 6, 7) 5 Good (4, 5, 6) 4 Preferable (3, 4, 5) 3 Not bad (2, 3, 4) 2 Weak advantage (1, 2, 3) 1 Equal (1, 1, 1)
2.2.3. Fuzzy AHP
Then, we will briefly introduce that how to carry out the fuzzy AHP in the following sections.
Step1: Construct pairwise comparison matrices among all the elements/criteria in the dimensions of the hierarchy sys-tem. Assign linguistic terms to the pairwise comparisons by asking which is the more important of each two dimensions, as following matrix eA
e A ¼ 1 ~a12 ~a1n ~ a21 1 ~a2n .. . .. . . . . .. . ~ an1 ~an2 1 2 6 6 6 6 4 3 7 7 7 7 5¼ 1 a~12 a~1n 1=~a12 1 a~2n .. . .. . . . . .. . 1=~a1n 1=~a2n 1 2 6 6 6 6 4 3 7 7 7 7 5 ð7Þ where ~ aij¼ ~ 91; ~81; ~71; ~61; ~51; ~41; ~31; ~21; ~11; ~1; ~2; ~3; ~4; ~5; ~6; ~7; ~8; ~9; 1; i – j 1 i ¼ j (
Step 2: To use geometric mean technique to define the fuzzy geometric mean and fuzzy weights of each criterion by
Hsieh et al. (2004)
~ri¼ ð~ai1 ~aij ~ainÞ1=n
~
wi¼ ~ri ½~r1 ~ri ~rn1
ð8Þ where ~aijis fuzzy comparison value of dimension i to criterion j, thus, ~riis a geometric mean of fuzzy comparison value of criterion i to each criterion, ~wiis the fuzzy weight of the ith criterion, can be indicated by a TFN, ~wi¼ ðlwi;mwi;uwiÞ. The lwi, mwiand uwistand for the low-er, middle, and upper values of the fuzzy weight of the ith dimension. There are numerous studies that apply fuzzy AHP method to solve different managerial problems. Huang, Chu, and Chiang (2008)adopt a fuzzy analytic hierarchy process method and utilize crisp judgment matrix to evaluate subjective expert judgments made by perception.Pan (2008)applied fuzzy AHP model for select-ing the suitable bridge construction method.Cakir and Canbolat (2008)propose an inventory classification system based on the fuz-zy analytic hierarchy process.Wang and Chen (2008)applied fuzzy linguistic preference relations to construct a pairwise comparison matrix with additive reciprocal property and consistency. Sambas-ivan and Fei (2008)evaluate the factors and sub-factors critical to the successful implementation of ISO 14001-based environmental management system and benefits.Sharma, Moon, and Bae (2008)
used AHP method to optimize the selection of delivery network de-sign followed by relevant choices for decision-making of Home plus distribution center.Costa and Vansnick (2008)discussed the mean-ing of the priority vector derived from the principal eigenvalue method used in AHP.Firouzabadi, Henson, and Barnes (2008) pre-sented a decision support methodology for strategic selection deci-sions used a combination of analytic hierarchy process and zero-one goal programming to address the selection problem from the point of view of an individual stakeholder.Wang, Luo, and Hua
(2008)showed by examples that the priority vectors determined
by the analytic hierarchy process method.Kuo, Tzeng, and Huang (2007)proposed group decision-making based on concepts of TOPIS technique for location section in fuzzy environment.Gumus (2009)
evaluates hazardous waste transportation firms containing the methods of fuzzy AHP and TOPSIS.Armillotta (2008)described a computer-based tool for the selection of techniques used in the manufacture of prototypes and limited production runs of indus-trial products. The underlying decision model based on the AHP methodology,Dagdeviren and Yuksel (2008)presented fuzzy AHP approach to determine the level of faulty behavior risk in work
sys-tems.Chen, Tzeng, and Ding (2008)used fuzzy analytic hierarchy process to determine the weighting of subjective/perceptive judg-ments for each criterion and to derive fuzzy synthetic utility values of alternatives in a fuzzy multicriteria decision-making environ-ment.Lin, Wang, Chen, and Chang (2008)proposed a framework that integrates the analytical hierarchy process and the technique for order preference by similarity to ideal solution to assist design-ers in identifying customer needs/requirements and design charac-teristics and help achieve an effective evaluation of the final design solution for achieving the aspired/desired levels.
3. The fuzzy TOPSIS method
In this study, we propose this method to evaluate the perfor-mance of global top four notebook computer ODM companies. TOPSIS views a MADM problem with m alternatives as a geometric system with m points in the n-dimensional space of criteria. The method is based on the concept that the chosen alternative should have the shortest distance from the positive-ideal solution (i.e., achieving the minimal gaps in each criterion) and the longest dis-tance from the negative-ideal solution (i.e., achieving the maximal levels in each criterion). TOPSIS defines an index called similarity to the positive-ideal solution and the remoteness from the nega-tive-ideal solution. Then, the method chooses an alternative with the maximum similarity to the positive-ideal solution (Hwang & Yoon, 1981; Wang & Chang, 2007). It is often difficult for a deci-sion-maker to assign a precise performance rating to an alternative for the attributes under consideration. The merit of using a fuzzy approach is to assign the relative importance of attributes using fuzzy numbers instead of precise numbers for suiting the real world in fuzzy environment. This section extends the TOPSIS to the fuzzy environment (Kuo et al., 2007; Yang & Hung, 2007). This method is particularly suitable for solving the group decision-mak-ing problem under fuzzy environment. We briefly review the ratio-nale of fuzzy theory before the development of fuzzy TOPSIS. The mathematics concept borrowed fromBüyüközkan, Feyziog˘lu, and Nebol (2007), Kuo et al. (2007)andWang and Chang (2007). Step 1: Determine the weighting of evaluation criteria.
This research employs fuzzy AHP to find the fuzzy prefer-ence weights.
Step 2: Construct the fuzzy performance/decision matrix and choose the appropriate linguistic variables for the alterna-tives with respect to criteria
ð9Þ i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n ~ xij¼ 1 K ~x 1 ij ~x k ij ~x K ij where ~xk
ijis the performance rating of alternativeAiwith re-spect to criterion Cj evaluated by kth expert, and ~
xk ij¼ ðl
k ij;mkij;ukijÞ.
Step 3: Normalize the fuzzy-decision matrix.
The normalized fuzzy-decision matrix denoted by eR is shown as following formula:
e
R ¼ ½~rijmn; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n ð10Þ
Then, the normalization process can be performed by follow-ing formula: ~rij¼ ulijþ
j ;mijuþ j ;uuijþ j ; uþ j ¼ maxifuijji ¼ 1; 2; . . . ; ng
or we can set the best aspired level uþ
j and j = 1, 2, . . . , n is equal one; otherwise, the worst is zero.
The normalized ~rijis still triangular fuzzy numbers. For trap-ezoidal fuzzy numbers, the normalization process can be conducted in the same way. The weighted fuzzy normalized decision matrix is shown as following matrix eV :
e
V ¼ ½~
v
ijnn; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n ð11Þwhere ~
v
ij¼ ~rij ~wj.Step 4: Determine the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS).
According to the weighted normalized fuzzy-decision matrix, we know that the elements ~
v
ij are normalized positive TFNand their ranges belong to the closed interval [0, 1]. Then, we can define the FPIS A+(aspiration levels) and FNIS A(the worst levels) as following formula:Aþ¼ ð~
v
1; . . . ; ~v
j; . . . ; ~v
nÞ ð12Þ A¼ ð~v
1; . . . ; ~v
j; . . . ; ~v
nÞ ð13Þ wherev
~ j ¼ ð1; 1; 1Þ ~wj¼ ðlwj;mwj;uwjÞ andv
~j ¼ ð0; 0; 0Þ, j = 1, 2, . . . , n.Step 5: Calculate the distance of each alternative from FPIS and FNIS.
The distances (~dþ
i and ~di) of each alternative from A +and Acan be currently calculated by the area compensation method ~ dþ i ¼ Xn j¼1 d ~
v
ij; ~v
j ; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n ð14Þ ~ d i ¼ Xn j¼1 d ~v
ij; ~v
j ; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; n ð15ÞStep 6: Obtain the closeness coefficients (relative gaps-degree) and improve alternatives for achieving aspiration levels in each criterion.
Opricovic and Tzeng (2004)proposed a compromise solution by
MCDM methods for comparative analysis of VIKOR and TOPSIS in EJOR; they pointed out the TOPSIS cannot be used for ranking pur-pose. Based on those concepts, the improved and chosen alterna-tive should have the shortest distance from the posialterna-tive-ideal solution (i.e., achieving the minimal gaps in each criterion) and the longest distance from the negative-ideal solution (i.e., achiev-ing the maximal levels in each criterion).
Therefore, we propose the fCCiis defined to determine the fuzzy gaps-degree based on fuzzy closeness coefficients for improving alternatives; once the ~dþ
i and ~di of each alternative have been cal-culated. Calculate similarities to ideal solution. This step solves the similarities to an ideal solution by formula:
f CCi¼ ~ d i ~ dþ i þ ~di ¼ 1 ~ dþ i ~ dþ i þ ~di ; i ¼ 1; 2; . . . ; m ð16Þ where we define ~di ~ dþ iþ~di
as fuzzy satisfaction degree in ith alternative and ~dþi
~ dþ
iþ~di
as fuzzy gap degree in ith alternative. We can know which and how fuzzy gaps should be improved for achieving aspiration levels and getting the best win–win strategy from among a fuzzy set of feasible alternatives.
In the last years, some fuzzy TOPSIS methods were developed in the different applied field.Lin and Chang (2008) adopted fuzzy TOPSIS for order selection and pricing of manufacturer (supplier) with make-to-order basis when orders exceed production capacity.
Chen and Tsao (2008)is to extend the TOPSIS method based on
interval-valued fuzzy sets in decision analysis.Büyüközkan et al. (2007) identified the strategic main and sub-criteria of alliance partner selection that companies consider the most important through fuzzy AHP and fuzzy TOPSIS model and achieved the final partner-ranking results. Abo-Sinna, Amer, and Ibrahim (2008)
focused on multiobjective large-scale non-linear programming problems with block angular structure and extended the technique for order preference by similarity ideal solution to solve them.
Wang and Chang (2007)applied fuzzy TOPSIS to help the Air Force Academy in Taiwan choose optimal initial training aircraft in a fuzzy environment.Li (2007)developed a compromise ratio (CR) methodology for fuzzy multiattribute group decision-making (FMAGDM), which is an important part of decision support system.
Wang and Lee (2007)generalized TOPSIS to fuzzy multiple-criteria group decision-making (FMCGDM) in a fuzzy environment. Kahr-aman, Sezi, Nüfer, and Gülbay (2007)proposed a fuzzy hierarchical TOPSIS model for the multicriteria evaluation of the industrial robotic systems.Benítez, Martín, and Román (2007)presented a fuzzy TOPSIS approach for evaluating dynamically the service qual-ity of three hotels of an important corporation in Gran Canaria is-land via surveys.Wang and Elhag (2006)proposed a fuzzy TOPSIS method based on alpha level sets and presents a non-linear pro-gramming solution procedure.Chen, Lin, and Huang (2006)applied fuzzy TOPSIS approach to deal with the supplier selection problem in supply chain system.
4. Numerical example
The performance measurement activity has paralleled the strat-egy activity throughout the period of the grant. This paper applies the focus group research method to get the evaluation relative dimensions. Focus group research is based on facilitating an orga-nized discussion with a group of individuals selected because they were believed to be representative of some class. Discussion is used to bring out insights and understandings in ways, which sim-ple questionnaire items may not be able to tap. The interaction among focus group participants brings out differing perspectives through the language that is used by the discussants. Interaction is the key to successful focus groups. In an interactive setting, dis-cussants draw each other out, sparking new ideas (Morgan, 1988). The reactions of each person spark ideas in others, and one person may fill in a gap left by others.
The host researcher raised a number of issues including: the rel-ative importance of notebook computer ODM companies perfor-mance evaluation criteria as recognized by participants, industrial analysts, professors and so on. After thorough discussion, and with the aid of answers to open-ended questionnaires and recording equipment, opinions were integrated and summarized. Finally, six potential evaluation dimensions are determined through the focus group process. They are manufacturing capabil-ity, supply chain capabilcapabil-ity, innovation capabilcapabil-ity, financial capa-bility, human resource capacapa-bility, and service quality capability. 4.1. Manufacturing capability
Manufacturing capability is considered to be an important ele-ment in a firm’s endeavor to improve firm performance. Manufac-turing capability management strategies have reduced inventory and manufacturing cycle times, and more complete and on-time shipments of better quality products (Himes, 2007). The enter-prises should focus on reducing costs; they also pay much more attention to building agility and flexibility into their manufacturing processes, seeking better market differentiation. Cost reductions remain the focus of all enterprises and many still struggle with data collection and cultural issues (Wainwright et al., 2005). The
manufacturing capability includes five aspects, such as reducing manufacturing cost, shrinking manufacturing cycle time, improv-ing schedule compliance, satisfyimprov-ing demand for more complete and on-time shipments (Gleich et al., 2008; Welch & Mann, 2001). 4.2. Supply chain capability
Supply chain management, analysis, and improvement are becoming increasingly important. Managers want to measure the performance of the supply chain and the results of improvement efforts across supplier, company, and customer operations. Supply chain management will affect more than costs, and managers must be able to sell the value created to senior executives, trading part-ners, and shareholders (Pollen & Coleman, 2005). Everyone agrees that ‘‘you can only manage what you measure,” but many compa-nies struggle with creating and using effective performance mea-surement systems for forecasting, purchasing, production, and distribution operations (Gupta & Selvaraju, 2006). The challenges may include lack of consistency, inability to share data, or poor buy-in, among others. This course provides a fast-paced overview of a proven approach for identifying measurement needs, develop-ing appropriate metrics, and implementdevelop-ing the infrastructure to support them. The course is essential for those who want to use measures to maximize supply chain performance and improve-ment (Welch & Mann, 2001).
4.3. Innovation capability
It is well known that industrial enlivenment must continually cope with extremely rapid changes, which demand an innovative technological and managerial response. Such a response must redefine the firms’ organizational assets in order to achieve a satis-factory degree of adaptation to the external environment. Innova-tion is a necessary condiInnova-tion, not only for increasing the firms’ competitiveness, but primarily to ensure their survival (Capaldo, Iandoli, Raffa, & Zollo, 2003). Innovation is about change, about doing different things, or doing things differently. The ability to innovate is critical to the survival and growth of your business.
Innovation shows up in the quality and quantity of ideas and the efficiency and effectiveness of implementation of those ideas (Jones & Kaluarachchi, 2008). The second face of R&D is called the absorptive capacity, and it is considered to be crucial particu-larly for assessing the effective contribution by spillovers from oth-ers. Defined as a set of knowledge and competencies, the firm’s knowledge base remains a preliminary condition in the assimila-tion of spillovers from R&D efforts of environment. R&D activity does not only stimulate innovation, but it also enhances the firms’ ability to assimilate outside knowledge.
4.4. Financial capability
Financial capability concerns itself with the application of this discipline to the finance function. It deals with how well the fi-nance organizations support a company’s strategic objectives (Maiga & Jacobs, 2004). The majority of empirical studies have found that firm’s cash flow as a measure of internal financial capa-bility is associated with higher levels of performance. The financial capabilities include five aspects, such as liquidity, financial lever-age, asset turnover, profitability, and market value.
Liquidity is particularly interesting to short-term creditors. Liquidity is the availability of credit or the ease with which institu-tions can borrow or take on leverage. The financial managers are working with banks and other short-term lenders, an understand-ing of liquidity is essential. Financial leverage takes the form of a loan or other borrowings, the proceeds of which are reinvested with the intent to earn a greater rate of return than the cost of
interest. The higher a firm’s financial leverage, the riskier the firm’s operations are considered to be. The most typical system of deter-mining an acceptable level of financial leverage is by comparing operations to others firms in the same industry. Asset turnover is a financial ratio that measures the efficiency of a company’s use of its assets in generating sales revenue or sales income to the com-pany. Profit generally is the making of gain in business activity for the benefit of the owners of the business. Market value is a concept distinct from market price, which is ‘‘the price at which one can transact”, while market value is ‘‘the true underlying value”. 4.5. Human resource capability
Successfully managing human resource capability is important for the high tech industry. Management techniques, such as re-cruit, train, apply, apprise and maintain combine organizational strategies and human resources plans that can effectively carry out human resources development and directly influence the Tai-wanese economy’s success or failure (Tai & Wang, 2006). Busi-nesses find success when they can establish clear strategic goals and marshal all resources to achieve those objectives. Human re-source performance management is a huge priority for competitive organizations. That is where superior software solutions come in. By automating much of the human resource performance manage-ment process, and adding much-needed knowledge and informa-tion access to the equainforma-tion, such soluinforma-tions can help to make these HR initiatives a source of success. Valued human resource development not only improves professional skills and capabilities, but also solves the problem of measuring the effect of human re-sources on an organization. We think that HRM as an instrument designed to enhance the labor extraction process and thus improve firm performance.
4.6. Service quality capability
SERVQUAL as the most often used approach for measuring service quality has been to compare customers’ expectations before a service encounter and their perceptions of the actual service delivered. For Parasuraman, Zeithaml, and Berry (1985, 1988a), service quality is measured in 10 phases: accessibility, communication, capability, courtesy, trustworthiness, reliability, responsiveness, safety, tangibility, and understanding with cus-tomers.Parasuraman et al. (1988a), Parasuraman, Zeithaml, and Berry (1988b) also reduced the 10 to 5: tangibility, reliability, responsiveness, assurance, and empathy.
Manufacturing Capability
Supply Chain Capability
Innovation Capability
Financial Capability
Human Resource Capability
Service Quality Capability
Ev
aluating the Performance
QuantaCompel
Wistron
Inventec
The hierarchical structure of this research decision problem is shown in Fig. 2. The whole hierarchy of accessing the perfor-mance of global top four notebook computer ODM companies can be easily visualized from Fig. 2. After the construction of the hierarchy, the different priority weights of each criteria, attri-butes and alternatives are calculated using the fuzzy AHP and fuz-zy TOPSIS approaches. The comparison of the importance or preference of one criterion, attribute or alternative over another can be done with the help of the questionnaire. The method of calculating priority weights of the different decision alternatives is discussed below.
Step 1: The weights of evaluation dimensions.
We adopt fuzzy AHP method to evaluate the weights of differ-ent dimensions for the performance of notebook computer ODM companies. Following the construction of fuzzy AHP model, it is ex-tremely important that experts fill the judgment matrix.
The following section demonstrates the computational proce-dure of the weights of dimensions.
(1) According to the committee with ten representatives about the relative important of dimension, then the pairwise com-parison matrices of dimensions will be obtained. We apply the fuzzy numbers defined inTable 1. We transfer the lin-guistic scales to the corresponding fuzzy numbers (as
Appendix A).
(2) Computing the elements of synthetic pairwise comparison matrix by using the geometric mean method suggested by
Buckley (1985)that is: ~ aij¼ ~a1ij ~a 2 ij . . . ~a 10 ij
; for ~a12as the example :
~
a12¼ ð1; 1; 1Þ ð1; 1; 1Þ ð2; 3; 4Þ1=10
¼ ðð1 1 2Þ1=10;ð1 1 3Þ1=10;
ð1 1 4Þ1=10Þ ¼ ð0:88; 1:14; 1:37Þ
It can be obtained the other matrix elements by the same computa-tional procedure, therefore, the synthetic pairwise comparison matrices of the five representatives will be constructed as follows matrix A:
(3) To calculate the fuzzy weights of dimensions, the computa-tional procedures are displayed as following parts
~r1¼ ð~a11 ~a12 ~a13 ~a14 ~a15 ~a16Þ1=6
¼ ðð1 0:88 1:06Þ1=6;ð1 1:14 1:28Þ1=6;
ð1 1:37 1:55Þ1=6Þ ¼ ð1:130; 1:358; 1:571Þ
Similarly, we can obtain the remaining ~ri, there are:
~r2¼ ð1:423; 1:699; 1:966Þ
~r3¼ ð1:017; 1:222; 1:478Þ
~r4¼ ð0:949; 1:101; 1:248Þ
~r5¼ ð0:440; 0:524; 0:655Þ
~r6¼ ð0:533; 0:615; 0:745Þ
For the weight of each dimension, they can be done as follows: ~
w1¼ ~r1 ð~r1 ~r2 ~r3 ~r4 ~r5 ~r6Þ1
¼ ð1:130; 1:358; 1:571Þ ð1=ð1:571 þ þ 0:745Þ; 1=ð1:358 þ þ 0:615Þ; 1=ð1:130 þ þ 0:533ÞÞ
¼ ð0:147; 0:208; 0:286Þ
We also can calculate the remaining ~wi, there are: ~ w2¼ ð0:186; 0:261; 0:358Þ ~ w3¼ ð0:133; 0:187; 0:269Þ ~ w4¼ ð0:124; 0:169; 0:227Þ ~ w5¼ ð0:057; 0:080; 0:119Þ ~ w6¼ ð0:070; 0:094; 0:136Þ
(4). To apply the COA method to compute the BNP value of the fuzzy weights of each dimension: To take the BNP value of the weight of D1(manufacturing capability) as an example, the calculation process is as follows
BNPw1¼ ½ðUw1 Lw1Þ þ ðMw1 Lw1Þ=3 þ Lw1
¼ ½ð0:286 0:147Þ þ ð0:208 0:147Þ=3 þ 0:147 ¼ 0:214
Then, the weights for the remaining dimensions can be found as shown in Table 2. Table 2 shows the relative weight of six dimensions of the evaluation of notebook computer
com-panies, which obtained by AHP method. The weights for each dimension are: manufacturing capability (0.214), supply chain capability (0.268), innovation capability (0.196), financial capabil-ity (0.173), human resource capabilcapabil-ity (0.086), and service quality capability (0.100). From the fuzzy AHP results, we can understand the first two important dimensions for the evalua-tion of notebook computer companies are supply chain capabil-ity (0.268) and manufacturing capabilcapabil-ity (0.214). Moreover, the less important dimension is human resource capability (0.086).
Step 2: Construct the fuzzy-decision matrix and choose the appropriate linguistic variables for the alternatives with respect to criteria.
This paper focus on evaluating the performance of global top four notebook computer ODM companies; so, we assume that questionnaire has collected completely and will start with building dataset that are collected. The evaluators have their own range for the linguistic variables employed in this study according to their subjective judgments (Hsieh et al., 2004).
For each evaluator with the same importance, this study employs the method of average value to integrate the fuzzy/ vague judgment values of different evaluators regarding the same evaluation dimensions. The evaluators then adopted linguistic terms (see Table 3), including ‘‘very poor”, ‘‘poor”, ‘‘fair”, ‘‘good” and ‘‘very good ” to express their opinions about the rating of every companies regarding each capability criteria, based on the technological data of the four companies listed in
Table 4.
Using Eq. (9), we can normalize the fuzzy-decision matrix as
Table 5.
Step 4: Establish the weighted normalized fuzzy-decision matrix.
The forth step in the analysis is to find the weighted fuzzy-deci-sion matrix; the resulting fuzzy-weighted decifuzzy-deci-sion matrix is shown asTable 6.
Step 5: Determine the fuzzy positive and fuzzy negative-ideal reference points.
Then, we can define the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) as: A+and A. This is the fifth step of the fuzzy TOPSIS analysis
A¼ ½ð0; 0; 0Þ; ð0; 0; 0Þ; ð0; 0; 0Þ; ð0; 0; 0Þ; ð0; 0; 0Þ; ð0; 0; 0Þ
Step 6: Estimating the performance and ranking the alternatives.
In order to calculate the closeness coefficients of each of the alternatives dþ
1 and d
1 calculation is used as an example as follows:
dþ1 ¼ 0:230; d
1¼ 0:936
Once the distances from FPIS and FNIS are determined, the closeness coefficient can be obtained with Eq.(15). The index CC1 of first alternative is calculated as:
f CC 1¼ 0:936 0:230 þ 0:936¼ 0:803 f CCþ 1¼ 0:230 0:230 þ 0:936¼ 0:197 We define fCC
i as satisfaction degree in ith alternative and fCCþi as gap degree in ith alternative. We can know which and how gaps should be improved for achieving aspiration levels and get-ting the best win–win strategy from among a fuzzy set of feasible alternatives. The aspired/desired satisfaction degree of fuzzy TOP-SIS is 1.00. From the results ofTable 7, we can find out the satis-faction degrees and gap degrees of each company. Then, the satisfaction degree value of Quanta, Compal, Wistron and Inven-tec are 0.803, 0.746, 0.72, and 0.601 levels respectively; i.e., 0.197, 0.254, 0.274, and 0.399 levels should be improved, respec-tively. On the other hand, we also can calculate the gap degrees between the policy tools and aspired/desired level by using Eq.
(15). The results ofTable 7reveal that the gap degree of Quanta and Compal is bigger than other companies. Therefore, we con-sider that the Quanta and Compal are similarities to aspired/de-sired level.
From the proposed method, fuzzy AHP and fuzzy TOPSIS, we find out the first two important dimensions for notebook computer ODM companies are supply chain capability and manufacturing capability. Moreover, the Quanta and Compel rank the first two performances for these companies.
Better manufacturing ability could predict resource capacities and competing resource requirements provides more accurate forecasts of production lead time. This ability comes from the Table 2
Weights of dimensions.
Dimensions Weights BNP Rank
Manufacturing capability (0.147, 0.208, 0.286) 0.214 2 Supply chain capability (0.186, 0.261, 0.358) 0.268 1 Innovation capability (0.133, 0.187, 0.269) 0.196 3 Financial capability (0.124, 0.169, 0.227) 0.173 4 Human resource capability (0.057, 0.080, 0.119) 0.086 6 Service quality capability (0.070, 0.094, 0.136) 0.100 5
Table 3
Linguistic scales for the rating of each company.
Linguistic variable Corresponding triangular fuzzy number Very poor (VP) (0, 1, 3) Poor (P) (1, 3, 5) Fair (F) (3, 5, 7) Good (G) (5, 7, 9) Very good (VG) (7, 9, 10) Table 4
Subjective cognition results of evaluators towards the five levels of linguistic variables.
Quanta Compal Wistron Inventec Manufacturing capability (5.0, 7.0, 8.9) (4.4, 6.4, 8.4) (4.4, 6.4, 8.3) (2.6, 4.6, 6.6) Supply chain capability (5.2, 7.2, 9.0) (4.6, 6.6, 8.6) (3.8, 5.8, 7.7) (2.6, 4.6, 6.6) Innovation capability (4.6, 6.6, 8.6) (3.6, 5.6, 7.6) (4.0, 6.0, 7.9) (3.0, 5.0, 7.0) Financial capability (5.6, 7.6, 9.2) (4.8, 6.8, 8.7) (4.6, 6.6, 8.4) (3.2, 5.2, 7.2) Human resource capability (4.8, 6.8, 8.7) (4.0, 6.0, 8.0) (3.8, 5.8, 7.8) (2.6, 4.6, 6.6) Service quality capability (5.0, 7.0, 9.0) (4.4, 6.4, 8.4) (4.2, 6.2, 8.1) (2.5, 4.4, 6.4) Aþ ¼ ½ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ ~wj ¼ ½ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ; ð1; 1; 1Þ ½ð0:147; 0:208; 0:286Þ; ð0:186; 0:261; 0:358Þ; ð0:133; 0:187; 0:269Þ; ð0:124; 0:169; 0:227Þ; ð0:057; 0:080; 0:119Þ; ð0:070; 0:094; 0:136Þ ¼ ð0:147; 0:208; 0:286Þ; ð0:186; 0:261; 0:358Þ; ð0:133; 0:187; 0:269Þ; ð0:124; 0:169; 0:227Þ; ð0:057; 0:080; 0:119Þ; ð0:070; 0:094; 0:136Þ
acuity gained through improved communication, scanning, and analysis. Then, greater responsiveness provides flexibility to react to schedule variations and changes. Competing in the market-place on the basis of cost efficiency requires striving for low cost production. In order to keep manufacturing costs competitive, managers must address materials, labor, overhead, and other costs. Inventories have long been the focus of cost reduction in factories and are one of the justifications of the JIT system. Therefore, inventory and inventory-related items, such as improving vendor’s quality, reducing waste of purchased materi-als, are considered as the indicators of the cost capability. Real-izing low inventory level, decreasing labor cost, and reducing machine time are all positive factors of the cost efficiency construct.
In addition, online tool launched to help companies improve supply chain capability. The web-based information system could provide sufficient detail and richness to steer supply chain performance. Then, the enterprises should design the demand planning, manufacturing planning, and transportation and logis-tics planning. Demand planning can gain advanced forecasting capabilities to more accurately predict and shape customer de-mand while sufficiently preparing for a multitude of unforeseen changes capable of both positively and negatively affecting de-mand. Manufacturing planning could help ensure maximized efficiency throughout entire supply chain by streamlining each of manufacturing process to make the most of valuable assets while reducing total costs. Transportation and logistics planning
could overcome the complex challenges of optimally coordinat-ing pick-up and delivery times across multiple worldwide loca-tions, while adhering to a growing number of international regulations to ensure customers consistently receive the right goods at the right time.
5. Conclusions and remarks
The aim of this research is to construct a fuzzy AHP and fuzzy TOPSIS model to evaluate different notebook computer ODM com-panies. In the performance evaluation for the notebook computer ODM companies including manufacturing capability, financial capability, innovation capability, supply chain capability, human resource capability, and service quality capability. These factors are to generate a final evaluation ranking for priority among these notebook computer ODM companies of the proposed model. The importance of the dimensions is evaluated by experts, and the uncertainty of human decision-making is taken into account through the fuzzy concept in fuzzy environment. From the pro-posed method, fuzzy AHP and fuzzy TOPSIS, we find out the first two important dimensions for notebook computer ODM compa-nies are supply chain capability and manufacturing capability. On the other hand, human resource ranks last priorities among these dimensions. Moreover, the Quanta and Compel rank the first two performances for these companies.
The integrated evaluation system is designed to provide practi-tioners with a fuzzy point of view to traditional performance eval-uation model for dealing with imprecision. The proposed method enables decision analysts to better understand the complete eval-uation process. Furthermore, this approach provides a more accu-rate, effective, and systematic decision support tool. Furthermore, the further research can explore that how to improve the gaps in each criteria based on Network Relationship Map (NRM) and cap-ture the complex relationships among these evaluation criteria. The NRM is not only to find out the most important criterion for the performance but also to measure the relationships among these evaluation criteria.
Table 5
Normalized fuzzy-decision matrix.
Quanta Compal Wistron Inventec
Manufacturing capability (0.543, 0.761, 0.967) (0.478, 0.696, 0.913) (0.478, 0.696, 0.902) (0.283, 0.500, 0.717) Supply chain capability (0.565, 0.783, 0.978) (0.500, 0.717, 0.935) (0.413, 0.630, 0.837) (0.283, 0.500, 0.717) Innovation capability (0.500, 0.717, 0.935) (0.391, 0.609, 0.826) (0.435, 0.652, 0.859) (0.326, 0.543, 0.761) Financial capability (0.609, 0.826, 1.000) (0.522, 0.739, 0.946) (0.500, 0.717, 0.913) (0.348, 0.565, 0.783) Human resource capability (0.522, 0.739, 0.946) (0.435, 0.652, 0.870) (0.413, 0.630, 0.848) (0.283, 0.500, 0.717) Service quality capability (0.543, 0.761, 0.978) (0.478, 0.696, 0.913) (0.457, 0.674, 0.880) (0.272, 0.478, 0.696)
Table 6
Weighted normalized fuzzy-decision matrix.
Quanta Compal Wistron Inventec
Manufacturing capability (0.080, 0.159, 0.277) (0.071, 0.145, 0.261) (0.071, 0.145, 0.258) (0.042, 0.104, 0.205) Supply chain capability (0.105, 0.204, 0.350) (0.093, 0.187, 0.335) (0.077, 0.164, 0.300) (0.052, 0.130, 0.257) Innovation capability (0.066, 0.134, 0.252) (0.052, 0.114, 0.222) (0.058, 0.122, 0.231) (0.043, 0.102, 0.205) Financial capability (0.075, 0.139, 0.227) (0.065, 0.125, 0.215) (0.062, 0.121, 0.207) (0.043, 0.095, 0.178) Human resource capability (0.030, 0.059, 0.113) (0.025, 0.052, 0.104) (0.024, 0.051, 0.101) (0.016, 0.040, 0.086) Service quality capability (0.038, 0.072, 0.133) (0.033, 0.066, 0.124) (0.032, 0.064, 0.119) (0.019, 0.045, 0.094)
Table 7
Closeness coefficients to aspired level among different companies. dþi d
i Gaps degree of CCþi Satisfaction degree of CC i Quanta 0.230 0.936 0.197 0.803 Compal 0.294 0.861 0.254 0.746 Wistron 0.315 0.832 0.274 0.726 Inventec 0.454 0.684 0.399 0.601
Appendix A. Linguistic scale of each expert
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