A fuzzy AHP evaluation model for buyer―supplier relationships with the consideration of benefits, opportunities, costs and risks

With increasingly fierce global competition, firms in various industries need to build a cooperative buyer–supplier relationship to survive and to acquire reasonable profit. Even though the literature on various types of collaboration between firms is abundant and the works on supplier selection models are numerous, the research that provides a mathematical model for the selection of the most appropriate form of buyer–supplier relationship is very limited. Existing buyer–supplier evaluation models usually only consider the benefits from the relationship, but not the opportunities, costs and risks that may need to be confronted. The main objective of this study is to propose an analytical approach to evaluate the forms of buyer–supplier relationship between a manufacturer and its supplier. A fuzzy analytic hierarchy process (AHP) model, which applies fuzzy set theory and the benefits, opportunities, costs and risks (BOCR) concept, is constructed to deal with uncertainty and to consider various aspects of alternatives. Multiple factors that affect the success of the relationship are analysed by incorporating experts' opinions on their priority of importance, and a performance ranking of the buyer–supplier forms is obtained. A case study of selecting the most appropriate buyer–supplier form between a TFT-LCD manufacturer and its colour filter supplier is presented, and the proposed model is applied to facilitate the decision process. The proposed model is a general form that can be tailored and applied by firms that are making decisions on buyer–supplier relationship.

Keywords: buyer–supplier relationship; fuzzy analytic hierarchy process; performance ranking; BOCR; TFT-LCD

During the past two decades, the nature of buyer–supplier relationships has been undergoing dramatic changes. One of the most important trends in industrial purchasing is the radical change in buying attitudes and behaviour. Buyer and supplier ties have become closer with a myriad of collaborative strategies instead of the traditional arm's length transaction. Many firms are shrinking and consolidating their supplier base and developing longer-term, closer inter-firm relationships, such as strategic alliances and joint ventures, with some of the remaining key suppliers to achieve strategic goals that range from cost and risk reduction to new skills or knowledge acquisition. These collaborations can improve the competitiveness of companies in complex and turbulent environments by providing access to external resources, providing synergies and fostering rapid learning and change (Hoffmann and Schlosser [17]).

Strategic alliances are defined as inter-firm cooperative arrangements aimed at pursuing mutual strategic objectives (Das and Teng [11]). There are various types of alliances, including joint ventures, joint R&D, contracted R&D, joint production, product bundling, joint bidding, co-marketing, licensing, and code-sharing. Strategic alliances are becoming an increasingly popular strategy, particularly in high-tech industries, in which the pace of new technology and product development is remarkably high and the lifecycle of products is short (Vilkamo and Keil [40]). A dramatic increase in strategic alliances is observed in the past two decades. The trend is attributed to the firm's strategic responses to the rapid environmental changes, such as sharing risk and resources, gaining knowledge, accelerating technology advancements, building new sources of competitive advantage, concentrating on the firm's core competencies, increasing capital requirements, increasing importance of customer relationships, obtaining access to new markets, and the globalisation of markets (Dacin and Hitt [9], Chen [1], Townsend [39], Yasuda and Iijima [44]).

Despite the popularity of developing alliances among firms, strategic alliances often fail, and the failure rate was reported to be as high as 70% (Das and Teng [10], Murray et al.[29]). Although the basic concept of alliances is well known, there are relatively few guidelines for implementing and developing strategic alliances. Therefore, in order to achieve the eventual success of the buyer–supplier relationship, a formal purchasing strategy development process, a supplier assessment and selection process, followed by the evaluation and selection of the type of collaborations are necessary.

In the digital era, thin film transistor-liquid crystal displays (TFT-LCD) are quickly becoming the preferred choice in many applications of human–machine interface. However, the profit margin of TFT-LCD is decreasing as the manufacturers enter into the mass production phase. In the fabrication of TFT-LCD panels, colour filter substrate is the key component for the display to perform at its brightest, most vivid and colourful potential. However, it is one of the most expensive raw materials. The cost ratio for TFT-LCD components is quite high, and the cost of colour filters is around 25% of total material cost. Colour filters are usually purchased from colour filter manufacturers, and each TFT-LCD panel requires a piece of colour filter. Therefore, sufficient amount of colour filters must be available in the plant to maintain a smooth production flow. To summarise, in order to reduce cost and ensure product availability, a good buyer–supplier relationship is especially important in TFT-LCD manufacturing.

This paper is organised as follows. Section 2 reviews the theories of buyer–supplier relationships. Section 3 goes over the key concepts of analytic hierarchy process (AHP), fuzzy AHP, and benefits, opportunities, costs and risks (BOCR) methods. A fuzzy analytic hierarchy process (FAHP) model is constructed to evaluate the forms of buyer–supplier relationship in Section 4. Section 5 provides a numerical example, and the proposed model is applied to evaluate the efficiency under different types of buyer–supplier relationships between a TFT-LCD manufacturer and a colour filter manufacturer. Some concluding remarks are made in the last section.

Inter-organisational relations can vary widely in their structure, reflecting various degrees of inter-organisational interdependency and levels of internalisation (Hagedoom [14]). These relations range from complete interdependency to total dependence between firms. One extreme are mergers and acquisitions, which represent complete interdependency between the firms and full internalisation. The other extreme are spot-market transactions, wherein totally independent firms engage in arm's-length buy/sell transactions in which either firm remains completely independent of the other. The possible domain of inter-firm linkages is shown by Yoshino and Rangan ([45]); Todeva and Knoke ([38]) further classified 13 basic forms of inter-organisational relations appearing in the theoretical and research literatures.

The proliferation of strategic alliances has been increasing at an amazing rate in the past two decades across all business sectors. Strategic alliance is attractive in today's global environment because firms often lack the resources, such as skills, technology, capital and market access, to achieve a sustainable competitive advantage on their own. Whereas an alliance offers the means to obtain the benefits of vertical integration without the investment in physical and human resources associated with actual ownership (Whipple and Frankel [42], Zineldin and Bredenlöw [48]). Between 1987 and 1992, over 20,000 new alliances were formed, with a growth rate of 25% a year (Harbison and Pekar [16]). According to Zineldin and Bredenlöw ([48]), the number of strategic alliances has almost doubled in the past 10 years and is expected to increase even more in the future. The collaboration among firms through strategic alliances, corporate mergers and acquisitions appears to have become an indispensable means for firms to carry out business strategy and may even determine a firm's potential for future growth. Various types of collaborations have grown rapidly in the last decade, and collaborations will grow continuously into the 21st century and is very likely to be a significant trend in the industrial corporate world (Wheelen and Hungar [41], Zineldin and Jonsson [49], Zineldin and Bredenlöw [48]).

Even though many firms enter into some kind of inter-organisational relationship, few firms succeed eventually (Malott [25], Michelet and Remacle [26], Soursac [36], Elmuti and Kathawala [12], Zineldin and Bredenlöw [48]). Research estimated that two-thirds of the strategic alliances formed between 1992 and 1995 were dissolved (The Economist[37], Cravens et al.[8]). The failure rate of strategic alliance strategies to meet partner expectations and of termination of alliances is projected to be as high as 70% (Kalmbach and Roussel [19], Whipple and Frankel [42]). In spite of the fact that strategic alliance is attractive in today's global environment, it is not easy to create, develop, implement and support an alliance (Whipple and Frankel [42], Zineldin and Bredenlöw [48]). One of the most cited reasons for alliance failure is the incompatibility of partners (Dacin and Hitt [9]). The choice of the right partner and right type of collaboration can yield important competitive benefits that lead to the success of the relationship, whereas the failure to establish compatible objectives, or to communicate effectively, can lead to detrimental problems (Dacin and Hitt [9]).

To summarise, the selection of an appropriate supplier and the right type of buyer–supplier relationship is an important factor affecting the performance of the relationship. Although the literatures on supplier selection methods and the reviews of the different forms of inter-firm links are abundant, there are very few mathematical models for evaluating the forms of relationship that is most appropriate for a firm to enter into with its supplier.

The analytic hierarchy process (AHP) was introduced by Saaty in 1971 for solving unstructured problems in different areas of human needs and interests, such as political, economic, social and management sciences (Saaty [33]). Since its introduction, the AHP has become one of the most widely used methods for multiple criteria decision-making (MCDM). The procedures of AHP to solve a complex problem involve six essential steps (Zahedi [47], Cheng et al.[6], Chi and Kuo [7], Murtaza [30], Lee et al.[24]):

• 1. Define the unstructured problem and state clearly the objectives and outcomes.
• 2. Decompose the problem into a hierarchical structure with decision elements (e.g. criteria and alternatives).
• 3. Employ pairwise comparisons among decision elements and form comparison matrices.
• 4. Use the eigenvalue method to estimate the relative weights of the decision elements.
• 5. Check the consistency property of matrices to ensure that the judgments of decision makers are consistent.
• 6. Aggregate the relative weights of decision elements to obtain an overall rating for the alternatives.

Good decision-making models should be able to tolerate vagueness or ambiguity since fuzziness and vagueness are common characteristics in many decision-making problems (Yu [46]). As a result, the use of fuzzy numbers and linguistic terms may be more suitable, and the fuzzy theory in AHP should be more appropriate and effective than conventional AHP in an uncertain pairwise comparison environment.

Different methods have been devised to rank fuzzy numbers, and each method has its own advantages and disadvantages (Klir and Yuan [22]). One of the methods is the centroid ranking method (Yagar [43]). Let fc(x) be a membership function for triangular fuzzy number C = (p, q, s), the centroid ranking method formula of triangular fuzzy number C is:

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Define Ci = (pi, qi, si), i = 1, 2, ..., n as n triangular fuzzy numbers. By the formula stated above, one can obtain the centroid rank value of triangular fuzzy number:

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Finally, the centroid rank value of triangular fuzzy numbers is:

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In recent years, fuzzy AHP has become a popular methodology to solve problems in various fields. For example, Haq and Kannan ([15]) proposed a fuzzy AHP model for evaluating and selecting a vendor in a supply chain. Lee et al. ([24]) applied fuzzy AHP to evaluate the efficiency under different priority mixes in semiconductor manufacturing.

One of the general theories of the analytic network process (ANP), which was also proposed by Saaty ([32]), enables one to deal with the benefits, opportunities, costs, and risks (the BOCR merits) of a decision. A network can consist of four sub-networks: benefits, opportunities, costs, and risks. In benefits (B) and opportunities (O) sub-networks, pairwise comparison questions ask which alternative is most beneficial or has the best opportunity under each control criterion/sub-criterion. In risks (R) and costs (C) subnets, the pairwise comparison questions ask which alternative is riskiest or costliest under each control criterion/sub-criterion. Therefore, while the best alternative gets the highest priority for B and C subnets, the worst alternative also gets the highest priority for R and C. We can first combine the weights of the alternatives according to the weights of the criteria, which are set by experts, for each subnet. Then the weights of the alternatives under B, O, C and R are further combined to get a single outcome for each alternative. Saaty ([31]) proposed five ways to combine the scores of each alternative under B, O, C and R:

• 1. Additive

•

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• where _I_B_i_, _I_O_i_, _I_C_i_ and _I_R_i_ represent the synthesised results and _Ii_, o, c and r are normalised weights of B, O, C and R subnets, respectively.
• 2. Probabilistic additive

•

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• 3. Subtractive

•

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• 4. Multiplicative priority powers

•

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• 5. Multiplicative

•

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The BOCR concept can also be applied by the AHP, and each subnet of the four merits is replaced by a hierarchy. The major drawback of ANP is that the questionnaire is too cumbersome, and experts may not have the patience to fill it out, not to say that the consistency of judgment can be met. Therefore, in this paper we will only adopt the BOCR concept, and propose a fuzzy AHP model instead.

In this research, we will divide the problem into two phases, and each phase has a hierarchy, as shown in Figure 1. For the hierarchy in phase I, the overall objective is to achieve the most efficient performance of a manufacturer through maintaining the best form of buyer–supplier relationship. The strategic criteria for achieving the overall objective are in the second level, and each of the strategic criteria can be considered as sub-goals that the firm is willing to realise (Erdogmus et al.[13]). The four merits, benefits (B), opportunities (O), costs (C) and risks (R), for the evaluation of the best form of buyer–supplier relationship are in the third level. The purpose of phase I is to calculate the relative weights, b, o, c and r, for the four merits B, O, C and R, respectively (Saaty and Ozdemir [35], Saaty [34]). It is very likely that the four merits are not equally important; thus, the priorities of the merits must be determined. However, it is not very easy for experts to pairwise compare the importance of the four merits. For instance, a question like 'which merit should be emphasised more (or what is the relative importance of benefits in compared with opportunities) in achieving the goal of the best form of buyer–supplier relationship' is abstract and very difficult, even if possible, to answer. Therefore, Satty ([34]) and Saaty and Ozdemir ([35]) propose the use of a control hierarchy to determine the relative weights, b, o, c and r, for the four merits B, O, C and R, respectively. For example, a question like: 'what level of benefit (opportunity, cost or risk) do you associate with strategic criterion S1?, is asked, and a rating is given by each expert on the level of benefit (opportunity, cost or risk) on that strategic criterion.

Graph: Figure 1. The framework.

In phase II, the overall objective is also to select the best form of buyer–supplier relationship. BOCR are considered simultaneously to achieve the goal. Under each merit, there are control criteria and other sub-criteria. The forms of buyer–supplier relationship are alternatives in the lowest level. The relative weights of BOCR obtained in phase I is input here to calculate the overall priority weight of each alternative. Fuzzy set theory is incorporated into the model to meet the uncertain decision-making environment.

A systematic fuzzy AHP model for evaluating the forms of buyer–supplier relationship is proposed in this section. The steps are summarised as follows:

Form a committee of experts in the industry and define the buyer–supplier relationship problem. Different forms of collaboration have different impacts on a manufacturer, and the selection of an appropriate relationship is essential to be competitive in the market.

Decompose the problem hierarchically. Two hierarchies, in the form as in Figure 1 are constructed based on literature review and experts' opinions.

Formulate a questionnaire based on the proposed structure, and experts in the field are asked to fill out the questionnaire. There are basically two types of questions. The first type of question is to pairwise compare the importance of strategic criteria with respect to the goal. The second type of question is to give a rating of the importance of each merit on each strategic criterion, the importance of each control criterion on each merit, the importance of each sub-criterion on each control criterion, and the performance of each strategy on each sub-criterion (Cheng [4], Chen and Cheng [2], Lee et al.[24], Kang and Lee [20], Saaty [34], Saaty and Ozdemir [35]).

Phase I calculations. Calculate the relative weights, b, o, c and r, for the four merits B, O, C and R.

From experts' questionnaire results, obtain pairwise comparison results of the importance of strategic criteria toward achieving the overall objective. A five-point scale is used to express preferences between strategic criteria p and q by experts, ηpqt, as equally (1), moderately (3), strongly (5), very strongly (7), or extremely preferred (9), and the reciprocal of the value is used to express less preference. For example, if strategic criterion S1 is more strongly important than strategic criterion S2 under the evaluation of expert 1, then η121 = 5/1 = 5. On the other hand, if S2 is more strongly important than S1, then η121 = 1/5. The consistency property of each expert's comparison results is examined. If an inconsistency is found in an expert's result, the expert is asked to revise the questionnaire until a consistency is met.

Combine experts' opinions on the importance weight for each strategic criterion. For a number of S experts, the synthetic set representing the relative importance level between strategic criteria p and q can be generated by geometric average as (Kuo et al.[23], Lee et al.[24]):

Graph

Graph

where

Graph

Graph

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Establish fuzzy importance weight for each strategic criterion. By synthesising experts' opinions, the weights of strategic criteria can be represented by a weight vector, (Mon et al.[27], Cheng et al.[6], Lee et al.[24]):

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where , and are defined as in Table 1.

Table 1. Characteristic function of the fuzzy numbers.

Calculate fuzzy importance (impact) of each merit on each strategic criterion. Obtain experts' opinions on the importance (impact) of the merit (B, O, C and R) on each strategic criterion by a five-point scale (from very unimportant (1) to very important (9)). The approach is not a pairwise comparison of two merits with respect to each strategic criterion, but is based on the approach proposed by Satty ([34]) and Saaty and Ozdemir ([35]). A rating is given by each expert on the level of benefit (opportunity, cost or risk) on that strategic criterion. A triangular fuzzy number is obtained by combining the experts' opinions.

Graph

where

Graph

Graph

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and kept is the importance weight of merit e (benefits, costs, opportunities, risks) on strategic criterion p from expert t.

Prioritise the relative importance of the four merits by considering their ratings on the strategic criteria. The fuzzy priority of a merit is obtained by summing up the multiplication of the fuzzy importance weight for each strategic criterion from Step 4.3 and the fuzzy importance (impact) of the merit on each strategic criterion from Step 4.4. The resulted fuzzy priority of each merit is assumed to be a triangular fuzzy number (Kaufmann and Gupta [21], Chen [3], Cheng et al. 1996). By applying the centroid method, a defuzzified priority for each merit is obtained. The defuzzified priorities for the four merits are normalised into b, o, c and r.

Phase II calculations. Calculate the fuzzy ranking of alternatives under each merit (B, O, C and R).

Obtain the importance weight of each control criterion (and sub-criterion) by a similar step as Step 4.4.

Calculate the integrated normalised priority of each sub-criterion under each merit. A fuzzy integrated priority of each sub-criterion is calculated by multiplying the importance weight of the sub-criterion with the importance weight of its upper-level control criterion. The fuzzy integrated priority of each sub-criterion is defuzzified into an integrated defuzzified priority by the centroid method. The integrated defuzzified priorities under the same merit are normalised into normalised integrated priorities.

Obtain the performances of each alternative under each quantitative sub-criterion by experts' forecasting. Normalise the value into a number between zero and one:

For direct sub-criterion j:

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For inverse sub-criterion j:

Graph

where , , 0 ≤ ρij ≤ 1, and rij is the value of sub-criterion j in evaluating alternative i.

Obtain the performances of each alternative under each qualitative sub-criterion. The performances of alternatives under each qualitative sub-criterion are generated through expert's evaluations since these data may not be quantified. Five levels of evaluation are used here and their linguistic values are as in Table 2. Experts' opinions are collected through questionnaire, and the same procedure as Step 4.4 is applied here.

Table 2. Linguistic value table.

Determine the relative performance of alternatives with respect to each control criterion by forming a matrix for each control criterion. Use the data generated from Steps 5.3 and 5.4, the performances of alternatives in each sub-criterion under the same control criterion are entered in the matrix.

Synthesise and establish the fuzzy ranking of alternatives under each merit (B, O, C and R) by combining the results from Steps 5.2 and 5.5.

Calculate overall priorities of alternatives by combining BOCR priorities of each alternative from Step 5.6 with corresponding normalised weights b, o, c and r from Step 4.5. As stated in section 3.3, there are five ways to combine the scores of each alternative under B, O, C and R.

As the TFT-LCD industry is becoming extremely competitive, various strategies and cost control efforts have been stressed by manufacturers. These include the increase in the size of the substrates, the decrease in the number of process steps, the simplification of the processes, the improvement in the utilisation of processes, the decrease in cycle time and the improvement in yields (Moslehi [28]). Among all the cost-control strategies, the reduction of the cost of materials and the increase in the utilisation rate of the materials are especially important since raw materials accounts for as high as 79% of the total manufacturing cost (Hsieh [18]).

Colour filter is the most critical material in TFT-LCD manufacturing. A TFT-array substrate and a colour filter substrate must be paired into the assembly station; therefore, an adequate amount of colour filters must be in the cell plant on time to fully utilise the capital-intensive equipment and to avoid any shortages and the stoppage of production flow. The cost of colour filters can be as high as 25% of raw material cost or 16% of total manufacturing cost, exceeding that for all other materials except backlight unit (Hsieh [18]). In addition, transportation and handling risk is high for newer-generation colour filters due to the continuous increases in the size of substrates. To summarise, in order to achieve cost reduction, ensure product availability and obtain leading-technology colour filters, the buyer–supplier relationship with colour filter manufacturers is especially important for TFT-LCD manufacturers.

Since colour filters is one of the most critical and the most expensive components in TFT-LCD manufacturing; therefore, in this paper, we propose to build a model for selecting the most appropriate buyer–supplier relationship between TFT-LCD manufacturer and colour filter manufacturer. A committee of experts in the TFT-LCD industry is formed to define the buyer–supplier relationship problem between TFT-LCD manufacturers and colour filter manufacturers. The research scope is on TFT-LCD plants with fifth generation or lower. With a comprehensive review of literature, consultation with domain experts and consideration of data accessibility, the hierarchy and the factors for determining the efficiency of a TFT-LCD manufacturer in terms of a buyer–supplier relationship form is organised. Four forms of buyer–supplier relationships, which are currently possible and are highly recommended to form with the target colour filter manufacturer, are considered here: contractual alliance (I), minority equity ownership (II), joint venture (III) and acquisition (IV). In a contractual alliance (I), the TFT-LCD manufacturer signs a long-term sourcing agreement with the colour filter manufacturer. In the agreement, the TFT-LCD manufacturer consigns manufacturing service to the colour filter manufacturer, and the colour filter manufacturer provides the TFT-LCD manufacturer with colour filters subject to the specification designated by the TFT-LCD manufacturer. Minority equity ownership (II) means that the TFT-LCD manufacturer holds minority equity of the colour filter manufacturer through a direct stock purchase. In a joint venture (III), the TFT-LCD manufacturer and the colour filter manufacturer create a jointly owned organisation that manufactures colour filters. Through acquisition (IV), the TFT-LCD manufacturer takes full control of the colour filter manufacturer's assets and coordinates actions by the ownership rights mechanism.

The control hierarchy, as displayed in Figure 2, shows the strategic criteria for the buyer–supplier relationship form. The management should select a relationship form that will optimise the performance of the firm, and the strategic criteria are the sub-goals. The control hierarchy is used to rate the relative importance, b, o, c and r, of benefits (B), opportunities (O), costs (C) and risk (R) respectively. The strategic criteria are verified by experts to pretty well capture TFT-LCD manufacturers' main corporate concerns about the form of buyer–supplier relationship. That is, the strategic criteria are very basic criteria that are used to assess the forms of relationship. 'Sufficient delivery of colour filters' measures whether the TFT-LCD manufacturer can receive the right amount of colour filters at the right time in its production. 'Lower colour filter unit cost' means that the cost of colour filters should be reduced in order to make a reasonable profit and increase the competitiveness of the firm. 'Quality of colour filters' is also essential for the firm to make final products with the required quality and to reduce rework and product failure, etc. 'Flexibility in service' is the ability of the colour filter manufacturer to provide flexible service in terms of quantity, product type and lead time, etc. 'Product/process technology' means the product/process technology possessed by the colour filter manufacturer that can lead to better quality and improved colour filters, and that can have a good impact to TFT-LCD manufacturing. For the BOCR hierarchy, which is used to evaluate the forms of buyer–supplier relationship, the four merits and their respective control criteria and sub-criteria are listed and defined in Table 3. Although the framework seems to be very complex, it is necessary for making such an important decision, which can have a serious impact on the success or failure of the TFT-LCD manufacturer. In addition, even though there are many control criteria and sub-criteria in total, they are grouped into four different sub-hierarchies. For instance, for the benefits sub-hierarchy, there are only four control criteria, and each control criterion has less than four sub-criteria.

Graph: Figure 2. The control hierarchy.

Table 3. The BOCR hierarchy.

A questionnaire is constructed and is targeted on the experts in the TFT-LCD industry. A total of five experts including senior managers of purchasing, finance and corporate development departments from an anonymous internationally-well-known TFT-LCD manufacturing company in the Science-Based Industrial Park in Taiwan are invited to contribute their professional experience. The company aims to choose the most suitable form of buyer–supplier relationship with a target colour filter supplier.

Based on the collected opinions of the experts and the proposed model, the performance results of the four forms of buyer–supplier relationship can be generated. The importance of strategic criteria toward achieving the goal is calculated first. The consistency of the pairwise comparison results of each expert needs to be examined. For instance, the pairwise comparison matrix for the strategic criteria of an expert is as follows (Saaty [33], Saaty [32]):

Graph

and

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The consistency test (Saaty [33], Saaty [32]) is performed by calculating the consistency index (CI) and consistency ratio (CR):

Graph

and

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where n is the number of items being compared in the matrix, and RI is the random index, the average consistency index of randomly generated pairwise comparison matrix of similar size (Saaty [33], Saaty [32]). Since CR is less than 0.1, the threshold for consistency, the expert's judgment is consistent in this case. If the consistency test is not passed, the expert will be asked to re-do part of the questionnaire.

After the experts' opinions on the relative importance of the strategic criteria are obtained, a synthesis of the opinions is generated and as shown in the first row in Table 4. Experts are also asked to evaluate BOCR according to the strategic criteria by using a five-point scale, and the opinions are combined as shown in Table 4. For example, the fuzzy priority for Benefits is:

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Table 4. BOCR rating.

The defuzzified priority for Benefits is calculated by the centroid method (Yagar [43]):

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The normalised priorities of BOCR are calculated and shown in the last column of Table 4.

The relative priorities of control criteria and sub-criteria under the four merits are listed in Table 5. Under the benefits merit, the most important sub-criterion, out of a total of 12 criteria, is 'purchase savings', with a priority of 0.22045. This means that the major benefit concern for the firm in forming a relationship with the colour filter manufacturer is to lower the cost of colour filters. The second and third sub-criteria are 'on-time delivery' (0.13411) and 'time from order to delivery' (0.11241), and this indicates that the delivery of colour filters in a short and prompt time is very important. Under the opportunities merit, 'time-to-market' (0.23425) and 'market share' (0.18101), both belonging to the control criterion 'access to markets', are the most important criteria. This implies that the firm hopes to reduce the time to introducing new TFT-LCD products to the market and to increase its (and colour filter's) market share. Under the costs merit, 'cost of forming the relationship' (0.54172) and 'time to forming the relationship' (0.19829) are the major concerns. The underlying reason is very straightforward since different forms of relationship lead to large differences in the cost and time that the firm must spend on. Under the risks merit, 'lack of coordination between management teams' (0.23881) and 'lack of trust' (0.21566) are the major concerns. This means that the firm worries more about the compatibility of the management of the two firms after forming the relationship.

Table 5. Relative priorities of control criteria and sub-criteria.

The relative performance of alternatives with respect to each merit is shown in Table 6. Under the benefits merit, acquisition (IV) performs the best with a priority of 0.33324, followed by joint venture (III) with 0.26483. Under the opportunities merit, acquisition (IV) also performs the best with a priority of 0.42064, followed by joint venture (III) with 0.24670. However, under the costs merit, contractual alliance (I) becomes the best with a priority of 0.38574, followed by minority equity ownership (II) with 0.38212. Under the risks merit, the least risky alternative becomes minority equity ownership (II) with a very high priority of 0.45885, followed by joint venture (III) with 0.22925.

Table 6. Priorities of alternatives under four merits.

Table 6. Priorities of alternatives under four merits.

The final ranking of the alternatives are calculated by the five methods to combine the scores of each alternative under B, O, C and R. The results are as shown in Table 7. Under all five methods of synthesising the scores of alternatives, minority equity ownership (II) ranks the first. Contractual alliance (I) ranks the second under all the methods except probabilistic additive method and subtractive method. Under probabilistic additive method, joint venture (III) ranks the second with a score of 0.46998 and contractual alliance (I) ranks the third with 0.46680 (an insignificant difference of 0.00318). Under subtractive method, acquisition (IV) ranks the second with a score of 0.05494 and contractual alliance (I) ranks the third with 0.03380. The major reason for minority equity ownership (II) being the best alternative is that it is the least risky and rather costless alternative. Even though minority equity ownership (II) performs the worst in the benefits and opportunities merits, but the difference from the performance of other alternatives are not tremendous. On the other hand, it is the second best in the costs merit, with an insignificant performance difference from the best alternative, contractual alliance (I). The most important thing is that it performs best in the risks merit, with the lowest normalised priority of 0.11023, which is two times better than the second best alternative, joint venture (III), and 3.5 times better than the worst alternative, acquisition (IV). Therefore, minority equity ownership (II) is the best alternative with experts' overall consideration of benefits, opportunities, costs and risks.

Table 7. Final synthesis of priorities of alternatives.

A sensitivity analysis is performed next, and the results are shown in Table 8. When the priorities of merits are changed, the ranking of alternatives may be different too. Use benefits as an example. No matter how the priority of benefits (b) decreases, the best alternative remains to be minority equity ownership (II). However, the best alternatives become both minority equity ownership (II) and acquisition (IV) when b increases to 0.9707, 0.3405 and 0.5341 under the additive, subtractive, and multiplicative priority powers method, respectively. When b increases to 0.4801, the best alternatives become both minority equity ownership (II) and joint venture (III) under the probabilistic additive method. Note that the priorities of merits have no effect on the solution under the multiplicative method. Based on Table 8, we can see that minority equity ownership (II) remains to be the best alternative when the priorities of merits change in a range. Even though contractual alliance (I) may be the best when the priority of costs (c) increases, the possibility of being the best is very slim because c needs to be as high as 0.9360, a very large number. Minority equity ownership (II) is the best option for the firm, and acquisition (IV) may be the best when the priorities of merits change in a rather large degree.

Table 8. Sensitivity analysis under different priorities of merits.

Even though contractual alliance (I) ranks the second under three of the five synthesising methods in Table 7, sensitivity analysis shows that acquisition (IV) may be the best if the priorities of merits change. Contractual alliance (I) ranks second mainly because of its good performance in costs merit, and it becomes the best alternative when the priority of costs (c) increases tremendously. On the other hand, acquisition (IV) performs very well in benefits and opportunities merits, and its overall ranking is not very good due to its poor performance in costs and risks merits. When the priority of benefits (b) or opportunities (o) increases, it may become the best alternative. In conclusion, minority equity ownership (II) is the best option for the anonymous TFT-LCD manufacturer in considering the relationship with its colour filter supplier.

Currently, there is a trend for TFT-LCD manufacturers to build their own colour filter factories; however, it is usually for newer generation factories because of the transportation issue of large-sized colour filters. To be cost-competitive and to acquire colour filters with different specification varieties, a TFT-LCD manufacturer may still want to build a relationship with an existing colour filter manufacturer, instead of building its own colour filter factory, for lower generation products. In this case study, acquisition is not preferred because the associated costs and risks are too high for buying this supplier even though the benefits and opportunities gained from acquisition are the highest among the four forms of relationship. This is another reason why many TFT-LCD manufacturers are beginning to build their own colour filter factories for higher generation products.

In this paper, a fuzzy analytic hierarchy process (AHP) model is constructed to evaluate the forms of buyer–supplier relationship. Even though there are many supplier selection models available, the models usually only consider the criteria that are required by the buyers, but not the opportunities, costs and risks that need to be faced by the buyers if they select a specific supplier. In addition, as far as the author is aware there is no mathematical model that can help a firm to evaluate the various types of buyer–supplier relationship. Therefore, the proposed model can help decision makers in the buyer–supplier relationship selection process by considering the benefits, opportunities, costs and risks (BOCR) perspectives. As human decision making process involves ambiguity and uncertainty, fuzzy theory is also incorporated into the model.

By applying the proposed model, decision makers in the TFT-LCD manufacturer can base on the results to examine the expected performance of each relationship form on various criteria and sub-criteria, and can select the most appropriate form of relationship with its colour filter manufacturer. The model can also be modified as required by a firm in any other industry to help it select the best form of buyer–supplier relationship.

If there are several suppliers that should be evaluated at the same time, a more complicated evaluation framework is necessary. For example, the framework can consist of two parts: the supplier selection stage and the relationship selection stage. The supplier selection stage is to select one supplier out of several suppliers first, and the relationship selection stage is to select the most appropriate relationship with this specific supplier. The two stages may be switched in sequence. Alternatively, the evaluation framework can contain alternatives that are in the forms of supplier-relationship, e.g. supplier A-contractual alliance and supplier B-acquisition. Solving such a complicated instance can be part of our future research direction.

This work was supported in part by the National Science Council in Taiwan under Grant NSC 96-2416-H-216-002.