Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

Lin, Chinho

ABSTRACT

We propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy-oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real-world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.

Subject Areas: Fuzzy Weighted Average, Integer Linear Programming, Portfolio Matrix, and Strategic Portfolio Management.

INTRODUCTION

Strategy formulation is the process of determining appropriate courses of action or a plan for achieving organizational objectives, and thus accomplishing the organizational purpose (Hatten & Hatten, 1987). The goal of formulating a strategic plan is to identify feasible strategic alternatives and then to select the best one. In multibusiness organizations, the evaluation and selection of appropriate strategic plans that the firm will pursue involve the business strength/industry attractiveness analysis of Strategic Business Units (SBUs) as well as the feasibility analysis of those strategic plans submitted by the SBUs. The whole process, from identifying the competitive position of SBUs to determining suitable strategic plans, is a very complicated task involving a structured evaluation procedure and requires experienced decision makers (Tan, Lin, & Hsieh, 2003). Generally, strategic planning approaches with structured procedures are employed to guide managers in establishing each level of a strategic plan so that a strategy can be completely formulated (Hax & Majluf, 1991; Archer & Ghasemzadeh, 1999; Ghasemzadeh & Archer, 2000; Tan & Platts, 2003). Most of these studies have focused on the fields of Research and Development (R&D) (Ringuest, Graves, & Case, 2004), information technology (Klapka & Pinos, 2002), marketing (Thieme & Song, 2000), customer relations management (Zhu, Sivakumar, & Parasuraman, 2004), and optimal portfolio of investments (Levary & Seitz, 1990). In these studies, the methods of capital budgeting (Levary & Seitz, 1990), Analytic Hierarchy Process (AHP) (Hahn, 2003), scoring model, and portfolio matrices used in conjunction with optimization models are popular among decision makers to consider a broad range of quantitative and qualitative characteristics, as well as multiple objectives. Of these methods, capital budgeting has been commonly applied to select capital investments, including physical assets like equipment and nonphysical investments like stocks (Levary & Seitz, 1990; Chan, 2004). However, Edvinsson and Malone (1997) stated that traditional financial data as presented in the annual report are no longer leading indicators of future financial performance. It has been gradually acknowledged that traditional financial measurement is inadequate in guiding strategic policy making (Waterhouse & Svendsen, 1998). Traditional financial methods, which are based on tangible assets and historical, transaction-based information, are inadequate for valuing intangible benefits of strategic plans. Hence, in evaluating and selecting strategic plans, capital budgeting should be supplemented by measurements covering intangible benefits of strategic plans.

In addition, in the aforementioned strategic planning approach, decision makers must confirm that all of the information available or needed is brought to bear on the problem or issue at hand. As previous cases indicate (Ansoff & McDonnell, 1990; Chien, Lin, Tan, & Lee, 1999), identifying all relevant information for a decision does not mean that the decision makers have complete information; in most instances, information is incomplete. Decisions must be made with limited information because decision makers do not have full knowledge of the problem they face and generally cannot even determine a reasonable probability for alternative outcomes; thus, they must make their decisions under conditions of uncertainty. In addition, many decisions in organizations, especially important decisions that have far-reaching effects on organizational activities and personnel, are made in groups. One problem with group decision making is that not every member in the decision group has the same knowledge of the problem as the others have. This means that decision makers will face a decision-making situation with various peers possessing different confidence levels regarding the problem to be handled. Thus, the domain of strategic management has already been recognized as a field appropriate for the application of a fuzzy set theory (Pap, Bosnjak, & Bosnjak, 2000). Some prior studies employed fuzzy set theory to do project evaluation and selection. However, existing studies generally concentrate on evaluating projects at the functional level, for example, R&D (Buyukozkan & Feyzioglu, 2004), information technology (Chiu, Shyu, & Tzeng, 2004), and operations management (Bozdag, Kahraman, & Ruan, 2003), and neglect the demands of making strategic evaluations at the corporate level. Therefore, a project selection method constructed with strategy-oriented evaluation and selection processes will meet many firms' practical needs. Furthermore, after identifying the competitive position of SBUs and the feasibility of strategic plans submitted by SBUs, a firm needs to select the most suitable strategic plans. The most common application of integer linear programming involves the general problem of finding the best way to allocate limited resources among competing activities (Walukiewicz, 1991; Robinson & Lawrence, 2004). Hence, a suitable technique, integer linear programming, will act as a tool to select the optimal strategic plans.

Hence, the focus of this research is to incorporate fuzzy set theory into a portfolio analysis and 3Cs model (customer relations, capabilities, and competencies) to provide a quantitative method to identify the competitiveness of SBUs and the feasibility of strategic plans, respectively. Furthermore, with the results derived from portfolio analysis and 3Cs model together with proper estimations of potential profit and implementation cost for each strategic plan, one can construct and solve an integer linear programming model to determine the strategic plans that best utilize a firm's budget and maximize the net financial payoff generated from implementing these strategic plans. The study is organized as follows. The portfolio matrix concept, 3Cs model, fuzzy set theory, and integer linear programming are introduced. The characteristics of the decision-making problem in determining strategic plans are conveyed. A case study is employed as an example to illustrate the proposed integrated approach. In addition, the implementation procedure of the proposed integrated approach illustrated by using the case firm's data are described. Discussion and analysis are presented. Finally, further research and the conclusions of the research are provided.

LITERATURE REVIEW

The Portfolio Matrix Concept and 3Cs Model

The entire thrust of the competitive analysis concept is based on the underlying assumption that corporate strategy starts with an analysis of competitive position. During the 1970s and early 1980s, a number of leading consulting firms developed the portfolio matrix concept to help managers reach a better understanding of the competitive position of the overall portfolio of businesses (Hax & Majluf, 1983). The most popular three portfolio matrices are: growth-share matrix, GE multifactor portfolio matrix, and life-cycle matrix (Rowe, Mason, & Dickel, 1994). Table 1 briefly summarizes the characteristics of the internal and external dimensions used by each one of the portfolio matrices. The portfolio matrix has been proven to be a powerful tool for companies to analyze products or SBUs and to provide strategic directions (Rowe et al., 1994). In the proposed example, the top managers of the cooperating company chose the GE portfolio matrix as a tool to position the competitive situation of their four SBUs. The GE portfolio matrix is a nine-cell matrix that helps managers understand the competitive position of SBUs and develop an organizational strategy based primarily on Industry Attractiveness (IA) and Business Strength (BS). The former is a subjective assessment based on external factors that are intended to capture the industry and the competitive structure on which the business operates. The latter is a subjective assessment based on the critical success factors that define the competitive position of a business within its industry. Each of these two dimensions is actually a composite of various factors that will be illustrated in the proposed example.

Besides considering the competitiveness of the business portfolio, managers also need to consider whether the businesses have the capabilities and resources necessary to implement their strategic plans. In addition, they must be sure that the plans will not threaten the attainment of other organizational goals. Therefore, for the purpose of selecting the strategic plans submitted by the same SBU, a set of criteria is also needed to differentiate the most feasible strategic plan from the others. The 3Cs model, presented by Hatten and Rosenthal (1999), is concerned with the business' customer relations, process capabilities, and functional competencies that constitute the resource platform for a business' future strategies and determine the feasibility of its plans. Customer preference, reciprocity, and loyalty define customer relations. Process capabilities refer to the physical capabilities to do things and are measures of the performance of business processes along dimensions defined by customers' needs and expectations (time, cost, quality, functionality, and flexibility). Knowing how to do things constitutes functional competencies, which are measures of the organization's potential to conduct state-of-the-art business in both the firm's input markets (labor, capital, information, and technology) and output markets with its customers. Thus, the business strategy is based on the strengths of the firm's customer relationships, the depth of its competencies, and the amount of its capabilities. Working under this concept, the selected strategic plan should be congruent with the requirement of meeting customers' needs as well as with the competencies and capabilities of the business.

Fuzzy Set Theory

Linguistic variable and fuzzy number

The first publication of fuzzy set theory was made by Zadeh (1965). Zadeh wrote: "The notion of fuzzy set provides a convenient point of departure for the construction of a conceptual framework which parallels in many respects the framework used in the case of ordinary sets, but it is more general than the latter and, potentially, may prove to have a much wider scope of applicability, particularly in the fields of pattern classification and information processing." Essentially, such a framework provides a natural way for dealing with problems where the source of imprecision is the absence of sharply defined criteria of class membership rather than the presence of random variables. Therefore, fuzzy set theory provides a strict mathematical framework in which vague conceptual phenomena can be precisely and rigorously studied (Zimmermann, 1991).

As indicated earlier, the fact that decision makers seldom have complete information to make decisions causes feelings of uncertainty among them during the decision-making process. Hence, under many circumstances, crisp numbers are inadequate in modeling real-life situations. The definition of a crisp number is as follows. If R is the universe, A is a subset of R. Assume A is a crisp set and x is an element in A. The characteristic function of A is λ^sub A^(x) : R [arrow right] {0, 1}. If x in A is a real number, we call it a "crisp number." Because human judgments, including preferences, are often vague, and individual preference is difficult to estimate with an exact numerical value, the major problem with humans using the classical portfolio matrix lies in precisely determining the numerical value of the criterion (Bohanec, 1995; Pap, Bosnjak, & Bosnjak, 2000). In this case, linguistic assessments instead of numerical indicators may be used, meaning that the ratings and weights of the criteria in the problem are evaluated by means of linguistic variables (Bellman & Zadeh, 1970; Herrera, Herrera-Viedma, & Verdegay, 1996). A linguistic variable is a variable with values that are not numbers but words or phrases in a natural or synthetic language. These linguistic variables are then replaced by suitable triangular fuzzy numbers that are used for arithmetical operations.

Fuzzy weighted average

When the environment is vague, the rating criteria and the weights of their corresponding importance are often evaluated as a fuzzy number (Liou & Wang, 1992). In order to obtain the weighted sum of those criteria evaluated by fuzzy numbers in terms of rating and importance, we use the fuzzy weighted average for the calculation. There has been some research involved in the field of fuzzy weighted average (Vanegas & Labib, 2001; Buyukozkan & Feyzioglu, 2004). Dong and Wong (1987) addressed the computational aspect of the extension principle when the principle is applied to the weighted average operations in risk and decision analysis. Their computational algorithm is based on the α-cut representation of fuzzy sets and interval analysis. Lee and Park (1997) proposed an efficient algorithm, named the Efficient Fuzzy Weighted Average (EFWA), to compute a fuzzy weighted average, which was an improvement over the previous methods by reducing the number of comparisons and arithmetical operations to O(n log n). We adopted the EFWA algorithm (Lee & Park, 1997) to do the calculations in the current work, which is described as follows:

Suppose x^sub i^ and w^sub i^, i = 1, 2, . . . , n, have the corresponding intervals [a^sub i^, b^sub i^] and [c^sub i^, d^sub i^] with c^sub i^ ≤ 0, respectively.

1. Sort a's in non-decreasing order. Let (a^sub 1^, a^sub 2^, . . . , a^sub n^) be the resulting sequence. Let first =1 and last = n.

2. Let δ - threshold = [(first + last)/2] = (n + 1)/2. For each i = 1, 2, . . . , δ - threshold, let e^sub i^ = d^sub i^, and for each i = δ - threshold + 1, . . . n, let e^sub i^ = c^sub i^. For an n-tuple S = (e^sub 1^, e^sub 2^, . . . , e^sub n^), evaluate δ^sub S^sub δ-threshold^^ and δ^sub S^sub (δ-threshold+1)^^. δ^sub S^sub i^^ = (a^sub 1^ - a^sub i^)e^sub 1^ + (a^sub 2^ - a^sub i^)e^sub 2^ + . . . + (a^sub n^ - a^sub i^)e^sub n^/e^sub 1^ + e^sub 2^ + . . . + e^sub n^.

3. If δ^sub S^sub δ-threshold^^ > 0 and δ^sub S^sub (δ-threshold+1)^^ ≤ 0; then L = f^sub L^(e^sub 1^, e^sub 2^, . . . , e^sub n^) = a^sub 1^ + δ^sub S^sub 1^^ = a^sub 2^ + δ^sub S^sub 2^^ = . . . = a^sub n^ + δ^sub S^sub n^^ and go to Step 4; otherwise execute the following step.

3.1. If δ^sub S^sub δ-threshold^^ > 0, then first =δ - threshold + 1; otherwise last = δ threshold, and go to Step 2.

4. Sort b's in non-decreasing order. Let (b^sub 1^, b^sub 2^, . . . , b^sub n^) be the resulting sequence. Let first = 1 and last = n.

5. Let ξ - threshold = [(first + last)/2] = (n + 1)/2. For each i = 1, 2, . . . , ξ - threshold, let e^sub i^ = c, and for each i = ξ - threshold + 1, . . . , n, let e^sub i^ = d^sub i^. For an n-tuple S = (e^sub 1^, e^sub 2^, . . . , e^sub n^), evaluate ξ^sub S^sub ξ-threshold^^ and ξ^sub S^sub (ξ-threshold+1)^^.ξ^sub S^sub i^^ = (b^sub 1^ - b^sub i^)e^sub 1^ + (b^sub 2^ - b^sub i^)e^sub 2^ + . . . + (b^sub n^ - b^sub i^)e^sub n^/e^sub 1^ + e^sub 2^ + . . . + e^sub n^.

6. If ξ^sub S^sub ξ-threshold^^ > 0 and ξ^sub S^sub (ξ-threshold+1)^^ ≤ 0; then U = f^sub U^(e^sub 1^, e^sub 2^, . . . , e^sub n^) = b^sub 1^ + ξ^sub S^sub 1^^ = b^sub 2^ + ξ^sub S^sub 2^^ = . . . = b^sub n^ + ξ^sub S^sub n^^ and stop; otherwise execute the following step.

6.1. If ξ^sub S^sub ξ-threshold^^ > 0 then first = ξ - threshold + 1; otherwise last = ξ threshold, and go to Step 5.

Integer Linear Programming (ILP)

In general, there is a trade-off between investment cost and financial potential in selecting a strategic plan, that is, the less expensive a project, the less its likely return. A zero-one integer linear programming model has been proposed as a tool to select an optimal project portfolio, based on the organization's objectives and constraints, such as resource limitations and interdependence among projects (Levary & Seitz, 1990; Burn, Liu, & Feng, 1996; Ghasemzadeh, Archer, & Iyogun, 1999). In the proposed example, we use the GE matrix to express the competitive position of SBUs and use the 3Cs model to evaluate the feasibility of the strategic plans. Then we use the analysis results of the GE matrix and 3Cs model as one of the input datasets for the ILP model. Besides considering the competitiveness of SBUs and the feasibility of strategic plans, a manager may consider the financial contribution of each strategic plan to the whole portfolio. Hence, with the help of a firm providing financial estimation information, we can construct and solve an ILP model to determine the strategic plans that best utilize a firm's annual budget to maximize the potential profit generated from implementing these strategic plans. Three basic assumptions are stated as follows. First, two parameters, required investment cost and anticipated profit, are considered when evaluating the financial feasibility of strategic plans. Second, all strategic plans are independent of one another. Third, each SBU can only implement one strategic plan a year.

The proposed ILP model includes the following notations:

r^sub ij^ = These are decision variables; unity if the jth strategic plan is implemented at the ith SBU; otherwise it is 0.

P^sub ij^ = Anticipated profit from implementing the jth strategic plan at the ith SBU.

C^sub ij^ = Required investment cost of implementing the jth strategic plan at the ith SBU.

U^sub i^ = Upper limit on the total investment amount budgeted to the ith SBU of the firm.

B = Overall investment budget of the firm for the year.

I^sub i^ - External construct (Industry attractiveness of the ith SBU).

A^sub i^ = Internal construct (Business strength of the ith SBU).

F^sub ij^ = Feasibility construct (Feasibility of jth strategic plan at the ith SBU).

THE CHARACTERISTICS OF THE DECISION-MAKING PROBLEM IN DETERMINING STRATEGIC PLANS

The decision-making problem studied in this research concerns the determination of strategic plans that best utilize a given firm's budget and maximize the net financial payoff generated from implementing these strategic plans (Figure 1). An integrated approach involving both the evaluation and selection processes is proposed to solve this type of decision-making problem. The evaluation process contains the portfolio matrix concept, 3Cs model, fuzzy set theory, and EFWA. In the selection process, the selection of strategic plans is viewed as an assignment problem which is solved by the integer linear programming model.

CASE STUDY

To evaluate the applicability of the proposed integrated approach, we implemented it in a strategic planning project for a food corporation in Taiwan. This company, with headquarters located in Taiwan's former capital, Tainan, was formally based on the concept "Beneficial to the Local Community." Starting with 82 employees and initial capital of about US$1 million, the company became not only a remarkable leader in Taiwan's food industry, but also globally based with annual revenues in billions of dollars. The company's top managers were very concerned with the issue of effectively allocating the firm's annual budget to the proposed strategic plans provided by the SBUs. Thus, the proposed integrated approach is used to assist the determination of strategic plans. The implementation procedure of the proposed integrated approach illustrated by using the case firm's data are shown in Figure 2. The implementation procedure contains 14 steps and involves an evaluation team. The evaluation team includes a group of the case firm's general managers, facilitators, members of a focus group, and the case firm's SBUs directors. Several researchers have previously discussed the role of a facilitator in the decision-making processes (Ngwenyama, Noel, & Ayodele, 1996). The functions of the facilitators in the implementation procedure include preparation and setup of the strategic selection, data-input and data collection, management of the group process, and promotion of effective task behaviors.

In Step 1, four SBUs and 11 strategic plans were selected by the group of the case firm's general managers. While SBU1 identified four alternative strategic plans, SBU2 identified two, SBU3 identified three, and SBU4 two. In addition, three general managers selected from the group of the case firm's general managers were invited to perform the evaluation. In Step 2, facilitators collected portfolio matrices from relative literatures as well as from other strategic planning cases, and consulted with the managers of different departments in the case company to solicit their opinions. In Step 3, facilitators conducted a focus group, which included 10 managers and 3 experts in strategic planning, to decide upon the portfolio matrix model and the corresponding evaluation constructs and factors. (In Table 2, we show the evaluation constructs and the factors used to evaluate the industry attractiveness and the business strength of SBUs.) Then, in Step 4, the three managers defined their linguistic variables and corresponding triangular fuzzy numbers. We show Manager 1's definition of linguistic variables and corresponding triangular fuzzy numbers in a graph in Figure 3.

In Step 5, the three managers used linguistic variables to evaluate the SBUs on internal and external factors, the strategic plans on feasibility factors, and these evaluation factors on their importance. In Step 6, the three managers decided upon the confidence levels. In step 7, because this was the first time they were using this approach, the three managers decided to simplify the arithmetical process of EFWA by using confidence level α = 0 to calculate the weighted scores of those criteria. As an example, we had Manager 1 evaluate Strategic Plan 2 submitted by SBU3 on the feasibility factors of customer relations, capabilities, and competencies. The evaluation results of the feasibility factors and their corresponding importance rates, presented in linguistic values, are medium/medium/very high and high/medium/medium, respectively. We replaced the linguistic values with triangular fuzzy numbers according to Manager 1's definition of linguistic variables and triangular fuzzy numbers. The computational procedure of EFWA for the example is shown in more detail in Example 1 of the Appendix. Accordingly, the interval for confidence level α = 0 is [3.818, 9.529] (α = 1 is 5.432). This represents the computational result of EFWA for Manager 1 evaluating Strategic Plan 2 submitted by SBU3 on the feasibility factors. The other computational results of EFWA for Manager 1 are shown in Table 3. We then repeated the computational procedure of EFWA for confidence level α = 0 to obtain the weighted score results of the other two managers.

In Step 8, the three managers decided the optimism levels that were used to transfer fuzzy numbers into crisp numbers in Step 9. In Step 10, facilitators used the average method to aggregate the evaluation results from the three managers. With the aggregation results of the weighted scores, the financial data collected from Steps 11 and 12, and the importance ratings of evaluation constructs obtained from Step 13, a corresponding ILP model was set up in Step 14. The ILP model maximizes 8r^sub 11^ + 6r^sub 12^ + 6r^sub 13^ + 7r^sub 14^ + 5r^sub 21^ + 6r^sub 22^ + 4r^sub 31^ + 5r^sub 32^ + 4r^sub 33^ + 7r^sub 41^ + 6r^sub 42^ and satisfies several constraints. Solving the ILP model using LINDO (Schrage, 1991), a commercial mathematical programming software, we obtained the optimal solution: r^sub 14^ = r^sub 22^ = r^sub 31^ = r^sub 42^ = 1, all other r^sub ij^' s = 0. The results imply that if SBU1 adopts its fourth strategic plan, SBU2 adopts its second strategic plan, SBU3 adopts its first strategic plan, and SBU4 adopts its second strategic plan, then the entire company can maximize its returns with acceptable cost resulting from implementing these strategic plans. The maximum profit that could thus be generated is estimated to be $30 million.

DISCUSSION AND ANALYSIS

In the above example, to simplify the arithmetical process of EFWA, the three managers decided to use confidence level α = 0 to calculate the weighted scores. However, it should be noted that the confidence levels of different managers toward a strategic plan may not be the same (Hsu & Chen, 1996). Thus, we asked the three managers to provide their own confidence levels in terms of SBUs, strategic plans, and the importance of evaluation factors (Table 4). We also take Manager 1 evaluating Strategic Plan 2 submitted by SBU3 on the feasibility factors as an example to show the computational procedure of EFWA by using different confidence levels (Example 2 of the Appendix). Accordingly, the interval for confidence level α = 0.5 is [5.073, 8.167] (α = 1 is 5.432). Then, we used the other two managers' confidence levels to recalculate the weighted score results. Consequently, different evaluation results were obtained. The optimal solution is r^sub 13^ = r^sub 22^ = r^sub 32^ = r^sub 42^ = 1, all other r'^sub ij^ s = 0 and the maximum profit is $28 million. Hence, the two evaluation results, the former obtained through using the same confidence level α = 0, and the latter obtained through using the three managers' own confidence levels (Table 4), are different. In practice, top managers will encounter plan selection situations in which they have different confidence levels in terms of SBUs, strategic plans, and the importance of evaluation factors. The proposed integrated approach containing EFWA can consider the diversity of confidence levels of managers instead of treating their confidence levels as equal when conducting evaluations.

After calculating the weighted sum of scores by using EFWA, we derived the results presented in triangular fuzzy numbers. The next step is to decide the optimism levels to use when we transfer the triangular fuzzy numbers into crisp numbers. The optimism level is an attitude a decision maker possesses regarding personal expectations of how things will proceed. The managerial meaning of optimism level has been mentioned above. Therefore, just like the role of the confidence level, the optimism level can be viewed as a factor expressing the diversity of the managers' attitudes toward the whole situation instead of seeing all of the managers' perspectives as equal. In this case, the three managers had the same medium optimism level. In addition, during the step of using integer linear programming to select the most suitable strategic plans, the different proportion of the values w^sub A^, w^sub I^, and w^sub F^ in the objective function will also affect the final selection results. The values w^sub A^, w^sub I^, and w^sub F^ presenting, respectively, the importance of constructs A, I, and F on the selection of strategic plans, will vary somewhat from industry to industry, or firm to firm, according to the evaluator's determination. In this case, the three managers assigned w^sub A^, w^sub I^, and w^sub F^ as .3, .3, and .4, respectively.

The top managers of the company were very pleased and totally agreed with our recommendations. Furthermore, by using the proposed integrated approach, they reduced the decision-making time for evaluation and selection of strategies from the normal two-month period to only 12 business days, a dramatic savings in time that the top managers had previously considered impossible. In addition, the top managers stated that the proposed integrated approach was a practical tool for selecting strategies, considering the uncertainty problem of decision makers in conducting evaluations, as well as the diversity of decision makers' confidence and optimism levels. Finally, the proposed integrated approach earned the confidence of top managers and will be implemented by the company to conduct its annual strategic planning in the future.

CONCLUSION

An interesting problem in group decision making is how to reach a higher degree of consensus existing among group members (Ray & Triantaphyllou, 1998). There are many researchers providing several approaches to solve this problem (Yeh, Lin, Kreng, & Gee, 1999; Juan Carlos & Eduardo, 2003; Shirland, Jesse, Thompson, & Iacovou, 2003). In the proposed example, the discrepancies among evaluators' results are not great. The reason could be that the three managers might have expected that their results would be investigated, which might have caused their conservative attitude on evaluation. Consequently, we can find that all of them tended to choose "medium" to present their preferences. In fact, we think this reason occurs in many real-world evaluation situations. An extension of the current approach could focus on measuring the discrepancies among evaluators' results as well as improving the consensus among group members. Furthermore, in the study, fuzzy set theory is applied to solve the uncertainty problem in the proposed decision makers' problem. Similar to fuzzy set theory, grey system theory is a mathematical means of resolving problems possessing uncertainty (Hsu & Wen, 2000; Wu & Chang, 2004). Fields covered by grey system theory contribute to dealing with prediction problems that are characterized by poor or insufficient information (Hsu & Chen, 2003; Lo & Lin, 2004). The proposed decision-making problem could be solved by extending or modifying the current grey system theory. However, fuzzy set theory has been recognized as a mature methodology with sound theoretical bases and has been used in many applications (Bozdag et al., 2003; Buyukozkan & Feyzioglu, 2004; Chiu et al., 2004). Therefore, fuzzy set theory is a suitable method applied in the current study.

Our research has emphasized several advantages of the proposed integrated approach. First, the proposed integrated approach is a complete procedure for managers using a strategy-oriented perspective to select strategic plans by appropriately considering the industry attractiveness and the business strength of SBUs, and the feasibility and the financial potential of strategic plans. Second, through the use of fuzzy set theory, this integrated approach helps to deal with the uncertainty problem of decision makers in conducting evaluations, thus providing a technique with the characteristic of presenting the diversity of confidence and optimism levels of decision makers facing different SBUs and strategic plans. Third, we also describe the process of selecting plans by means of an integer linear programming model, which appears to be an effective quantitative method for managers to select strategic plans. Fourth, this research can increase the practical value of the academic methods (portfolio matrix, 3Cs model, fuzzy set theory, and integer linear programming), which are applied and logically integrated in the proposed integrated approach. Fifth, the proposed integrated approach is supported by several sound theories which are appropriately introduced and presented in the research and described by using a clear and detailed implementation procedure for practical application. Although we adopted the GE matrix as the portfolio model in evaluating the strategic positions of the SBUs and 3Cs model in assessing the feasibility of strategic plans, our approach can also work with other evaluation measures. [Received: October 2003. Accepted: February 2005.]

* We thank two anonymous referees and the associate editor for their constructive comments, which led to noticeably improved exposition of the research.

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Chinho Lin[dagger]

Department of Industrial and Information Management and Institute of Information Management, National Cheng Kung University, Tainan, Taiwan, ROC, e-mail: linn@mail.ncku.edu.tw

Bertram Tan

Department of Business Administration, Kun Shan University, Tainan, Taiwan, ROC, e-mail: tanb@mail.ksut.edu.tw

Ping-Jung Hsieh

Department of Business Administration, National Huwei University of Science & Technology, Huwei, Taiwan, ROC, e-mail: pj901028@yahoo.com.tw

[dagger] Corresponding author.

Chinho Lin is a distinguished professor at the Department of Industrial and Information Management and Institute of Information Management, National Cheng Kung University, Taiwan (R.O.C.). He received his PhD in business administration (management planning systems) from the City University of New York. He has contributed articles to Decision Support Systems, Information & Management, Journal of the Operational Research Society, International Journal of Prodution Research, Computers & Operations Research, TQM, Expert Systems with Applications, and others. His research interests are focused on the interface of strategic management and decision support systems. Specific research areas include knowledge management, supply chain management, quality management, and technology management.

Bertram Tan is a professor and dean of the College of Commerce and Management at Kun Shan University in Taiwan. His current research interests include strategic management, supply chain management, and knowledge management.

Ping-Jung Hsieh is an assistant professor at the Department of Business Administration, National Huwei University of Science and Technology, Taiwan. She received her PhD in business administration from National Cheng Kung University in Taiwan, MHA in health service administration from the University of Southern California and BS in medical technology from National Yang Ming University in Taiwan. In addition to health service management, her current research interests focus on artificial intelligence methods for supporting decision-making processes.

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