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Andres Delgado. A short summary of this paper. Download Download PDF. Translate PDF. Decision Support Systems 38 — www. In order to decide which of the proposed projects should be retained in the final project portfolio, numerous conflicting criteria must be considered. They include economic, personnel development, and corporate image. Although there are many studies available to assist decision-makers in doing the process of portfolio selection, there are no integrated frameworks that one can use to systematically do the portfolio selection.
In addition, in most decision-making situations, decision-makers have to make decisions with incomplete information and under uncertain circumstances. These situations have been recognized by many researchers as a suitable field to use fuzzy set theory.
Therefore, based on the concepts of decision support system DSS , we developed an integrated framework that incorporates fuzzy theory into strategic portfolio selection. This framework provides managers with a flexible, expandable and interactive DSS to select projects for portfolio management. We used a real-world case to demonstrate the proposed approach. D Elsevier B.
All rights reserved. Keywords: Strategic portfolio; Fuzzy weighted average; Fuzzy integer linear programming; Decision support system 1. Introduction choices must be made in creating a suitable project portfolio [13]. In order to decide which of the The selection of a strategic portfolio, which proposed projects should be retained in the final requires the consideration of corporation goals, project portfolio, a number of conflicting criteria resources, and constraints, is an important and must be taken into account.
They include environ- challenging task. Usually, there are more projects mental advantages and disadvantages, tangible and available for selection than can be undertaken within intangible benefits, and risk level of the project the physical and financial constraints of a firm, so portfolio. Several studies have been proposed to help organizations make good project selection decisions.
In Tel. Lin, P. In addition, many decisions that consider a broad range of quantitative and qualita- have far-reaching effects on the organizational activ- tive characteristics, as well as multiple objectives. One problem The evaluation models found in present portfolio of group decision-making is that every member has selection methods are mainly numerical, e. The draw- This means that the situation where different deci- back of these studies is that decision makers generally sion-maker possesses different confidence level for have vague perceptions instead of clear knowledge the problem will occur.
Therefore, the field of stra- about the evaluation criteria and are unable to provide tegic management has been recognized as an appro- exact numbers. To overcome the problem, some prior priate field for the application of the fuzzy set theory, studies employed fuzzy theory to do the evaluation because of the fuzziness of the main concepts and [7,23,27,31].
Of these, Coffin and Taylor [7] and terms, and the contexts of strategic management Machacha and Bhattacharya [27] applied fuzzy logic belong to the area of uncertainty and vagueness [30]. The proposed tion of individual projects; and Rasmy [31] constructed approach takes advantage of the characteristics of a fuzzy expert system to solve the multiobjective linear some existing methods, which include portfolio ma- programming problem. These methods have sound theoretical bases must change his perspective from product-orientation and are commonly used because of their good or market-orientation to strategy-orientation when decision support characteristics.
In order to increase making project selection decisions. Existing studies the user acceptability, we use a computer-based generally concentrate on evaluating projects for their group decision support approach to project strategic functional level, e.
The process, from project portfolio. The conceptual framework that requires a structured evaluation procedure and experienced evaluators. However, in the evaluation Conceptually, our approach for project portfolio process, evaluators must confirm that all the infor- selection in the group decision support system is a mation available or needed is brought to bear on the three phase process: 1 pre-evaluation, 2 prefer- problem or issue at hand.
As previous cases indicated ence elicitation, and 3 data analysis and reporting. One of the most popular portfolio 4 deciding the type of the fuzzy integer linear matrices is the GE Multifactor Portfolio Matrix that programming model and the relative importance of developed jointly by General Electric and McKinsey coefficients.
The four activities are common to any and Company Fig. This tool helps managers group decision-making process, and are well dis- understand the competitive position of SBUs based cussed in the literature [12,21,22]. Industry attractiveness is a two activities: 1 collecting the individual confi- subjective assessment based on external factors, dence level, and the definition of the linguistic which is uncontrollable by the firm.
Business variables and the corresponding triangular fuzzy strength is a subjective assessment based on the numbers; and 2 deriving the scores of weighing critical success factors, which is largely controllable the criteria and rating the alternatives. The first by the firm. Each of these two dimensions is a activity is the basic preparation step for the utiliza- composite of various factors. In practice, the confidence levels of different managers toward one strategic plan 2.
The feasibility analysis of strategic plans might vary [20]. Sometimes there are experienced managers in a decision group, such as a project Besides considering the competitiveness of the manager who is familiar with the field of the business portfolio, managers also need to consider strategic plan, or some managers who have more whether the businesses have the capabilities and experience with evaluation than others, thus the resources that are necessary for the implementation final evaluation result is influenced by these man- of the strategic plan.
In addition, they must be sure agers with different confidence levels. The second that the plans will not threaten the attainment of activity of the preference elicitation phase is com- other organizational goals.
Therefore, for the pur- mon in group decision-making situations, which is pose of selecting the strategic plans submitted by generally supported by most DSS environments. The third phase, which is the calculation pro- cess, includes data analysis and reporting. This phase employs two algorithms, one is the fuzzy weighted average for identifying the competitive advantage of SBUs and the feasibility of strategic plans, and the other is the fuzzy integer linear programming for selecting the optimum strategic plans.
The portfolio matrix model During the s and early s, a number of leading consulting firms developed the concept of portfolio matrix to help managers better understand the competitive position of the overall portfolio of Fig. Industry attractiveness vs. To remedy tegic plan from the others. A linguistic variable is a future strategies and determine the feasibility of its variable whose values are not numbers but words or plans. Trust, integrity and reciprocity define the phrases in a natural or synthetic language.
Herein, customer relations. The basic definitions of the fuzzy set flexibility and acuity. Knowing how to do things theory, which are necessary for this paper, are pre- constitutes functional competencies, which are sented in Appendix A. Dong and Wong [10] competencies, and its capabilities.
Their computational algorithm is based on the business. Liou and Wang [26] suggested a modifi- 2. Fuzzy weighted average cation of the fuzzy weighted average method that was developed by Dong and Wong [10]. This The initial publication of fuzzy set theory was by modification provided similar computational results Zadeh [37].
Fuzzy set theory provides a strict but required less evaluation and computations. Lee mathematical framework in which vague conceptual and Park [25] proposed the efficient fuzzy weighted phenomena can be precisely and rigorously studied average EFWA for the computation of a fuzzy [38]. It can also be considered as a modeling weighted average, which improved on the previous language that is well suited for situations that works by reducing the number of comparisons and contains fuzzy relations, criteria and phenomena.
We adopt the EFWA algo- The portfolio matrix and 3Cs model have been rithm for the calculations in the current work [25]. However, as Liou and Wang [26]. Since human judg- Generally, there is a trade-off between investment ments and preferences are often vague and difficult cost and financial potential in selecting a strategic to be estimated with an exact numerical value, the plan; the less expensive projects will have lower main problem with the usage of the classical returns.
Decision-making prob- submitted by the ith SBU. In this study, we use the GE matrix to express the where z is the value function to be maximized; and aij, competitive position of SBUs, the 3Cs model to baR are real coefficients. Generally, a strategic plan with a higher 3. The decision support system score on the analysis of GE matrix, 3Cs model and financial potential will have more competitive ad- The portfolio selection prototype, an application vantage for high return and be more likely to be within the group work environment discussed here, selected for implementation.
Hence, by using the was developed using Visual Basic 6. The functional evaluation results of the GE matrix, 3Cs model and architecture of the application can be divided into four financial potential as the input data, we can con- modules, as illustrated in Fig. However, the optimal portfolio selection module, and 4 reporting evaluation process implemented in the proposed module. Therefore, we is to collect the off-line information for the subse- adopt the fuzzy integer linear programming FILP quent modules.
The information includes the alter- to do the selection of an optimal project portfolio natives for evaluation, the required implementation [18], see Appendix B.
In FILP classification time or cost and potential returns of alternatives, the [17,18], we find that there are either fuzzy numbers resources a firm can provide, the portfolio matrix and as coefficients in the objective function or fuzzy the corresponding evaluation criteria, and the fuzzy numbers defining the set of constraints.
In the integer linear programming model and the relative current work, we use the FILP with fuzzy numbers importance of coefficient. Several researchers have as coefficients in the objective function. The programming model used in the paper are defined major functions of the facilitator include the prepa- by: ration and setup of the strategic selection, the man- agement of the group process, and promotion of 8 effective task behaviors.
System application architecture. In addition, users can individual decision-maker to obtain an aggregate decide the type of portfolio matrix, how many criteria group result, 3 deriving the optimal portfolio through and the corresponding sub-criteria for evaluating the the utilization of the fuzzy integer linear program- alternatives.
The next flexibility advantage of our ming. Until the implemen- management module, the preference elicitation mod- tation of first function, the data files of the preference ule can offer the decision-makers a set of user-friendly elicitation module collect the evaluation data from interfaces. Each decision-maker inputs data by inter- individual decision-makers separately. There are two decision- performing the fuzzy integer linear programming. The first one is for collecting the fuzzy integer linear programming utilizes the aggre- individual confidence level, and defining the linguistic gate group data instead of separately individual data to variables and the corresponding triangular fuzzy conduct the arithmetic process.
Therefore, the purpose numbers. The other is for deriving the scores of of the second function is to apply an averaging method weighing the criteria and rating the alternatives. All to aggregate the weighted scores that are from indi- of the data are loaded into the data file of the vidual decision-makers to become an aggregate group preference elicitation module. After every decision- result. Furthermore, we collected the important managing the report generation and distribution pro- factors from several strategic planning cases, and cess.
The reporting module provides several types of consulted with different departmental managers for results, which include scatter plot and table format.
This step can help the managers to Due to the difficulties of plotting fuzzy numbers on identify the relevant internal and external factors of graphs, the facilitator needs to select a method [aver- positioning the SBUs, as well as the feasibility factors age, optimistic, pessimistic, median] see Appendix of the strategic plans. We then conducted a focus group A to transfer fuzzy numbers into crisp numbers that included 10 top managers and 3 experts in the field before positioning SBUs and strategic plans on the of strategic planning to decide two major things.
The graphs. However, the information that decision-mak- first set of actions is to select the following factors: 1 ers obtained from scatter plot is displayed in crisp the internal factors to assess the business strength of numbers that were transferred from fuzzy numbers.
With the fuzzy numbers tencies. The second set of actions is to choose the type of the fuzzy integer linear programming model, and the relative importance of coefficients in the objective 4. A case illustration function. The fuzzy integer linear programming model that was decided by the focus group is as follows. In order to evaluate the applicability of the pro- Three basic assumptions are stated as follows: posed approach, we implemented it in a strategic planning project for a food corporation in Taiwan.
The follow- 2. All strategic plans are independent of one another. Each SBU can only implement one strategic plan Fig. Phase I: pre-evaluation The fuzzy integer linear programming model pro- posed includes the following notations: The firm runs four SBUs.
The first SBU 1 identified four alternative strategic plans, the second rij Unity if the jth strategic plan is implemented SBU 2 identified two, the third SBU 3 prepared at the ith SBU; otherwise it is 0 three, and the fourth SBU 4 submitted two alternative Pij Anticipated profit resulted from implement- strategic plans.
Flow chart of the proposed procedure. It includes Marketing procurement, Competitive barriers to the scores of industry attractiveness, competitive ad- brand loyalty, factors exit, barriers business image to entry, vantage, feasibility and financial potential.
The weight wij is a ratio patents factors legislation, taxation that is equal to the potential profit of the plan divided Management management Social factors ecological by total potential profit of whole proposed plans. It is competence, impacts, designed to present the level of financial potential of a planning and consumer specific strategic plan to maximize returns, compared control systems, protection, to the plans proposed overall.
A strategic plan with a financial strength degree of unionization higher financial potential will have a higher weight, which leads to a higher score in the objective function. Constraint Eqs. Meanwhile, constraint Eq. Finally, constraint The fuzzy integer linear programming model can Eq. Phase III: data analysis and reporting Membership functions for linguistic values Linguistic Fuzzy numbers In this phase, the facilitator performed three values Manager 1 Manager 2 Manager 3 actions: 1 checking to make sure that all participat- Very low 0,0,3 0,0,1 0,0,2 ing decision-makers had finished Phase II; 2 run- Low 0,3,5 0,1,5 0,2,5 ning the optimal portfolio selection module that Medium 3,5,9 1,5,9 2,5,8 encompasses two major algorithm-fuzzy weighted High 5,9,10 5,9,10 5,8,10 average and fuzzy integer linear programming; 3 Very high 9,10,10 9,10,10 8,10,10 defining the format of report graph or table , which was generated at the end of Phase III.
In Figs. Phase II: preference elicitation scatter plot format. Also the initial budget of investment is million Rials.
Running the Model: Since it is difficult to find the optimal solution of the proposed model [42] in traditional ways, we use linear and nonlinear hybrid approximation methods simultaneously. We can use the technique of simulation [43] and genetic algorithm [44] based on fuzzy non linear integer simulation to help find the optimal solution with hybrid algorithm.
When fuzzy simulation is integrated into GA, the algorithm will take a fairly long WorldAppl. Li, U. In order to lessen the computational work, we employ neural networks NNs. NNs are famous for approximating any nonlinear continuous functions over a closed bounded set [20]. In order to neural network modeling, we use one input layer, one hidden layer and two neurons as output layer.
In this research, one training data set for objective function employed and for training theses data, back propagation algorithm investigated. And also, logistic sigmoid function used in hidden layer. Expected values and chances were calculated by them. The probability of crossover and probability of mutation are. Step 2: Train a neural network to approximate the objective function according to the generated training input-output data.
Step 3: Initialize pop size chromosomes whose feasibility may be checked by the trained neural network. Step 4: Update the chromosomes by crossover and mutation operations. Table 2: Comparisons of object values by hybrid intelligent system Population size Crossover function f 20 0. Step 7: Select the chromosomes by spinning the roulette wheel according to the different fitness values. Step 8: Repeat the fourth to seventh steps for a given number of cycles.
Step 9: Report the best chromosome as the optimal solution of portfolio selection problem. This paper considered a fuzzy mixed portfolio selection with fuzzy return and linear and integer constraints to set output as integer values WorldAppl.
Fuzzy set theory is applied to model uncertain and flexible information. To solving mixed fuzzy model, a hybrid intelligent algorithm is provided to estimate objective function with combinational constraints that used fuzzy linear integer programming to selection stocks. An example was given to illustrate the proposed fuzzy integer portfolio selection using real data from Tehran Stock Exchange results were showed the high fitness of model. Gupta, P. Saxena, Asset portfolio optimization using fuzzy mathematical programming.
Information Sci. Markowitz, H. Portfolio selection, Journal of Finance, 7: Campbell, J. Kinlay, Elton, E. Jorion, P. Portfolio optimization in practice, Financial Analysis J. Carlsson, C. Fuller, Onpossibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, Lintner, B.
Valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, Mossin, J. Equilibrium in capital asset markets, Econometnca, 34 4 : Sharpe, W. Capital asset prices: a theory of market equivalent under conditions of risk, J.
Finance, 19 3 : Luenberger, D. Bawa, V. Lindenberg, Capital market equilibrium in a mean-lower partial moment framework, J. Financial Economics, 5: Hasuike, T.
Katagin and H. Ishn, Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets and Systems, Watada, J. Fuzzy portfolio selection and its applications to decision making, Tatra Mountains Mathematical Publications, Aouni, B. Ben Abdelaziz, J. Martel, Decision-maker's preferences modeling in the stochastic goal programming, European J. Operational Res. Kumar, P. Ezzell, Goal programming and the selection of portfolios by dual-purpose funds, The J. Finance, Lee, S. Chesser, Goal programming for portfolio selection, The J.
Portfolio Manage. Abdelaziz, F. Lang and R. Nadeau, Efficiency in multiple criteria under uncertainty, Theory and Decision, Mejri, Application of goal programming in a multi-objective reservoir operation model in Tunisia, European J. Ziemba, W. Mulvey, Inuiguchi, M. Ramik, Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems, Leon, R. Liern andE. Vercher, Validity of infeasible portfolio selection problems: fuzzy approach, European J.
Tanaka, H. Guo andl. Turksen, Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Sets and Systems, Vercher, E. Segura, Fuzzy portfolio optimization under downside risk measures, Fuzzy Sets and Systems, Lacagnina, V. Pecorella, A stochastic soft constraints fuzzy model for a portfolio selection problem, Fuzzy Sets and Systems, Huang, X.
Two new models for portfolio selection with stochastic returns taking fuzzy information, European J. Ammar, E. On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem, Information Sciences, Available Online 4 April. Guo, Portfolio selection based on upper and lower exponential possibility distributions, European J.
Lin, C. Hsieh, A fuzzy decision support system for strategic portfolio management, Decision Support Systems, Ehrgott, M. Schwehm,
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