In this paper, considering the two-level linear programming problem, which is a numerical model for the optimization of a hierarchical system by two decisionmakers, we focus on the situation where the coefficients are...
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In this paper, considering the two-level linear programming problem, which is a numerical model for the optimization of a hierarchical system by two decisionmakers, we focus on the situation where the coefficients are stochastic variables and reduce the formulated two-level stochastic linear programming problem to an ordinary two-level programming problem based on the probability maximization model in chance-constrained programming. Based on the assumption that motivation exists for cooperation between the high-level decisionmaker and the low-level decisionmaker in this resulting two-level programming problem, we consider interactive fuzzy programming that interactively derives a satisfactory solution of the high-level decisionmaker while considering the balance with the degree of satisfaction of the low-level decisionmaker. (c) 2005 Wiley Periodicals, Inc.
As an approach to the optimization of systems containing fuzziness and uncertainty, the probabilistic programming method including uncertainty based on probability theory and the fuzzy mathematical programming method ...
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As an approach to the optimization of systems containing fuzziness and uncertainty, the probabilistic programming method including uncertainty based on probability theory and the fuzzy mathematical programming method representing fuzziness in terms of fuzzy theory are typical ones that have been developed in various forms. In the present research, we target multiobjective linear programming problems in which the coefficients included in the program are random variables. We develop a formulation based on the probabilistic maximizationmodel in which the probability that several objective functions are below certain values is maximized under the stochastic constraint condition that the constraints need not be satisfied all the time but only above a certain probability. For the multiobjective probability maximization model, the fuzzy target of the decision maker is introduced. Also, an interactive algorithm based on the reference point method that derives a solution satisfactory to the decision maker by interaction with the decision maker is applied. The new decision making process is a combination of the probabilistic programming method and the fuzzy programming method. (C) 2003 Wiley Periodicals, Inc.
This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to co...
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This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.
This paper considers product mix problems including randomness of future returns, ambiguity of coefficients and flexibility of upper value with respect to each constraint such as budget, human resource, time and sever...
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This paper considers product mix problems including randomness of future returns, ambiguity of coefficients and flexibility of upper value with respect to each constraint such as budget, human resource, time and several costs. Particularly, the flexibility is assumed to be a fuzzy goal. Then, several models based on maximizing total future profits under a level of satisfaction to each fuzzy goal are proposed. Furthermore, the model considering preference ranking to each fuzzy goal of constraints is proposed. Since these problems are basically formulated as nonlinear programming problems, the transformations into deterministic equivalent problems are introduced and the efficient solution methods are developed. A numerical example for product mix problem is given to illustrate our proposed models. (C) 2008 Elsevier Ltd. All rights reserved.
This paper considers multiobjective linear programming problems with fuzzy random variables coefficients. A new decision making model is proposed to maximize both possibility and probability, which is based on possibi...
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This paper considers multiobjective linear programming problems with fuzzy random variables coefficients. A new decision making model is proposed to maximize both possibility and probability, which is based on possibilistic programming and stochastic programming. An interactive algorithm is constructed to obtain a satisficing solution satisfying at least weak Pareto optimality. (c) 2007 Elsevier B.V. All rights reserved.
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