Stackelberg solutions have been derived for two-level linear programming problems using genetic algorithms which in recent years have shown their efficacy in optimization problems having discrete variables. two-level ...
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Stackelberg solutions have been derived for two-level linear programming problems using genetic algorithms which in recent years have shown their efficacy in optimization problems having discrete variables. two-level linear programming problems are converted into single-levelprogrammingproblems by including the optimal conditions of lower-levelproblems in the conditions of higher-levelproblems. The obtained one-levelprogrammingproblems become 0-1 mixed programmingproblems. A computational method for obtaining Stackelberg solutions by generating initial population and using corresponding genetic opera tors based on the characteristics of the problems by expressing the 0-1 variables as individuals of the genetic algorithms is proposed. The efficacy of the proposed method is shown in computational experiments by comparing it with the variable elimination method. (C) 2002 Scripta Technica.
In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-levellinear prog...
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In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, alpha-level sets of fuzzy random variables are introduced and an alpha-stochastic two-levellinearprogramming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the alpha-stochastic two-levellinearprogramming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization, the transformed stochastic two-levelprogramming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. (C) 2012 Elsevier Ltd. All rights reserved.
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