The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independ...
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The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independently on each right-hand-side or objective coefficient without affecting the optimality of the given basis. Some extensions have been proposed in the literature, which allow for individual tolerances for each coefficient, thus enlarging the tolerance region. In this paper we review the main results concerning the approach, giving new and simpler proofs, and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion. We compare our method with the existing ones on two examples, showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances. (c) 2004 Elsevier B.V. All rights reserved.
In this paper we present a pivotal-based algorithm for the global minimization of composite concave quadratic functions subject to linear constraints. It is shown that certain subclasses of this family yield easy-to-s...
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In this paper we present a pivotal-based algorithm for the global minimization of composite concave quadratic functions subject to linear constraints. It is shown that certain subclasses of this family yield easy-to-solve line search subproblems. Since the proposed algorithm is equivalent in efficiency to a standard parametric complementary pivoting procedure, the implication is that conventional parametric quadratic programming algorithms can now be used as tools for the solution of much wider class of complex global optimization problems. (C) 1998 Elsevier Science B.V. All rights reserved.
In this paper, the problem of solving multiparametric 0-1 mixed-integer linear programming models is considered. A novel Branch and Bound algorithm is described based on successive solutions of parametric linear progr...
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In this paper, the problem of solving multiparametric 0-1 mixed-integer linear programming models is considered. A novel Branch and Bound algorithm is described based on successive solutions of parametric linear programs where n right-hand side parameters are allowed to vary independently. Numerical examples are presented to illustrate the basic steps and the potential of the proposed procedure. (C) 1999 Elsevier Science B.V. All rights reserved.
Ln this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the m...
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Ln this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kuno et al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]-[8] and its techniques.
In the present paper, a novel solution approach is proposed for a class of fuzzy programming models. In this direction, we prove that the lower and upper bounds of their fuzzy optimal objective values at a possibility...
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In the present paper, a novel solution approach is proposed for a class of fuzzy programming models. In this direction, we prove that the lower and upper bounds of their fuzzy optimal objective values at a possibility level, a 2 0;1 , can be calculated solving a pair of crisp mathematical programming models. Thus, their membership functions are simulated enumerating the upper and lower bounds obtained from a series of a-level calculations. Motivated from real-world project scheduling applications, several numerical examples are considered to evaluate the accuracy, efficiency and applicability of our treatment. The results derived are compared with those of Chen and Tsai (Eur J Oper Res 212(2): 386-397, 2011) to demonstrate that our method is easier to be utilized, with lower computational complexity, nonetheless without losing its effectiveness. Finally, the new approach does not suffer from the limitation to be applicable only to linear programming models that makes it suitable for a wider range of models and applications.
The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the objective function is a family of 0-1-ILP problems in which the problems are related by having identical constraint matrix and right...
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The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the objective function is a family of 0-1-ILP problems in which the problems are related by having identical constraint matrix and right-hand side vector. In this paper we present an algorithm to perform a complete multiparametric analysis. (C) 2000 Elsevier Science B.V. All rights reserved.
In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solvi...
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In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solving (FMOINLP) problems by using the compromise weights from the pay-off table of membership function for each objective function is presented. (c) 2005 Elsevier Inc. All rights reserved.
For the problemP(λ): Maximizec T z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives at every point \(\ba...
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For the problemP(λ): Maximizec T z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives at every point \(\bar \lambda \)such thatP( \(\bar \lambda \) ) and its dual are both superconsistent. To compute these directional derivatives a min-max-formula, well-known in convex programming, is derived. In addition, it is shown that derivatives can be obtained more easily by a limit-process using only convergent selections of solutions ofP(λ n ), λ n → \(\bar \lambda \)and their duals.
In this paper, we study multiparametric sensitivity analysis for programming problems with linear-plus-linear fractional objective function using the concept or maximum volume in the tolerance region. We construct cri...
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In this paper, we study multiparametric sensitivity analysis for programming problems with linear-plus-linear fractional objective function using the concept or maximum volume in the tolerance region. We construct critical regions for simultaneous and independent perturbations of one row or one column of the constraint matrix in the given problem. Necessary and sufficient conditions are given to classify perturbations parameters as 'focal' and 'nonfocal'. Nonfocal parameters can have Unlimited variations, because of their low sensitivity in practice, these parameters can be deleted from the analysis. For focal parameters, a maximum volume tolerance region is characterized. Theoretical results are illustrated with the help of a numerical example. (c) 2005 Elsevier Inc. All rights reserved.
This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fracti...
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This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the alpha -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the alpha -cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration. (C) 2001 Elsevier Science BY. All rights reserved.
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