We consider the parametric Uncapacitated Facility Location Problem (UFLP) where the demand of each customer is allowed to vary over a certain interval. Despite the value of parametric analysis, no such efforts are fou...
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We consider the parametric Uncapacitated Facility Location Problem (UFLP) where the demand of each customer is allowed to vary over a certain interval. Despite the value of parametric analysis, no such efforts are found for the UFLP, that mainly seems to be due to the fact that parametric analysis usually requires the computation of a number of UFLP's with heavy computational burden. In this paper, we will show that the special structure of the UFLP provides a nice property for its parametric version, based on which an efficient branch and bound procedure for the parametric analysis is developed.
This paper deals with parametric knapsack problems where the costs resp. weights are replaced by linear functions depending on a parameter t. The aim is to find the smallest parameter t* such that the optimal solution...
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This paper deals with parametric knapsack problems where the costs resp. weights are replaced by linear functions depending on a parameter t. The aim is to find the smallest parameter t* such that the optimal solution value of the knapsack problem is equal to a prespecified solution value. For this inverse-parametric problem pseudopolynomial algorithms are developed and search methods making use of the special properties of the parametric value function are constructed. Using computational experiments the behaviour of these algorithms is investigated and the favourable practical performance of different search methods is exhibited.
In many decentralized organizations, resource planning with sequential decision making can be formulated as a multi-level programming problem. In such cases, the decision variables are partitioned among the decision m...
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In many decentralized organizations, resource planning with sequential decision making can be formulated as a multi-level programming problem. In such cases, the decision variables are partitioned among the decision makers. Each of the decision makers optimizes his/her own objective function. This paper presents an algorithm using parametric analysis to solve a typical kind of nonlinear integer multilevel programming problems, called separable integer monotone bilevel programming (SIMBP), and then extends the algorithm for solving a parametric SIMBP problem. A numerical example with application of reliability optimization is given to illustrate the solution method.
For the study of mathematical programming problems and solution methods the duality theory forms a powerful tool. There are also some concepts of regularization and stabilization of a given problem for a better behavi...
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For the study of mathematical programming problems and solution methods the duality theory forms a powerful tool. There are also some concepts of regularization and stabilization of a given problem for a better behavior in practical solution procedures. The aim of this paper is the investigation of duality aspects of such regularizations and the forming of hullfunctions on the other hand. Applications for handling of so-called ill-posed problems (Eremin) using some parametrizations of the original problem will emphasize the importance for practical numerical methods, especially. This results will inspire some applications to solution methods for parametric and multicriteria optimization.
In this paper, we use a robust policy concept that is an extension to nonlinear systems of the mean-variance approach for linear models. In the linear case, the approach reduces to the minimization of a convex combina...
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In this paper, we use a robust policy concept that is an extension to nonlinear systems of the mean-variance approach for linear models. In the linear case, the approach reduces to the minimization of a convex combination of the mean and variance of the stochastic problem. We also discuss a method for computing expectations of nonlinear systems based on evaluating the bias from certainty equivalence using Monte Carlo simulations. The method computes robust strategies. If desired, these can be in the form of simple decision rules, as aggregate parametrisations of full feedback strategies. The parameters are determined to minimize a convex combination of the original objective function and a sensitivity (variance) expression. The latter can either be chosen as the sensitivity (variance) of the original objective function or the sensitivity (variance) of the individual endogenous variables.
This paper investigates local behavior of optimal solutions of parametrized optimization problems with cone constraints in Banach spaces. The corresponding first-order optimality conditions are formulated in a form of...
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This paper investigates local behavior of optimal solutions of parametrized optimization problems with cone constraints in Banach spaces. The corresponding first-order optimality conditions are formulated in a form of generalized equations (variational inequalities) and solutions of these generalized equations are studied. It is shown that under certain second-order sufficient optimality conditions and a regularity assumption related to the associated Lagrange multipliers, the considered optimal solutions are Lipschitzian stable. This is compared with a similar result in Shapiro and Bonnans [SIAM J. Control Optim., 30 (1992), pp. 1409-1422]. Under the additional assumption of uniqueness of the Lagrange multipliers, first-order expansions of the optimal solutions are given in terms of solutions of auxiliary optimization problems. Finally, as an example, semi-infinite programming problems are discussed.
A parametric program may use rules and algorithms to define the relationships between dimensions and elements of designs, and it may thus generate variants of a design. Programs currently in use have technical limitat...
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A parametric program may use rules and algorithms to define the relationships between dimensions and elements of designs, and it may thus generate variants of a design. Programs currently in use have technical limitations in their ability to handle time-varying and imprecise data, the search for suitable existing designs and their maintain-ability. The paper suggests how these and other limitations can be overcome to widen the field of application of parametric programs.
parametric analysis in linear fractional programming is significantly more complicated in case of an unbounded feasible region. We propose procedures which are based on a modified version of Martos' algorithm or a...
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parametric analysis in linear fractional programming is significantly more complicated in case of an unbounded feasible region. We propose procedures which are based on a modified version of Martos' algorithm or a modification of Charnes-Cooper's algorithm, applying each to problems where either the objective function or the right-hand side is parametrized.
This study intends to propose an alternative approach to the multi-parametric sensitivity analysis of a linear programming problem by the concept of a maximum volume in the tolerance region. For the purposes of manage...
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This study intends to propose an alternative approach to the multi-parametric sensitivity analysis of a linear programming problem by the concept of a maximum volume in the tolerance region. For the purposes of management and control, the study first proposes the necessary and sufficient conditions of the focal parameters. Then, those nonfocal parameters that have unlimited variations can be identified and thus because of their low sensitivity in practice and simplicity in analysis, they will be deleted. For those focal parameters, their different levels of sensitivity are investigated and conceived by the proposed Maximum Volume Region so that they can be handled with the greatest flexibility, simultaneously and independently. This Maximum Volume Region is bounded by a symmetrically rectangular parallelepiped. It can be characterized by a maximization problem and solved by the existing technique - Dynamic programming. Besides, an extension to the Extended Maximum Volume Region for the case of semi-bounded region is considered. Theoretical proofs are provided with numerical illustrations. The result has been compared to Wendell's approach.
The purpose of this paper is to discuss the various pivot rules of the simplex method and its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland....
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