Vector optimization in the system optimal
Decision-making in economic and technical
systems

Yu. K. Mashunin

Abstract The purpose of work to give theoretical justification and to formulate methods of the solution of the vector problems of mathematical programming (VPMP) at equivalent criteria. Methods of the solution of VPMP are based on normalization of criteria and the principle of the guaranteed result. Methods of vector optimization are intended for system adoption of optimal solutions, first, for modeling and adoption of optimal solutions in economic systems, and, secondly, for modeling and adoption of optimal solutions in technical systems in the conditions of definiteness and uncertainty. When modeling economic systems there is a problem of the choice of the optimum choice of goods at which their production is estimated by system of economic indicators. The model of economic system is presented by a vector problem of linear programming. The model of technical system is created as a nonlinear vector problem of mathematical programming. Criteria (characteristics) are formed in the conditions of definiteness (functional dependence of each characteristic and restrictions on parameters is known) and in the conditions of uncertainty (there is no sufficient information on functional dependence of each characteristic on parameters). Numerical implementation of methods of the solution of problems of vector optimization is shown: in economic sciences on an example with a vector problem of linear programming with three criteria; in technical science it is shown on a numerical example of a vector problem of nonlinear programming with five criteria (characteristics). Both tasks are realized in the Matlab system. Keywords: The Vector optimization, Economic systems, Technical systems, System optimum decision-making

Title:	Vector optimization in the system optimal Decision-making in economic and technical systems
Author Name:	Yu. K. Mashunin
Abstract:	Abstract The purpose of work to give theoretical justification and to formulate methods of the solution of the vector problems of mathematical programming (VPMP) at equivalent criteria. Methods of the solution of VPMP are based on normalization of criteria and the principle of the guaranteed result. Methods of vector optimization are intended for system adoption of optimal solutions, first, for modeling and adoption of optimal solutions in economic systems, and, secondly, for modeling and adoption of optimal solutions in technical systems in the conditions of definiteness and uncertainty. When modeling economic systems there is a problem of the choice of the optimum choice of goods at which their production is estimated by system of economic indicators. The model of economic system is presented by a vector problem of linear programming. The model of technical system is created as a nonlinear vector problem of mathematical programming. Criteria (characteristics) are formed in the conditions of definiteness (functional dependence of each characteristic and restrictions on parameters is known) and in the conditions of uncertainty (there is no sufficient information on functional dependence of each characteristic on parameters). Numerical implementation of methods of the solution of problems of vector optimization is shown: in economic sciences on an example with a vector problem of linear programming with three criteria; in technical science it is shown on a numerical example of a vector problem of nonlinear programming with five criteria (characteristics). Both tasks are realized in the Matlab system. Keywords: The Vector optimization, Economic systems, Technical systems, System optimum decision-making
Cite this article:	Yu. K. Mashunin , " Vector optimization in the system optimal Decision-making in economic and technical systems " , International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Volume 6, Issue 1, January - February 2017 , pp. 042-057 , ISSN 2278-6856.
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