Dual prices and objective harmonization of multicriteria programming models

Abstract

Investigations in this paper are connected to quantitative determination of additional indices related to the solution of multi objective programming models that might be useful for practical implementation. When preparing and making decisions, one can not surpass the idea of multiple objectives, i.e. very often it is not enough only to define one specific decision but there is a need for preparing alternatives along with additional indices, especially in case of coefficients being variable and uncertain. In this paper two techniques of generating of additional indices of multi objective programming models are given. First, the intervals of validity of dual prices considered necessary for economic analysis are given. Second, the formulation of the system of dual prices is presented. Investigation of system of dual prices and their intervals of validity is required whenever the amount of a resource is not exactly given or there are alternative resources. These results are of special interest in case of multi objective programming, i.e. for a given goal for every interval of validity of system of dual prices another basis is relevant, and for every basis dual prices are to be determined for all the other given objective functions. By investigating and comparing basic solutions, it is possible to find a solution that would be optimal for the system of objective functions as a whole. It is known that solutions of multi objective program contain some degree of subjectivity of decision makers. This can be reduced by formulating a system of dual prices along with their intervals of validity, which would be the basis for determining of the target values for goal programming models. So, the necessary information feedback between target values determination and optimal solution is obtained. Based on methods developed for single criteria models a method of analysis and coordination of coefficients of objective functions of multicriteria models is presented. A proposal is given in the sense of coordination of values in the case of models with preferential goals. A modification of input coefficients of higher order objective function is needed to produce alternative solutions while it is important to observe the structure of those alternatives. With objective functions of lower order, the appropriate modifications of coefficients of basic variables are needed.