The method for solving the multi-criteria linear-fractional optimization problem in integers

Abstract

In the papers we propose a method for solving the linear-fractional multi-criteria optimization model with identical denominators in whole numbers. Such models are in increasing demand, especially from an application point of view. The solving procedure of these models initially involves assigning utilities (weights) to each criterion [15] and building the optimization model with a single criterion, which is a synthetic function of all criteria weighted. It was found that the optimal solution of the model does not depend on the values optimum of the criteria obtained in R+ or in Z+. So, the decision maker can combinatorially select the types of optimal values of criteria, a fact that represents the essential priority of the algorithm. By changing the utility values, at the decision maker's discretion, we will obtain a new optimal compromise solution of the model. Theoretical justification of the algorithm as well as a solved example are brought to work.