SOLUTION OF A MULTICRITERIA ASSIGNMENT PROBLEM USING A CATEGORICAL EFFICIENCY CRITERION

Context. The paper considers a problem of assigning a set of employees to a finite set of operations in a multicriteria statement, under condition of a hierarchical structure of a partial efficiency criterion of performing a set of operations, being presented in such a way that each employee possesses a finite set of competencies and each operation has a finite set of characteristics. Numerical and categorical data types are provided for the use as exogenous parameters of the problem. The relevance of the assignment problem being considered is determined by an extremely wide range of practical applications, both in the classical statements and new modifications, the high demand for which is constantly generated by the dynamically developing economic environment. At the same time, a critically smaller number of scientific publications propose means of modeling and solving multi-criteria assignment problems, despite the importance of this type of problems in decision-making, both in theoretical and practical aspects. In general, in conditions of lack of information, the exogenous parameters of the problem cannot be specified in numerical form, therefore there is a need to use categorical data with further numerical coding. Objective. The goal of the work is to build a multicriteria mathematical model and, on this basis, carry out a numerical study of the optimization assignment problem, taking into account a hierarchical structure of a partial efficiency criterion of the selection of «operation – employee» pairs. Method. The study proposes a novel method of solving the assignment problem that implemented as a multi-stage process, which includes the stage of transformation of exogenous parameters of the model, given by categorical variables, based on the implementation of the Pareto principle and logistic mapping, the stage of constructing linear scalarization of the efficiency and the cost criteria.