SUMMARY
The subject matter of the article is mathematical models for solving particular problems of sorting out candidates for a project team. The aim is to create a region of compromises for a variety of particular criteria for selecting candidates and to develop an integral optimization function as a utility function for selecting preferred alternatives. The tasks are: developing the approximate area of compromises for solving single-criterion optimization problems; selecting the utility function of partial criteria; using general principles of utility theory application for solving personnel problems; sorting out the best option on the ground of multi-criteria evaluation and optimization methods; defining the degree of particular criteria importance; analyzing the peculiarities of multi-criteria assessment of problems in human resource management. The methods used are: multi-criteria assessment and optimization methods, utility function. The following results are obtained. The problem of estimating the relative importance of particular criteria in the utility function is considered. The procedure of determining the approximate region of compromises is described with account of a number of personal and psychological characteristics by successive solving single-criterion optimization problems for each particular criterion. The problem of developing the integral multi-criteria function for selecting preferred alternatives is considered. The peculiarities of using general principles of utility theory for personnel problems solving are analyzed. The function of multi-criteria optimization as a utility model for partial criteria is formulated. The general task of assessing and producing labour force with account of professional, personal and psychological properties of a candidate is formulated. Conclusions. The task of building a project team is considered in the article. The stages of team building are considered. The procedure for determining the approximate region of compromises is described with account of a number of personal and psychological characteristics by successive solving single-criterion optimization problems for each particular criterion. The function of multi-criteria optimization is formulated as a utility model for partial criteria. The method for selecting and evaluating personnel for planned projects is suggested on the basis of the procedure for sorting out candidates for a new project team from the workers who were previously involved in similar projects.