One of the goals of the university is to achieve the maximum values of the competencies of the graduated specialists, which ensures their success in work, increases the competitiveness of the university, and contributes to the influx of more trained applicants. Ultimately, this indicator characterizes the maximum performance of the university in terms of impact on the national economy. The task of optimal construction of the educational process is the task of optimal management of the resources of the university and the student (university resources: labor, time, financial, computing, territorial, informational, etc.; student resources: labor, financial, time, etc.) – the search for an option that provides the maximum of the indicator that evaluates the result. As for the criteria of optimality, The authors believe that it is possible to accept the competencies of the graduates as a criterion to assess the outcome of their training. Then the research task is formulated as achieving the maximum of competencies in conditions of limited available resources. Graduate’s competencies are a consequence of the level of study of academic disciplines, which, in turn, depends on the resources invested. In this formulation of the problem, we do not touch upon the issue of individual abilities and focus on the maximum result for each of the students within the framework of their abilities. This approach is focused not on a specific student, but on the creation of preferable conditions of the educational process, passing through which, the students achieve the maximum mastery of the system of competencies. The formulation of the problem of optimal resource allocation permits several options: a static model (one time interval); a system of hierarchical models (consideration of competencies by levels of detail); taking into account the duration of the impact of resources (dividing resources into capital and one-time); dynamic model (covering the entire training period); optimization of the structure of the curriculum (optimization of the time resource); the relationship between the competencies of the personnel and the performance of the enterprise. The article presents a system of mathematical models for optimizing the allocation of university resources when organizing the educational process. The relationship between the competencies of the personnel and the performance of the enterprise has been analyzed. The issues of interaction between universities and the real sector of the economy through the formation of the competencies of a university graduate are considered.