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Algorithms and mathematical models that help predict, on the basis of macroeconomic analysis, the needs of regional economies for professionals with higher, secondary, and basic vocational education and form the enrolment plans of educational establishments on the basis of these needs are considered. The model is based on the matrices of profession-qualification matches; it uses job rotation coefficients and average annual employment data by industry and by education level. The methodology of predicting the needs for vocational education graduates is standardized for all the constituent entities of the Russian Federation.

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162Forecasting student admissions, student body, and graduations at institutions of vocational education is a vital task. Graduates of the vocational education sys tem represent a major source of labor resources for the job market, and their quantitative forecast assessment is fundamental for the calculation of the prospective workforce balance. Furthermore, graduates of the vocational education system largely contribute to admissions at other levels of vocational education, which has to be taken into account in their assessment. For example, graduates of primary vocational educa tion (PVE) institutions of the current year and previ ous periods represent 8% of admissions to secondary vocational education (SVE) institutions, and SVE graduates account for 28% of admissions to higher vocational education (HVE) institutions. Thus, a proper assessment of admissions requires the calcula tion of graduations from the institutions of the voca tional education system.Forecasting student numbers allows one to make long term assessments of public funding required for education; since 2011, it is calculated per capita for institutions of HVE.Concept model. Earlier developed models [1-3] considered the numbers of graduates from institutions of vocational education as a linear function of students who were admitted late. Meanwhile, it was assumed that the duration of study for all students admitted to educa tional institutions was the same, irrespective of the mode and area of study. This period was two years for PVE, four years for SVE, and five years for HVE. This approach only relied on admission and graduation data, which made it easy for use but complicated exact assessments of student numbers. For example, in [4], there was intro duced a model describing admissions to institutions of higher vocational education, based on school graduate numbers in the current and previous years. This model did not take into account graduations from and admis sions to PVE and SVE institutions. Admissions to SVE and HVE largely depended on the 11th grade graduations in the preceding years (in 2010, the respective share amounted to 15.7% for admissions to HVE and 14.2% for SVE).In [5], it is suggested to assess the numbers of cur rent year applicants with secondary (full) general edu cation obtained in the previous years on the basis of data on 11th graders, who were not admitted to voca tional education institutions during the graduation year. These data were collected for the three preceding years. However, this model did not provide any quan titative estimates to prove its relevance. The experi mental testing of the model did not bring any accept able results.Analyzing changes in student numbers of voca tional education institutions by years and courses lie at the core of the developed model. In this case, the stu dent numbers in the j course and i year are determined in respect of the student numbers in the j 1 course and i 1 year. The graduations in the i year are defined in respect of the student body enrolled in senior courses in the ...

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