The research develops an eight-dimensional framework based on four dimensions, namely, financial resources of education, socio-economic conditions, the wider social context, and properties of the student population. The variables studied are spending on higher vocational education, expenditure per student, GDP, level of household spending, overall retail sales of consumer products, the urban unemployment rate, population size, and the number of secondary school graduates. Grey relational analysis is used to identify those factors that have the strongest relationship with the trends in enrollment in a private higher vocational education. Based on these results, the paper incorporates the outcomes into a BP neural network and the GM(1,1) model, overcoming the natural shortcomings of a stand-alone GM(1,1) forecast by developing a combined prediction model of GM-BP. This structure is then used to predict the size of the private higher vocational education sector between 2025 and 2035, as well as the expected changes in the volume of enrollment and the disciplinary mix during this period. The findings show that the total enrollment of students within the private higher vocational institutions will peak at 946,062 in 2035, and the fields of transportation, medicine, and healthcare are the ones that will attract the largest proportion of students.
