An Analysis of the Application of Mathematical and Statistical Models in the Optimization of Educational Resource Allocation in Colleges and Universities

This paper focuses on the practical application of mathematical statistical models for the allocation of educational resources in higher education institutions under the premise of resource optimization. It takes factors such as the level of resource investment, resource utilization efficiency, and the degree of research platform development as entry points to explore their impact on the efficiency of educational resource allocation. Using Data Envelopment Analysis (DEA) models, Structural Equation Modeling (SEM) methods, and factor analysis, this study analyzes the allocation of educational resources in selected Chinese higher education institutions. Based on a survey of educational resources in 256 Chinese higher education institutions, it was found that the efficiency of educational resource allocation in Chinese universities is generally low, with only 9.38% of institutions achieving effective resource allocation. The study also concluded that the level of regional economic development significantly influences the efficiency of resource allocation in higher education institutions, with universities in eastern regions generally achieving higher resource allocation efficiency than those in central and western regions. Technological progress remains the primary factor driving improvements in resource allocation efficiency, with its contribution rate to resource allocation efficiency reaching as high as 68.4%. Therefore, this paper suggests establishing a data-driven dynamic resource allocation mechanism, building a cross-regional resource-sharing platform, implementing categorized guidance for resource allocation, strengthening internal management within universities, fully utilizing university resources, optimizing resource allocation, and enhancing the overall educational quality of universities.