Optimizing training efficiency amid postgraduate enrollment expansion: A new parallel network DEA allocation model

Against the backdrop of the continuous expansion of postgraduate enrollment in China, ensuring the quality of postgraduate education has become a long-term focus of concern for the entire society. Currently, the allocation model of postgraduate enrollment quotas among Chinese universities and within universities has not formed an effective competitive mechanism, making it difficult to reflect quality orientation and improve training efficiency. Therefore, a new parallel network data envelopment analysis (DEA) enrollment quotas allocation model based on shared investment is proposed to achieve efficiency and fairness. An empirical analysis is conducted using the allocation of enrollment quotas for professional degree postgraduates at a university in Shanghai as an example. The study shows that (1) the existing allocation schemes only follow a single high average principle, which neglects allocation efficiency. Through optimization, the allocation efficiency has been improved from 0.76 to 1. (2) When the subjective stage weight coefficient ${\gamma }_1$ = 0.9, the Gini coefficient of the allocation scheme is the lowest, which is the optimal allocation scheme under the condition of efficiency priority. (3) When the coefficient of the subjective efficiency stage and the input-oriented weight coefficient within the subjective efficiency stage change by 11 % and 40 %, respectively, there is no significant difference between the test and control groups in the allocation results (P > 0.05), and the Pearson correlation coefficient (R²) is 0.96. Therefore, this allocation model demonstrates good stability and can be applied to the allocation of enrollment quotas among different universities and other types of postgraduates.