Constrained Weighted DEA Method Based on Volume Under Surface: A Case Study in Large Industrial Sectors

The efficiency of large industrial sectors plays a critical role in promoting high‐quality economic growth and enhancing total factor productivity. Data envelopment analysis (DEA) is widely used for such evaluations due to its flexibility and nonparametric structure; however, its core mechanism, which allows each decision‐making unit (DMU) to select optimal weights, often yields extreme and unreasonable weighting schemes that distort efficiency scores and weaken discriminatory power. This study addresses this foundational challenge through three key contributions. First, it introduces the weight extremity function (WEF), a mathematical construct that quantifies the degree of weight concentration within any given weighting scheme. Second, it develops a novel DEA model that incorporates WEF‐based constraints, effectively preventing DMUs from adopting unreasonable weight distributions while preserving the method’s inherent flexibility. The proposed framework transforms the resulting nonlinear programming problem into an equivalent linear formulation, ensuring computational tractability. Third, to eliminate subjective parameter selection, the model employs a volume‐under‐the‐surface calculation method to derive efficiency scores, relying solely on objective statistical properties of the data. An empirical study of China’s large‐scale industrial sectors across 31 provinces (2019–2022) demonstrated the enhanced discrimination capability and evaluation consistency of the proposed approach. The findings reveal significant geographical disparities in industrial efficiency across China, with the proposed model providing more nuanced and robust rankings than existing alternatives.