Performance evaluation and quota allocation for multiple undesirable outputs based on the uniform frontier
针对零和收益DEA模型在可变规模报酬下多投入多产出时可能无解的问题，提出两种改进模型和通用迭代算法，确保总能确定统一前沿面并完成配额分配，并以中国30个行政区的环境绩效评价为例说明。
The zero sum gains data envelopment analysis (ZSG-DEA) models and the corresponding uniform frontier method are widely applied for performance evaluation and resource/quota allocation in practice. Nevertheless, assuming variable returns-to-scale (VRS) and a situation with multiple ZSG inputs/outputs, the existing ZSG-DEA models may have no feasible solution for some efficient decision-making units and hence the uniform frontier cannot always be determined. In this study, two improved ZSG-DEA models are proposed, one assuming constant returns-to-scale (CRS) and the other VRS. Then, a general iterative algorithm is developed for resource/quota allocation based on the uniform frontier. We prove that the proposed method can always allocate multiple resources/quotas under both CRS and VRS assumptions, which extends the existing uniform frontier method research. An application to environmental performance evaluation and quota allocation for 30 administrative regions in China is presented to elucidate the main ideas.