A general cross-efficiency evaluation framework for non-homogeneous DMUs and a lexicographic-based method for Pareto-optimal cross-efficiency scores
针对数据包络分析中决策单元非齐次性的长期难题，提出一个允许各单元自主选择投入分配策略的一般交叉效率评估框架，并引入字典序方法确保唯一效率排名和帕累托最优结果。
The non-homogeneity of decision-making units (DMUs) has been a long-standing challenge in data envelopment analysis (DEA) when assessing relative performance. In response to this issue, this article proposes a general cross-efficiency evaluation framework for the performance evaluation of non-homogeneous DMUs. Unlike traditional methods, which assume uniform input allocation proportions across all DMUs when calculating self-evaluated efficiency, the proposed framework allows each DMU the autonomy to adopt a tailored input distribution strategy. Additionally, it supports scenarios with multiple subgroups of non-homogeneous DMUs, extending beyond the conventional focus on just two groups. Building upon this foundational framework, we introduce new models for self-evaluation, as well as aggressive and benevolent cross-efficiency evaluations. Furthermore, we present a lexicographic-based approach to cross-efficiency evaluation, ensuring unique efficiency rankings and generating a set of Pareto-optimal results for the DMUs. The effectiveness of the proposed method is demonstrated through comparisons with existing approaches, using both a benchmark dataset and a case study of the nonferrous metal mining industry.