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<p>This paper addresses the challenges of ranking efficient units in Data Envelopment Analysis (DEA) by introducing a set of novel models grounded in the deviation variables framework. These models provide a systematic approach to ranking under both constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. The proposed methodology enhances the precision and consistency of efficiency assessments by resolving two major issues in existing approaches: (i) the occurrence of negative efficiency scores, which are both theoretically and practically invalid, and (ii) the presence of multiple optimal solutions, which undermine the reliability of ranking outcomes. To overcome these limitations, we develop a pair of benevolent and aggressive DEA models that incorporate deviation variables while ensuring all efficiency scores remain positive. To validate the effectiveness of our models, we present two numerical examples that highlight the shortcomings of traditional methods and demonstrate the improvements offered by our approach. The results show the superiority of the deviation-based framework in delivering more accurate and interpretable rankings within the DEA context.</p>

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Improving cross-inefficiency analysis by eliminating negative scores and solution multiplicity

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Bohlool Ebrahimi

摘要

This paper addresses the challenges of ranking efficient units in Data Envelopment Analysis (DEA) by introducing a set of novel models grounded in the deviation variables framework. These models provide a systematic approach to ranking under both constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. The proposed methodology enhances the precision and consistency of efficiency assessments by resolving two major issues in existing approaches: (i) the occurrence of negative efficiency scores, which are both theoretically and practically invalid, and (ii) the presence of multiple optimal solutions, which undermine the reliability of ranking outcomes. To overcome these limitations, we develop a pair of benevolent and aggressive DEA models that incorporate deviation variables while ensuring all efficiency scores remain positive. To validate the effectiveness of our models, we present two numerical examples that highlight the shortcomings of traditional methods and demonstrate the improvements offered by our approach. The results show the superiority of the deviation-based framework in delivering more accurate and interpretable rankings within the DEA context.