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<p>The traditional Data Envelopment Analysis (DEA) model assumes non-negative resources and outputs, but in real-world business scenarios, negative data can often arise. This paper introduces modified slack-based measure (SBM) and super-efficiency SBM (SupSBM) models designed to handle negative data under variable returns to scale. These models are consistent with the standard SBM and SupSBM frameworks. The developed models preserve the nature of the data, allowing for direct evaluation of negative values. They are feasible, unit-invariant, and capable of generating efficient projections. Notably, the simplicity and ease of use of these models are significant advantages. Additionally, the modified SBM and SupSBM models are extended to address nonpositive data, which includes both zero and negative values. A criterion for ranking units is also presented, offering more logical and realistic ratings compared to existing methods. The analysis demonstrates that the modified models not only effectively accommodate negative data but also enhance the robustness of efficiency evaluation in complex scenarios. Four numerical examples are provided, with a complete ranking presented to showcase the performance of the developed models and their comparison with other methods.</p>

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A modified slacks-based measure of efficiency and super-efficiency under zero and negative data

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Ehsan Zanboori

摘要

The traditional Data Envelopment Analysis (DEA) model assumes non-negative resources and outputs, but in real-world business scenarios, negative data can often arise. This paper introduces modified slack-based measure (SBM) and super-efficiency SBM (SupSBM) models designed to handle negative data under variable returns to scale. These models are consistent with the standard SBM and SupSBM frameworks. The developed models preserve the nature of the data, allowing for direct evaluation of negative values. They are feasible, unit-invariant, and capable of generating efficient projections. Notably, the simplicity and ease of use of these models are significant advantages. Additionally, the modified SBM and SupSBM models are extended to address nonpositive data, which includes both zero and negative values. A criterion for ranking units is also presented, offering more logical and realistic ratings compared to existing methods. The analysis demonstrates that the modified models not only effectively accommodate negative data but also enhance the robustness of efficiency evaluation in complex scenarios. Four numerical examples are provided, with a complete ranking presented to showcase the performance of the developed models and their comparison with other methods.