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<p>As a nonconvex class of data envelopment analysis, free disposal hull (FDH) has become a commonly used method in productivity and efficiency analysis. However, existing FDH models often generate many efficient units, ignore the slacks of production variables, and compute efficiency and super-efficiency in separate steps. Meanwhile, FDH models typically lead to mixed-integer linear or nonlinear programming problems, which are more complicated to solve than conventional DEA models. To address these issues, we first propose two new slack-based FDH and feasible super-efficiency FDH models. The former explicitly accounts for variable slacks and thus yields more accurate efficiency measures, while the latter overcomes the challenges of numerous efficient units and infeasible solutions in conventional FDH super-efficiency evaluation. Then, an integrated slack-based FDH model is developed to simultaneously compute efficiency and super-efficiency in a one-stage approach. The proposed framework is applicable to performance measurement involving both desirable outputs and undesirable outputs, by incorporating their corresponding slacks in a unified formulation. Enumeration algorithms for the proposed models are theoretically derived, which transform the mixed-integer nonlinear programming problems into explicit enumeration procedures over a finite set of observed DMUs. The proposed measures satisfy several desirable properties, including feasibility, strict monotonicity, unit invariance, and invariance to alternate optima. The validation is conducted by assessing the performance of the Chinese thermal power industry.</p>

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Integrating slack-based measure with free disposal hull optimization for performance measurement: modeling, characterization, and algorithms

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Xiaohong Liu,
  • Jiwu Zhang,
  • Yi Liu,
  • Yang Liu,
  • Qingchun Meng

摘要

As a nonconvex class of data envelopment analysis, free disposal hull (FDH) has become a commonly used method in productivity and efficiency analysis. However, existing FDH models often generate many efficient units, ignore the slacks of production variables, and compute efficiency and super-efficiency in separate steps. Meanwhile, FDH models typically lead to mixed-integer linear or nonlinear programming problems, which are more complicated to solve than conventional DEA models. To address these issues, we first propose two new slack-based FDH and feasible super-efficiency FDH models. The former explicitly accounts for variable slacks and thus yields more accurate efficiency measures, while the latter overcomes the challenges of numerous efficient units and infeasible solutions in conventional FDH super-efficiency evaluation. Then, an integrated slack-based FDH model is developed to simultaneously compute efficiency and super-efficiency in a one-stage approach. The proposed framework is applicable to performance measurement involving both desirable outputs and undesirable outputs, by incorporating their corresponding slacks in a unified formulation. Enumeration algorithms for the proposed models are theoretically derived, which transform the mixed-integer nonlinear programming problems into explicit enumeration procedures over a finite set of observed DMUs. The proposed measures satisfy several desirable properties, including feasibility, strict monotonicity, unit invariance, and invariance to alternate optima. The validation is conducted by assessing the performance of the Chinese thermal power industry.