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Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis
European Journal of Operational Research ( IF 6.0 ) Pub Date : 2023-06-01 , DOI: 10.1016/j.ejor.2023.05.034
Juan F. Monge , José L. Ruiz

Data Envelopment Analysis (DEA) very often sets unrealistic targets, which require from the decision-making units (DMUs) a huge amount effort, perhaps non-assumable, for their achievement. For the identification of best practices in the benchmarking, this paper proposes considering as peers not only DEA efficient DMUs but also those that are Pareto efficient, and allowing for reference sets spanning convex combinations that are not dominated by observed DMUs. It is therefore an approach that somehow relaxes the convexity in DEA, and sets targets representing best practices in the sense that they define a course of action leading to results that are not worse than those of the real plans. A bi-level linear programming (BLP) DEA model is developed which finds the closest targets from a convex combination of the DMUs in a reference set satisfying such non-dominance requirement. This approach has proven to be successful in setting targets that require an effort significantly smaller than that needed to achieve the closest targets on the strong efficient frontier of both the DEA and the free disposal hull (FDH) technologies. In the empirical illustration, we have observed reductions in the order of 40 percentage points on average in the total effort required for their achievement, thus setting more realistically implementable directions for improving performance towards best practices than those provided by conventional DEA and FDH.



中文翻译:

基于帕累托有效单位的非支配凸组合设定更接近的目标:数据包络分析中的双层线性规划方法

数据包络分析 (DEA) 经常设定不切实际的目标,这需要决策单元 (DMU) 付出巨大的努力(也许是不可假设的)才能实现。为了识别基准测试中的最佳实践,本文建议不仅将 DEA 高效 DMU 视为对等体,而且还考虑那些帕累托有效的 DMU,并允许跨越不受观察到的 DMU 支配的凸组合的参考集。因此,这是一种以某种方式放松 DEA 凸性的方法,并设定代表最佳实践的目标,因为它们定义了导致结果不比实际计划差的行动方针。开发了双层线性规划 (BLP) DEA 模型,该模型从满足此类非支配性要求的参考集中的 DMU 凸组合找到最接近的目标。事实证明,这种方法可以成功地设定目标,所需的努力远远小于在 DEA 和自由处置船体 (FDH) 技术的强大有效前沿实现最接近目标所需的努力。在实证例证中,我们观察到实现这些目标所需的总努力平均减少了约 40 个百分点,从而为提高绩效以实现最佳实践设定了比传统 DEA 和 FDH 提供的更现实可实施的方向。事实证明,这种方法可以成功地设定目标,所需的努力远远小于在 DEA 和自由处置船体 (FDH) 技术的强大有效前沿实现最接近目标所需的努力。在实证例证中,我们观察到实现这些目标所需的总努力平均减少了约 40 个百分点,从而为提高绩效以实现最佳实践设定了比传统 DEA 和 FDH 提供的更现实可实施的方向。事实证明,这种方法可以成功地设定目标,所需的努力远远小于在 DEA 和自由处置船体 (FDH) 技术的强大有效前沿实现最接近目标所需的努力。在实证例证中,我们观察到实现这些目标所需的总努力平均减少了约 40 个百分点,从而为提高绩效以实现最佳实践设定了比传统 DEA 和 FDH 提供的更现实可实施的方向。

更新日期:2023-06-01
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