In recent years, significant development has been made in efficiency evaluation for Decision-Making Units (DMUs) with fixed-sum outputs. The Generalized Equilibrium Efficient Frontier Data Envelopment Analysis (GEEFDEA) approach introduced by Yang et al. (2015) is one of the most representative methods. In the GEEFDEA approach, all DMUs are adjusted to become efficient under the same set of weights, indicating that the Equilibrium Efficient Frontier (EEF) constructed consists of only one hyperplane. However, in practical scenarios under the Variable Return to Scale (VRS) assumption, the production frontier always consists of multiple hyperplanes, presenting a more complex shape. To fill this research gap, we propose an improved Equilibrium Efficient Frontier Data Envelopment Analysis approach. Our approach allows DMUs to have different weights for inputs, variable-sum outputs, and fixed-sum outputs, resulting in an EEF with multiple hyperplanes. It is noted that our new approach uses a non-linear model to obtain the EEF. We show that the model can be linearized in the case of a single fixed-sum output. In situations involving multiple fixed-sum outputs, we propose an algorithm based on the Expectation Maximization (EM) mechanism to solve the model to obtain an EEF. Finally, we illustrate the advantages of our new approach through a numerical example and a case study in the global motor vehicle industry.

中文翻译：

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一种改进的均衡有效前沿数据包络分析方法，用于评估具有固定总和输出的决策单元


近年来，具有固定总和输出的决策单元（DMU）的效率评估取得了重大进展。 Yang 等人提出的广义均衡有效前沿数据包络分析 (GEEFDEA) 方法。 （2015）是最具代表性的方法之一。在GEEFDEA方法中，所有DMU都被调整为在同一组权重下变得有效，这表明所构造的平衡有效边界（EEF）仅由一个超平面组成。然而，在规模收益可变（VRS）假设下的实际场景中，生产前沿总是由多个超平面组成，呈现出更复杂的形状。为了填补这一研究空白，我们提出了一种改进的均衡有效前沿数据包络分析方法。我们的方法允许 DMU 对输入、可变和输出和固定和输出具有不同的权重，从而产生具有多个超平面的 EEF。值得注意的是，我们的新方法使用非线性模型来获得 EEF。我们证明该模型可以在单个固定和输出的情况下线性化。在涉及多个固定和输出的情况下，我们提出了一种基于期望最大化（EM）机制的算法来求解模型以获得EEF。最后，我们通过数值示例和全球机动车辆行业的案例研究来说明我们新方法的优势。