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A balanced data envelopment analysis cross-efficiency evaluation approach

机译：平衡数据包络分析交叉效率评估方法

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摘要

Data envelopment analysis (DEA) is a frontier analysis procedure for evaluating the relative performance of decision making units (DMUs) with multiple inputs and multiple outputs. To improve its discrimination power, an important extension is proposed as cross-efficiency, which uses peer DMUs' optimal relative weights to evaluate the relative performance. However, the existing cross-efficiency methods show an inconsistent and unbalanced evaluation standard, since each DMU might determine a different total (or mean) efficiency value across all DMUs. The different values imply that the DMUs that have assigned larger cross-efficiency scores will have a larger effect in aggregating the ultimate cross-efficiency scores and different DMUs' effects are unbalanced in cross-efficiency methods. In this paper, we will deal with this unbalanced cross-efficiency evaluation problem. To this end, we first suggest a practical adjustment measure to rectify the traditional cross-efficiency, which will provide a common evaluation standard for all DMUs and make each DMU dispatch an identical total efficiency score across all DMUs. Further, we propose a game-like iterative procedure to obtain the optimal balanced cross-efficiency. Finally, we present both a numerical example and an empirical study derived from the literature and a real-world problem to demonstrate the usefulness and efficacy of the new balanced cross-efficiency evaluation approach. The work presented in this paper can extend the traditional cross-efficiency approaches to situations involving unbalanced evaluation standards, and make the evaluation results more practical significance. (C) 2018 Elsevier Ltd. All rights reserved.
机译：数据包络分析（DEA）是一种前沿分析程序，用于评估具有多个输入和多个输出的决策单元（DMU）的相对性能。为了提高其区分能力，提出了一个重要的扩展，即交叉效率，该效率使用对等DMU的最佳相对权重来评估相对性能。但是，现有的交叉效率方法显示出不一致且不平衡的评估标准，因为每个DMU可能会在所有DMU上确定不同的总（或平均）效率值。不同的值表示分配了较大交叉效率得分的DMU将在汇总最终交叉效率得分中产生更大的影响，并且不同的DMU的效果在交叉效率方法中是不平衡的。在本文中，我们将处理这种不平衡的交叉效率评估问题。为此，我们首先提出一种实用的调整措施来纠正传统的交叉效率，这将为所有DMU提供通用的评估标准，并使每个DMU在所有DMU上分配相同的总效率得分。此外，我们提出了一种类似于游戏的迭代程序来获得最佳的平衡交叉效率。最后，我们同时提供了一个数值示例和一个来自文献和一个实际问题的实证研究，以证明新的平衡交叉效率评估方法的有用性和有效性。本文提出的工作可以将传统的交叉效率方法扩展到涉及不平衡评估标准的情况，并使评估结果更具实际意义。 （C）2018 Elsevier Ltd.保留所有权利。

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