Abstract The data envelopment analysis technique produces higher efficiency scores for the assessed decision making units (DMUs) when more input/output factors are considered. This feature generates an intuitively unreasonable result in which the efficiency of a DMU measured considering the accompanying undesirable outputs is greater than or equal to that measured without considering them. In order to obtain a reasonable measure of efficiency, this paper proposes a concept for determining the minimum amount of undesirable outputs that a DMU is allowed to generate based on the assertion of weak disposability, and the results are used to construct the production frontier. The efficiency of the DMUs measured from this frontier can be decomposed into two parts, one of which shows the efficiency of consuming the observed inputs to produce the observed desirable outputs and the other of which, a reduction factor, shows the effect of producing excessive amounts of undesirable outputs on efficiency. A case of thirty paper mills taken from the literature is used to illustrate this idea. The results are helpful for DMU decision-makers to identify sources of inefficiency and for the government to formulate standards for generating allowable amounts of undesirable outputs.

中文翻译：

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衡量不良产出对生产单位效率的影响

摘要 当考虑更多的输入/输出因素时，数据包络分析技术为评估的决策单元 (DMU) 产生更高的效率分数。此特征会产生一个直观上不合理的结果，其中考虑到伴随的不良输出而测得的 DMU 的效率大于或等于未考虑它们时测得的效率。为了获得合理的效率度量，本文提出了一种基于弱可处置性断言来确定允许 DMU 产生的最小不良输出量的概念，并将结果用于构建生产前沿。从这个前沿测量的 DMU 的效率可以分解为两部分，其中一个显示消耗观察到的输入以产生观察到的理想输出的效率，另一个是减少因子，显示产生过多的不良输出对效率的影响。从文献中选取的 30 家造纸厂的案例来说明这一想法。结果有助于 DMU 决策者确定效率低下的根源，并有助于政府制定产生允许数量的不良输出的标准。