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首页> 外文期刊>Applied Mathematical Modelling >The role of non-Archimedean epsilon in finding the most efficient unit: With an application of professional tennis players
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The role of non-Archimedean epsilon in finding the most efficient unit: With an application of professional tennis players

机译：非阿基米德epsilon在寻找最高效单位方面的作用：通过职业网球运动员的应用

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摘要

The determination of a single efficient decision making unit (DMU) as the most efficient unit has been attracted by decision makers in some situations. Some integrated mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) data envelopment analysis (DEA) models have been proposed to find a single efficient unit by the optimal common set of weights. In conventional DEA models, the non-Archimedean infinitesimal epsilon, which forestalls weights from being zero, is useless if one utilizes the well-known two-phase method. Nevertheless, this approach is inapplicable to integrated DEA models. Unfortunately, in some proposed integrated DEA models, the epsilon is neither considered nor determined. More importantly, based on this lack some approaches have been developed which will raise this drawback. In this paper, first of all some drawbacks of these models are discussed. Indeed, it is shown that, if the non-Archimedean epsilon is ignored, then these models can neither find the most efficient unit nor rank the extreme efficient units. Next, we formulate some new models to capture these drawbacks and hence attain assurance regions. Finally, a real data set of 53 professional tennis players is applied to illustrate the applicability of the suggested models.
机译：在某些情况下，决策者已将单一的高效决策单位（DMU）确定为最高效的单位。已经提出了一些集成的混合整数线性规划（MILP）和混合整数非线性规划（MINLP）数据包络分析（DEA）模型，以通过最佳的通用权重集找到单个有效单位。在传统的DEA模型中，如果避免采用权重从零开始的非阿希米德无穷小ε，那么如果它采用了众所周知的两阶段方法就没有用了。但是，这种方法不适用于集成DEA模型。不幸的是，在一些建议的集成DEA模型中，既没有考虑也没有确定ε。更重要的是，基于这种不足，已经开发出一些方法来提高这一缺点。在本文中，首先讨论了这些模型的一些缺点。确实，这表明，如果忽略非阿基米德ε，那么这些模型既不能找到最有效的单位，也不能对极端有效的单位进行排名。接下来，我们制定一些新模型来捕捉这些缺点，从而获得保证范围。最后，使用53位职业网球运动员的真实数据集来说明所建议模型的适用性。

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