不确定性数据包络分析：框不确定性
Uncertain Data Envelopment Analysis: Box Uncertainty
摘要：
数据包络分析（DEA）是一种非参数的、数据驱动的技术，用于在一组可比的决策单元（DMU）之间进行相对性能分析。通过线性规划比较每个决策单元的输入和输出数据来评估效率。传统上，在DEA中，数据被认为是精确的。然而，在许多实际应用中，分析中使用的输入和输出数据的值可能是不精确的。为了说明这一点，我们开发了不确定的DEA问题的情况下，框的不确定性。我们引入了DEA距离的概念，以确定所需的最小数量的不确定性的DMU被认为是有效的。对于小问题，可以精确地找到最小量的不确定性，对于较大的问题，这变得计算密集。因此，我们提出了一种迭代法，其中的不确定性的量是逐渐增加的。这导致了一个鲁棒的DEA问题，可以有效地解决。这项研究的不确定性的动机是固有的不确定性性质的放射治疗计划过程中的肿瘤。我们应用该方法来评估一组前列腺癌放射治疗计划相对于彼此的质量。
英文摘要：
Data Envelopment Analysis (DEA) is a nonparametric, data driven technique used to perform relative performance analysis among a group of comparable decision making units (DMUs). Efficiency is assessed by comparing input and output data for each DMU via linear programming. Traditionally in DEA, the data are considered to be exact. However, in many real-world applications, it is likely that the values for the input and output data used in the analysis are imprecise. To account for this, we develop the uncertain DEA problem for the case of box uncertainty. We introduce the notion of DEA distance to determine the minimum amount of uncertainty required for a DMU to be deemed efficient. For small problems, the minimum amount of uncertainty can be found exactly, for larger problems this becomes computationally intensive. Therefore, we propose an iterative method, where the amount of uncertainty is gradually increased. This results in a robust DEA problem that can be solved efficiently. This study of uncertainty is motivated by the inherently uncertain nature of the radiotherapy treatment planning process in oncology. We apply the method to evaluate the quality of a set of prostate cancer radiotherapy treatment plans relative to each other.
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