Data envelopment analysis is a linear programming-based operations research technique for performance measurement of decision-making units. In this paper, we investigate data envelopment analysis from a multiobjective point of view to compute both the efficient extreme points and the efficient facets of the technology set simultaneously. We introduce a dual multiobjective linear programming formulation of data envelopment analysis in terms of input and output prices and propose a procedure based on objective space algorithms for multiobjective linear programmes to compute the efficient frontier. We show that using our algorithm, the efficient extreme points and facets of the technology set can be computed without solving any optimization problems. We conduct computational experiments to demonstrate that the algorithm can compute the efficient frontier within seconds to a few minutes of computation time for real-world data envelopment analysis instances. For large-scale artificial data sets, our algorithm is faster than computing the efficiency scores of all decision-making units via linear programming.

中文翻译：

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计算数据包络分析有效边界的多目标优化方法

数据包络分析是一种基于线性规划的运筹学技术，用于决策单位的绩效评估。在本文中，我们从多目标的角度研究数据包络分析，以同时计算技术集的有效极点和有效方面。我们介绍了一种基于投入和产出价格的数据包络分析的双重多目标线性规划公式，并提出了一种基于目标空间算法的多目标线性规划程序来计算有效边界。我们表明，使用我们的算法，可以在不解决任何优化问题的情况下计算出技术集的有效极限点和方面。我们进行了计算实验，以证明该算法可以在几秒钟到几分钟的计算时间内为实际数据包络分析实例计算有效边界。对于大规模的人工数据集，我们的算法比通过线性规划计算所有决策单元的效率得分更快。