基于公共权重的鲁棒DEA模型研究

Robust Data Envelopment Analysis Based on Common Weights

传统DEA模型允许决策单元自由选取对其最为有利的投入产出权重,以获得最大的效率。相比之下,公共权重DEA模型采用统一的权重,更加适合统一管理的组织对各部门进行效率评价。此外,由于DEA方法是一种基于现有数据进行建模的方法,而现实生活中的数据往往是不精确的,因此,在建模的过程中考虑数据的不确定性十分重要。本文对Chen等提出的多目标公共权重DEA模型进行了简化。在此基础上,利用鲁棒优化方法,建立了基于公共权重的鲁棒DEA模型,并与Omrani提出的模型进行了对比。数值算例表明本文提出的方法有效,求解计算量更少,得到的公共权重更加合理。

In traditional DEA models, different decision making units （DMUs） are free to choose weights that are beneficial for themselves to obtain a high efficiency. While the common weights DEA models use common weights to assess different DMUs, which seems more suitable for the centralized organizations. Besides, DEA is a data-oriented method. However, the inputs and outputs data in real-life problems are often imprecise. Thus we should take the data uncertainty into consideration. In this paper, we simplify a multi-objective common weights DEA model proposed by Chen et al： Under the consideration of data uncertainty, we establish a robust muhi-objective DEA model and make a comparison between our model and Omrani＇ s. The results of numerical example show that our approach is reasonable and acceptable, our computation amount is less and the common weights derived from our model are more reasonable.