关键词: 数据包络分析, 决策单元, 交叉效率, 区间效率值, 多个基最优解

Abstract: A traditional CCR model of data envelopment analysis (DEA) is to evaluate decision-making units (DMUs) optimistically in self-appraisal method. The maximum of relative ratio of weighted sum of outputs to that of inputs is regarded as the relative efficiency of a DMU. However, since all possible ratios of weighted sum of outputs to that of inputs can be assumed as possible efficiencies, the efficiencies of DMUs can be measured within the range of an interval. On applying cross-efficiency method, interval efficiencies of DMUs can be constructed based on CCR model. A factor that possibly reduces the usefulness of original cross-efficiency evaluation method is that cross-efficiency scores may not be unique due to the presence of alternate optima in CCR model. To solve the problem, a two-phased approach is adopted in cross-efficiency evaluation. With respect to the shortcoming of need to solve many additionally auxiliary linear programming problems that is due to non-uniqueness of cross efficiency score in cross efficiency evaluation method, this paper proposes a new computational method to obtain interval efficiencies by means of finding multiple basic optimal solutions of the traditional DEA linear programming model. Thus, the amount of computational work is greatly decreased. The above is the first issue of this article. The second issue in the paper is the problem of ranking of interval efficiencies for DMUs. The maximum efficiency of a DMU in CCR model is regarded as its upper bound of interval efficiency. On the condition of keeping the maximum efficiencies of other DMUs, cross efficiencies of a rated DMU is minimized and the minimum of all minimum cross efficiencies of a rated DMU is regarded as its lower bound of efficiency interval. At the same time, because the attitude to risk of most decision-makers lies between pessimism and optimism, a ranking method for interval efficiencies of DMUs, which can consider decision-makers' levels of optimism, is constructed by Hurwicz decision criterion, and a stability analysis of interval efficiencies ranking to optimistic coefficient is conducted in this article. Finally, a computational example is also given to illustrate the effectiveness of the method. Since CCR model under the condition of constant returns to scale can not divide overall efficiency of a DMU into technical efficiency and scale efficiency, the analysis of the paper can be applied to evaluation of overall efficiencies of DMUs when inputs and outputs are precise data and decision-makers' risk preferences need to be taken into consideration.

Key words: data envelopment analysis (DEA), decision-making unit, cross efficiency, interval efficiency, multiple basic optimal solutions