考虑决策者偏好结构的交叉效率评价方法

A Cross-efficiency Evaluation Method Considering Decision Maker Preference Structure

经典DEA交叉效率评价方法为了追求评价结果的客观性,往往忽略了决策者在评价过程中的主观性,从而导致主观决策信息的丢失,使得评价结果有效性较弱。针对这一问题,本文将决策者的主观心理偏好纳入研究中,提出一种结合数据包络分析和有序加权平均算子的心理偏好结构交叉效率评价方法。利用该方法,首先,采用对抗型数据包络分析模型求得决策单元的初始交叉效率矩阵;其次,使用偏度和标准差测量出决策者在对决策单元进行评价时所产生的心理偏好结构,即偏好优先级与偏好差距,并修正初始交叉效率矩阵;随后,基于最小偏好差异最大化的思想对决策单元进行偏好权重分配,同时结合有序加权平均算子对交叉效率评价信息进行集结,得出决策单元最终交叉效率值。本文所提方法不仅充分考虑了决策者的主观心理偏好,而且最大程度地利用了原始数据信息,减少了评价信息的丢失,提高了评价结果的合理性和有效性。

In practice,managers or decision-makers usually need to make strategic decisions among similar decision-making units,such as team performance,project performance,etc.Due to the same external environment,evaluation indicators,and other characteristics of similar decision-making units,it is difficult for decisionmakers to make correct evaluations.Scholars have proposed and employed the cross-efficiency evaluation method to solve the above problems.However,the classic cross-efficiency of DEA pursues the absolute objectivity of the evaluation results and ignores the subjectivity of decision-makers in the evaluation process,which leads to the loss of decision-making information and weakens the validity of the evaluation results.In response to this problem,a cross-efficiency evaluation method is given considering the decision-maker preference structure,which combines with DEA and OWA operators.Specifically,the radical DEA model is used to obtain the initial cross-efficiency matrix of the decision-making units at first.Second,skewness and standard deviation are used to measure the preference structure of decision-makers,that is preference difference and priority,and to modify the initial cross-efficiency matrix.Subsequently,the weights of decision-making units are obtained based on maximizing the minimum preference difference.The final cross-efficiency values of the decision-making units are received by the OWA operator to aggregate the evaluation information.The statistical data of 27 industrial robots from the study of Wang and Chin are used to test the proposed method.Further,the proposed method is compared with the traditional DEA and Chen's method.The perspective of overall ranking,the changing trend of ranking obtained by the three methods is similar;the perspective of specific ranking,the cross-efficiency difference of the proposed method is bigger than that of the other two methods.In sum,the evaluation results of the proposed method have excellent consistency,and it is more conducive for decisionmakers or managers to further understand and compare the differences between decision-making units.