管理评论

管理评论 ›› 2024, Vol. 36 ›› Issue (8): 212-223.

• 运作管理 • 上一篇    

基于指标比值的交叉DDF投影点效率评价方法

王庆1,2, 孟海宁1, 武华琛1, 李岸达1,2   

  1. 1. 天津商业大学管理学院, 天津 300134;
    2. 天津商业大学管理创新与评价研究中心, 天津 300134
  • 收稿日期:2022-12-12 发布日期:2024-09-03
  • 作者简介:王庆，天津商业大学管理学院教授，硕士生导师，博士;孟海宁，天津商业大学管理学院硕士研究生;武华琛，天津商业大学管理学院硕士研究生;李岸达(通讯作者)，天津商业大学管理学院副教授，硕士生导师，博士。
  • 基金资助:
    国家社会科学基金项目(16BGL096)。

Crossing Efficiency Evaluation Method through DDF Projections According to Indicator Ratios

Wang Qing1,2, Meng Haining1, Wu Huachen1, Li Anda1,2   

  1. 1. School of Management, Tianjin University of Commerce, Tianjin 300134;
    2. Management Innovation and Evaluation Research Center in Tianjin University of Commerce, Tianjin 300134
  • Received:2022-12-12 Published:2024-09-03

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摘要： 为解决传统DEA和DDF存在的问题,学者们提出交叉DDF,但现有交叉DDF仍存在一些问题:因忽略指标松弛量导致评价结果不精准;决策单元之间的评价基准(参照点)不一致;可能存在多个最优解;无法实现决策单元的效率全排序。为解决以上问题,本文给出基于指标比值的交叉DDF投影点效率评价方法。首先给出基于参照点的相对效率定义,即决策单元相对于参照点的综合投入指标比率和综合产出指标比率的比值,这样能将决策单元指标的所有信息考虑到效率评价中;其次,构建以最小化松弛量之和为第二目标函数的DDF模型,以尽可能得到决策单元唯一的投影点和评价结果;最后,以DDF投影点为参照,根据相对效率定义对决策单元进行交叉评价,使得评价参照点一致,评价结果不受方向向量长度影响且共识性强,同时实现决策单元的效率全排序。算例说明该方法具有一定的科学性和可行性。

关键词: DEA, DDF, 指标比值, 投影点, 交叉评价

Abstract: To solve the problems of the traditional data envelopment analysis (DEA) and directional distance function (DDF), scholars have proposed crossing DDF methods, but those methods are still defective in that evaluation results are inaccurate for the slacks of indicators being neglected; evaluation benchmarks (reference points) are inconsistent among DMUs; there may be multiple optimal solutions; and the efficiency of decision-making units cannot be fully ranked. In order to solve the above defects, this paper gives a cross efficiency evaluation method through DDF projections according to the indicator ratios between two DMUs. Firstly, this method gives the definition of relative efficiency based on reference DMUs, i.e., the ratio of comprehensive input ratio and comprehensive output ratio of DMUs, and makes all indicators' information of DMUs to be taken into account in efficiency evaluation. Secondly, based on the DDF method, the second objective function model that minimizes the sum of the slacks of inputs and outputs is constructed to obtain unique projection and unique evaluation result for DMUs. Finally, taking the DDF projections as references, the crossing efficiency of DMUs is evaluated according to the definition of relative efficiency, which ensures that evaluation reference points are consistent among the DMUs, evaluation results are not affected by the length of direction vectors and have strong consensus, and all DMUs are fully ranked according to their efficiencies. Two numerical examples are used to show that to a certain extent, the proposed method is scientific and feasible.

Key words: DEA, DDF, indicator ratio, projection, crossing-evaluation