基于SMAA和公共权重的决策单元效率评价与排序

Efficiency Evaluation and Ranking for Decision Making Units Based on SMAA and Common Weight

在数据包络分析(DEA)中,公共权重模型是决策单元效率评价与排序的常用方法之一。与传统DEA模型相比,公共权重模型用一组公共的投入产出权重评价所有决策单元,评价结果往往更具有区分度且更为客观。本文考虑决策单元对排序位置的满意程度,提出了基于最大化最小满意度和最大化平均满意度两类新的公共权重模型。首先,基于随机多准则可接受度分析(SMAA)方法,计算出每个决策单元处于各个排名位置的可接受度;然后,通过逆权重空间分析,分别求得使最小满意度和平均满意度最大化的一组公共权重;最后,利用所求的公共权重,计算各决策单元的效率值及相应的排序。算例分析验证了本文提出的基于SMAA的公共权重模型用于决策单元效率评价与排序的可行性。

Common weight model has been one of widely used efficiency evaluation and ranking methods for decision making units(DMUs)in Data Envelopment Analysis(DEA).Compared with the traditional DEA models which are based on self-evaluation efficiency,the common weight model assesses all DMUs with a common set of input and output weights;thus,the evaluation results are more discriminating and objective.This study considers the satisfaction degree of a DMU to its ranking position and proposes two types of common weight models:the one is to maximize the minimum satisfaction and the other is tomaximize the average satisfaction.Firstly,the acceptability index of each DMU in each ranking position is obtained using Stochastic Multi-criteria Acceptability Analysis(SMAA).Secondly,the weight space is explored to find the weight which maximizes the minimum or average satisfaction as a set of common weight.Finally,we calculate the efficiency scores for all the DMUs and rank them using the obtained common weight.The feasibility and effectiveness of our proposed method for efficiency evaluation and ranking are illustrated by a numeral example.