Qualitative data envelopment analysis by affinity set: a survey of subjective opinions for NPOs

Measuring the performance of Non-Profit Organizations (NPOs) is a complicated issue: data envelopment analysis (DEA) is a popular quantitative tool in the past literature. However, the subjective opinions of NPOs could disturb their actual performance, and this problem is seldom considered. In this study, we use the qualitative DEA as a tool to find the emphasized inputs and outputs for these NPOs. Most DEA models are established by the basis of quantitative data, they are difficult to describe the qualitative performance of NPOs. This paper proposes a new perspective for computing the efficiency of a Decision Making Unit based on qualitative data by affinity Set. The DEA model for qualitative data could be traced back to the work of Cook et al. early in 1993. Our contribution prevents the identical efficiency scores from the model of Cook et al., and a combinatorial optimization technique is used to solve the new problem. Finally, we found most NPOs would like to get more resources from outside; but interestingly, they don’t like to be officially monitored. Therefore, we should use the quantitative DEA on NPOs very carefully.