Modeling Hierarchical Levels Of Targeted Variables In Operational Efficiency Evaluation With DEA

Data Envelopment Analysis (DEA) is a non-parametric performance evaluation method with extensive applications. In the evaluation process, Decision Making Unit (DMU) with fewer inputs and more outputs is more efficient. With the development of DEA theory and applications, classic DEA models cannot properly handle variables with target levels, which are known as targeted variables, and these models are apt to overrate performances. Within DEA framework, Lim and Zhu made a pioneering research on variables with targets, and the findings were utilized to evaluate efficiencies of 36 American universities. However, they took no consideration for attainable targets. Moreover, in daily life, there are some situations where targeted variables may have discrete multiple targets. On account of these problems, this paper explores the way to model hierarchical targeted variables in DEA, and an application is presented.The main content and findings of this paper are as follows:Firstly, targeted variables with discrete multi-targets when all targets are unattainable are studied. Variables with mono-target, bi-targets and multi-targets are investigated respectively, when the whole production possibility set (PPS) is symmetric. Then the assessment under asymmetric PPS is stated briefly.Secondly, when targets are attainable, these targets are within the PPS, and it is inspiring to pursue how to assess performance. Based on Slack-based-measure (SBM), we propose a Slack-based-measure for Discrete multiple Targets (SBM-DT) to evaluate efficiency when all of the targets are achievable. And with discussions on that only part of the targets can be achieved, we make a thorough analysis on target attainability.Thirdly, the proposed approach is applied to evaluate performance of Chinese education and training institutes. Most of Chinese training institutes are operated by private organizations, and adopt the Small Class Teaching Mode. Existing research shows that students can gain a better performance when the class size is less than 20 persons. Thus when recruiting amounts are 20,40,60, etc., the training institutes will outperform other ones. The results of SBM and our provided approach differ, and offer diverse suggestions to make decisions much flexible.This paper extends DEA theory about targeted variables, and enriches the application of DEA approach in non-tertiary education. Meanwhile, this paper sketches out the Chinese education and training markets, and provides the participants with practical advice in the light of the performance evaluating results.