关键词: 数据包络分析, 网络DEA, 链形系统, 最近目标, 单调性

Abstract: Chain production system is a typical class of production system in real life, and the study of it has important theoretical and practical significance. At present, research on chain systems is mostly based on the farthest distance projection, i.e. finding improvement paths for ineffective decision-making units (DMUs) to maximize their efficiency. However, the improvement process is difficult and faces huge improvement costs, which discourages many managers. Therefore, it is necessary to study the chain network data envelopment analysis (DEA) method based on nearest distance projection.
From the latest research, it can be found that, in non-cooperative mode, the traditional two-stage network DEA method based on the nearest distance projection can reduce the difficulty of efficiency improvement while considering the internal structure. However, it still has the following aspects to be improved. Firstly, there are greater limitations in the selection of evaluation reference sets. Secondly, operation errors may occur when the index data is the same. Thirdly, the efficiency measured by it does not satisfy monotonicity.
In order to solve the above problems, this paper proposes a chain network DEA method based on generalized the nearest distance projection. Specifically, firstly, in order to be able to freely select the evaluation reference set according to the actual problem, the proposed method extends the evaluation reference set of the traditional two-stage network DEA method based on the nearest distance projection. Secondly, in order to avoid the occurrence of operational errors, the proposed method gives a modified invalidity index. Thirdly, in order to satisfy weak monotonicity in efficiency, based on the concept of free disposal sets, the proposed method uses virtual points instead of evaluated DMUs for efficiency evaluation.
In order to further verify the reasonability and feasibility of the proposed method, a comparative study is conducted between the proposed method and the traditional method through an empirical analysis of the operating efficiency of Chinese listed banks. The empirical results indicate that compared to the traditional two-stage network DEA method based on the nearest distance projection, in addition to avoiding operational errors, the proposed method has the following advantages in effectiveness evaluation. Firstly, the proposed method is more flexible in application, which can provide evaluation results under different reference sets according to the needs of managers. Secondly, the proposed method that satisfies weak monotonicity can provide managers with more reliable efficiency results and projection information. In summary, the efficiency result analysis under the proposed method is more worthy of reference by managers.
The proposed method is only a beneficial attempt in the evaluation of chain network systems and still has incomplete considerations. Further meaningful research in the future includes the following aspects. Firstly, consider the situation where there are exogenous inputs or final outputs in the intermediate stage. Secondly, expand the proposed method based on the assumption of variable returns to scale to other returns to scale scenarios. Thirdly, the application scenario of the proposed method should be extended to chain-parallel organizational structures or more general organizational structures, taking into account the fact that the internal structure of real systems is often not a single chain network structure.

Key words: data envelopment analysis, network DEA, chain system, nearest targets, monotonicity