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

摘要： 非合作模式下的基于最近距离投影的传统两阶段网络DEA方法在考虑内部结构的同时,很好地降低了改进难度。然而,其仍有以下不足:①无法依据实际问题自由地选择评价参考集;②在指标数据相同时可能无法运算;③所测效率不满足单调性。因此,本文首先通过拓展评价参考集,且在修正的无效性指数和自由处置集的基础上,提出了一种满足弱单调性的基于广义最近距离投影的链形网络DEA方法。为了验证本文方法的可行性,通过对中国上市银行运营效率的实证分析,将本文方法与传统方法进行了比较研究。结果表明,本文方法不仅可以根据管理者的需求基于不同评价参考集进行效率测度,而且满足“弱单调性”的效率测度可提供更为可靠的效率结果和投影信息。

关键词: 数据包络分析, 网络DEA, 链形系统, 最近目标, 单调性