Primal-dual correspondence and frontier projections in two-stage network DEA models
Primal-dual correspondence and frontier projections in two-stage network DEA models
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DOI：
10.1016/j.omega.2018.06.005
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发表时间：
2019-03
期刊：
影响因子：
--
通讯作者：
Sungmook Lim;Joe Zhu
中科院分区：
文献类型：
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作者：
Sungmook Lim;Joe Zhu
标准的数据包络分析（DEA）过程涉及求解一对两类模型，即乘数模型和修正模型，而DEA最有趣的特征之一是这两类模型由于线性规划中的对偶性而等价。然而，虽然一些突出的网络DEA模型已经提出了在文献中的乘数和/或修正形式，它仍然是可疑的或不清楚是否以及如何保持相同的原始-对偶对应关系的两种类型的网络DEA模型之间的标准DEA。为了解决这个问题，我们开发了一个公理化推导的一些两阶段网络DEA模型在本文中侧重于基本的两阶段串行过程结构。基于一些合理的公理性质，定义了基本两阶段串行过程的产生可能集。随后，我们开发了基于不同距离测度的网络DEA模型，并将其转化为乘数形式的两阶段网络DEA模型。
The standard data envelopment analysis (DEA) procedure involves solving a pair of two types of models, multiplier model and envelopment model, and one of the most interesting features of DEA is that these two types of models are equivalent due to duality in linear programming. However, while several prominent network DEA models have been proposed in the literature in multiplier and/or envelopment forms, it is still doubtful or unclear whether and how the same primal-dual correspondence can be retained between the two types of network DEA models as in the standard DEA. To address this issue, we develop an axiomatic derivation of some two-stage network DEA models in this paper focusing on the basic two-stage serial process structure. We define the production possibility set for the basic two-stage serial process based upon some reasonable axiomatic properties. Subsequently we develop envelopment network DEA models using different distance measures, which are then shown to result in well-known existing two-stage network DEA models in the multiplier form.