This study proposes a two-stage game–data envelopment analysis (DEA) approach for cost-efficiency (CE) measurement using centralized and Stackelberg game models. Each decision-making unit (DMU) is proposed to make up two-stage network structures (or processes), where all the first-stage outputs are the only second-stage inputs. The main contribution of this study is the development of cooperative and non-cooperative models for CE measurement and implies a unique CE decomposition. We apply centralized and Stackelberg approaches for cooperative and non-cooperative assumption between two stages. We proposed a simplified version of the two-stage DEA network CE model. Applying the proposed model for CE calculation reduces both the number of constraints and variables, resulting in a sharp reduction in computational requirements. The applicability of the presented model is demonstrated in the context of studying the output of the electrical network in Iran. The results of the case study show that in a two-stage network, the proposed DEA model can provide accurate estimates of CE. This paper aids the two-stage network structures to control the costs by weak DMUs management. To the authors’ knowledge, this paper is the first research on the CE in a network by the DEA approach so that the relationships between the internal stages of the network are considered.

这项研究提出了一种使用集中式和Stackelberg博弈模型的两阶段博弈数据包络分析（DEA）方法，以进行成本效益（CE）测量。建议每个决策单元（DMU）组成两阶段网络结构（或过程），其中所有第一阶段输出都是唯一的第二阶段输入。这项研究的主要贡献是开发了用于CE测量的合作和非合作模型，并暗示了独特的CE分解。我们在两个阶段之间采用集中式和Stackelberg方法进行合作和非合作假设。我们提出了两阶段DEA网络CE模型的简化版本。将提出的模型用于CE计算可减少约束和变量的数量，从而大大减少了计算需求。在研究伊朗电网输出的情况下证明了所提出模型的适用性。案例研究结果表明，在两阶段网络中，提出的DEA模型可以提供对CE的准确估计。本文通过弱DMU管理来帮助两阶段网络结构控制成本。据作者所知，本文是首次通过DEA方法对网络中的CE进行研究，从而考虑了网络内部各阶段之间的关系。本文通过弱DMU管理来帮助两阶段网络结构控制成本。据作者所知，本文是首次通过DEA方法对网络中的CE进行研究，从而考虑了网络内部各阶段之间的关系。本文通过弱DMU管理来帮助两阶段网络结构控制成本。据作者所知，本文是首次通过DEA方法对网络中的CE进行研究，从而考虑了网络内部各阶段之间的关系。