Data envelopment analysis (DEA) is a very effective management tool in assessing the performance of a set of decision making units (DMUs). In the efficiency evaluation using classic single stage DEA models, the internal processes of the DMUs are often neglected. In most real-world problems, it may be more realistic to evaluate the efficiency evaluation in two-stage production systems. In some cases: however, the decision-maker must need to identify the most efficient single unit. Numerous methods have been introduced to find the most efficient unit in single stage systems whereas no methods have been proposed for this aim in two stage production systems. Therefore, a new model based on mixed-integer programming was proposed to determine the most efficient DMU in two-stage systems and sub-stages in this study. The most important innovation of the suggested approach is that the most efficient DMUs of both stages can be found separately using only one model. Numerical examples for real world problems and a simulation study were provided for the validity of the proposed model.

数据包络分析（DEA）是评估一组决策单元（DMU）绩效的非常有效的管理工具。在使用经典的单阶段DEA模型进行效率评估时，DMU的内部过程通常被忽略。在大多数实际问题中，评估两阶段生产系统中的效率评估可能更为现实。但是，在某些情况下，决策者必须确定最有效的单个单元。为了在单级系统中找到最有效的装置，已经引入了许多方法，而在两级生产系统中没有为此目的提出任何方法。因此，本研究提出了一种基于混合整数编程的新模型，以确定两阶段系统和子阶段中最有效的DMU。建议方法的最重要创新是，仅使用一种模型就可以分别找到两个阶段中最有效的DMU。给出了实际问题的数值示例和仿真研究，以验证所提出模型的有效性。