Evaluation of efficiency using the product method in two-stage systems with undesirable outputs

Data envelopment analysis is a non-parametric method based on mathematics, which is used to evaluate the performance of a set of homogeneous decision-making units in a production technology with multiple inputs and outputs. The idea of performance evaluation in two-stage systems is one of the topics. It is of interest in data coverage analysis. In two-stage systems, all or part of the outputs of the first stage is considered as the input of the tail stage. This input of the second stage can be considered favorable or unfavorable. Arithmetic or geometric models can be used to calculate the efficiency of the decision-making units. Therefore, in this article, the evaluation of efficiency in two-stage systems with undesirable outputs is discussed using the product method. According to the new model presented, the efficiency of 6 regions in China was measured. It should be noted that every region of China has provinces and cities that have the same geographical, natural, etc. conditions.