**2. Literature Review**

This method has extended for incorporating environmental issues into the efficiency analysis. Before that, the production function estimation operates for a single output case while DEA models can consider multiple outputs by [2]. A linear programming model was developed by [3] to analyze the efficiency of multi-plant firms in a DEA framework. An extension of the previous paper for the limited data was performed by [4]. They also used the multi-plant technology for efficiency analysis of multi-units [5]. Unlike the classical DEA models that were extended for dealing with pollution generating technology, the multi-plant DEA models cannot consider environmental issues. Analyzing the environmental performance of production units by DEA methods is growing, and this method has been intensively used for environmental efficiency analysis of different sectors in the last decades. A review for the application of DEA models in environmental and energy studies was done by [6]. A study for the UK's regional environmental efficiency using directional distance function DEA models was implemented by [7]. They investigate the link between regional environmental efficiency and economic growth and found a "U" shape form for the link mentioned above. An investigation of the environmental efficiency of transportation sectors in 30 Chinese provinces was done by [8] between 2003 and 2012. They found the transportation sectors to be inefficient in most provinces. Another study by [9] used the DEA model to determine greenhouse gas emissions and carbon sequestration in small-scale maize production in Niger State, Nigeria. An environmental DEA model capable of handling zero and negative data was proposed by [10] and used for US industrial sectors' environmental efficiency analysis. An investigation of the corporate suitability of US industrial sectors was performed by [11] via an environmental efficiency analysis. They emphasized the role of the proposed DEA environmental assessment for corporate leaders in identifying how to invest in technology innovation to reduce undesirable output. A study on the role of the Central Government's policy was doen by [12] in China. They performed provincial level environmental analysis and concluded that though the Central Government's environmental policies fail to solve the inner contradiction between economic and environmental systems. In another study, the economic and environmental performance of wastewater treatment plants was investigated by [13] to find how it is potentially possible to reduce greenhouse gas emissions in the Valencia region on the Mediterranean coast of Spain. Classical DEA models were used by [14] for efficiency analysis and ranking of Iranian power plants at the country level. In another study by [15], classical DEA models were utilized for the environmental efficiency of thermal and hydroelectric power plants in Iranian provinces. They found the average technical efficiency for the hydroelectric power plant in 2011 and 2010 are 62% and 53%, respectively, and 82% and 77%, for thermal power plants in 2011 and 2010, respectively. The technical and environmental efficiency of 16 selected thermal power plants in Iran was investigated by [16] during 2011–2015, using DEA. The technical efficiency of 26 thermal power plants in Iran was analyzed by [17] in the period of 2003–2008 using DEA and the Malmquist index. Iranian industrial sector emissions was studied by [18] using the input-output analysis during 1380–1390. They found that the production of final goods with the highest positive change is the most important factor affecting the increase of emissions. Another investigation was performed by [19] to measure the CO2 emission levels of Iranian provinces. They considered and analyzed the impact of population, urbanization, energy intensity, and per capita income on environmental degradation. The interactions between the Iranian

industries' productive activities, the intensity of energy consumption by these activities, and the resulting environmental impacts (specifically CO2 emissions) were implemented by [20]. The current paper contributes to the literature in two ways. As a theoretical contribution, in this paper, we extend the multi-plant DEA model for dealing with undesirable outputs like pollution. We propose uniform and non-uniform multi-plant DEA models that consider the undesirable outputs. Moreover, other indices are also proposed for analyzing the local and global classical and environmental performance of production units. For the application side, we utilized the proposed model for the local and global classical and environmental efficiency analysis of 46 power plants in 21 provinces in Iran.
