Cap-and-trade is regarded as the most effective approach to control and reduce greenhouse gas emission. How to perform the reallocation in a fair way is very critical to control total amount of emissions and improve trade mechanism. It has been proved that data envelopment analysis (DEA) is an effective way for reallocation. The objective of the present paper is to develop a centralized DEA model to reallocate emission permits in the cap and trade system based on countries efficiencies. Presented model considers all decision making units (DMUs) together and improves whole efficiency of them by reducing total emission permit as undesirable outputs. Also, this model determines amount of emitted gases that can be reduced without reducing other outputs. To demonstrate the applicability of model, a case study is presented. Sensitivity analysis is carried out to investigate the impact of the some parameters on the results.

Introduction

Economic development of countries has caused many environmental problems. Interconnection between economic development and environmental worsening has led to a key trend in environmental policy and socio-economic development (Redclift, 2005). Environmental problems have seriously threatened human survival and development (Cohen and Winn, 2007). Since 1970, level of total greenhouse gas emissions has reached to 80%.1 Large amount of greenhouse gas emissions (mostly methane, carbon dioxide, and nitrous oxide) has changed chemical composition of atmosphere and, in turn, resulted into global warming and other related damages. Considerable damage could be caused by potential impacts of global warming (Mabey, 1997). To reach sustainable development, countries should focus on environmental, social, and economic aspects. Environmental performance is one of the significant research areas (Zhou et al., 2008). Growing public awareness on pernicious effects of greenhouse gas emissions on human life and pressure of environmentally friendly organizations in the world have led to approval of Kyoto protocol in December 1997. Based on Kyoto protocol, EU-152 committed to reduce six greenhouse gases including carbon dioxide, methane, nitrous oxide, sulfur hexafluoride, fluorocarbons, and hydro fluorocarbon from 2008 to 2012. Following commitment of EU-15, Paris agreement was approved by 195 countries at 21st Conference of Parties based on United Nations Framework Convention on Climate Change (Sutter et al., 2015). Paris agreement deals with decrease of greenhouse gas emissions and it will be adopted in 2020. Countries agreed to mitigate greenhouse gas emissions with their national contributions and provide a green climate fund to control increase in global average temperature to no more than 2
C, and preferably to 1.5
C (Lee, 2016).