## 2 Literature Review  
### Related Research on Carbon Quota Allocation Based on DEA Models  
Many studies have studied the allocation issue based on a single criterion: either efficiency or equality. [PERSON] and [PERSON] [19] proposed that the ZSG-DEA model is particularly suitable for equilibrium models and used it to analyze the allocation of CO2 emission rights among countries under the Kyoto Protocol. [PERSON] et al. [20] proposed an allocation plan for the provincial carbon quota allocation of China based on the 2030 emission reduction target by improved DEA models. [PERSON] et al. [21] used an environmental DEA model to propose that carbon quotas could be allocated through two principles: incremental efficiency improvements and emissions abatement planning. [PERSON] et al. [22] proposed a DEA model based on the eco-efficiency values of electricity generators to analyze carbon emissions and carbon quotas. However, when allocating carbon quotas among regions, there is also a need to consider equality of allocation in addition to efficiency. [PERSON] et al. [23] conducted a study on the allocation of carbon quotas in various geographic regions of China based on the entropy method and DEA model. In this work, the authors introduced an environmental Gini coefficient as a measure of equality of allocation schemes. [PERSON] et al. [9] combined the entropy method, the Super-SBM model, and the ZSG-DEA model and applied them to allocate the 2030 emission abatement target for China. From the perspectives of efficiency, equality, and equity, [PERSON] et al. [24] constructed a ZSG-SBM-based allocation model to obtain a reasonable scheme for the allocation of carbon quotas among provinces in China in 2019. [PERSON] et al. [25] considered the implied emissions of inter-provincial power transfer, combined with the DEA model and environmental Gini coefficient, and designed a dynamic carbon quota allocation model. Their model utilized four criteria: egalitarianism, historical responsibility, emission reduction capacity, and emission efficiency. [PERSON] and [PERSON] [5] combined environmentally relevant DEA and equilibrium efficient frontier DEA models to integrate a carbon quota allocation scheme and a carbon quota trading scheme into a framework that effectively translates the overall reduction target into a reduction target for each country. In addition, the differences in industrial structure and economic development among provinces cause concerns in solving the allocation issue. Scholars have studied the allocation of provincial-level carbon quotas in China from the perspective of industries and sectors. [PERSON] et al. [26] used the DEA method to allocate carbon quotas in provincial industrial sectors of China to reduce energy intensity. [PERSON] et al. [27] allocated thermal power carbon quotas in 30 provinces in China. [PERSON] et al. [28] integrated a fixed-cost allocation model and a zero-sum DEA model to allocate carbon quotas to the public building sector in China for 2030. Table 1 summarizes the above research related to carbon quota allocation based on DEA models. As can be seen from Table 1, scholars have balanced equity and efficiency criteria when developing carbon quota schemes in recent years, and this paper is no exception. Next, most of the decision variables in the literature consist of energy consumption, capital stock, and population as input variables, and GDP and carbon emissions as output variables. Some scholars use CO\({}_{2}\) as an input in their studies. However, CO\({}_{2}\) is a by-product of the production activity, and it would be more in line with the physical production process to consider it as an undesirable product. Some scholars have broken down the emission reduction targets by sector, considering the characteristics of sectors to generate a quota allocation scheme for the sectors in each province. However, no scholars have yet considered the differences among the three major industries in each province.