Optimal allocation of CO2 emission quotas at the city level in Bohai Rim Economic Circle based on multi-objective decision approach

As the most developed city circle in northern China, allocating CO2 emission quotas at the Bohai Rim Economic Circle (BREC) city level is essential for developing specific abatement policies. Thus, with reflecting multi-principles (fairness, efficiency, sustainability, and feasibility), this paper formulates the CO2 emission quota allocation among cities in BREC in 2030 based on the multi-objective decision approach. We first propose three allocation schemes based on the principles of fairness, efficiency, and sustainability, which are conducted by entropy method, zero-sum gains data envelopment (ZSG-DEA) model, and CO2 sequestration share method, respectively. Then, the CO2 allocation satisfaction is defined and used to measure the feasibility principle which is integrated as the objective function of the multi-objective decision model together with three allocation schemes to obtain the optimal allocation results. The results show that Beijing, Tianjin, Dalian, Shijiazhuang, Yantai, Weifang, and Linyi enjoy the largest CO2 emission quotas, having 1179.94 Mt in total and accounting for 31%. Beijing has the highest quotas, and Laiwu has the lowest emission quotas. Cities with large energy consumption and less CO2 sequestration capacity, such as Tianjin, Handan, and Tangshan, experience a decrease in the emission quota shares from 2017 to 2030, indicating that these cities would undertake large emission reduction obligations. Sensitivity analysis shows that Beijing, Zibo, and Jinan are more sensitive to minimum satisfaction changes, and the total satisfaction experiences an increase first and declines thereafter. Based on the results above, cities with large pressure to reduce CO2 emissions should not only promote economic development but also improve the capacity of CO2 sequestration by enhancing environmental protection to realize emission reduction targets.


Introduction
In order to combat climate change, the Chinese government has undertaken to reduce the national carbon emission intensity by 60-65% in 2030 compared with 2005 and reach the CO 2 emissions peak before 2030. Besides, in October 2020, China made further commitments to achieve carbon neutrality before 2060. To reduce carbon emission intensity, China has committed to implementing the emission trading scheme (ETS), which is an effective way to reduce CO 2 emissions through the market mechanism (Han et al. 2017;Kong et al. 2019;Hu et al. 2020). After implementing seven carbontrading pilot programs in 2011, China's national ETS was officially launched in December 2017 and started by covering the power sector in this system, while the remaining sectors will be incorporated gradually.
As one of the most essential prerequisites for national ETS, allocating CO 2 emission quotas scientifically and reasonably has attracted increasing attention. Studies have focused on CO 2 emission quota allocation at different levels, for example, country level (Benestad 1994;Pan et al. 2014;Momeni et al. 2019), China's provincial-level (Yi et al. 2011;Kong et al. 2019;He and Zhang 2020;Zhou et al. 2021), and several provinces within specific regions (Han et al. 2016;Chang Responsible editor: Roula Inglesi-Lotz et al. 2020). With respect to determining the CO 2 emission quotas by cities, Li et al. (2018a) constructed a comprehensive index using the maximum deviation method to allocate CO 2 emission quotas among nine cities in the Pearl River Delta region by 2020. Zhou et al. (2018) evaluated emission performance and allocated CO 2 emission quotas to Chinese 71 cities based on the data envelopment analysis (DEA) model. Besides, Liu et al. (2018) determined the CO 2 emission quotas among 25 cities in the Yangtze River Delta region by constructing a comprehensive index. The same case study was conducted by Zhang et al. (2020), who simulated the CO 2 emission quotas allocation by the ZSG-DEA model. In summary, few studies and methods are focusing on the CO 2 emission quota allocation at the city level.
As the main subject of CO 2 emissions, cities play an essential role in achieving carbon emission reduction targets, providing more accurate information than the provincial level to formulate targeted policies for emission reduction. Besides, as the most developed area in northern China, BREC consumed a lot of energy, accounting for 25.4% of the national total in 2017 (Chang et al. 2020). The realization of its regional coordinated carbon reduction has strategic importance for realizing China's national emission reduction target. Chang et al. (2020) proposed a two-stage allocation model to simulate the CO 2 emission quota allocation for five provinces in BREC in 2030. Han et al. (2016) issued CO 2 emission quotas to three provinces in the Beijing-Tianjin-Hebei region using the composite index approach. However, few studies have been conducted to allocate the CO 2 emission quotas among the cities in BREC. Therefore, it is of great importance to investigate provincial emission quota allocation among cities. This paper aims to formulate the CO 2 emission quota allocation for cities in BREC in 2030.
Furthermore, the principles and methods used can be induced from the existing literature. Generally, fairness and efficiency are two main principles followed by the most current studies. For example, Pan et al. (2014) formulated the fair CO 2 emission quota allocation at national levels following equal cumulative emission per capita. As for the efficiency principle, three allocation strategies (spatial, temporal, and spatial-temporal) were adopted by Zhou et al. (2014), who formulated the optimal allocation of CO 2 emission quotas using centralized DEA models. Also, Dong et al. (2018) applied an improved fixed cost allocation model by taking fairness and efficiency principles both into consideration. The same principles were considered by Kong et al. (2019) and He and Zhang et al. (2020), who combined the entropy method with the DEA model to establish a comprehensive index for the allocation of provincial CO 2 emission quotas. Although the principle of fairness and efficiency is most commonly used, the indicators measuring the fairness and efficiency principles failed to reach a unified conclusion. Besides, considering production consistency, feasibility principle was also proposed in the various studies since they believe the CO 2 emission quotas should be allocated with strong operational and more readily accepted in practice (Zetterberg et al. 2012;Zhou and Wang 2016;Li et al. 2018a;Zhu et al. 2018;Fang et al. 2018b;Fang et al. 2019). In addition, increasing attention has been paid to the principle of sustainability, which caters to the CO 2 emission demand of future development (Fang et al. 2018b;Fang et al. 2019;Cui et al. 2020;Li et al. 2020;Zhou et al. 2021). For instance, the environmental factors, including the absorptive capacity to sequestrate CO 2 and ecosystem service value, are used to reflect the sustainability principle Zhou et al. 2021).
To improve adaptability, the multi-criteria scheme has been proposed. For example, Fang et al. (2019) considered the indicators quantifying the principles of fairness, efficiency, feasibility, and sustainability into an improved ZSG-DEA model to determine the CO 2 emission quotas at the provincial level. Zhou et al. (2021) carried out a study of China's CO 2 emission quota allocation program design and efficiency evaluation by 2020, which integrated the principles of fairness, efficiency, and sustainability together to construct a comprehensive index based on the entropy method. Li et al. (2021) combined the Shapley value method, the entropy method, and the ZSG-DEA model to formulate the CO 2 emission quotas reflecting the principles of fairness, efficiency, feasibility, and sustainability. Generally, considering multiple principles to explore a compromise scheme is increasingly recognized. Thus, this paper aims to explore the CO 2 emission quota allocation of cities to achieve the multi-criteria objective.
The commonly used allocation methods to build multicriteria allocation schemes can be concluded as indicator approach, DEA, nonlinear programming models, game theory, and hybrid or other approaches. The indicator approach, especially the composite index, has been widely used to respond to different principles. For example, Yi et al. (2011) simulated the allocation of the national emission target by 2020, integrating carbon reduction responsibility, potential, and capacity. Similar studies were conducted by Chang et al. (2016), Han et al. (2016), Tang et al. (2019), and Zhou et al. (2021). Besides, many studies also constructed the comprehensive index combining the DEA model (Qin et al. 2017;Zhou et al. 2017;Liu et al. 2018;Kong et al. 2019;Zhou and Jin 2019). However, its subjectivity and arbitrariness have been criticized . For one thing, most of the indicators selected by previous studies are inconsistent, and the differences in natural resources and the environment have been ignored to a certain extent, except for the studies of Fang et al. (2018b) and Zhou et al. (2021). The environmental factor, especially carbon absorption, has a significant impact on the ecosystem's carbon cycle, which affects the realization of carbon neutrality. Besides, how to determine the weights for different indicators is still controversial. DEA and ZSG-DEA models have emerged to solve the problem by focusing on the whole system's efficiency. As a typical optimization method, researchers have proposed various improved DEA models, which provide more innovative ideas and solutions for CO 2 emission quota allocation. Similar models can be found in the studies of Zhou et al. (2014), Feng et al. (2015, Wu et al. (2016), An et al. (2017), Momeni et al. (2019), Xie et al. (2019), and Yu et al. (2019a). On the basis of the DEA model, the ZSG-DEA model was developed by reallocating the remaining resources based on the cooperation or competition among DMUs (decision-making units). Wang et al. (2013), Miao et al. (2016), Cucchiella et al. (2018), Cai and Ye (2019), Yu et al. (2019b), andFang et al. (2019) used the ZSG-DEA model, selecting different indicators as input and output variables to allocate the CO 2 emission quotas. Besides, Yang et al. (2020) proposed a ZSG-DEA model by improving the iterative approach, which introduces the fairness principle into the efficiency-oriented model to optimize the CO 2 emission reduction scheme for Chinese provinces by 2030. The mechanism of DEA gives priority to the efficiency principle, which may underestimate the effects of other principles. Besides, some studies regarded collaborative carbon abatement as the basis of allocation by game theory (Filar and Gaertner 1997;Li and Piao 2013;Zhang et al. 2014). However, the game theory is too complicated to be suitable for the allocation of the Chinese city level.
By contrast, the nonlinear optimization model has emerged as another common method, which explores using the multi-objective decision approach for resource allocation. Table 1 describes the use of nonlinear optimization models with their constraint condition, specifically, considering optimization based on fairness principle (Fang et al. 2018a), efficiency principle (Li et al. 2018b;Ye et al. 2019), and both fairness and efficiency principles Ma et al. 2020). Besides, Zhu et al. (2018) proposed a multi-objective decision model incorporating the principles of fairness, efficiency, and feasibility to allocate CO 2 emission quotas to six industries in Guangdong. The environmental Gini coefficient is mainly used to realize fairness optimization, while the optimization of efficiency mostly focuses on maximizing economic benefits and minimizing carbon reduction costs. However, the environmental Gini coefficient minimization model cannot consider historical emissions. This study intends to build CO 2 emission quota allocation solutions with more consensus on fairness and efficiency. In addition, as increasing guidelines are applied to multi-criteria, most nonlinear optimization models for CO 2 emission quota allocation need to be improved in defining and reflecting allocation principles other than the principles of fairness and efficiency. Thus, it is of great significance to integrate the feasibility and sustainability principles into the multi-objective decision with carbon intensity reduction targets towards 2030.
Considering the prevalence of the multi-objective decision approach, which can transform the allocation principles into specific mathematical models with constrained boundary condition, this paper proposes a multi-objective decision model, integrating the principles of fairness, efficiency, sustainability, and feasibility, to formulate the allocation of CO 2 emission quotas among cities in BREC by 2030. Specifically, we put forward three allocation schemes based on fairness, efficiency, and sustainability, respectively. The first allocation scheme is based on the principle of fairness. We construct a composite index integrating different fair indicators, including population, GDP, historical CO 2 emissions, and historically accumulated net CO 2 emission, where the historically cumulative net CO 2 emissions are calculated by deducting the CO 2 sequestration of vegetation. Based on this composite index, we use the entropy method to allocate the emission quotas to each city in BREC. As for the second allocation scheme, we simply take the efficiency principle into consideration and use the ZSG-DEA model to obtain each city's CO 2 emission quotas. The third allocation scheme is based on the sustainability principle and conducted using the proportion of regional carbon sequestration. After receiving three schemes, we further define the CO 2 allocation satisfaction to reflect the feasibility principle. Ultimately, three allocation schemes, as well as the allocation satisfaction (feasibility principle), are integrated into the multi-objective decision model as objective functions. Thus, this multi-objective decision model is proposed to explore the optimal allocation results.
Overall, the contributions of this paper can be described as (1) selecting the cities in BREC as the research object to analyze its CO 2 emission quotas allocation in 2030; (2) integrating the principles of fairness, efficiency, sustainability, and feasibility into a multi-objective decision model; (3) proposing and optimizing the allocation schemes based on the principles of fairness, efficiency, and sustainability to improve the adaptability of schemes; and (4) integrating the CO 2 allocation satisfaction for each city to ensure the feasibility of allocation scheme.
The remainder of this paper is conducted as follows. The "Methodology and data sources" section interprets the methods and data sources. The "Results" section introduces the CO 2 emission quota allocation results under single and multi-principles. The sensitivity analysis is provided in the "Sensitivity analysis" section. The "Conclusions and policy implications" section concludes this paper and provides some policy implications. Figure 1 illustrates the schematic of the CO 2 emission quota allocation adopted by this paper. First, three allocation schemes based on fairness, efficiency, and sustainability are conducted, respectively. Second, we define the CO 2 allocation satisfaction to measure the feasibility principle of the allocation scheme. Finally, a multi-objective model is established to explore the optimal CO 2 emission quota allocation solution considering the principles of fairness, efficiency, sustainability, and feasibility together.

Methodology and data sources
In this section, we begin with the method of allocation scheme based on the fairness principle. Then, we introduce the method of allocation schemes based on the principles of efficiency and sustainability, respectively, following which we explain the measurement of feasibility principle. "The multi-objective CO2 emission quota allocation" section presents the multi-objective decision model integrating the principles of fairness, efficiency, sustainability, and feasibility. Finally, this section introduces the data sources.

Allocation scheme based on the fairness principle
This paper intends to build the compromise allocation scheme considering the fairness principle by constructing a composite index. The indicators selected in this paper follow different perspectives of the fairness principle, as shown in Table 2. It should be noted that the accumulated historical net CO 2 emissions are the accumulated historical CO 2 emission minus CO 2 sequestration over the period 2005-2017, which reflects the attention on environmental factors.
To quantify the comprehensive index, we employ the entropy method to determine the weight of each indicator, which has been widely used to build the comprehensive index of CO 2 emission quota allocation (Feng et al. 2015;Liu et al. 2018;Kong et al. 2019;He and Zhang 2020). The methods are shown as follows: The following equation can normalize the positive indicator and negative indicator: where p ij is the value of indicator j of the city; max i p ij and min i p ij are the maximum and minimum values of cities, respectively; and x ij is the normalized value of p ij . Then, we calculate the entropy value of indicator j using Eqs. (3) and (4):  (Fang et al. 2018a) Minimize the sum of Gini coefficients (accumulated percentage of population, ecological productive land, GDP, and fossil energy resources) Gini coefficient constraint CO 2 emission intensity reduction constraint The restraint of CO 2 emission intensity reduction ratio in different regions Allocating CO 2 emission quotas to the Pearl River Delta cities (Li et al. 2018b) The minimization of regional abatement costs The maximization of individual interests where y ij is the share of indicator j of the city i in the sum of indicator j of all cities and m j is the entropy of indicator j. And if y ij = 0, then ln(y ij ) = 0. Next, we calculate the weight of each indicator and construct a comprehensive index.
The weight of indicator j (r j ) can be calculated using Eq. (5).
The comprehensive index (h i ) can be built by Eq. (6):  Finally, we calculate the weight for the city i by Eq. (7): After the comprehensive index of each city was obtained, we calculate the CO 2 emission quotas that each city should be allocated, represented as the Eq. (8).
where C fi is the CO 2 emission quota of the city i allocated based on the fairness principle and C 2030 is the total CO 2 emissions in BREC in 2030. The optimization of fairness requires the allocation results to be as close as possible to C fi with the constraints. We develop the fair evaluation function of CO 2 emission allocation If F 1 = 0, the allocation results are consistent with the fairness scheme. The objective function of fairness is expressed as: The allocation scheme based on the efficiency principle This paper applies the ZSG-DEA model to search for optimal CO 2 emissions with all cities on the DEA efficiency frontier. As the total CO 2 emissions in 2030 remain constant, the ZSG-DEA model can obtain the optimal allocation results by reallocating the redundant CO 2 emission among all cities. And it has been widely used to allocate CO 2 emission quotas, for example, taking CO 2 emissions as undesirable output; Wang et al. (2013) and Miao et al. (2016) adopted output-oriented ZSG-DEA model to formulate the allocation of CO 2 emission quotas. Conversely, the input-oriented ZSG-DEA models are also developed considering CO 2 emission as an input variable to formulate the allocation of CO 2 emission quotas (Cai and Ye 2019;Fang et al. 2019;Yu et al. 2019b). We adopt an input-oriented ZSG-DEA model to obtain optimal CO 2 emissions for each city. We consider energy consumption, labor, and GDP as three output variables and CO 2 emissions as an input variable, as shown in Table 3. The initial CO 2 emissions for each city in 2030 are obtained by the proportion of CO 2 emissions in 2017, where it is called grandfathering.
The input-oriented ZSG-DEA model is expressed as: where φ 0 is the efficiency value of the DMU being evaluated; C 0 , Y 0 , L 0 , E 0 , A 0 are the values of the corresponding variables of the DMU being evaluated; and E i , L i , Y i are the energy consumption, labor, and GDP of the ith DMU in 2030, respectively. λ i is the share of the ith DMU; C gi is the actual CO 2 emission of the ith DMU in 2030.
For an inefficient DMU k (k = 1, …, 44) (with initial DEA efficiency of φ k and initial CO 2 emission quota of C k ), its initial CO 2 emission quota must be reduced by C k (1 -φ k ). The remaining DMUs must increase their CO 2 emissions by Fang et al. 2019). Finally, we can obtain the optimal CO 2 emission of each city, expressed by C ei .
After obtaining each city's optimal CO 2 emissions (C ei ), the efficiency evaluation function of CO 2 emission allocation is built as If F 2 = 0, the allocation results follow the optimal efficiency scheme. The optimal solution is built to minimize ∑ n i¼1 C i −C ei ð Þ 2 , which can be described by the following equation: The allocation scheme based on sustainability principle When allocating CO 2 emission quotas, increasing attention has been paid to the principle of sustainability. Fang et al. (2018b) used urbanization rate, the proportion of the tertiary industry, and forest coverage rate to represent the sustainability principle of social, economic, and environmental dimensions, respectively. A similar approach was used by Li et al.  (2020), who applied forest coverage rate, population growth rate, and GDP growth rate as sustainability indicators. Zhou et al. (2021) adopted ecosystem service value as the indicator to reflect the sustainability principle. This paper uses carbon sequestration capacity as the sustainability principle of CO 2 emission quota allocation. We can calculate the CO 2 emission quotas based on the CO 2 sequestration capacity of each city, as shown in the following equation: where C si is CO 2 emission quotas of the city i, allocated based on the sustainability principle. S i is CO 2 sequestration of city i in 2017.
Similarly, the sustainability evaluation function of CO 2 emission allocation can be built as F 2 ¼ ∑ n i¼1 C i −C si ð Þ 2 . If F 2 = 0, the allocation results are equal to C si for each city. The objective function is shown as: The feasibility of CO 2 emission quota allocation The feasibility principle means that the allocation of CO 2 emission quotas should maintain production consistency, which is easy to be accepted and implemented (Zhu et al. 2018). This paper uses the "CO 2 allocation satisfaction" to estimate the feasibility of CO 2 emission quota allocation. For each city, if the allocated CO 2 emission quotas are larger than the CO 2 emission expectation, the degree of satisfaction is 1; by contraries, if the minimum CO 2 emission expectation is not met, the satisfaction degree is 0. The CO 2 allocation satisfaction function degree is described as follows: where C max i and C min i are the upper and lower limits of CO 2 emission feasibility interval for the city i, respectively. Although grandfathering has less impact on production and fewer political barriers (Zetterberg et al. 2012;Zhu et al. 2018), it has been criticized for its limitations on punishing efficient carbon firms while rewarding carbon-intensive firms (Zhou and Wang 2016). Feng et al. (2015) proposed a weighted voting model to quantify the voting rights of each city to select the CO 2 allocation schemes based on population, GDP, and historical emissions, which are intuitive and clear. Besides, Dong et al. (2018) analyzed the allocation schemes based on historical emissions, population, and per capita GDP (pays ability egalitarian), and then selected the allocation results based on pays ability egalitarian as constraint condition in the modified fixed cost allocation model to determine CO 2 emission quotas of each province in China optimized the CO 2 emission quotas based on a modified fixed cost allocation model. Inspired by the work of Dong et al. (2018) and Feng et al. (2015), this paper analyzes the three scenarios (population, GDP, and historical emissions) to determine the feasibility of CO 2 emission quota allocation as well as allocation satisfaction interval, presented as: where C popi , C gdpi and C gi are allocation results based on population, GDP, and historical emissions. The year 2017 is considered as a reference.
As for the feasibility of CO 2 emission quota allocation, there is no doubt that the higher CO 2 allocation satisfaction, the easier it is to accept and implement. And the most acceptable scheme requires maximizing the satisfaction of each city. However, it is impossible for all of the cities to reach their maximum CO 2 allocation satisfaction. We aim at maximizing the sum of minimum CO 2 allocation satisfaction for all cities, described as: The multi-objective CO 2 emission quota allocation As stated in "Allocation scheme based on the fairness principle", "The allocation scheme based on the efficiency principle", "The allocation scheme based on sustainability principle", and "The feasibility of CO 2 emission quota allocation" sections, the multi-objective CO 2 emission quota allocation model can be described as follows: The proposed model (18) is a multi-objective model. We can convert multiple goals into a single-objective model to seek the optimal value. Although Eq. (17) maximizes the total minimum CO 2 allocation satisfaction, it may be based on sacrificing the satisfaction of some cities. Considering the feasibility of allocation for each city, Eq. (17) is converted by the following constraint: where α is the minimum satisfaction acceptable to each city.
The CO 2 emission quota allocation needs to consider the relationships among different principles comprehensively. However, these four principles cannot be optimal at the same time due to the conflicts and contradictions between different principles. For example, the efficiency principle departs from fairness and sustainability. Therefore, the core issue of the multi-objective CO 2 emission quota allocation is not to pursue the optimal solution for each principle but to seek a non-inferior solution. More precisely, on the premise of meeting the CO 2 constraints, the allocation of the quotas is a trade-off between the four principles. Besides, as stated in "Allocation scheme based on the fairness principle", "The allocation scheme based on the efficiency principle", and "The allocation scheme based on sustainability principle" sections, we establish the evaluation functions of fairness, efficiency, and sustainability principles, and the deviations of the specified values are required to be as small as possible, respectively. Inspired by Zhu et al. (2018), C fi , C ei , and C si are considered to be ideal points of the three goals; thus, this paper uses a weighted sum approach to integrate the three objective functions, which is reasonable. The original model (18) can be converted into the following form.
where b 1 , b 2 , and b 3 are the weights of fairness, efficiency, and sustainability principles. Original data of provincial energy consumption in this paper is collected from the China Energy Statistical Yearbook (China National Bureau of Statistics, 2006-2018c). The historical CO 2 emissions and CO 2 sequestration capacity are collected from the work of Chen et al. (2020). More information about the calculation of CO 2 emissions at the city level can be found in the study of Chen et al. (2020). To ensure that the sum of CO 2 emissions in all cities is in line with the provincial total CO 2 emissions, this paper makes correction about the CO 2 emissions in each city by dividing a correction factor, which is calculated as the ratio of total CO 2 emissions in all cities to the provincial CO 2 emissions. The provincial CO 2 emissions are calculated from fossil energy consumption. Based on the city's CO 2 emissions, we calculate the standard coal consumption of each city by dividing the CO 2 emissions by the emission coefficient.

Data sources
Since we do the emission allocation in 2030, the total CO 2 emissions in BREC in 2030 are required. China's emission reduction target is to reduce the carbon intensity by 60-65% in 2030, compared with 2005. We set the same reduction target for BERC and assume that the emission target of 60% in 2030 will be realized. The total CO 2 emissions in BREC in 2030 (C 2030 ) can be calculated as C 2030 = (1 − 60%) × CI 2005 GDP 2030 , where CI 2005 is the CO 2 intensity in 2005 and GDP 2030 is the GDP in 2030.
As illustrated in the methods, the population, labor, GDP, and energy consumption in this paper should be predicted to 2030. We first calculate the total population of each city in 2030 based on the annual average growth rate of population for each city from 2005 to 2017. According to the development plan of each province, the populations in Beijing, Tianjin, Hebei, Shandong, and Liaoning in 2030 are 2300, 2150, 7910, 4500, and 10,667, respectively. To ensure that the sum of the population of cities in each province is consistent with the provincial predictions from provincial development planning, we correct the estimated population of each city in 2030 using the reference data of the total provincial population. The initial estimate data is divided by a correction factor, defined as the ratio of the sum of the population in all cities to the provincial predictions. Based on the population forecast, we multiply the population by the share of the labor force in the population of each city to calculate the labor, which is calculated by the proportion of employees to the population in 2017.
To estimate the GDP of each city, we first forecast provincial GDP using the annual average growth rate of GDP for each province from 2005 to 2017. According to Energy Outlook 2050 (2019), China's GDP growth rate will be approximately 6.7% before 2020 and approximately 5% between 2021 and 2035. Based on the related growth rate of China's GDP, we predict China's GDP until 2030. Then using China's GDP, we correct the provincial GDP by a correction factor, which is calculated by the ratio of the sum of GDP in all provinces to the national predictions. All the values are converted into the 2005 constant price. After the provincial GDP is obtained, we use the same prediction method with population to estimate the GDP of each city in 2030. Following the same method, we estimate the energy consumption of each city in 2030. We assume that China's total energy consumption is 6 billion tons of standard coal for reference. The reference data is from the energy production and consumption revolution strategy (2016-2030).

Scenario setting
We attempt to analyze the CO 2 emission quota allocation results under various decision preferences of decision-makers.
Four scenarios include equal weights, preferring fairness, preferring efficiency, and preferring sustainability. b 1 , b 2 , and b 3 in Table 4 are the weights of the allocation principles of fairness, efficiency, and sustainability, respectively.

Allocation results based on the fairness principle
According to the interpretation of fair CO 2 emission quota allocation in previous literature, this paper uses four indicators selected from different perspectives of fairness principle to obtain the allocation scheme based on fairness, including population, GDP, historical cumulative net CO 2 emissions, and historical carbon emission. We calculated the weights of these four indicators using the entropy method. As shown in Table 5, the weight of GDP is the largest, followed by population and historical CO 2 emission, while historical cumulative net CO 2 emissions appear the minimal importance. The environmental Gini coefficient based on population is 0.115 less than 0.2, which means that the allocation results are absolutely fair.
G pop is the environmental Gini coefficient based on population, which is calculated by the trapezoidal area method referring to the formula of Kong et al. (2019) Figure 2 displays the results of CO 2 emission quota allocation based on fairness in 2030. The regions with higher GDP, population, and historical CO 2 emission tend to obtain more CO 2 emission quotas, even though their historical responsibility may be larger, as the weight of historical cumulative net carbon emissions is the smallest. For example, Beijing, Tianjin, Qingdao, and Shijiazhuang, are the four cities having the highest emission quota allocation, accounting for more than 25.10% of the total. The share of CO 2 emission quotas in fourteen cities is less than 1.0 % in 2030. Among them, Laiwu and Fuxin enjoy the lowest CO 2 emission quota allocation proportions of 0.31% and 0.38%, respectively.

Allocation results based on the efficiency principle
This paper uses the ZSG-DEA model to attain each city's CO 2 emission quotas based on the efficiency principle. Figure 3 depicts the DEA efficiency changes for each allocation. The allocation efficiency using the ZSG-DEA model in twentyone cities is less than the average initial allocation efficiency of 0.89. Only five out of 44 cities have reached the DEA frontier. Tangshan experiences the lowest initial allocation efficiency of 0.8. After the first reallocation, tremendous changes are found, in which the DEA efficiency of all cities is above 0.97 and the average efficiency increases to 0.99, even though no additional cities achieve optimal DEA efficiency. With the completion of the second reallocation, twelve cities have the efficiency of 1, while the remaining cities are close to the DEA frontier. Ultimately, all the cities obtain the optimal efficiency of 1. Figure 4 describes the initial CO 2 emission and reallocation results for each city. The initial CO 2 emission is completely dependent on each city's historical emissions. We can find that CO 2 emission quotas increase in fifteen cities (e.g., Tianjin, Beijing, Dalian). Conversely, a decrease in the CO 2 emission quotas is witnessed in nineteen cities, including Tangshan, Shijiazhuang, Cangzhou, and Langfang. Besides, the CO 2 emission quotas in Jining, Taian, Rizhao, Linyi, Liaocheng, Zaozhuang, Shenyang, and Xingtai remain stable. The reallocation results indicate that Tianjin reports the largest CO 2 emission quotas with the value of 302 million tons (Mt), followed by Beijing (183 Mt Allocation results based on sustainability principle Figure 5 compares each city's CO 2 emission with their CO 2 sequestration and measures the environment pressure defined as CO 2 emission minus CO 2 sequestration in 2017. It can be found that the majority of cities have produced excessive CO 2 emissions, and the CO 2 sequestration of BREC is 776.45 Mt in 2017, which is far lower than the CO 2 emissions (1485 Mt) in the same period. Thus, it is difficult to achieve carbon neutralization only through the absorption effect of the environment on CO 2 . Meanwhile, negative environment pressure can be found in Chengde, Zhangjiakou, Dandong, Chaoyang, Fushun, Benxi, and Dalian, whose CO 2 sequestration has already exceeded their CO 2 emission by 41Mt, 31 Mt, 21 Mt, 10 Mt, 7 Mt, 6 Mt, 5 Mt, respectively. Fuxin, Tieling, and Huludao having a slight surplus of CO 2 sequestration are approaching the breakeven point (less than 0.30 Mt). By contrast, Laiwu, Rizhao, Jinzhou, Yingkou, Qinhuangdao, Weihai, and Liaoyang are under relatively low environmental pressure (less than 10.0 Mt). The remaining cities, including Beijing, Tianjin, and Shijiazhuang, are facing higher environmental pressure with a massive shortage of CO 2 sequestration (more than 10.0 Mt). The CO 2 emission quota allocation based on sustainability in 2030 is shown in Fig. 6. The cities with higher carbon sequestration capacity will be allocated with larger shares of emission quotas. Chengde, Zhangjiakou, and Dalian account for the largest proportion with 7.1 %, 7.0%, and 5.4%, respectively. The emission quotas in five cities, including Laiwu, Panjin, Liaoyang, Langfang, and Zaozhuang, stay at the lowest level and account for less than 1% of the total in 2030.

The feasibility interval of CO 2 emission quotas
Different from the principles of fairness, efficiency, and sustainability, this paper defines CO 2 allocation satisfaction to measure the feasibility principle. Specifically, inspired by Feng et al. (2015), who provided three allocation schemes, including population-based, GDP-based, and historical emissions-based, for each region to select its incline one, we analyze the above three scenarios to determine the allocation interval. Although there is no allocation scheme that can satisfy the favor of all cities, it is deemed better to obtain more emission quotas (Feng et al. 2015;Xie et al. 2019). Therefore, each city tends to choose the option that is most beneficial to them. Table 6 presents the allocation selected by each city, and the CO 2 allocation satisfaction interval is also given. The allocation based on GDP is dominant in fifteen cities, such as Beijing, Tianjin, and Xingtai. There are sixteen cities that choose the allocation scheme based on historical CO 2 emission, classified into the second echelon, while the population-based allocation scheme contributes the most to the remaining thirteen cities. As for the satisfaction interval span, the gap between the maximum and minimum CO 2 emissions of Beijing is the largest (287 Mt), followed by Tianjin (220 Mt), Tangshan (144 Mt), Baoding (142 Mt), and Handan (133 Mt). The differences between upper and lower bounds of CO 2 allocation satisfaction interval in Laiwu, Rizhao, Benxi, Anshan, Dongying, Fushun, Yingkou, Zhangjiakou, and Zaozhuang are less than 20 Mt. Among them, those of Laiwu and Rizhao are 9 and 10 Mt, respectively. Figure 7 delineates the contributions of the principles of fairness, efficiency, and sustainability to each city. Generally, there are both conflicts and agreements between the principles of fairness, efficiency, and sustainability. The fairness principle has gained prominence in eleven cities, including Beijing, Xingtai, Tianjin, Jinan, Zibo, Qingdao, and Shijiazhuang, whose proportion of allocation results based on the fairness principle is the largest compared with the other two principles. In the case of Beijing, for example, results indicate that the proportion of fairness has reached 52.2%. Eleven cities (e.g., Langfang, Tangshan, Tianjin, Shenyang) have the advantage of reflecting the efficiency principle, many of which are Additionally, the agreements exist in the remaining ten cities, in which the principles contribute similarly. For example, the proportion of fairness, efficiency, and sustainability principles in Linyi is 35.9%, 32.0%, and 32.1%. We further calculate the satisfaction of the single principlebased allocation scheme using Eqs. (14), (15), and (16). As shown in Fig. 8, the average of CO 2 allocation satisfaction based on the efficiency principle is the largest (0.53), followed by the principles of sustainability (0.44) and fairness (0.40). Thus, the allocation scheme based on the efficiency principle is the most feasible one. However, there are thirteen cities with low satisfaction (less than 0.2), among which the CO 2 allocation satisfaction in six cities is equal to 0. Only eight cities' satisfaction is lower than 0.2 in the fairness allocation scheme. Furthermore, this situation in the allocation scheme based on sustainability appears even worse than the principles of fairness and efficiency, which emerges as eighteen cities have low CO 2 allocation satisfaction, with which less than 0.1. The standard variance of CO 2 allocation satisfaction is the smallest in the fairness allocation scheme (0.12) among the three allocation schemes.

Multi-objective CO 2 quota allocation results
In order to improve the allocation results based on the single principle, this paper proposes a multi-objective CO 2 emission Fig. 3 The DEA efficiency of initial allocation and reallocation Fig. 4 The initial CO 2 emission and its reallocation results quota allocation model. The results of different cases are reported in Table 7. The minimum CO 2 allocation satisfaction a=0.3 is set as the baseline scenario. The CO 2 emission quotas in seventeen cities, such as Shijiazhuang, Chaoyang, Huludao, Jinan, and Liaocheng, are approximately equal in different cases. We also find that the satisfaction of those cities is close to the upper and lower limits of constraints, which means the CO 2 allocation satisfaction constraint decides their allocation results. Different characteristics are shown in the remaining cities. For example, Dalian obtains the largest CO 2 emission quotas under case 4 (preferring sustainability) with 180 Mt. In comparison, the lowest one is case 3 (preferring efficiency) with 143 Mt. Beijing is allocated with the highest CO 2 emission quotas in case 2 (preferring fairness) with 260 Mt. Emission quotas obtained by Beijing are the same in remaining cases. For Tianjin, the allocation results in cases 1 and 4 are equal to 231 Mt, and the largest quota is from case 2 (255 Mt), followed by case 3 (251Mt).
In case 1 (equal weights), Beijing, Tianjin, Dalian, Shijiazhuang, Yantai, Weifang, and Linyi enjoy the largest CO 2 emission quotas, 1180 Mt in total, and accounting for 31%. Compared with the initial CO 2 emissions obtained by grandfathering, the final results under the case of equal weights indicate that fifteen out of the 44 cities are found to cut down their CO 2 emission quotas, including Langfang, Tangshan, and Cangzhou, while ten cities (Qinhuangdao, Anshan, Fushun, and Benxi) remain stable, and the remaining nineteen cities such as Beijing, Qingdao, and Yantai experience the increase of emission quotas. Table 7 shows that case 2 is beneficial to Beijing, Tianjin, Dongying, Weifang, Linyi, and Heze, in which they obtain the largest emission quotas among the four cases. Conversely, it is not beneficial to Tangshan, Qinhuangdao, Jinzhou, and Yingkou. Some cities such as Tangshan, Handan, Cangzhou, Shenyang, Liaoyang, and Panjin prefer case 3, while Qinhuangdao, Baoding, Dalian, and Yantai incline to choose case 4. Figure 9 displays the sum of CO 2 allocation satisfaction of 44 cities with different decision cases. The greatest CO 2 allocation satisfaction is case 4 with 25.58. The following are cases 1 and 3, which are 25.12 and 24.07, respectively, while the lowest one is case 2 with 23.72. Therefore, the allocation preferring sustainability is the most feasible among the four cases. Compared with the single principle-based allocation scheme, fewer differences exist in the results of multi-object models with various cases, which means that allocation results of multi-objective models under different cases present a smaller variance. For example, the CO 2 emission quotas of Heze are equal to 37 Mt in multi-objective models under four cases. In contrast, the largest CO 2 emission quotas in the single principle-based allocation scheme are 6.26 times the size of the smallest. Allocation schemes based on fairness and sustainability principles have low CO 2 allocation satisfaction, conflicting with the feasibility principle. The scheme based on efficiency cannot achieve a fair allocation. Serious conflicts exist in the principles of fairness, efficiency, and sustainability in some cities (e.g., Beijing, Langfang, Tieling). Therefore, the scheme based on a single principle inevitably distorts the allocation results. However, the multi-objective model can effectively integrate the principles of fairness, efficiency, sustainability, and feasibility; the results can eliminate the conflicts between multiple principles and become more reasonable with less discrepant across various cases.

Sensitivity analysis
The minimum CO 2 allocation satisfaction (a) measures the feasibility of the allocation scheme, which is exogenously set by estimation and the authority. The value of a decides the CO 2 emission constraint for each city and plays an Fig. 7 The contribution of fairness, efficiency, and sustainability principles to each city allocation. Expressly, we set a at low and high levels: 0 and 0.48 and search the optimal solutions, respectively. When the minimum CO 2 allocation satisfaction (a) is higher than 0.48, the model has no feasible solution.
The sum of minimum CO 2 emissions of all cities would exceed the targeted total CO 2 emission. We take the case of equal weight as an example. The allocation results of choosing different values of a are shown in Table 8.
When a is up from 0 to 0.48, cities with low CO 2 allocation satisfaction increase their CO 2 emission quotas; typical examples include Beijing, Tianjin, Shijiazhuang, Jinan, Zibo, Zaozhuang, Jining, and Taian. Conversely, eighteen cities (e.g., Tangshan, Qinhuangdao, Chaoyang) first keep their CO 2 emission quotas constant with the increase of value a. Then their emission quotas decrease when a exceeds a specific value. Besides, the CO 2 emission quotas in some cities such as Handan, Baoding, Linyi, and Heze decrease first and increase thereafter. The emission quotas in Beijing increase by 38.2%, followed by Zibo and Jinan, with 22.2% and 21.8%, respectively. Fuxin, Chaoyang, and Tieling show the largest reduction proportion of their emission quotas (more than 30%). Some cities are less sensitive to the change of value a, for instance, Shenyang only increases by 0.9%, and Weifang decreases by 2.0%. Figure 10 reflects the tendency of the sum of CO 2 allocation satisfaction in all cities under various values of a. The sum of CO 2 allocation satisfaction experiences an increase first and then declines continuously, and it peaked when a is close to 0.1 at 26.211. The total CO 2 allocation satisfaction is 26.206 when a is equal to 0, which is only a little lower than the peak. When a is at high levels (more than 0.2), the sum of CO 2 allocation satisfaction is sensitive to increasing value a, presenting a faster decrease trend; therefore, it is more likely to obtain a higher level of satisfaction by controlling the value of a at lower levels (less than 0.2). However, it may cause low CO 2 allocation satisfaction in some cities. For example, the CO 2 allocation satisfaction in Shijiazhuang is 0 in the case of a=0. Thus, the policymakers must adopt reasonable minimum CO 2 allocation satisfaction to ensure the feasibility of all cities.

Conclusions and policy implications
This paper develops a multi-objective decision model integrating the principles of fairness, efficiency, sustainability, and feasibility to allocate the CO 2 emission quotas at the city level. Taking BREC as an example, we formulate the CO 2 emission quotas allocation for 44 cities in 2030. The main findings are as follows: Results in the case of equal weights show that Beijing, Tianjin, Dalian, Shijiazhuang, Yantai, Weifang, and Linyi Fig. 8 The satisfaction of CO 2 allocation of cities based on each principle enjoy the largest CO 2 emission quotas 1179.94 Mt in total and accounting for 31%. Compared with the initial CO 2 emissions obtained by grandfathering, fifteen out of the 44 cities are found to cut down their CO 2 emission quotas including Langfang, Tangshan, and Cangzhou, while nineteen cities such as Beijing, Qingdao, and Yantai have increased their emission quotas in 2030 that can be sellers in the carbon trading market. The emission quotas in the remaining ten cities (Qinhuangdao, Anshan, Fushun, and Benxi) remain stable, compared to initial CO 2 emissions.
The single principle-based allocation results display that the principles of fairness, efficiency, sustainability, and feasibility significantly conflict with each other in most cities. Generally, the allocation scheme that considers only the single principle tends to be less satisfactory. Fairness and sustainability principles, with low satisfaction of CO 2 emission quotas allocation, apparently partially go against the feasibility. Similarly, the efficiency principle departs from fairness and sustainability, even though it is more feasible. The sustainability principle, which only considers the environmental factors, cannot achieve fair and efficient allocation results.
Compared with the single principle allocation scheme, the multi-objective allocation model performs much better integrating the four principles (fairness, efficiency, sustainability, and feasibility) and effectively avoiding distorting the allocation results. Results in the multi-objective allocation model under various cases show fewer differences from each other. The satisfaction degree function in CO 2 emission quota allocation ensures that the results are more reasonable and acceptable. Also, it avoids sacrificing the satisfaction of any city effectively. Furthermore, the multi-objective allocation model provides various available options for policymakers by simply adjusting the weights of each principle. Sensitivity analysis indicates that the total CO 2 allocation satisfaction experiences an increase first and then declines constantly, and it reaches the peak when a is close to 0.1 at 26.211.
Based on the empirical results, we further put forward several policy implications. First, policymakers need to select reasonable indicators to allocate emission quotas so that it adapts to the development stages of different cities. In addition to focusing on the economic development level, population, and emission efficiency, attention also should be paid to the environmental factors. To achieve the emission reduction target, for one thing, the local governments should develop and use clean and renewable energy sources. For Fig. 9 The sum of CO 2 allocation satisfaction with various decision preferences Table 8 The CO 2 emission quota allocation results with the change of value a (unit: Mt) another, the investment in afforestation should be promoted to improve the CO 2 sequestration capacity.
Second, local governments should formulate targeted policies for emission reduction based on quota allocation and their situation. The policy orientation must be suitable for local development. By comparing the CO 2 emissions share of each city in 2017, cities with heavy emission reduction burdens, namely Langfang, Tangshan, Cangzhou, Handan, Panjin, Liaoyang, and Binzhou, besides developing the economy, the governments should also practice the concept of green development and promote green consumption at both enterprise and individual levels. While cities with relatively small emission reduction burdens, such as Beijing, Dalian, Zhangjiakou, Chaoyang, and Xingtai, can be sellers in the carbon trading market.
Third, the results show that the principles of fairness, efficiency, sustainability, and feasibility are irreconcilable. Thus, policymakers should explore a compromise solution to eliminate the limitations of allocation schemes based on a single principle. The multi-objective allocation model provides options for decision-makers and can be advocated when allocating CO 2 emission quotas at the city level.
Finally, policymakers must pay attention to the relationship between the total CO 2 allocation satisfaction and the individual city's CO 2 allocation satisfaction. Although a at low levels can achieve higher total satisfaction, it is based on sacrificing the satisfaction of some cities. Therefore, it is of critical importance to set the value of a to make the CO 2 emission quota allocation for cities more reasonable.