# A Multi-Objective Decision Model for Water Pollution Load Allocation under Uncertainty

^{1}

^{2}

^{*}

## Abstract

**:**

_{3}-N are reduced by different ranges. The comprehensive Gini coefficient after COD optimization decreased by 2.4–4.6%, and the comprehensive Gini coefficient after NH

_{3}-N optimization decreased by 25.1–32.5%, which verified the feasibility and rationality of the model in the optimal allocation of the total discharge of regional water pollutants. The model takes into account uncertain subjective and objective factors that have an important impact on water pollutant discharge targets and decision variables, thus optimizing the total emissions of the entire regional control unit in both space and time.

## 1. Introduction

_{3}-N as the target pollution has a significant decrease in the comprehensive Gini coefficient conforming to the allocation scheme, indicating the superiority of the optimal allocation scheme. The contents of the following sections of this paper are as follows: Section 2 firstly introduces the basic concept and calculation method of EGC, then gives the information entropy calculation method of EGC control index weight, the third describes the calculation formula of each control index contribution coefficient, and the fourth introduces the current situation of the 13th Five-Year Plan of Anhui Province in the study area. Section 3 presents the results of EGC calculation and water pollution load distribution in the study area and discusses the rationality of the reduction plan and the decline of the comprehensive Gini coefficient before and after the reduction of COD and NH

_{3}-N target pollutants. Section 4 summarizes the main research conclusions of this paper.

## 2. Materials and Methods

#### 2.1. Environmental Gini Coefficient

_{ij}represents the cumulative percentage of the jth metric in the ith unit, %; Y

_{i}indicates the cumulative proportion of pollutants discharged or allocated in Unit i, %; i = 1, 2, …, n (n is the number of partitions), when i = 1, (X

_{i}− 1, Y

_{i}− 1) = (0, 0). In the application example (see Table 1), the Gini coefficient of different pollutants based on each indicator in the base year can be calculated according to the above formula. This allows for a fair analysis of pollutant emissions in the base year and provides the underlying data for the next step of optimal allocation. It is worth noting that when plotting the Lorenz curve, the sub-regions should be sorted by the amount of contaminants per unit of index load. Normally, planning does not exceed 5 years, during which time there is generally no qualitative change in the situation in each sub-region. Therefore, when calculating Gini(j), the order of sub-regions under the same contaminants and indicators should be roughly consistent with the base year [25].

#### 2.2. Determination of Environmental Gini Coefficient Evaluation Indicators

_{3}-N) emissions and social, economic, natural, and other influencing factors, the control indicators represented by GDP, total population, total water resources, gross industrial production, and industrial wastewater emissions are finally selected [26] to construct an index system for calculating the Gini coefficient.

#### 2.3. The Environmental Gini Coefficient Controls the Determination of the Weight of the Indicator

- Calculate the unit pollutant loads for different indicators in each sub-zone:$${r}_{ij}={x}_{i}/{z}_{ij}$$
_{ij}represents the unit pollutant load of the jth indicator of the ith region; x_{i}indicates the existing sewage discharge in the ith zone; z_{ij}is the indicator value corresponding to the jth indicator in the ith subregion (i = 1, 2, …, n; j = 1, 2, …, m); n is the number of subregions (where, n = 16); m represents the number of indicators (here, m = 5). - Calculate the proportion of regional indicator values for the overall region under different indicators:$${p}_{ij}={r}_{ij}/{\displaystyle \sum}_{i=1}^{n}{r}_{ij}$$
- Calculate the information entropy of the unit pollutant load for each indicator:$${\theta}_{j}=-\frac{1}{\mathrm{ln}n}{\displaystyle \sum}_{i=1}^{n}\left({p}_{ij}\mathrm{ln}{p}_{ij}\right)$$
_{j}≤ 1. - Combined with the above calculation results, the weight value of each indicator can be expressed as:$${w}_{j}=\left(1-{\theta}_{j}\right)/{\displaystyle \sum}_{j=1}^{m}\left(1-{\theta}_{j}\right)$$

#### 2.4. Contribution Factor

_{ij}represents the contribution coefficient of each index, and j = 1, 2, 3, 4, 5 represents the population contribution coefficient, GDP contribution coefficient, total water resource contribution coefficient, industrial production contribution coefficient, and industrial wastewater discharge contribution coefficient, respectively. M

_{ij}refers to the value of the jth indicator in the ith region; M

_{j}is the total value of the jth indicator in the study area; M

_{ij}/M

_{j}represents the contribution rate of the jth indicator in Region I; W

_{ik}stands for the emissions of k different pollutants in Region i; W

_{k}represents the total emissions of the kth pollutant across all study areas, where k = 1, 2. COD and NH

_{3}-N are represented respectively. W

_{ik}/W

_{K}represents the contribution rate of different pollutant emissions in Region i. If the contribution coefficient is greater than 1, it means that the contribution rate of the indicator is greater than the contribution rate of pollutant emissions. If the contribution coefficient is less than 1, it means that the contribution rate of the indicator is less than the contribution rate of pollutant emissions, and there are unfair characteristics, and the smaller the value of the contribution rate, the unfairness increases.

#### 2.5. Optimal Allocation Model of Water Pollution Load Based on Multi-Objective Decision Making under Uncertain Conditions

#### 2.5.1. Fairness Goals

_{j}is the weight value of each index obtained according to the above information entropy method.

#### 2.5.2. Economic Goals

_{i}represents the environmental benefit coefficient of the ith region, where a

_{i}= x

_{0i}/GDP

_{i}(i = 1, 2, …, n); x

_{i}represents the pollutant load distribution in the ith region.

#### 2.5.3. Conditions of Constraint

- Total pollutant discharge constraint. The reduction of pollutants during the planning period determined by the relevant government planning documents is a target that must be achieved, so the model developed in this study sets it as the primary constraint. That is, the sum of pollutant emissions in each sub-region is not greater than the control target after reduction. The details are as follows:$$\sum}_{i=1}^{n}{x}_{i}\le E$$
- Gini coefficient constraint. To make sure the comprehensive Gini coefficient is not larger than the current value after model optimization, the fairness after optimization will not be reduced. Model constraints should satisfy Gini
_{(Comprehensive)}≤ Gini_{0 (Comprehensive)}. “Rigid” constraint makes the allocation scheme inflexible, and in order to increase the feasible domain, the maximum possible optimal value of the objective function is sought. Under the premise of ensuring the global optimum, the Gini coefficient of 0.4 is used as the warning value. Appropriate relaxation is given to the index constraint that the Gini coefficient is less than the warning value; that is, the current Gini coefficient in the fairness constraint ranges. For the index constraint where the Gini coefficient is greater than the warning value, there is no need to give looseness. When Gini_{0j}≤ 0.4, Gini_{j}≤ Gini_{0j}^{±}. When Gini_{0j}> 0.4, Gini_{j}≤ Gini_{0j}. The relaxation of the constraint here is the fuzzy interval of the constraint. The specific constraint formula is determined based on the Gini coefficient of the base year of the study area. - Pollution load reduction rate constraint. For the overall target reduction given in the planning document, each sub-area should be tasked. Therefore, this model needs to set limits on the pollutant reduction rate of each sub-region (that is, the upper and lower limits of pollution load allocation) based on the given regional pollutant reduction rate, combined with the economic development level and actual emission reduction capacity of each sub-region. Due to different subjective and objective reasons, the data information often has certain deviations or statistical inaccuracies—that is, it is ambiguous. In order to better reflect the inaccuracy and incompleteness of statistical information, and also to improve the flexibility of decision-making schemes, it is necessary to consider setting an elastic constraint.$${U}_{\mathrm{min}\left(i\right)}^{\pm}\le \frac{{x}_{0\left(i\right)}-{x}_{i}}{{x}_{0\left(i\right)}}\le {U}_{\mathrm{max}\left(i\right)}^{\pm}$$

#### 2.5.4. The Solution of the Model

- (1)
- Characterization of the number of intervals. Aiming at the uncertainty parameters in the model, the model is intervalized, and the maximum and minimum values of the interval are obtained by taking a certain amount of expansion. The specific values vary within the interval. For this feature, let X
^{±}= [X^{−}, X^{+}] = {x∈X^{±}∣X^{−}≤ x ≤ X^{+}}, which is a uniformly distributed number of intervals with known upper and lower bounds. X^{−}and X^{+}are the upper and lower bounds of the interval number X^{±}, respectively; when X^{−}= X^{+}, the X^{±}becomes a definite value. For the number of intervals [X^{−}, X^{+}] that follow a uniform distribution, a random simulation is performed using the rand function provided by MATLAB to generate random numbers that follow a uniform distribution. For this purpose, a sampling function for the number of intervals is constructed as follows:$${X}_{\left(k\right)}^{\pm}={X}^{-}+\left({X}^{+}-{X}^{-}\right)\mathrm{rand}\left(\xb7\right)\left(k=1~K\right)$$ - (2)
- Solving the multi-objective decision model. The weighted objective programming method is adopted to solve the above nonlinear multi-objective optimization problem, a. The multi-objective function is firstly dimensionless processed, and then converted with weights into a single objective function to facilitate the optimization and screening of subsequent solutions. For the fairness goal and efficiency target, the equal weight coefficient method is used to construct the evaluation function. At the same time, consider that if each objective function order of magnitude is not in the same order of magnitude, there will be a phenomenon of large numbers eating small numbers. In order to prevent this situation, the function is also normalized by orders of magnitude. Due to the introduction of a genetic algorithm to solve the problem, the total target value is first converted into a minimization function, and the multi-objective evaluation function after preprocessing is as follows:$$\mathrm{min}F\left(x\right)={\lambda}_{1}{G}_{\mathrm{Comprehensive}}\left(x\right)/\alpha -{\lambda}_{2}Eb(x)/\beta $$
_{1}and λ_{2}are multi-objective weight coefficients and 0 < λ_{1}, λ_{2}<1, λ_{1}+ λ_{2}= 1; α, β are regularization factors.

#### 2.6. Case Study

#### 2.6.1. Overview of the Study Area

^{2}and a land area of 139,400 km

^{2}, accounting for 1.45% of the country and ranking 22nd. Anhui Province has a total of 16 prefecture-level cities under the jurisdiction of the province. The specific location of Anhui is as follows in Figure 2, in which the diagonally filled part is the location of Anhui Province.

#### 2.6.2. Status of Sewage Discharge in the Base Year of Anhui Province

_{3}-N loads were selected as the main control factors to construct an optimal distribution model for water pollution load. In 2015, the total COD emissions in the province reached 870,900 tons, so at least 85,900 tons need to be reduced within five years; the total ammonia nitrogen emissions reached 96,800 tons, which needs to be reduced by 13,800 tons. According to the 2016 Anhui Statistical Yearbook [33] and the water resources annual reports provided by the municipal water bureaus, the specific values of water pollution discharge and evaluation indicators in each city can be calculated, as shown in Table 1. Among them, the total population of the province is 69.4911 million, the total GDP is CNY 2.254162 trillion, the total water resources are 91.412 billion m

^{3}, the total industrial output value is CNY 3.987566 trillion, and the total discharge of industrial wastewater is 714.3569 million tons.

## 3. Results and Discussions

#### 3.1. Rationality Evaluation of the Current Situation of Pollutants

#### 3.1.1. Study of the Regional Environmental Gini Coefficient

_{0(j)}based on the corresponding pollutant emissions under different indicators is calculated, and the calculation results are shown in Table 2.

_{3}-N Gini coefficients are less than 0.2 and are considered highly average. The COD and NH

_{3}-N Gini coefficients based on GDP, industrial output value, and industrial wastewater discharge are between ~0.2 and 0.4, which is already in a relatively unfair state, but does not exceed the warning value. COD and NH

_{3}-N Gini coefficients based on total water resources were the largest, exceeding the warning value of 0.4. It shows that there is still a big conflict between the distribution of pollutant loads in Anhui Province and the current situation of the regional water resources environment, and the pollutant discharge in different regions is not balanced enough, and it is necessary to optimize the distribution. In addition, the reduction of the Gini coefficient of the total water resources should be paid attention to in the total water pollution load allocation model.

_{3}-N allocation models are calculated according to the data in Table 1, as shown in Table 3.

#### 3.1.2. Study of the Environmental Contribution Factor of the Region

_{3}-N indicators in Anhui Province in the benchmark year. Since the index (population) with a Gini coefficient of less than 0.2 is highly average, other indicators were selected for analysis. The Gini coefficient of total water resources-COD/NH

_{3}-N is the largest, and the analysis of the distribution map of the contribution coefficient to total water resources shows that the contribution coefficient of total water resources in Anhui Province shows an increasing trend from northwest to southeast. The contribution coefficients of the northern and central eastern parts of Anhui Province are less than 1. The water contribution coefficients of Fuyang, Bozhou, Huaibei, Suzhou, Bengbu, Huainan, and Tongling are less than 0.5, which is the main unfair factor. Combined with the data in Table 1, these cities accounted for 13.23% of the total water resources in Anhui Province, but COD and NH

_{3}-N emissions accounted for 49.81% and 48.56% of the total pollutant emissions. This shows a high degree of inequity in the indicator of total water resources. Due to the excessive weight of the index of total water resources, the distribution map of the comprehensive contribution coefficient of COD/NH

_{3}-N is basically consistent with the distribution map of the contribution coefficient of total water resources. Regional differences in total water resources are a major contributor to the uneven distribution of pollutants, indicating that the amount of water resources varies from region to region and the rate of economic development. Therefore, for regions with a large amount of water resources, the amount of pollutants allocated should be increased to indirectly promote the development of a regional economy. Areas with less water resources should pay attention to controlling and reducing the allocation of pollutants to control the discharge of pollutants from the source and avoid pollutants exceeding the carrying capacity of the water environment. The analysis of the contribution coefficient of GDP shows that the contribution coefficients of Hefei, Wuhu, Ma’anshan, and Tongling are greater than 1 based on the two pollutants, among which Hefei and Wuhu are among the best. It shows that the contribution rate of the city’s GDP is greater than the contribution rate of pollutant emissions, and the benefits brought by the discharge of pollutants are relatively high, which is manifested as a green economic development model. The contribution coefficients of Fuyang, Suzhou, Lu’an, Huainan, Bozhou, and Chuzhou are less than 1, especially Fuyang City, which is less than 0.5, which is the main factor causing inequality. Combined with the distribution map of the contribution coefficient of gross industrial production-COD/NH

_{3}-N, it can be found that the distribution of the two is basically the same in Anhui Province, indicating that the main source of GDP in Anhui Province is industrial production. In terms of future economic development, it is necessary to gradually realize industrial upgrading, reduce or even abandon high-pollution, low-value-added industries, and improve the efficiency of pollutant treatment.

#### 3.2. Optimal Allocation Results of Pollution Load in Anhui Province

_{max}(COD) = [20%, 25%], and the upper limit of ammonia nitrogen emissions is U

_{max}(NH

_{3}-N) = [30%, 35%].

#### 3.3. Discussions

_{3}-N pollutants in the base year and the Gini coefficient after the optimized distribution scheme.

_{3}-N optimization decreased by 25.1~32.5%. Obviously, COD is reduced relatively little. This is directly related to the pollutant reduction target in the 13th Five-Year Plan, and the appropriate emission reduction target needs to be formulated on the basis of a comprehensive review of the actual emission situation and the bearing capacity of the study area, and it is impossible to require a one-time emission reduction in order to reduce the Gini coefficient, which is often unrealistic. The control of total pollutant emissions is a long-term and continuous task, and the fairness of distribution is gradually optimized and adjusted [34].

## 4. Conclusions

- (1)
- Under the principles of sustainable development of the water environment, economic and social fairness, and efficiency, this paper proposes a comprehensive management model of multi-objective and uncertain optimization of the total amount of regional water pollution discharge and constructs a multi-objective decision-making optimization model of water pollution load (COD and NH
_{3}-N) allocation that takes into account economic optimum and fairness. - (2)
- A solution method for the uncertain multi-objective allocation model is designed in this study, and the practicability and feasibility of the model solution method are verified by a case study. The results of multiple simulation–optimization can generate a series of decision schemes under uncertain objective functions and constraints and provide a more reasonable decision range for decision makers.
- (3)
- The model was applied to the allocation of total pollutant reduction in Anhui Province’s 13th Five-Year Plan for Environmental protection. Based on the environmental Gini coefficient, the rationality of the total pollutant distribution system in Anhui Province was evaluated, and the comprehensive Gini coefficients of COD and NH3-N were calculated to be 0.43152 and 0.42952, respectively. The Gini coefficients based on the total water resources were 0.59 and 0.57, which exceeded the warning value and were the main inequity factors.
- (4)
- After the optimization of water pollution load distribution, the comprehensive Gini coefficients of COD and NH
_{3}-N are reduced in different ranges. The comprehensive Gini coefficient decreases by 2.4~4.6% after COD optimization and 25.1~32.5% after NH_{3}-N optimization. The control of total pollutant discharge is a long-term and continuous task, and the fairness of distribution is also gradually optimized and adjusted, which is the direction of further research.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Wang, Z.; Ye, A.; Liu, K.; Tan, L. Optimal Model of Desalination Planning Under Uncertainties in a Water Supply System. Water Resour. Manag.
**2021**, 35, 3277–3295. [Google Scholar] [CrossRef] - Cui, Y.; Ning, S.; Jin, J.; Jiang, S.; Zhou, Y.; Wu, C. Quantitative Lasting Effects of Drought Stress at a Growth Stage on Soybean Evapotranspiration and Aboveground BIOMASS. Water
**2021**, 13, 18. [Google Scholar] [CrossRef] - Pan, Z.; Jin, J.; Li, C.; Ning, S.; Zhou, R. A Connection Entropy Approach to Water Resources Vulnerability Analysis in a Changing Environment. Entropy
**2017**, 19, 591. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Wang, J.; Zhou, R. Attribution Analysis of Hydrological Drought Risk Under Climate Change and Human Activities: A Case Study on Kuye River Basin in China. Water
**2019**, 11, 1958. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Zhou, J.; Zhou, R. Interval Multi-Attribute Decision of Watershed Ecological Compensation Schemes Based on Projection Pursuit Cluster. Water
**2018**, 10, 1280. [Google Scholar] [CrossRef] [Green Version] - Xiang, X.; Wu, X.; Chen, X.; Song, Q.; Xue, X. Integrating Topography and Soil Properties for Spatial Soil Moisture Storage Modeling. Water
**2017**, 9, 647. [Google Scholar] [CrossRef] [Green Version] - Deng, Y.; Zheng, S.; Li, Z.; Hao, C.; Zheng, B. The innovation and future development of total pollutant control system. Res. Environ. Sci.
**2021**, 34, 382–388. [Google Scholar] - Chen, L.; Han, L.; Tan, J.; Zhang, F.; Lin, Y. Optimization distribution model of point-point source pollution load in river network based on multi-section water quality standard. Water Resour. Prot.
**2021**, 37, 128–134+141. [Google Scholar] - Yang, Y.; Zhao, Q.; Han, C.; Xing, C.; Song, L.; Hu, Z. Research on total amount allocation of sea and watershed water pollutants based on fairness principle. Mar. Environ. Sci.
**2019**, 38, 796–803. [Google Scholar] - Zhang, X.; Wang, P.; He, Y.; Du, Z.; Luo, J.; Xie, J. Study of two-layer multi-objective optimization model for water pollution load distribution in rivers. J. Xi’an Univ. Technol.
**2020**, 36, 475–485. [Google Scholar] - Li, R.; Shu, K. Model for wastewater load allocation based on multi-objective decision making. Acta Sci. Circumst.
**2011**, 31, 2814–2821. [Google Scholar] - Wang, X.; Pang, M.; Zhao, M. Pollution Load Capacity Calculation Study Based on Multi-objective System in Trans-boundary Area, Plain River Network. Bull. Environ. Contam. Tox.
**2021**, 106, 600–607. [Google Scholar] [CrossRef] [PubMed] - Liu, Q.; Li, Z.; Yao, G. Research on equity of total water pollutant distribution based on Gini coefficient. China Water Wastewater
**2016**, 32, 90–94. [Google Scholar] - Wu, F.; Cao, Q.; Zhang, D.; Sun, F.; Shen, J. Allocation of flood drainage rights of Sunan Canal based on environmental Gini coefficient. J. Hohai Univ. (Nat. Sci.)
**2020**, 48, 314–319. [Google Scholar] - Kolluru, M.; Semenenko, T. Income Inequalities in EU Countries: Gini Indicator Analysis. ECONOMICS-Innov. Econ. Res.
**2021**, 9, 125–142. [Google Scholar] [CrossRef] - Zaeimi, M.B.; Rassafi, A.A. Designing an integrated municipal solid waste management system using a fuzzy chance-constrained programming model considering economic and environmental aspects under uncertainty. Waste Manag.
**2021**, 125, 268–279. [Google Scholar] [CrossRef] - Liu, Q.; Jiang, J.; Jing, C.; Liu, Z.; Qi, J. A New Water Environmental Load and Allocation Modeling Framework at the Medium—Large Basin Scale. Water
**2019**, 11, 2398. [Google Scholar] [CrossRef] - Wang, M.; Gong, H. Imbalanced Development and Economic Burden for Urban and Rural Wastewater Treatment in China—Discharge Limit Legislation. Sustainability
**2018**, 10, 2597. [Google Scholar] [CrossRef] [Green Version] - Chen, W.; Zhang, M.; Zhao, W. Study on multi-objective optimal allocation of water resources system under uncertainties. J. Hydro. Eng.
**2021**, 40, 12–24. [Google Scholar] - Xie, Y.; Zhou, X. Income inequality in today’s China. Proc. Natl. Acad. Sci. USA
**2014**, 111, 6928–6933. [Google Scholar] [CrossRef] [Green Version] - Zhang, F. Study on the Total Pollution Distribution in the Middle Reaches of Fenhe Based on Information Entropy and Gini Coefficient Method. Master’s Thesis, Xi’an University of Technology, Xi’an, China, 2021. [Google Scholar]
- Shu, H.; Xiong, P. Construction of Gini Coefficient of a mixed environment and its Application in the evaluation of industrial economy and ecological spatial equilibrium. Math. Pract. Theory
**2018**, 48, 9–17. [Google Scholar] - Steinberger, J.K.; Krausmann, F.; Eisenmenger, N. Global patterns of materials use: A socioeconomic and geophysical analysis. Ecol. Econ.
**2010**, 69, 1148–1158. [Google Scholar] [CrossRef] - Cheng, Y.; Li, Y.; Zhu, X.; Shi, Y.; Zhu, Y.; Pan, H.; Xu, Y.; Cheng, Y. Total pollutant load allocation in plain river network based on the entropy-environmental Gini coefficient method. J. Lake Sci.
**2020**, 32, 619–628. [Google Scholar] - Shu, K. Model and Method of Water Waste Loads Allocation in a Region-Case of Chaohu Lake Basin. Master’s Thesis, Hefei University of Technology, Hefei, China, 2010. [Google Scholar]
- Yu, S.; Lu, H. Integrated watershed management through multi-level and stepwise optimization for allocation of total load of water pollutants at large scales. Environ. Earth Sci.
**2018**, 77, 373. [Google Scholar] [CrossRef] - Wu, W.; Jiang, H.; Duan, Y.; Liu, N.; Lu, Y.; Zhang, W.; Yu, S. Application of total water pollutant load distribution in control-unit based on the environmental Gini coefficient. China Popul. Resour. Environ.
**2017**, 27, 8–16. [Google Scholar] - Marler, R.T.; Arora, J.S. The weighted sum method for multi-objective optimization: New insights. Struct. Multidiscip. Optim.
**2010**, 41, 853–862. [Google Scholar] [CrossRef] - Jin, J.; Ding, J. Genetic Algorithm and Its Application in Water Science; Sichuan University Press: Chengdu, China, 2000. [Google Scholar]
- Li, C.; Chen, J.; Wang, R.; Huang, J.; Qian, Z.; Xu, Y. Multi-indices analysis of heavy precipitation changes in Anhui Province, China. Meteorol. Atmos. Phys.
**2021**, 133, 1317–1325. [Google Scholar] [CrossRef] - Tan, W.; Zhang, C.; Liu, X. Research on the compilation of the Atlas of the First National Census of Geographical Conditions in Anhui Province. Intell. City
**2020**, 6, 52–53. [Google Scholar] - Anhui Provincial Department of Environmental Protection. 13th Five-Year Plan for Environmental Protection of Anhui Province; Anhui Provincial People’s Government: Hefei, China, 2017.
- Anhui Provincial Bureau of Statistics. Anhui Statistical Yearbook-2016; China Statistics Press: Beijing, China, 2016. [Google Scholar]
- Qin, D.; Wei, A.; Lu, S.; Luo, Y.; Liao, Y.; Yi, M.; Song, B. Total water pollutant load allocation in Dongting Lake area based on the environmental Gini coefficient method. Res. Environ. Sci.
**2013**, 26, 8–15. [Google Scholar]

**Figure 1.**Schematic diagram of Lorentz curve. A is the area between the actual distribution curve and the absolute equal distribution curve; B is the area under the actual distribution curve.

**Figure 2.**Location of Anhui Province in China. From the website of the Ministry of Natural Resources of the People’s Republic of China, Figure Number: GS (2019) No.1674, downloaded at: http://bzdt.ch.mnr.gov.cn/index.html (accessed on 10 November 2022). The broken line indicated by the arrow on the map is the study area of Anhui Province.

**Figure 8.**Distribution of COD index contribution coefficient in the benchmark year of Anhui Province. (

**a**) GDP contribution factor. (

**b**) Contribution factor of industrial wastewater discharge. (

**c**) Population contribution factor. (

**d**) Contribution factor of gross industrial production. (

**e**) Total water contribution factor. (

**f**) Comprehensive contribution factor.

**Figure 9.**Distribution of NH

_{3}-N index contribution coefficient in Anhui Province in the benchmark year. (

**a**) GDP contribution factor. (

**b**) Contribution factor of industrial wastewater discharge. (

**c**) Population contribution factor. (

**d**) Contribution factor of gross industrial production. (

**e**) Total water contribution factor. (

**f**) Comprehensive contribution factor.

**Figure 10.**Distribution chart of comparison between COD optimized distribution results and base year.

**Table 1.**Specific values of water pollution emissions and evaluation indicators of cities in Anhui Province in 2015.

Region | Pollutant Discharge | Indicators of Evaluation | |||||
---|---|---|---|---|---|---|---|

COD (10,000 tons) | NH_{3}-N (10,000 tons) | Population (10,000 People) | GDP (CNY 100 million) | Water Volume (100 million m ^{3}) | Industrial Output Value (CNY 100 million) | Wastewater Discharge (10,000 tons) | |

Hefei | 11.4 | 0.92 | 717.72 | 5660.27 | 48.63 | 9345.59 | 5334.98 |

HuaiBei | 2.8 | 0.36 | 216.5 | 760.39 | 5.99 | 1814.6 | 5377.67 |

Bozhou | 6.81 | 0.7 | 634.95 | 942.61 | 22.25 | 959.39 | 3501.66 |

Suzhou | 10.43 | 0.97 | 649.51 | 1235.83 | 22.39 | 1,623.25 | 6126.77 |

Bengbu | 4.33 | 0.48 | 376.35 | 1253.05 | 20.82 | 2,596.82 | 2474.02 |

Fuyang | 10.73 | 1.24 | 1042.65 | 1267.45 | 30.28 | 1989.69 | 2946.11 |

Huainan | 5.9 | 0.7 | 383.39 | 901.08 | 9.94 | 970.42 | 9112.06 |

Chuzhou | 6.67 | 0.89 | 449.06 | 1305.7 | 54.83 | 2567.11 | 5859.72 |

Lu’an | 5.36 | 0.67 | 580.53 | 1016.49 | 123.57 | 1542.1 | 2443.29 |

Ma’anshan | 2.79 | 0.35 | 228.5 | 1365.3 | 22.15 | 2540.75 | 7694.53 |

Wuhu | 4.8 | 0.62 | 384.79 | 2457.32 | 41.34 | 5829.01 | 4933.27 |

Xuancheng | 4.02 | 0.4 | 279.95 | 971.46 | 126.68 | 1796.38 | 3664.98 |

Tongling | 2.38 | 0.25 | 170.43 | 911.6 | 9.25 | 2269.01 | 5338.25 |

Chizhou | 1.92 | 0.22 | 161.61 | 544.74 | 103.13 | 740.43 | 1422.11 |

Anqing | 5.15 | 0.7 | 525.48 | 1417.43 | 123.52 | 2723.16 | 4469.63 |

Huangshan | 1.6 | 0.21 | 147.69 | 530.9 | 149.35 | 567.95 | 736.62 |

Total | 87.09 | 9.68 | 6949.11 | 22,541.6 | 914.12 | 39,875.7 | 71,435.7 |

**Table 2.**Gini coefficient of corresponding pollutants under each evaluation index in Anhui Province in 2015.

Evaluation Indicators | Population | GDP | Total Water Resources | Gross Industrial Output | Industrial Wastewater Discharge |
---|---|---|---|---|---|

COD | 0.11 | 0.30 | 0.59 | 0.33 | 0.34 |

NH_{3}-N | 0.10 | 0.32 | 0.57 | 0.39 | 0.32 |

Pollutants | Population | GDP | Total Water Resources | Gross Industrial Output | Industrial Wastewater Discharge |
---|---|---|---|---|---|

COD | 0.022 | 0.130 | 0.417 | 0.247 | 0.184 |

NH_{3}-N | 0.021 | 0.126 | 0.430 | 0.232 | 0.191 |

Pollutants | Region | Benchmark Annual Emissions (×10^{4}t) | Distributed Emissions (×10 ^{4}t) | Amount of Reduction (×10 ^{4}t) | Rate of Reduction/% | Reduction of Quotas/% |
---|---|---|---|---|---|---|

COD | Hefei | 11.4 | [10.69, 10.83] | [0.57, 0.71] | [5.0, 6.2] | 6.5 |

HuaiBei | 2.8 | [2.51, 2.66] | [0.14, 0.29] | [5.0, 10.4] | 2.1 | |

Bozhou | 6.81 | [5.11, 5.60] | [1.21, 1.70] | [17.8, 24.9] | 14.6 | |

Suzhou | 10.43 | [7.82, 8.52] | [1.91, 2.61] | [18.3, 25.0] | 22.9 | |

Bengbu | 4.33 | [3.97, 4.11] | [0.22, 0.36] | [5.1, 8.3] | 2.9 | |

Fuyang | 10.73 | [8.05, 8.68] | [2.05, 2.68] | [19.1, 25.0] | 24 | |

Huainan | 5.09 | [4.43, 4.83] | [0.26, 0.66] | [5.1, 13.0] | 4.4 | |

Chuzhou | 6.67 | [6.11, 6.34] | [0.33, 0.56] | [5.0, 8.4] | 4.4 | |

Lu’an | 5.36 | [4.76, 5.09] | [0.27, 0.60] | [5.0, 11.2] | 4.2 | |

Ma’anshan | 2.79 | [2.56, 2.65] | [0.14, 0.23] | [5.0, 8.2] | 1.8 | |

Wuhu | 4.80 | [4.47, 4.56] | [0.24, 0.33] | [5.0, 6.9] | 2.9 | |

Xuancheng | 4.02 | [3.75, 3.82] | [0.20, 0.27] | [5.0, 6.7] | 2.4 | |

Tongling | 2.38 | [2.16, 2.26] | [0.12, 0.22] | [5.0, 9.0] | 1.6 | |

Chizhou | 1.92 | [1.72, 1.82] | [0.10, 0.20] | [5.0, 10.4] | 1.5 | |

Anqing | 5.15 | [4.76, 4.89] | [0.26, 0.39] | [5.0, 7.6] | 3.2 | |

Huangshan | 1.60 | [1.46, 1.52] | [0.08, 0.14] | [5.0, 8.8] | 1.0 | |

Total | 87.09 | [74.33, 78.28] | [8.00, 11.95] | [9.2, 13.7] | 100 | |

NH_{3}-N | Hefei | 0.92 | [0.68, 0.828] | [0.09, 0.24] | [10, 26.1] | 8.4 |

HuaiBei | 0.36 | [0.25, 0.32] | [0.04, 0.11] | [11, 30.6] | 3.8 | |

Bozhou | 0.7 | [0.49, 0.63] | [0.07, 0.21] | [10, 30] | 7.1 | |

Suzhou | 0.97 | [0.68, 0.84] | [0.13, 0.29] | [13.4, 29.9] | 10.6 | |

Bengbu | 0.48 | [0.34, 0.43] | [0.05, 0.14] | [10.4, 29.2] | 4.8 | |

Fuyang | 1.24 | [0.87, 1.03] | [0.21, 0.37] | [16.9, 29.8] | 14.7 | |

Huainan | 0.7 | [0.49, 0.63] | [0.07, 0.21] | [10, 30.0] | 7.1 | |

Chuzhou | 0.89 | [0.62, 0.80] | [0.09, 0.27] | [10.1, 30.3] | 9.1 | |

Lu’an | 0.67 | [0.48, 0.60] | [0.07, 0.19] | [10.4, 28.4] | 6.6 | |

Ma’anshan | 0.35 | [0.25, 0.31] | [0.04, 0.10] | [11.4, 28.6] | 3.5 | |

Wuhu | 0.62 | [0.44, 0.55] | [0.07, 0.18] | [11.3, 29.0] | 6.3 | |

Xuancheng | 0.4 | [0.29, 0.36] | [0.04, 0.11] | [10, 27.5] | 3.8 | |

Tongling | 0.25 | [0.18, 0.22] | [0.03, 0.07] | [12.0, 28] | 2.5 | |

Chizhou | 0.22 | [0.16, 0.19] | [0.03, 0.06] | [13.6, 27.3] | 2.3 | |

Anqing | 0.7 | [0.49, 0.63] | [0.07, 0.21] | [10.0, 30] | 7.1 | |

Huangshan | 0.21 | [0.15, 0.18] | [0.03, 0.06] | [14.2, 28.6] | 2.3 | |

Total | 9.68 | [6.86, 8.60] | [1.13, 2.82] | [11.7, 29.1] | 100 |

Pollutants | Benchmark Year | After Optimization | Range of Reduction |
---|---|---|---|

COD | 0.4315 | [0.4117, 0.4210] | [−4.6%, −2.4%] |

NH_{3}-N | 0.4295 | [0.2901, 0.3216] | [−32.5%, −25.1%] |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhou, R.; Sun, Y.; Chen, W.; Zhang, K.; Shao, S.; Zhang, M.
A Multi-Objective Decision Model for Water Pollution Load Allocation under Uncertainty. *Water* **2023**, *15*, 309.
https://doi.org/10.3390/w15020309

**AMA Style**

Zhou R, Sun Y, Chen W, Zhang K, Shao S, Zhang M.
A Multi-Objective Decision Model for Water Pollution Load Allocation under Uncertainty. *Water*. 2023; 15(2):309.
https://doi.org/10.3390/w15020309

**Chicago/Turabian Style**

Zhou, Runjuan, Yingke Sun, Wenyuan Chen, Kuo Zhang, Shuai Shao, and Ming Zhang.
2023. "A Multi-Objective Decision Model for Water Pollution Load Allocation under Uncertainty" *Water* 15, no. 2: 309.
https://doi.org/10.3390/w15020309