Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model
Abstract
:1. Introduction
2. Literature Review
3. Materials and Methods
3.1. Problems Statement
3.2. Upper-Level Programming Model
3.2.1. Objective Functions
- (1)
- Objective function of basin economic benefits
- (2)
- Objective function of basin social benefits
- (3)
- Objective function of basin eco-environmental benefits
3.2.2. Constraints
- (1)
- Constraint for total amount of pollutant discharge
- (2)
- Constraint for regional coordinated development
- (3)
- Constraint for social justice
- (4)
- Nonnegative constraint
3.3. Lower-Level Programming Model
3.3.1. Objective Functions
3.3.2. Constraints
- (1)
- Constraint for total distributable amount
- (2)
- Output constraint
- (3)
- Convex constraint
- (4)
- Nonnegative constraint
3.4. Solution of Model
3.5. Materials and Data
3.5.1. Study Area
3.5.2. Data Collection and Parameter Identification
- (1)
- Data collection
- (2)
- Parameter identification
4. Results and Discussion
4.1. Solutions of the LFHDM Model
4.2. Comparisons with Single-Level Models
4.3. Comparisons under Different Allowable Assimilative Capacities of Water Bodies
4.3.1. Allocation and Variation Trend of Initial Emission Rights
4.3.2. Reduction Plan of Emission Rights in Each Province
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Indicators | Unit | Explanation | Attribute |
---|---|---|---|
Population size | 10,000 persons | It reflects the population differences within each region. The larger the value, the more people enjoy equal emission rights. | Income-type |
Area size | km2 | It reflects the area difference under the jurisdiction of regional water sources. The larger the value, the higher the natural rationality of distribution. | Income-type |
Total water resources amount | 100 million tons | It reflects the difference of regional water resources. The larger the value, the better the regional resource endowment. | Income-type |
Water consumption per 10,000 yuan GDP | ton | It reflects the utilization efficiency of water resources in each region. The larger the value, the more water is used per unit of GDP. | Cost-type |
Pollution emission per 10,000 yuan GDP | ton | It reflects the pollutant emission efficiency of each region. The greater the value, the greater the pollutant emission per unit of GDP. | Cost-type |
Sewage reuse rate | % | It reflects the sewage reuse efficiency of each region. The larger the value, the higher the sewage treatment capacity of the region. | Income-type |
Standard rate of water quality in water function area | % | It reflects the water quality status of water functional areas in each region. The larger the value, the better the regional water environment. | Income-type |
Appendix B
Year | QH | SC | GS | NX | IM | |||||
---|---|---|---|---|---|---|---|---|---|---|
2006 | 44.27 | 493.99 | 19.89 | 203.07 | 58.56 | 510.74 | 17.45 | 233.10 | 86.57 | 1153.77 |
2007 | 51.92 | 598.66 | 23.54 | 248.33 | 67.98 | 612.63 | 20.33 | 280.57 | 106.66 | 1468.85 |
2008 | 61.68 | 708.02 | 27.34 | 287.15 | 78.32 | 702.78 | 23.95 | 329.11 | 131.46 | 1802.52 |
2009 | 70.23 | 807.80 | 32.36 | 340.59 | 89.30 | 802.84 | 27.70 | 381.49 | 158.87 | 2182.76 |
2010 | 83.57 | 949.23 | 37.23 | 386.93 | 102.96 | 914.12 | 31.81 | 432.62 | 188.52 | 2557.58 |
2011 | 98.57 | 1063.84 | 44.52 | 439.57 | 121.17 | 1022.23 | 37.07 | 479.09 | 224.01 | 2887.88 |
2012 | 118.49 | 1220.17 | 53.68 | 505.74 | 146.33 | 1177.77 | 44.27 | 545.81 | 267.49 | 3290.10 |
2013 | 135.55 | 1397.28 | 60.94 | 574.76 | 167.48 | 1349.46 | 50.17 | 619.17 | 300.91 | 3705.12 |
2014 | 151.52 | 1570.60 | 67.68 | 641.85 | 186.86 | 1513.93 | 55.46 | 688.27 | 332.03 | 4110.95 |
2015 | 169.50 | 1765.63 | 75.52 | 719.75 | 209.02 | 1701.92 | 61.94 | 772.52 | 369.81 | 4601.34 |
2016 | 200.60 | 2115.53 | 89.22 | 860.87 | 246.70 | 2033.53 | 73.38 | 926.55 | 434.47 | 5472.86 |
2017 | 223.55 | 2683.16 | 100.09 | 1099.08 | 265.36 | 2489.50 | 82.16 | 1180.75 | 469.32 | 6728.48 |
2018 | 266.19 | 3309.75 | 120.11 | 1366.25 | 313.42 | 3045.93 | 97.68 | 1454.17 | 549.11 | 8154.93 |
Year | SaX | SX | HN | SD | ||||||
2006 | 66.46 | 643.31 | 89.07 | 748.18 | 131.68 | 1334.18 | 150.15 | 1532.70 | ||
2007 | 79.55 | 795.63 | 107.07 | 929.32 | 155.97 | 1632.98 | 177.38 | 1871.05 | ||
2008 | 96.88 | 964.76 | 121.44 | 1049.43 | 182.77 | 1905.26 | 208.04 | 2184.97 | ||
2009 | 113.78 | 1135.31 | 132.45 | 1146.88 | 209.74 | 2190.74 | 239.17 | 2516.89 | ||
2010 | 134.54 | 1325.63 | 155.66 | 1330.96 | 243.25 | 2508.89 | 277.13 | 2879.85 | ||
2011 | 159.31 | 1491.59 | 182.86 | 1485.76 | 283.23 | 2775.89 | 319.51 | 3155.03 | ||
2012 | 192.61 | 1720.67 | 215.81 | 1672.96 | 334.25 | 3125.65 | 376.05 | 3542.89 | ||
2013 | 220.66 | 1973.27 | 242.77 | 1883.98 | 376.71 | 3526.37 | 425.37 | 4011.75 | ||
2014 | 247.77 | 2228.00 | 260.67 | 2034.11 | 419.91 | 3952.55 | 473.28 | 4488.32 | ||
2015 | 276.47 | 2498.41 | 277.66 | 2177.40 | 470.29 | 4448.69 | 528.59 | 5037.72 | ||
2016 | 326.03 | 2982.71 | 318.00 | 2524.58 | 557.68 | 5340.66 | 623.34 | 6014.25 | ||
2017 | 365.73 | 3808.06 | 353.74 | 3196.30 | 624.42 | 6805.86 | 695.35 | 7635.82 | ||
2018 | 440.09 | 4746.87 | 419.38 | 3925.43 | 746.53 | 8428.88 | 822.06 | 9351.30 |
Appendix C
Provinces (Autonomous Regions)/Lower Limit Value | Population Size | Area Size | Total Water Resources Amount | Water Consumption per 10,000 yuan GDP | Pollution Emission per 10,000 yuan GDP | Sewage Reuse Rate | Standard Rate of Water Quality in Water Function Area |
---|---|---|---|---|---|---|---|
QH | 0.095 | 0.486 | 0.577 | 0.129 | 0.135 | 0.128 | 0.365 |
SC | 0.002 | 0.054 | 0.131 | 0.135 | 0.060 | 0.000 | 0.384 |
GS | 0.349 | 0.457 | 0.345 | 0.204 | 0.159 | 0.428 | 0.346 |
NX | 0.135 | 0.164 | 0.029 | 0.036 | 0.048 | 0.291 | 0.288 |
IM | 0.163 | 0.482 | 0.155 | 0.272 | 0.288 | 0.266 | 0.146 |
SaX | 0.554 | 0.426 | 0.322 | 0.420 | 0.224 | 0.286 | 0.211 |
SX | 0.452 | 0.310 | 0.203 | 0.397 | 0.202 | 0.124 | 0.250 |
HN | 0.323 | 0.116 | 0.162 | 0.397 | 0.368 | 0.128 | 0.242 |
SD | 0.165 | 0.043 | 0.065 | 0.086 | 0.406 | 0.190 | 0.192 |
Provinces (Autonomous Regions)/Upper Limit Value | Population Size | Area Size | Total Water Resources Amount | Water Consumption per 10,000 yuan GDP | Pollution Emission per 10,000 yuan GDP | Sewage Reuse Rate | Standard Rate of Water Quality in Water Function Area |
QH | 0.116 | 0.486 | 0.861 | 0.187 | 0.257 | 0.338 | 0.508 |
SC | 0.002 | 0.054 | 0.196 | 0.185 | 0.115 | 0.000 | 0.508 |
GS | 0.426 | 0.457 | 0.515 | 0.300 | 0.303 | 0.723 | 0.503 |
NX | 0.166 | 0.164 | 0.043 | 0.056 | 0.092 | 0.506 | 0.419 |
IM | 0.199 | 0.482 | 0.232 | 0.427 | 0.550 | 0.459 | 0.212 |
SaX | 0.677 | 0.426 | 0.482 | 0.650 | 0.429 | 0.506 | 0.307 |
SX | 0.552 | 0.310 | 0.304 | 0.620 | 0.385 | 0.434 | 0.363 |
HN | 0.395 | 0.116 | 0.242 | 0.606 | 0.702 | 0.427 | 0.352 |
SD | 0.201 | 0.043 | 0.097 | 0.129 | 0.776 | 0.500 | 0.279 |
Provinces (Autonomous Regions) | QH | SC | GS | NX | IM | SaX | SX | HN | SD |
---|---|---|---|---|---|---|---|---|---|
0.485 | 0.897 | 0.348 | 0.799 | 0.476 | 0.252 | 0.404 | 0.474 | 0.696 | |
0.542 | 0.130 | 0.679 | 0.229 | 0.552 | 0.775 | 0.623 | 0.554 | 0.332 |
Provinces (Autonomous Regions) | QH | SC | GS | NX | IM | SaX | SX | HN | SD |
---|---|---|---|---|---|---|---|---|---|
0.528 | 0.127 | 0.661 | 0.223 | 0.537 | 0.755 | 0.607 | 0.539 | 0.323 | |
0.528 | 0.125 | 0.646 | 0.226 | 0.569 | 0.744 | 0.587 | 0.535 | 0.322 |
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Category | (Low Allowable Assimilative Capacity of Water Bodies Scenario) | (Moderate Allowable Assimilative Capacity of Water Bodies Scenario) | (High Allowable Assimilative Capacity of Water Bodies Scenario) | |||
---|---|---|---|---|---|---|
COD | NH3-N | COD | NH3-N | COD | NH3-N | |
Total amount control | [58.63, 63.43] | [5.32, 5.77] | [61.52, 68.23] | [5.68, 6.21] | [66.18, 73.03] | [6.11, 6.65] |
Province | K = 1 | K = 2 | |||||||
---|---|---|---|---|---|---|---|---|---|
Initial Solution | Initial DEA Efficiency Value | ZSG-DEA Efficiency Value | Initial Solution | Initial DEA Efficiency Value | |||||
Initial Value | Adjusted Plan | Iteration 1 | Iteration 2 | Adjusted Plan | |||||
QH | 5.800 | 1.000 | 1.000 | 5.310 | 1.000 | 1.000 | 5.432 | 5.906 | 1.000 |
SC | 1.101 | 1.000 | 1.000 | 1.123 | 1.000 | 1.000 | 5.150 | 0.907 | 1.000 |
GS | 8.337 | 1.000 | 1.000 | 7.913 | 1.000 | 1.000 | 6.866 | 9.293 | 1.000 |
NX | 5.740 | 0.883 | 0.904 | 5.858 | 0.975 | 1.000 | 5.523 | 3.565 | 1.000 |
IM | 7.024 | 1.000 | 1.000 | 7.168 | 1.000 | 1.000 | 6.342 | 7.947 | 1.000 |
SaX | 8.982 | 1.000 | 1.000 | 9.166 | 1.000 | 1.000 | 9.191 | 10.684 | 1.000 |
SX | 8.215 | 0.916 | 0.938 | 8.383 | 0.976 | 1.000 | 7.513 | 8.677 | 1.000 |
HN | 7.668 | 1.000 | 1.000 | 7.825 | 1.000 | 1.000 | 6.958 | 7.996 | 1.000 |
SD | 5.763 | 1.000 | 1.000 | 5.881 | 1.000 | 1.000 | 5.656 | 3.655 | 1.000 |
Province | (Low Allowable Assimilative Capacity of Water Bodies) | (Moderate Allowable Assimilative Capacity of Water Bodies) | (High Allowable Assimilative Capacity of Water Bodies) | |||
---|---|---|---|---|---|---|
COD | NH3-N | COD | NH3-N | COD | NH3-N | |
QH | [5.989, 6.479] | [0.585, 0.635] | [6.284, 6.969] | [0.625, 0.683] | [6.760, 7.460] | [0.672, 0.731] |
SC | [0.907, 0.981] | [0.124, 0.135] | [0.952, 1.055] | [0.133, 0.145] | [1.024, 1.130] | [0.143, 0.155] |
GS | [9.336, 10.101] | [0.789, 0.856] | [9.797, 10.865] | [0.842, 0.921] | [10.539, 11.629] | [0.906, 0.986] |
NX | [3.088, 3.340] | [0.281, 0.305] | [3.240, 3.593] | [0.300, 0.328] | [3.485, 3.846] | [0.323, 0.351] |
IM | [7.984, 8.638] | [0.777, 0.842] | [8.378, 9.292] | [0.829, 0.907] | [9.013, 9.945] | [0.892, 0.971] |
SaX | [10.868, 11.758] | [0.997, 1.081] | [11.404, 12.648] | [1.065, 1.164] | [12.268, 13.538] | [1.145, 1.246] |
SX | [9.324, 10.088] | [0.781, 0.847] | [9.784, 10.851] | [0.834, 0.911] | [10.525, 11.614] | [0.897, 0.976] |
HN | [8.024, 8.681] | [0.701, 0.760] | [8.419, 9.338] | [0.749, 0.818] | [9.057, 9.995] | [0.805, 0.876] |
SD | [3.110, 3.364] | [0.285, 0.309] | [3.263, 3.619] | [0.304, 0.333] | [3.510, 3.873] | [0.327, 0.356] |
satisfaction | [0.925, 0.933] | [0.920, 0.928] | [0.921, 0.928] | [0.916, 0.921] | [0.920, 0.923] | [0.915, 0.917] |
Model | Economic Benefit | Social Benefit | Ecological Benefits | Comprehensive Benefit Satisfaction | Social and Economic Development Index | Emission Efficiency |
---|---|---|---|---|---|---|
LFHDM-U | 591.141 | 0.236 | 58.630 | 0.913 | Satisfied | Partial invalid |
LFHDM-L | 611.288 | 0.236 | 58.630 | 0.918 | Unsatisfied | validity |
LFHDM | 589.041 | 0.187 | 58.630 | 0.933 | Satisfied | validity |
Province | Current Annual Emission (10,000 tons) | ||||||
---|---|---|---|---|---|---|---|
Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | ||
QH | 5.592 | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] |
SC | 0.251 | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] |
GS | 15.527 | [5.426, 6.190] | [34.946, 39.869] | [4.662, 5.730] | [30.024, 36.905] | [3.897, 4.988] | [25.101, 32.126] |
NX | 15.259 | [11.919, 12.171] | [78.109, 79.766] | [11.666, 12.019] | [76.453, 78.768] | [11.413, 11.774] | [74.796, 77.160] |
IM | 19.572 | [10.934, 11.588] | [55.865, 59.205] | [10.280, 11.194] | [52.526, 57.194] | [9.627, 10.559] | [49.186, 53.952] |
SaX | 26.592 | [14.834, 15.723] | [55.783, 59.129] | [13.944, 15.188] | [52.436, 57.114] | [13.054, 14.324] | [49.090, 53.866] |
SX | 20.583 | [10.496, 11.259] | [50.992, 54.700] | [9.732, 10.800] | [47.283, 52.468] | [8.969, 10.058] | [43.575, 48.867] |
HN | 15.854 | [7.173, 7.830] | [45.245, 49.389] | [6.516, 7.435] | [41.102, 46.894] | [5.859, 6.797] | [36.958, 42.871] |
SD | 6.275 | [2.911, 3.166] | [46.388, 50.445] | [2.656, 3.012] | [42.331, 48.002] | [2.402, 2.765] | [38.274, 44.063] |
Province | Current Annual Emission (10,000 tons) | ||||||
---|---|---|---|---|---|---|---|
Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | Reduction Interval (10,000 tons) | Reduction Rate Interval (%) | ||
QH | 0.450 | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] |
SC | 0.022 | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] | [0.000, 0.000] |
GS | 1.598 | [0.742, 0.809] | [46.437, 50.614] | [0.677, 0.755] | [42.352, 47.272] | [0.611, 0.691] | [38.268, 43.281] |
NX | 1.025 | [0.720, 0.744] | [70.268, 72.587] | [0.697, 0.725] | [68.000, 70.731] | [0.674, 0.702] | [65.733, 68.516] |
IM | 1.318 | [0.476, 0.541] | [36.085, 41.069] | [0.411, 0.489] | [31.211, 37.082] | [0.347, 0.426] | [26.337, 32.318] |
SaX | 2.465 | [1.384, 1.468] | [56.135, 59.556] | [1.301, 1.401] | [52.790, 56.819] | [1.219, 1.320] | [49.445, 53.550] |
SX | 2.199 | [1.352, 1.418] | [61.494, 64.497] | [1.288, 1.366] | [58.558, 62.095] | [1.223, 1.302] | [55.622, 59.225] |
HN | 1.404 | [0.644, 0.703] | [45.847, 50.071] | [0.586, 0.656] | [41.718, 46.692] | [0.528, 0.599] | [37.588, 42.656] |
SD | 0.552 | [0.243, 0.267] | [43.990, 48.359] | [0.219, 0.247] | [39.719, 44.864] | [0.196, 0.224] | [35.448, 40.690] |
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Yu, Q.; Sun, Z.; Shen, J.; Xu, X.; Chen, X. Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model. Int. J. Environ. Res. Public Health 2023, 20, 1511. https://doi.org/10.3390/ijerph20021511
Yu Q, Sun Z, Shen J, Xu X, Chen X. Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model. International Journal of Environmental Research and Public Health. 2023; 20(2):1511. https://doi.org/10.3390/ijerph20021511
Chicago/Turabian StyleYu, Qianwen, Zehao Sun, Junyuan Shen, Xia Xu, and Xiangnan Chen. 2023. "Interactive Allocation of Water Pollutant Initial Emission Rights in a Basin under Total Amount Control: A Leader-Follower Hierarchical Decision Model" International Journal of Environmental Research and Public Health 20, no. 2: 1511. https://doi.org/10.3390/ijerph20021511