*3.3. Data Collection and Analysis*

This article takes Handan City as the research region and selects 2030 as the planning year. Due to the administrative adjustment of the city in recent years, this paper merged the Fuxing district, the Congtai district and the Hanshan district into the urban district to facilitate data compilation and calculation. The data needed in this model are related to economy, society, environment and water resources. All of these data are collected from related literature, field surveys, local statistical yearbooks and website information. Specifically, the water distribution relationship between water sources and users is obtained from the water resources bulletin [46]. The weight coefficient *α* is calculated based on the proportion of the added value of different users in each region in the recent two years' yearbooks [47]. The planned annual water transport capacity is obtained by combining the water conveyance capacity over the years and the pipeline network construction in

recent years (https://www.h2o-china.com/news/295843.html, accessed on 14 June 2021). The unit oxygen consumption *d* and regional COD emissions are derived from related papers [48,49]. The benefit coefficient of agricultural water and industrial water is determined by the method of net output value allocation [48], and the benefit coefficient of domestic and ecological water use is obtained from relevant literatures [50,51]. According to the priority principle of domestic and ecological water use, the benefit coefficient was adjusted appropriately in this pater to rationalize the results, which are shown in Table 1.


**Table 1.** Net benefit coefficient of water use (yuan/m<sup>3</sup> ).

The available water supply of surface water, groundwater and diverted water in the planning year were predicted by the trend analysis method. The amount of recycled water was obtained according to the predicted regeneration rate of water consumption in the planning year. By comparing the predicted results with the water situations in recent years, it can be seen that there is similar water inflow situation in 2019. Thus, the water inflow situation of each stage in the planning year can be obtained based on the analysis of water supply proportion in 2019. 110% and 90% of the inflow were taken as the upper and lower bounds individually, and the results are shown in Figure 3.

It is necessary to calculate the planned annual water demand for optimal allocation of water resources. In this paper, the quota method was employed to forecast the water demand for agricultural, domestic and ecological use, whilst the equidimensional complementary residuals-residual modified GM (1, 1) model [52] was adopted to forecast the industrial water demand. Then, the water consumption situation in 2019 was analyzed to derive the water demand of every user at different stages of the planning year. Among them, the proportion of water demand at different stages of agriculture in the planning year is 15.80%, 49.80%, 23.40% and 11.00% respectively. The proportion of industrial water demand is 23.50%, 24.00%, 26.60% and 25.90%. The proportion of domestic water demand is 23.00%, 29.00%, 23.00% and 24.00%. The proportion of ecological water demand is 23.40%, 28.20%, 25.00% and 23.40%. In the planning year, 110% and 90% of the predicted water demand of different users in each region are taken as the upper and lower bounds of their water demand, respectively. The predicted results are shown in Table 2.

**Figure 3.** The amount of different water sources in the planning year (104 m3). **Figure 3.** The amount of different water sources in the planning year (10<sup>4</sup> m<sup>3</sup> ).

It is necessary to calculate the planned annual water demand for optimal allocation **Table 2.** Water demand (10<sup>4</sup> m<sup>3</sup> ).


#### Qiu [1834.11, 2241.69] [11.93, 14.58] [1027.04, 1255.27] [214.86, 262.60] Quzhou [2713.14, 3316.06] [851.19, 1040.35] [1945.83, 2378.23] [19.10, 23.34] **4. Results and Discussion**

#### Guantao [5127.48, 6266.92] [10.67, 13.05] [853.80, 1043.54] [190.99, 233.43] *4.1. Results Analysis*

She [11,532.15, 14,094.85] [2262.35, 2765.09] [2552.62, 3119.86] [582.51, 711.95] Guangping [2309.04, 2822.16] [0.00, 0.00] [764.05, 933.83] [895.73, 1094.78] Chengan [6932.34, 8472.86] [29.06, 35.52] [968.93, 1184.25] [236.83, 289.45] Wei [17,979.03, 21,974.37] [654.69, 800.17] [1832.58, 2239.82] [477.47, 583.57] In this study, the FIDP model suitable for Handan's water management was established to obtain the objective function values and water resources allocation schemes, which can be seen in Table 3. The *λ* <sup>+</sup>, *λ* − represent the maximum subordinate degree and the minimum subordinate degree respectively. In detail, by solving the model, the value of *λ* + *opt* is 0.993, the corresponding economic benefit is 2989.33 <sup>×</sup> <sup>10</sup><sup>8</sup> yuan, the satisfaction of users is 96.50%, and the social benefit is 1.23 <sup>×</sup> <sup>10</sup><sup>8</sup> kg. On the contrary, the value of *<sup>λ</sup>* − *opt*

Ci [1717.47, 2099.13] [574.94, 702.70] [1674.10, 2046.12] [582.51, 711.95]

is 0.985, whilst the corresponding economic benefits, satisfaction and social benefits are 2264.72 <sup>×</sup> <sup>10</sup><sup>8</sup> yuan, 87.50% and 1.65 <sup>×</sup> <sup>10</sup><sup>8</sup> kg, respectively.

**Table 3.** Solutions of objective functions (FIDP).


Table 4 shows the total amount of water allocated to different users in different regions of Handan City in the planning year, while Table 5 shows the total amount of water allocated from different water sources to different regions. It can be seen that the total amount of allocated water in Handan City in 2030 will be [175,412.60, 219,210.86] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , and the total water shortage will reach [34,051.91, 36,800.32] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> according to the water demand forecasting results. As the minimum water demand in the planning year will reach [167,571.50, 204,809.62] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , which is less than the allocated water, the water allocation in the planning year can meet its minimum guaranteed water demand on the whole.



In 2030, the agricultural water consumption in Handan City will account for[52.90, 53.60] % of the total water distribution with the detailed allocation being [92,754.97, 117,454.65] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . Since the agricultural water demand is affected by the season and climate, the water demand also changes at different stages of the planning year. In detail, the second stage is the main growth period of crops, and the agricultural water demand in this stage also increases correspondingly, accounting for [48.80, 49.80] % of the annual water demand. On the contrary, the amount of water distribution in the fourth stage accounts for the least proportion, which is only [11.10, 11.50] % of the total agricultural water distribution. The difference between these two stages is [35,988.55, 43,789.37] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . The calculation results show that the satisfaction of the agricultural is [80.00, 82.90] % in 2030, and it reaches 80% in each stage, meeting its minimum water demand. Supported by the soil characteristics of each region, the leading agricultural industries in Urban, Weixian, Daming, and Yongnian have been developing rapidly, and the agricultural water consumption in these four regions would account for [54.40, 56.40] % of the total agricultural water consumption in the city. The agricultural water distribution in the planning year is shown in Figure 4.


**Table 5.** Water allocations of different water sources in each region in the planning year (10<sup>4</sup> m<sup>3</sup> ).

**Figure 4.** Water allocations for agricultural use in the planning year. **Figure 4.** Water allocations for agricultural use in the planning year.

By solving the model, the industrial water distribution of Handan City in 2030 will be [36,210.94, 46,203.93] × 104 m3, accounting for [20.60, 21.10] % of the total water distribution. The satisfaction of industrial water consumption is [80.00, 83.50] % in the whole year, and such satisfaction is higher than 80.00% in each stage, meeting its minimum water demand. According to the solution results as shown in Figure 5, the third stage has the largest industrial water distribution, which is [9631.84, 12,290.27] × 104 m3, whereas the water distribution in the first stage is least with the allocation amount of [8509.83, 10,859.91] × 104 m3, and the difference between the two stages is [1122.11, 1432.34] × 104 m3. Among them, Urban, Wu 'an and Fengfeng are the major industrial water users, making a contribution of [78.90, 82.40] % for the whole city's industrial water consumption. By solving the model, the industrial water distribution of Handan City in 2030 will be [36,210.94, 46,203.93] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , accounting for [20.60, 21.10] % of the total water distribution. The satisfaction of industrial water consumption is [80.00, 83.50] % in the whole year, and such satisfaction is higher than 80.00% in each stage, meeting its minimum water demand. According to the solution results as shown in Figure 5, the third stage has the largest industrial water distribution, which is [9631.84, 12,290.27] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , whereas the water distribution in the first stage is least with the allocation amount of [8509.83, 10,859.91] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , and the difference between the two stages is [1122.11, 1432.34] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . Among them, Urban, Wu'an and Fengfeng are the major industrial water users, making a contribution of [78.90, 82.40] % for the whole city's industrial water consumption.

In 2030, the domestic water distribution in Handan City will be [34,907.31, 41,915.24] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , accounting for [19.10, 19.90] % of the total water distribution. The satisfaction of domestic water use in the whole year is [93.40, 95.10] %, and it is higher than 92.00% in each stage indicating a high degree for guaranteed domestic water. With the change of temperature, the domestic water consumption at different stages also changes slightly to some extent. Specifically, the proportion of domestic water in the four stages of the

In 2030, the domestic water distribution in Handan City will be [34,907.31, 41,915.24] × 104 m3, accounting for [19.10, 19.90] % of the total water distribution. The satisfaction of domestic water use in the whole year is [93.40, 95.10] %, and it is higher than 92.00% in

**Figure 5.** Water allocations for industrial use in the planning year.

planning year is [23.01, 23.44] %, [28.80, 29.00] %, [23.40, 24.10] % and [24.00, 24.40] % respectively. Obviously, the second stage consumes the most domestic water, whereas the first stage consumes the least proportion. During the planning year, the population in Urban and Yongnian will reach 3.40 <sup>×</sup> <sup>10</sup><sup>6</sup> , and the water allocated to these two areas will be [12,953.41, 15,082.32] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> correspondingly, accounting for [36.00, 37.10] % of the domestic water distribution to the whole city. The annual domestic water distribution in the planning year is shown in Figure 6. year, and such satisfaction is higher than 80.00% in each stage, meeting its minimum water demand. According to the solution results as shown in Figure 5, the third stage has the largest industrial water distribution, which is [9631.84, 12,290.27] × 104 m3, whereas the water distribution in the first stage is least with the allocation amount of [8509.83, 10,859.91] × 104 m3, and the difference between the two stages is [1122.11, 1432.34] × 104 m3. Among them, Urban, Wu 'an and Fengfeng are the major industrial water users, making a contribution of [78.90, 82.40] % for the whole city's industrial water consumption.

mestic water distribution to the whole city. The annual domestic water distribution in the

sustainability level of the region. In 2030, the ecological water distribution in Handan will be [11,539.41, 13,638.02] × 104 m3, with a contribution of [6.20, 6.60] % for the total water distribution. The satisfaction of ecological water use is [96.70, 100.00] % in the whole year with the satisfaction degree over 93.00% in each stage, which reflects the priority in ecological development. It can be seen from Figure 7 that the distribution of ecological water reaches the annual maximum amount of [3254.21, 3704.50] × 104 m3 in the second stage, which is [404.34, 554.02] × 104 m3 more than the least water distribution in the first stage. The ecological water consumption in the third and fourth stage is [2884.81, 3333.10] × 104 m3 and [2700.24, 3300.23] × 104 m3 respectively, accounting for [24.40, 25.00] % and [23.40, 24.20] % of the ecological water consumption in the whole year. Among them, the ecological water consumption in the urban area and Daming county is relatively huge, contribution [32.10, 34.30] % and [23.10, 23.90] % to the total ecological water consumption respectively. This indicates that these two regions pay close attention to ecological environment

By solving the model, the industrial water distribution of Handan City in 2030 will be [36,210.94, 46,203.93] × 104 m3, accounting for [20.60, 21.10] % of the total water distribution. The satisfaction of industrial water consumption is [80.00, 83.50] % in the whole

**Figure 4.** Water allocations for agricultural use in the planning year.

**Figure 5.** Water allocations for industrial use in the planning year. **Figure 5.** Water allocations for industrial use in the planning year. planning year is shown in Figure 6.

**Figure 6.** Water allocations for domestic use in the planning year. **Figure 6.** Water allocations for domestic use in the planning year.

construction.

To a certain extent, the development degree of ecological environment reflects the sustainability level of the region. In 2030, the ecological water distribution in Handan will be [11,539.41, 13,638.02] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , with a contribution of [6.20, 6.60] % for the total water distribution. The satisfaction of ecological water use is [96.70, 100.00] % in the whole year with the satisfaction degree over 93.00% in each stage, which reflects the priority in ecological development. It can be seen from Figure 7 that the distribution of ecological water reaches the annual maximum amount of [3254.21, 3704.50] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> in the second stage, which is [404.34, 554.02] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> more than the least water distribution in the first stage. The ecological water consumption in the third and fourth stage is [2884.81, 3333.10] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> and [2700.24, 3300.23] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> respectively, accounting for [24.40, 25.00] % and [23.40, 24.20] % of the ecological water consumption in the whole year. Among them, the ecological water consumption in the urban area and Daming county is relatively huge, contribution [32.10, 34.30] % and [23.10, 23.90] % to the total ecological water consumption respectively. This indicates that these two regions pay close attention to ecological environment construction.

**Figure 7.** Water allocations for ecological use in the planning year. **Figure 7.** Water allocations for ecological use in the planning year.

Based on the analysis above, it can be known that FIDP model can provide global optimal solutions for the planned annual water distribution scheme, as well as specific water distribution schemes at different stages of the year under dynamics and uncertainties. In the planning year, the second stage has the largest water distribution of [68,246.70, 84,190.91] × 104 m3, while the fourth stage has the smallest water distribution of [30,648.40, 39,012.42] × 104 m3. The water distribution difference between the two stages is [37,598.12, 45,178.58] × 104 m3, and the difference accounts for [20.60, 21.40] % of the annual water distribution. Based on the analysis above, it can be known that FIDP model can provide globaloptimal solutions for the planned annual water distribution scheme, as well as specific water distribution schemes at different stages of the year under dynamics and uncertainties. In the planning year, the second stage has the largest water distribution of[68,246.70, 84,190.91] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , while the fourth stage has the smallest water distribution of [30,648.40, 39,012.42] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . The water distribution difference between the two stages is [37,598.12, 45,178.58] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , and the difference accounts for [20.60, 21.40] % of the annual water distribution.

#### *4.2. Model Comparison 4.2. Model Comparison*

[2171.42, 3124.16] × 108 yuan, 2

In order to verify the effectiveness of the proposed FIDP model, the application of FILP model to the case study is provided for comparison, which is shown in Appendix A. The difference between FILP model and FIDP model is that it deletes dynamic programming and parameter *t*, but their objective functions, constraints, decision variables and solution methods remain the same. Because the FIDP model takes into account the dynamic factors in different stages of water resources system, the solution results cannot In order to verify the effectiveness of the proposed FIDP model, the application of FILP model to the case study is provided for comparison, which is shown in Appendix A. The difference between FILP model and FIDP model is that it deletes dynamic programming and parameter *t*, but their objective functions, constraints, decision variables and solution methods remain the same. Because the FIDP model takes into account the dynamic factors in different stages of water resources system, the solution results cannot only

whole planning year without considering the dynamic variability of regional water resources system, which would imply that the water use efficiency, water consumption, water demand, water supply and other factors in the FILP model cannot be adjusted correspondingly with the seasonal changes. Therefore, the FIDP model has better optimal so-

λ

<sup>±</sup> = [0.952, 0.992], 1

λ

<sup>±</sup> = [1.17, 1.85] × 108 kg, and the com-

*f* <sup>±</sup> =

> *f* ±

<sup>±</sup> of the FIDP

lutions and stronger applicability than FILP. The detailed analysis is as follows.

<sup>±</sup> = [75.00, 84.00] %, 3

parison result of two models is shown in Figure 8. It can be seen that, compared with the FILP model, the ranges of the solution results of the FIDP model are reduced in different

model is not only reduced in scope, but also presents increases in its overall value, with its upper bound and lower bounds increased by 0.10% and 3.30% respectively. For 1

*f*

Based on the FILP model, the membership function

degrees, making the results more specific and accurate. In detail, the

*f*

conform to the case study, but also achieve global optimization under the local optimal conditions of each stage. However, the FILP model only aims at optimality over the whole planning year without considering the dynamic variability of regional water resources system, which would imply that the water use efficiency, water consumption, water demand, water supply and other factors in the FILP model cannot be adjusted correspondingly with the seasonal changes. Therefore, the FIDP model has better optimal solutions and stronger applicability than FILP. The detailed analysis is as follows.

Based on the FILP model, the membership function *λ* ±= [0.952, 0.992], *f* ± 1 = [2171.42, 3124.16] <sup>×</sup> <sup>10</sup><sup>8</sup> yuan, *<sup>f</sup>* ± 2 = [75.00, 84.00] %, *f* ± 3 = [1.17, 1.85] <sup>×</sup> <sup>10</sup><sup>8</sup> kg, and the comparison result of two models is shown in Figure 8. It can be seen that, compared with the FILP model, the ranges of the solution results of the FIDP model are reduced in different degrees, making the results more specific and accurate. In detail, the *λ* ± of the FIDP model is not only reduced in scope, but also presents increases in its overall value, with its upper bound and lower bounds increased by 0.10% and 3.30% respectively. For *f* ± 1 and *f* ± 3 , not only the ranges of their value are reduced by 23.90% and 38.20%, but also their lower bounds are increased by 93.30 <sup>×</sup> <sup>10</sup><sup>8</sup> yuan and 0.06 <sup>×</sup> <sup>10</sup><sup>8</sup> kg respectively, which are more accurate. The value of *f* ± 2 in FIDP model is improved by 12.50%, which will alleviate the conflicts between local government and users, and among different users more effectively. Consequently, it can be concluded that FIDP model proposed in this paper performs better and is more suitable for the optimization of water resources allocation in this area. and 3 *f* <sup>±</sup> , not only the ranges of their value are reduced by 23.90% and 38.20%, but also their lower bounds are increased by 93.30 × 108 yuan and 0.06 × 108 kg respectively, which are more accurate. The value of 2 *f* <sup>±</sup> in FIDP model is improved by 12.50%, which will alleviate the conflicts between local government and users, and among different users more effectively. Consequently, it can be concluded that FIDP model proposed in this paper performs better and is more suitable for the optimization of water resources allocation in this area.

**Figure 8.** Comparison of the objective functions between FILP and FIDP. **Figure 8.** Comparison of the objective functions between FILP and FIDP.

The water distribution scheme of FILP model is shown in Table 6, and the water shortage rate of the two models is compared in Figure 9. As presented in Table 6, the total water distribution of the FILP model is [167,643.11, 205,259.94] × 104 m3, which is reduced by [7769.43, 13,951.80] × 104 m3 compared with the FIDP model. As the water distribution decreases, the corresponding water shortage rate will be [19.70, 20.00] %, with an increase of [5.10, 9.10] % compared with [10.60, 14.90] % from the FIDP model. Compared with FILP, the water shortage rate from FIDP has declined in all regions, especially in Qiu, Quzhou, Guangping, Ci and Feixiang, with a decrease of [7.90, 16.70] %, [7.00, 15.00] %, [8.30, 20.00] %, [9.90, 20.00] %, and [9.80, 14.30] % respectively. Therefore, the model has good applicability to water resources allocation in water-scarce areas. The water distribution scheme of FILP model is shown in Table 6, and the water shortage rate of the two models is compared in Figure 9. As presented in Table 6, the total water distribution of the FILP model is [167,643.11, 205,259.94] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , which is reduced by [7769.43, 13,951.80] <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> compared with the FIDP model. As the water distribution decreases, the corresponding water shortage rate will be [19.70, 20.00] %, with an increase of [5.10, 9.10] % compared with [10.60, 14.90] % from the FIDP model. Compared with FILP, the water shortage rate from FIDP has declined in all regions, especially in Qiu, Quzhou, Guangping, Ci and Feixiang, with a decrease of [7.90, 16.70] %, [7.00, 15.00] %, [8.30, 20.00] %, [9.90, 20.00] %, and [9.80, 14.30] % respectively. Therefore, the model has good applicability to water resources allocation in water-scarce areas.

> [10,424.35, 12,740.87]

Jize [4396.03, 5372.93] [652.51, 797.52] [720.90, 881.11] [0.00, 0.00] Qiu [1467.29, 1793.35] [11.92, 14.58] [813.41, 994.17] [171.89, 262.60] Quzhou [2170.51, 2652.85] [680.95, 832.28] [1541.09, 1883.56] [19.10, 23.34] Guantao [4101.98, 5013.54] [10.67, 13.05] [676.21, 826.48] [152.79, 233.43] She [9225.72, 11,275.88] [1809.88, 2212.07] [2021.67, 2470.93] [466.01, 569.56]

**Agricultural Industrial Domestic Ecological** 

[8824.00,

17,422.01] [2091.95, 2556.83] [143.23, 175.07]

10,784.89] [3167.30, 3871.15]

Urban [16,518.74,

20,189.58]

Wuan [2287.87, 2796.29] [14,254.37,


**Table 6.** Water allocation of different users in different regions in the planning year (10<sup>4</sup> m<sup>3</sup> ). Wei [14,383.22, 17,579.50] [523.75, 640.14] [1451.40, 1773.94] [381.97, 484.41]

Guangping [1847.23, 2257.73] [0.00, 0.00] [605.12, 739.60] [716.58, 875.82] Chengan [5545.87, 6778.29] [29.06, 35.52] [767.39, 937.93] [189.46, 289.45]

**Figure 9.** Comparison of water shortage rates between FILP and FIDP. **Figure 9.** Comparison of water shortage rates between FILP and FIDP.

**5. Conclusions**  This study combines fuzzy-interval linear programming and dynamic programming to establish a fuzzy-interval dynamic programming (FIDP) method. The system uncertainty is expressed in the form of interval numbers in the model establishment and results presentation. In order to solve the conflicts among users caused by uneven distribution of In summary, the FIDP model has the following advantages over the FILP model: (i) The obtained target value intervals are more specific and accurate. (ii) This model can improve the overall satisfaction of the water users and alleviate the water contradiction among them. (iii) The water shortage rate of FIDP model is lower than that of FILP, which effectively alleviates the contradiction between water supply and demand. (iv) Last but

not least, FIDP model can get the allocation schemes of each stage in the planning year, and provide theoretical basis for water distribution decision-making in more detail way. Therefore, the model has a good performance in dealing with the dynamic changes of water resources system, and has advantages in optimizing the target value and reducing the water shortage rate.
