Abstract

Water resource scarcity increases societal instability, poverty, and economic recession. Therefore, sound water resource management is vital to alleviating water crises in the agricultural, domestic, and industrial sectors. Southeast Iran, which currently lacks good water resource management, is experiencing a severe water crisis. Taking Zabol and Zahedan as examples, this paper seeks to optimize water allocation between the two cities using a dynamic bi-level programming model; the upper level objective minimizes the deviation between water demand and supply, and the lower level objective maximizes the net economic benefits in each sector. A sensitivity analysis is then conducted on the different sources of available water to provide more information on water allocation over time.

INTRODUCTION

The competition for water resources has attracted increasing attention, with one of the main conflicts being the imbalance between water supply and demand (Dehgan et al. 2014). Water demand varies from country to country primarily because of differences in the hydrological indicators. For example, global warming has increased the water requirements for some flora and fauna. Further, economic development and reduced precipitation has decreased the water available for human use. As the agricultural, domestic, and industrial sectors and other water needs (ecology, recreation and navigation) compete for limited water resources, the indiscriminate allocation of water resources is unworkable; therefore, it is urgent to modify water use patterns and develop water allocation plans to more equitably distribute the limited water resources.

As available water is necessary for food security, daily life, and economic development, there have been many research attempts to alleviate water scarcity. Xu et al. (2016) proposed a dynamic equilibrium strategy for drought emergency temporary water transfers and allocation management, Hu et al. (2016) resolved water allocation issues using a multi-objective bi-level programming model that considered equality and stability, and Wang et al. (2015) optimized water resource allocation in the Heihe River Basin, China. Tamošaitienė & Zavadskas (2013) developed a multi-stage model to improve decision-making processes in different seasons and particularly in drought seasons. Fang et al. (2013), Kucukmehmetoglu & Guldmann (2005) and Roozbahani et al. (2013) all developed multi-objective models to resolve water resource allocation problems. However, little previous research has analyzed the complicated relationship between the authorities and water users. In this paper, bi-level programming is used to consider the different types of decision-makers.

As stream flow can have a significant influence on water availability, some water allocation research has considered the changes in the seasons. Ke et al. (2016) proposed a comprehensive dynamic model and Niayifar & Perona (2017) defined dynamic flow release rules to improve the global efficiency of storage systems. Therefore, to achieve sustainable development, in this paper, the climatic influences on stream flows in spring, summer, autumn, and winter are considered. There has been a call for the development of market systems to resolve water surplus and shortage problems (Raffensperger et al. 2009), with water rights trading being considered an effective method for promoting efficient water allocations (Wang et al. 2017). Therefore, in this paper, possible water transactions are considered to be incorporated into the optimization model.

Based on the above analysis, this paper develops a dynamic bi-level programming model to enable trade-offs between two different decision-makers to optimize water allocation planning. The Karush–Kuhn–Tucker (KKT) technique, one of the most widely used techniques (Shi et al. 2005; Lu et al. 2007), is then used to solve the model. Therefore, the purpose of the paper is to optimize water resource allocation by using bi-level programming. Thus, the major contributions of this paper are as follows:

  • To propose a multi-stage bi-level programming model to relieve water crises.

  • To consider a water market strategy to deal with the seasonal surplus water.

  • To incorporate a water tariff to achieve water sustainability.

The remainder of the paper is organized as follows. The second section gives the main details of the problem. The third section describes the multi-stage bi-level model that includes a consideration of the water market and water tariffs. The fourth section illustrates the model using a case study and gives the solution method. Results and analysis are presented in the fifth section. Four separate seasonal scenarios are described in the sixth section. Finally, the seventh section gives the conclusions.

CONCEPTUAL FRAMEWORK OF THE WATER ALLOCATION PROCESS

In this paper, a bi-level framework is constructed to describe the water allocation process. The decision-maker on the upper level decides on the initial water allocation to the sub-areas. Then, the managers on the lower level seek to optimize the distribution of the pre-determined water between the agricultural, industrial, and domestic sectors, as shown in Figure 1. On the upper level, the available water, denoted Wi(i = 1,2, … ,n), is transferred from the basin reservoir to the sub-areas and is stored in the city reservoirs, denoted Ri(i = 1,2, … ,n), after which on the lower level, the pre-determined water and ground water (GW) are distributed to the agricultural (AGR), industrial (IND), and domestic (DOM) sectors. Water efficiency allocation is further increased through trading on the government monitored water market; that is, if sub-areas need to buy additional water or sell excess water, they must only purchase or sell on the water market.

Figure 1

Conceptual water allocation process framework.

Figure 1

Conceptual water allocation process framework.

As water demand and supply fluctuates across seasons, accounting for each season is vital for accurate and efficient water allocations (Xu et al. 2013). Therefore, multi-stage decision making is incorporated into the developed model.

MODELING

There are two decision-making levels: the Basin Reservoir Manager (WM), who makes water allocation decisions based on the water demand in spring, summer, autumn, and winter, and Sub-area Authorities (SA), who are responsible for the water distribution across the sectors and water transactions between n sub-areas. In this section, the upper- and lower-level objectives, constraints, and state transit equations are proposed.

Assumptions

There is a water market between the sub-areas, in which the sub-area manager has the rights under government regulation to sell any excess water stored in the reservoirs to another sub-area.

Notation

Indexes:

     
  • t

    Decision stage, t= 1,..,T

  •  
  • i

    City reservoir order number i= 1, 2, … , n

  •  
  • k

    Water using sectors k= 1, 2, 3

Certain parameters:

     
  • Ecosystem use

  •  
  • Water demand in sector j in city i

  •  
  • Actual water resource in city reservoir i in stage t

  •  
  • Water supply unit price to sector k in city i

  •  
  • Water supply unit cost to sector k in city i

  •  
  • AWt

    Actual water resource in the basin reservoirs

  •  
  • Quantity of ground water supplies to city reservoir i in stage t

  •  
  • Additional water tariff

  •  
  • Stream flow quantity in stage t

Decision variables:

     
  • Quantity of water transferred from the basin reservoirs to city reservoir i in stage t based on the WM decision

  •  
  • Quantity of fresh water supply to sector k

  •  
  • Water bought from () or sold ( to the water market by lower level manager in city i in stage t.

Lower level decision-making process

Objective function

On this level, the water comes from the basin reservoir and the ground water and the SA seeks to maximize the net benefits by equitably distributing the water to the three sectors, as shown in Equation (1): 
formula
(1)
where TRF is the additional tariff for water usage and sewage disposal. If the volume of fresh water used or sewage generated is higher than allocated, then the sub-areas must pay more for the consumed water and the generated waste water. Therefore, a pricing policy is developed by the government for optimal water consumption in each sector: 
formula
(2)
A water rights transaction price is also taken into account using a price function, Equation (3) (Fitzmaurice 1997): 
formula
(3)
When the desired water exceeds the fresh water allocated to the city or the desired water is less than the water allocated, the decision-makers must choose to buy or sell excess water on the government-controlled water market (Xu et al. 2013): 
formula
(4)
in which is the amount of water bought from the water market and is the amount of water sold to the water market.

Constraints

The constraints on the lower level are as follows:

  • 1.
    The city reservoir fresh water storage at each stage is denoted: 
    formula
    (5)
     
    formula
    (6)
  • 2.
    The fresh water withdrawn for the different sectors must be less than the ground water and surface water transferred from the basin reservoirs to the city reservoirs: 
    formula
    (7)

Upper level decision-making process

As water demand increases, water crises can lead to disputes and conflicts between the regions; therefore, water resource allocations need careful attention. WM is the upper level decision-maker who decides the water transfer from the basin reservoirs to the cities.

The objective function on the upper level is to minimize water scarcity, which is denoted by Equation (8): 
formula
(8)

The constraints are as follows:

  • 1.
    As noted earlier, four stages are considered in this model. As the water stored in the basin reservoirs to be allocated to the cities in each stage is changeable, the relationship can be expressed as: 
    formula
    (9)
  • 2.
    Total water quantity transfer to the cities cannot exceed the available water in the basin reservoirs in stage t: 
    formula
    (10)
  • 3.
    Water transfer continues until the deviation between the water demand in the sectors and the actual water transfer quantity in each city is greater than zero: 
    formula
    (11)
  • 4.
    The total water sold and bought via the water market must be equal to zero: 
    formula
    (12)
  • 5.
    The total water transferred via the water market should be less than the water quantity allocated to the sub-areas: 
    formula
    (13)

Global model

The global model, Equation (14), in this paper is a multi-stage bi-level programming to optimize the water allocation to the different cities on the upper level and water distribution to the three sectors on the lower level. The WM as the leader focuses on minimizing the deviation between water demand and water allocation in each city in each stage and the SAs as the followers focus on maximizing the net economic benefits of the water distribution and transactions. 
formula
(14)

CASE STUDY

The proposed model is applied to Iran, which has long grappled with water shortages. In this section, the applicability and efficiency of the proposed model is demonstrated by solving the complex situation between the basin reservoir and SA in Zahedan and Zabol, Iran.

Site description and data collection

Because of the water scarcity in Iran, farming has virtually disappeared, making life difficult for people (United Nations 2010). Two areas that have been seriously affected are Zahedan and Sistan Provinces. Zahedan is located in the southeast of Iran with a population of more than 550,000 inhabitants, and Zabol is located in the northern part of Iran with a population of around 225,000 inhabitants.

Water demand in the different sectors and especially for agriculture increases in the dry season, causing conflicts and disputes across the sectors in both Zabol and Zahedan. In Sistan basin, water scarcity has resulted in a reduction in crop yields and a corresponding decline in farm income. Some other effects of water stress are immigration and village evacuations and sand and dust storms. Therefore, the regional authorities need to focus on water resource allocation optimization to improve equitable and sustainable access to fresh water in the agricultural, industrial, and domestic sectors.

The only water source for Hamoon Lake and the Sistan Basin is the Helmand River Basin, a trans-boundary river (Moghaddamnia et al. 2009). After the recent drought, the available water in Hamoon Lake and Sistan Basin decreased, after which the SA diverted the river into the four Chahnimeh reservoirs to store additional water for irrigation, and the industrial and domestic sectors (see Figure 2). Chahnimeh 1, 2 and 3 were constructed around 35 years ago and have an overall capacity of around 660 million cubic metres, with the capacity of Chahnimeh 4 being significantly larger at 820 million cubic metres.

Figure 2

Sistan Basin and four Chahnimeh reservoirs.

Figure 2

Sistan Basin and four Chahnimeh reservoirs.

On average, the irrigation water fees are less than for the other sectors to encourage farmers. Based on historical data from the regional water authority and expert assessment, the water demand is shown in Table 1. The available water in the reservoirs and the expected water demand vary across the four seasons due to climate and temperature changes and precipitation fluctuations. Over the past few decades, the average precipitation rate has decreased with most rain falling during winter and the early spring months, at which time the stream flow rate is higher (Moghaddamnia et al. 2009), as shown in Table 2; therefore, the available water in the reservoirs varies, especially in the drier seasons. The initial available water volumes at the beginning of each stage/season in the four Chahnimeh reservoirs are respectively 290, 380, 171, 180 and 354 million m³. Table 3 shows the water volumes stored in the reservoirs in the two cities, which are influenced by the water withdrawals and stream flows in each season.

Table 1

Water demand in the two states ()

CityZabol (1)
Zahedan (2)
SeasonSpringSummerAutumnWinterSpringSummerAutumnWinter
DOM 2.11 2.99 2.93 2.53 9.01 11.09 8.76 8.00 
AGR 123.00 146.00 139.00 103.00 31.00 46.00 34.00 30.00 
IND 2.85 3.66 3.12 1.67  7.87 15.46 10.09 6.22 
CityZabol (1)
Zahedan (2)
SeasonSpringSummerAutumnWinterSpringSummerAutumnWinter
DOM 2.11 2.99 2.93 2.53 9.01 11.09 8.76 8.00 
AGR 123.00 146.00 139.00 103.00 31.00 46.00 34.00 30.00 
IND 2.85 3.66 3.12 1.67  7.87 15.46 10.09 6.22 
Table 2

Stream flows in the different seasons ()

SeasonSpringSummerAutumnWinter
Stream flow 270 80 145 310 
SeasonSpringSummerAutumnWinter
Stream flow 270 80 145 310 
Table 3

Water volumes stored in the reservoirs in the two cities

S1S2S3S4S5Total
City 1 123.0 101.9 41.1 0.0 73.8 339.8 
City 2 141.0 121.7 60.9 5.9 42.2 371.7 
S1S2S3S4S5Total
City 1 123.0 101.9 41.1 0.0 73.8 339.8 
City 2 141.0 121.7 60.9 5.9 42.2 371.7 

Results and analysis

The results of the water allocation to each sector in Zabol and Zahedan are shown in Tables 46. Table 4 shows the initial water allocated to Zabol and Zahedan in the different stages, and Table 5 shows the water volumes distributed to each sector in the four stages. The total demand from all sectors in the two cities is also compared, which verifies the water scarcity in these two cities.

Table 4

Initial water allocation in different stages

1234
Zabol 93.18 128.97 100.01 90.48 
Zahedan 40.09 43.96 36.60 39.22 
Total 133.27 172.93 136.61 129.70 
1234
Zabol 93.18 128.97 100.01 90.48 
Zahedan 40.09 43.96 36.60 39.22 
Total 133.27 172.93 136.61 129.70 
Table 5

Water distribution in the different stages

1
2
3
4
DomAgrIndDomAgrIndDomAgrIndDomAgrInd
Zabol 1.68 90.40 2.29 2.38 116.8 2.92 2.34 111.2 2.50 2.02 82.40 1.33 
Zahedan 7.21 24.80 6.29 8.87 36.80 12.36 7.01 27.20 8.07 6.40 24.00 4.97 
1
2
3
4
DomAgrIndDomAgrIndDomAgrIndDomAgrInd
Zabol 1.68 90.40 2.29 2.38 116.8 2.92 2.34 111.2 2.50 2.02 82.40 1.33 
Zahedan 7.21 24.80 6.29 8.87 36.80 12.36 7.01 27.20 8.07 6.40 24.00 4.97 
Table 6

Demand and supply comparisons

1
2
3
4
DomAgrIndDomAgrIndDomAgrIndDomAgrInd
Supply 8.89 123.2 8.58 11.25 153.60 15.28 9.35 138.40 10.57 8.42 106.40 6.30 
Demand 11.12 154.00 10.72 14.08 192.00 19.11 11.69 173.00 13.21 10.53 133.00 7.89 
1
2
3
4
DomAgrIndDomAgrIndDomAgrIndDomAgrInd
Supply 8.89 123.2 8.58 11.25 153.60 15.28 9.35 138.40 10.57 8.42 106.40 6.30 
Demand 11.12 154.00 10.72 14.08 192.00 19.11 11.69 173.00 13.21 10.53 133.00 7.89 

The water allocation plan shown in Table 5, which was solved using the proposed model, gives priority to the agricultural sector in each city, followed by the industrial sector. More than 92% of the water withdrawn (22% higher than the global average) is used in the agricultural sector. The water allocated to Zabol is higher than to Zahedan because of the higher level of farming. However, because there are more factories and a higher population in Zahedan, the water allocated to the industrial and domestic sectors is higher in Zahedan than in Zabol.

As stream flow has a significant influence on water allocations, the water allocated to each sector in different stages varies. For example, at the end of the winter and at the beginning of spring, the stream flow is greater, and therefore the reservoir water demand from the three sectors reduces.

The economic benefits, which reflect the effectiveness of the allocation optimization, are shown in Table 7.

Table 7

Economic utility of sub-areas in each stage

DomAgrIndDomAgrInd
 
Zabol 1,364 38,016 1,967 2,367 51,392 2,933 
Zahedan 16,254 10,912 11,225 23,851 16,192 39,369 
Total 17,618 48,928 13,192 26,218 67,584 42,302 
 
Zabol 2,302 41,448 2,269 1,819 36,256 848 
Zahedan 15,437 11,968 17,707 13,086 10,560 7,346 
Total 17,740 53,416 19,976 14,904 46,816 8,194 
DomAgrIndDomAgrInd
 
Zabol 1,364 38,016 1,967 2,367 51,392 2,933 
Zahedan 16,254 10,912 11,225 23,851 16,192 39,369 
Total 17,618 48,928 13,192 26,218 67,584 42,302 
 
Zabol 2,302 41,448 2,269 1,819 36,256 848 
Zahedan 15,437 11,968 17,707 13,086 10,560 7,346 
Total 17,740 53,416 19,976 14,904 46,816 8,194 

As can be seen in Table 7, in Zabol, agriculture provides 85% of the food energy intake and is the most important economic sector, followed by the industrial sector, with the domestic sector contributing the lowest net economic benefit. The price of the water allocated to the agricultural sector is lower than for other sectors in Zabol City; however, any increases in farm water prices could lead to crop yield reductions. In Zahedan, there is a high net profit from the domestic sector because of the higher residential density. Further, as the water price in Zabol is cheaper than in Zahedan, the net economic benefit in Zabol is lower than in Zahedan in each stage; therefore, it is concluded that water prices and costs are not the main factors affecting water allocation.

Sensitivity analysis

As the initial parameter values used in the model were based on a specific period, this limits the model's use for future planning. Therefore, a sensitivity analysis was conducted to examine the effect of available water on the optimal solution to the decision-making problem to guide strategy development (Dong et al. 2013).

As the available water usually fluctuates in water allocation models, this affects water allocation strategies. Therefore, because the available water greatly influences an optimal solution and the water allocations, four stages are considered.

Four scenarios are considered; extreme drought, moderate drought, slight drought and normal. The available water in each scenario is due to the trade-offs between stream flow rate and geological diversions in each season. However, as there is decision-making uncertainty about the amount of available water, this variable is characterized using interval fuzzy sets. For the solution, therefore, the expected value of the fuzzy variable is used, as shown in Table 8.

Table 8

Sensitivity analysis with different volumes of available water

Water allocated to sectors
Net economic benefit
StagesAvailable waterDomAgrIndDomAgrInd
Extreme drought  Zabol 1.77 104.80 2.39 1,478.21 46,112.00 2,108.20 
 Zahedan 8.30 32.80 7.83 21,083.08 14,432.00 16,746.26 
 Zabol 2.74 114.40 3.40 2,982.25 50,336.00 3,792.36 
 Zahedan 9.36 75.25 14.7 26,566.15 33,110.00 54,767.79 
Moderate drought  Zabol 1.67 89.07 2.10 1,351.09 39,190.80 1,711.71 
 Zahedan 6.43 23.92 7.90 13,193.54 10,524.80 17,007.79 
 Zabol 3.02 102.40 2.65 3,507.80 45,056.00 2,496.69 
 Zahedan 7.73 27.83 8.12 18,484.77 12,245.20 17,910.45 
Slight drought  Zabol 1.61 78.10 1.60 1,277.32 34,363.00 1,119.36 
 Zahedan 6.46 23.20 5.59 13,305.70 10,208.00 9,063.01 
 Zabol 1.76 93.60 2.87 1,465.26 41,184.00 2,849.82 
 Zahedan 8.03 25.90 7.30 19,831.15 11,396.00 14,718.99 
Normal stream flow  Zabol 1.68 76.00 1.19 1,363.57 33,440.00 568.94 
 Zahedan 5.83 20.80 4.40 11,049.09 9,152.00 5,924.16 
 Zabol 2.83 86.30 1.64 3,146.71 37,972.00 1,162.50 
 Zahedan 6.87 27.00 5.10 14,885.62 11,880.00 7,691.31 
Water allocated to sectors
Net economic benefit
StagesAvailable waterDomAgrIndDomAgrInd
Extreme drought  Zabol 1.77 104.80 2.39 1,478.21 46,112.00 2,108.20 
 Zahedan 8.30 32.80 7.83 21,083.08 14,432.00 16,746.26 
 Zabol 2.74 114.40 3.40 2,982.25 50,336.00 3,792.36 
 Zahedan 9.36 75.25 14.7 26,566.15 33,110.00 54,767.79 
Moderate drought  Zabol 1.67 89.07 2.10 1,351.09 39,190.80 1,711.71 
 Zahedan 6.43 23.92 7.90 13,193.54 10,524.80 17,007.79 
 Zabol 3.02 102.40 2.65 3,507.80 45,056.00 2,496.69 
 Zahedan 7.73 27.83 8.12 18,484.77 12,245.20 17,910.45 
Slight drought  Zabol 1.61 78.10 1.60 1,277.32 34,363.00 1,119.36 
 Zahedan 6.46 23.20 5.59 13,305.70 10,208.00 9,063.01 
 Zabol 1.76 93.60 2.87 1,465.26 41,184.00 2,849.82 
 Zahedan 8.03 25.90 7.30 19,831.15 11,396.00 14,718.99 
Normal stream flow  Zabol 1.68 76.00 1.19 1,363.57 33,440.00 568.94 
 Zahedan 5.83 20.80 4.40 11,049.09 9,152.00 5,924.16 
 Zabol 2.83 86.30 1.64 3,146.71 37,972.00 1,162.50 
 Zahedan 6.87 27.00 5.10 14,885.62 11,880.00 7,691.31 

Based on the analysis, when the available water is less than its initial value in the different stages (−20), the water allocated to the sectors and the respective net economic benefits in each stage reduce and vice versa. When the available water increases (+20), the water distributed to each sector increases; however, in the extreme drought scenario, a few sectors such as the agricultural sector are sensitive at 114.4, and the economic benefit fluctuation is insignificant. Therefore, in such cases, water needs to be bought on the market or rain generated through cloud seeding.

CONCLUSIONS

Many efforts have been made in the Middle East to reduce the impact of the water crisis; however, water scarcity problems are pushing many areas closer to the brink of disaster. Each sector must compete for the available water for food production, human survival, and economic development. Therefore, dynamic bi-level programming was developed to optimize water allocations.

The model was applied to two cities in Iran that have long grappled with water scarcity. This study found that the total demand in all sectors in the two cities could not be satisfied with the limited water resources. The agricultural sector has allocated 92% of the water in both Zabol and Zahedan, which is significantly greater than in the other sectors. The water allocated to the industrial and domestic sectors in Zahedan was found to be higher than that in Zabol because of the great level of industrialization and the larger population. To derive more in-depth information on the water allocations, this paper examined the effect of the available water on an optimal solution under extreme drought, moderate drought, slight drought and normal situations.

A sensitivity analysis was conducted by changing the available water. It was found that buying additional water on the water market could increase the economic benefits.

ACKNOWLEDGEMENTS

Support was provided by the National Natural Science Foundation of China (Grant No. 660 71771157, 71301109), Funding of Sichuan University (Grant No. skqx201726), and China Postdoctoral Science Foundation Funded Project (Grant No. 2017M610609).

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