Enhancing Disparity in Water Distribution within Irrigation Systems Aimed at Improving the Conflict Domain under Alternative Perspectives: A Reliable Multi-Objective Framework

Abstract

In general, decision makers in irrigation systems prioritize the cultivation of diverse crops to ensure sufficient food supply and maximize economic profit, while overlooking ecological resilience. This study proposes a novel reliable multi-objective framework designed to minimize disparities in water distribution between multi-crops, thereby addressing conflicts related to irrigation timing and distribution space. To assess the feasibility of the proposed model, a reliability evaluation technique is employed to examine the conflict ratio of the water distribution policy corresponding to constraints concerning the available water and the water allocated to various crops ($C\text{-}value$). Next, to evaluate the reliable optimal multi-objective model, we examined the disparity of water distribution among four crops—fodder, watermelon, wheat, and grape—cultivated in three sub-areas of the Zayandehroud watershed, a watershed experiencing water shortage in the center of the Iranian plateau. Subsequently, given the overlooking of water conservation policies, this study investigates the impact of alternative perspectives on the disparity of water distribution and the conflict domain. The final results indicate that grapes exhibit lower sensitivity to water consumption, whereas watermelon is the most sensitive. In terms of the conflict domain, the city of Lenjanat recorded the least sensitivity.

1. Introduction

The term “disparity” denotes an imbalance in the distribution of a valuable resource among stakeholders [1]. Therefore, enhancing the optimization of the disparity index within the system will enhance the equitable distribution of system resources among users, ultimately leading to reduced conflicts [2,3]. Nonetheless, addressing disparities in accessing irrigation pose significant impacts on the sustainability of large-scale irrigation systems, resulting in heightened food security and income levels [4]. Yet the optimization of water distribution within the irrigation system is imperative to alleviate disparities in water allocation and enhance the efficiency of accessible water resources [5].

The significance of irrigation monitoring in managing scarce water resources has long been acknowledged. Numerous studies have investigated climate variability and the main factors influencing water distribution within irrigation systems at regional and global scales [5,6,7,8,9,10,11,12,13,14]. In this context, several programming frameworks have been proposed to develop water resource management concerning the disparity index. For instance, Yin et al. [5] enhanced irrigation water consumption efficiency by assessing the disparity in Unit Irrigation Water Consumption (UIWC) and Total Irrigation Water Consumption (TIWC) across cropping systems in China from 2018 to 2014. Li et al. [12] constructed a model framework to optimize the multi-dimensional conflict arising from the interaction between limited water supply and escalating water demand. Their objective was to address the challenge of effectively managing the synergy between Agricultural Land and Water Resources (ALWR) within a dynamic environment. Hassan et al. [6] proposed a two-stage mechanism for demand-based water allocation to ensure equitable distribution among farmers. In the first stage, surface water is initially allocated based on individual water rights. In the second stage, water is distributed according to demand, accompanied by an auction-based pricing mechanism. Siebert and Döll [13] devised a crop water balance model aimed at estimating irrigation water consumption for each crop and grid cell, adhering to principles of water balance. Hashemy Shahdany [15] introduced a novel configuration of the water level difference error method to expedite error sharing within the framework of model predictive control (MPC), aimed at achieving equitable water distribution between upstream and downstream users in water-scarce main channels. This scheme utilizes an Integral-Delay (ID) model to represent channel pool responses within the model predictive controller.

The referenced studies typically explore the application of various frameworks to examine water distribution in agricultural irrigation systems considering different objectives. While previous research has made substantial advances in the economic and social aspects of agricultural irrigation systems, particularly in terms of equity between diverse crops, the development of reliable multi-objective frameworks to optimize disparity within an irrigation system has been infrequent. Indeed, equilibrium in water distribution promotes sustainable irrigation by balancing water demand with available water resources, leading to more consistent and reliable irrigation schedules. In practice, unreliability of the water distribution system to meet the water requirements of multi-crops during a drought exacerbates instability, thereby amplifying the conflict domain within the irrigation system. To tackle this challenge, it is crucial to develop an optimal water distribution framework characterized by high reliability, particularly focusing on the critical factors linked to this process.

Accordingly, the main contribution of this study is outlined a reliable multi-objective framework aimed at minimizing the disparity of water distribution between multi-crops within an irrigation system, and thereby mitigating conflict domain. Moreover, given that decision makers in irrigation systems often prioritize the cultivation of a variety of crops to ensure sufficient food supply and maximize economic profit—while neglecting the specific water requirements of individual crops—this study explores alternative approaches. It examines the regulation of high-water-consumption crops in contrast to alternative, less-water-intensive crops and assesses the impact on conflict domain levels as well as the disparity range of water distribution.

2. Methods

2.1. Assessment of Conflict Domain within the Irrigation System

Two critical contradictions concerning water distribution within irrigation systems must be addressed: (1) the space conflict in the distribution of water within the system, and (2) the temporal conflict related to irrigation scheduling. In order to mitigate damage, it is essential to ensure sufficient water supply to cultivated areas, while also ensuring that scarce water resources maintain adequate water to satisfy regular requirements of multi-crops. Since water resources are scarce, the decision maker cannot prioritize one crop over others when distributing water resources to address the water requirement gap. This is because in the irrigation system, total losses encompass the losses of all individual crops. Consequently, conflicts concerning the space distribution of water resources, such as access issues or unequal distribution across different geographical areas within the system, lead to space conflicts in water distribution.

In addition, irrigation timing conflict can occur due to seasonal variations in precipitation, competing requirements for water, and inadequate scarce water resources. Delayed distribution of water resources may exacerbate damage in the region, leading to challenges in scheduling irrigation cycles. Farmers may struggle to irrigate their crops at the optimal times, which can impact crop yields and overall benefits. Thus, distributing scarce water resources based on current benefits poses an irrigation timing conflict as water resources are required for future water distribution (Figure 1).

Figure 1. Conflict perspective concerning the water demand and insufficient water supply.

Therefore, solely prioritizing immediate benefits may pose the risk of future water shortages, particularly if unexpected deterioration in rainfall occurs.

To effectively address space and timing conflicts, it is imperative to establish equilibrium in the distribution of scarce water resources within the irrigation sector to ensure stable irrigation.

Based on the above analysis, the equity of irrigation considering the drought rate is one of the key points to solve the conflict domain. In this regard, this study proposes a reliable multi-objective optimization framework aimed to minimize the impacts of drought disparity within the irrigation system, ensuring an improved conflict domain. According to the criteria proposed for irrigation disparity, three objective functions are developed to maintain the disparity of water distribution between multi crops with regard to shortage.

Figure 2, as the framework of this study, shows the process of water distribution between multi-crops, wherein the demand–supply curves have placed the main focus on the rate of irrigation disparity.

Figure 2. Conceptual framework of the water supply system in terms of the disparity index.

2.2. An Optimal Multi-Objective Disparity Framework

The objective functions in this study, denoted as $f^1$, $f^2$, and $f^3$, are defined as follows:

$f^1$: According to the definition of the water stress index provided by Li et al. [16], the $f^1$ is represented in Equation (1). In the given equation, the decision maker aims to minimize the disparity between the ratio of total water withdrawal for irrigation and the available scarce water designated for the crop $i$. Essentially, the distribution of water depends on the availability of water.

$$\underset{X_i^t}{\min f^1}={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{i^{\prime }=2}^n\left|\frac{X_i^t}{W_i^t}-\frac{X_{i^{\prime }}^t}{W_{i^{\prime }}^t}\right|}}$$

(1)

where $i$ is the number of crops, $X_i^t$ is the total water withdrawal for irrigation (decision variable) at time $t$, and $W_i^t$ refers to the volume of available water resources. In total, the parameter $f^1$ varies between 0 and 1, with a tendency towards 0 representing the absence of stress and the least irrigation disparity.

$f^2$: Based on the definition of scarce water resources delineated by Ren et al. [17], $f^2$ is shown in Equation (2). In this equation, the decision maker seeks to minimize the disparity in water scarcity per unit of water demand within the irrigation system of each sub-area.

$$\underset{X_i^t}{\min } f^2={\displaystyle \frac{1}{T}}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{i^{\prime }=2}^n\left|\frac{\max (R_i^t{A}_i^t-X_i^t{A}_i^t,0)}{R_i^t}-\frac{\max (R_{i^{\prime }}^t{A}_{i^{\prime }}^t-X_{i^{\prime }}^t{A}_{i^{\prime }}^t,0)}{R_{i^{\prime }}^t}\right|}}$$

(2)

where $R_i^t$ refers to the water requirement for crop i at time $t$, $A_i^t$ is the assigned area for crop $i$ at time $t$, and $T$ is total operation years. However, the tendency of $f^2$ towards 0 shows minimum irrigation disparity.

$f^3$: Given the principle of equity, the authority seeks to minimize the disparity of water distribution per unit of economic benefit across each sub-area. This approach enables the leader to determine the necessary initial water distribution among the sub-areas. Therefore, $f^3$ aims to minimize the disparity of water distribution per unit of net benefit within an irrigation system [18]:

$$\underset{X_i^t}{\min }{f}^3={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{i^{\prime }=2}^m\left|\frac{X_i^t{A}_i^t}{E_i^t}-\frac{X_{i^{\prime }}^t{A}_{i^{\prime }}^t}{E_{i^{\prime }}^t}\right|}}$$

(3)

${\displaystyle \frac{X_i^t{A}_i^t}{E_i^t}}$ simulates the acquisition of an optimal supply pattern within the concept of “boosting crop yield while minimizing water consumption”, which pertains to the amount of water supplied per unit of economic profit. However, a reduction in $f^3$ to 0 signifies minimum irrigation disparity with regard to net benefit of crop $i$. Conversely, an increase in the $f^3$ suggests that the decision maker of an irrigation system needs to supply more water to crop $i$ to sustain the net benefit. In addition, $E_i^t$ shows the net benefit as follows:

$$\begin{array}{l}{E}_i^t={\displaystyle \sum _{i=1}^m({\mu }_i.P_i^t.A_i^t-\rho .X_i^t.A_i^t)}\\ t=1,2,\dots T\end{array}$$

(4)

where ${\mu }_i$ presents the benefit parameter for crop $i$ per unit of allocated water, $P_i^t$ is the quantity of yield per unit of acreage, and $\rho$ refers to the price of water.

Constraints:

The level of water in the reservoir is defined by the available water from the previous stage and the streamflow volume as follows:

$$s^{t+1}=\min \left[s^t-{\displaystyle \sum _{i=1}^n{X}_i^t+z^t , \overline{s}}\right]$$

(5)

where $s^t$ denotes the level of scarce water in the reservoir during period $t$, $z^t$ is the amount of effective streamflow during the period $t$, and $\overline{s}$ is the maximum storage capacity of the reservoir.

Furthermore, the rate of water allocated to multi-crops must not exceed the rate of available water in a reservoir:

$$0\le {\displaystyle \sum _{i=1}^n{X}_i^t\le s^t}$$

(6)

The rate of available water in the reservoir should fall within the range of the reservoir’s maximum and minimum storage capacities:

$$s^{t\_\min }\le s^t\le \overline{s}$$

(7)

In addition, a correlation exists between crop yield and water absorption. As a result, we use a mathematical representation (a parabolic model) to explain how water affects crop productivity [19].

$$\begin{array}{l}{P}_i=a\cdot [z^t+\beta {\displaystyle \sum _{i=1}^n{X}_i^t{]}^2+b\cdot [z^t}+\beta {\displaystyle \sum _{i=1}^n{X}_i^t]+c}\\ i=1,2,\dots n.\end{array}$$

(8)

where $P_i$ refers to the quantity of yield from crop $i$ per unit of acreage, $\beta$ is the irrigation coefficient, and $a,b,c$ are positive parameters in the water production function.

Following the application of the weighted sum approach to address the multi-objective model, the resulting equation incorporating $f^1$, $f^2$, and $f^3$ is presented as follows:

$$Min f=w_{\alpha }\ast f^1+w_{\mu }\ast f^2+w_{\rho }\ast f^3$$

(9)

where $w_{\alpha }$, $w_{\mu }$, and $w_{\rho }$ represent the weights associated with the three objective functions, wherein their values are defined by the decision maker of the irrigation system to satisfy the system status with regard to $w_{\alpha }+w_{\mu }+w_{\rho }=1$.

Additionally, to assess the feasibility of the proposed model, a reliability assessment technique outlined by Shuai et al. [20] is employed to examine the conflict ratio of the water distribution policy corresponding to the constraints regarding the disparity between the available water volume and the water allocated to multi-crops $z^t-{\displaystyle \sum _{i=1}^n{X}_i^t}$($C\text{-}value$) over the specified duration.

$$L={\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T{\eta }^t}}{T}}, {\eta }^t=\{\begin{array}{l}1, if C\text{-}value\ge 0\\ 0, Others\end{array}$$

(10)

2.3. Case Study and Data Collection

Zayandehroud (identified by latitude ${31}^{\circ }11^{\prime }$ and longitude ${53}^{\circ }61^{\prime }$) stands as one of the main watersheds situated in Iran’s central plateau [21]. Its source lies in the Zagros mountains in the western part of Isfahan province, and it eventually drains into the Gavakhoni wetland [22,23]. A significant portion of the hydrological resources within this watershed is allocated to providing irrigation water for the Isfahan, Najafabad, and Lenjanat sub-areas, all of which have been experiencing pronounced water scarcity in recent years [24]. Indeed, a range of factors including the construction of dams along the riverbed, extensive water extraction from the headwaters of this watershed, shifts in climatic conditions, low irrigation efficiency, and a substantial decrease in precipitation have been identified as contributing to the increased water stress within this particular watershed [25,26,27]. Hence, conventional methods of water distribution are insufficient to meet the water requirements of the irrigation system at the sub-regional level. Therefore, the Zayandehroud watershed was considered as the studied area (Figure 3).

Figure 3. Zayandehroud watershed, Iran.

In this context, the initial data related to the rate of precipitation was acquired from the Water and Sewerage Department of Isfahan province, and historic water requirements of multi-crops were derived from the statistical data documented by the Regional Water Resources Center. Given the growth periods of four economically significant crops outlined in Table 1, this study implements a seasonal cropping schedule. Coefficients of the water production function and price of the crops were acquired from the experts affiliated with the Regional Agricultural Jihad organization (Table 2).

Table 1. Parameters of precipitation $\left(m^3{s}^{-1}\right)$, water requirement ($M{m}^3)$, and crop areas ($ha$).

	Isfahan			Najafabad			Lenjanat
	Crop Area	Water Requirement	Precipitation	Crop Area	Water Requirement	Precipitation	Crop Area	Water Requirement	Precipitation
Fodder	117	88	2.64	102	65	2.44	134	81	2.27
Watermelon	169	93	3.21	121	79	2.89	83	68	1.59
Wheat	164	95	1.75	146	88	3.37	120	73	2.02
Grape	123	76	2.37	98	80	1.84	102	78	2.62

Table 2. The value of coefficients in water production function and the crops’ price.

Crops	Grain	Fodder	Wheat	Grape
a	−0.0168	−0.0299	−0.0698	−0.0373
b	17.37	27.687	49.314	53.180
c	−694	−11,476	−10,461	−7823
Price (IRR/Kg)	4500	1500	9500	6500

3. Results and Analysis

3.1. Investigating the Reliability Index with Regard to Available Water Resources and the Overall Distribution of Water Among Multi-Crops

Figure 4 illustrates the reliability results with regard to available water constraints. The results obtained from three sub-areas exhibit considerable variability concerning the volume of available water and the $C\text{-}value$. In this regard, drought has a significant impact on the level of storage and the C-value. At the onset of the period, the C-value in Isfahan city is below $50 {Mm}^3,$ whereas it exceeds $50 {Mm}^3$ in the other two cities. Ultimately, the value drops below this threshold for all three sub-areas.

Figure 4. Reliability of optimal solution with regard to C-value ($M{m}^3$).

Based on the annual cultivation period, this figure is in a satisfactory condition for all three sub-areas in September. The actual value and mean distribution of water resources exhibited more moderate fluctuation in the cities of Lenjanat and Isfahan. Overall, the total number for all three sub-areas varied by less than 30% throughout the entire cultivation period, indicating a reliability of 70%. Consequently, this led to a notable feasible status regarding the C-value.

Table 3 provides the optimal distribution of irrigation water for multi-crops across three sub-areas. The results indicate that decision makers in the Isfahan and Najafabad regions allocated the highest amounts of water for wheat irrigation ($83.76 {Mm}^3 and 79.68 {Mm}^3$, respectively). In contrast, Lenjanat county allocated the highest amount of water to fodder ($71.47 {Mm}^3$). The highest average net profit across the three sub-areas is derived from wheat and fodder, each attaining an average value of $13 {Mm}^3$. In terms of $f^i$, Lenjanat city has nearly reached the optimal values across all three objective functions ($0.396$), whereas the first objective function has not achieved a notably optimal figure for Isfahan and Najafabad ($0.559, 0.582$). In summary, despite optimizing the distribution of irrigation water, addressing the total water requirements of each sub-region remains the primary challenge, resulting in a growing disparity.

Table 3. Optimal water distribution alongside disparity rate.

		Fodder	Watermelon	Wheat	Grape	${\mathit{f}}^1$	${\mathit{f}}^2$	${\mathit{f}}^3$
Isfahan						0.559	0.490	0.478
	$X_i$ ($M{m}^3)$	73.46	83.05	83.76	62.50
	EBs (${10}^{9}IRR)$	13.162	15.947	16.008	10.473
	$\mathrm{Harvest} \mathrm{crops} ({\displaystyle \frac{kg}{ha}})$	3284	5539	4612	4680
Najafabad						0.582	0.441	0.403
	$X_i$ ($M{m}^3)$	59.24	72.99	79.68	71.09
	EBs (${10}^{9}IRR)$	10.562	9.482	12.397	9.132
	$\mathrm{Harvest} \mathrm{crops} ({\displaystyle \frac{kg}{ha}})$	2486	3856	3071	3984
Lenjanat						0.396	0.421	0.430
	$X_i$ ($M{m}^3)$	71.47	64.02	65.25	67.96
	EBs (${10}^{9}IRR)$	15.730	7.841	10.956	9.603
	$\mathrm{Harvest} \mathrm{crops} ({\displaystyle \frac{kg}{ha}})$	4081	2689	2860	4146

EBs: Economic benefits.

3.2. Optimal Trade-Off for Irrigation Disparity Under Various Weight Scenarios

As the impact of each objective function varies in the presence of disparity, the present study employs weight adjustment scenario introduced by Tokos et al. [28]. This approach is adopted to investigate the relative importance of objective functions as perceived by decision makers [29]. Indeed, decision makers may place varying emphasis on disparity assessment; in other words, ${\mathit{f}}^1$, ${\mathit{f}}^2$, and ${\mathit{f}}^3$ present different degrees of importance to decision makers. Thus, to offer more information to managers, this study conducts 36 potential objective weights $(w_{\alpha }, w_{\mu }, w_{\rho })$ to determine solutions to the water balance issue with respect to $w_{\alpha }+w_{\mu }+w_{\rho }=1$.

As shown in Figure 5, in Najafabad and Lenjanat, increasing the weight associated with ${\mathit{f}}^1$ results in the mitigation of disparity. Conversely, for Isfahan, elevating the weight of ${\mathit{f}}^2$ and ${\mathit{f}}^3$ notably diminishes disparity.

Figure 5. Disparity scores across diverse sets of objective weights, (0.1, 0.1, and 0.8 denote ${\mathrm{w}}_{\alpha }=0.1,{ w}_{\mu }=0.1,$ and $w_{\rho }$ = 0.8).

3.3. Enhancing Crop Water Management Aimed at Improving Conflict Domain

Since decision makers of irrigation systems primarily seek to cultivate a variety of crops to ensure sufficient food supply and maximize economic benefit, while overlooking the specific water requirements of each crop, this study investigates some alternative perspectives. In this context, this study examines enhancing crop water management to analyze the potential water conservation policy in more detail. The advancement of modern mechanisms, such as regulated deficit irrigation, advanced irrigation technologies, and drought-resistant crops, among others, can play a crucial role in supporting this policy. This approach provides decision makers of irrigation systems the potential to effectively address alternative demands and shortages. Therefore, this study investigates the impact of the proposed approach by analyzing the effects of reductions in crop water requirements (5% and 10% less than the current demand) on the rate of disparity in the irrigation system.

According to the results presented in Table 4, despite the notable impact on the harvesting situation, the efficiency of water distribution relative to water demand improved significantly. In terms of the disparity index, the enhancement of crop water management leads to a more effective response to water requirements, satisfying a greater volume of the demanded water. Consequently, the disparity index value approaches 0, signifying a reduction in the conflict domain within the water distribution process.

Table 4. Analysis of enhancing crop water management approach.

Reduction in Water Requirements		Fodder	Watermelon	Wheat	Grape	${\mathit{f}}^1$	${\mathit{f}}^2$	${\mathit{f}}^3$
		−5%	−5%	−5%	−5%	−5%	−5%	−5%
		−10%	−10%	−10%	−10%	−10%	−10%	−10%
Isfahan						0.512	0.467	0.435
						0.473	0.420	0.391
	$X_{i }$ ($M{m}^3$)	71.62	82.84	80.14	60.62
		68.26	79.02	78.39	59.87
	Harvest crops $({\displaystyle \frac{kg}{ha}})$	3071	5408	4569	4496
		2897	5262	4337	4248
Najafabad						0.551	0.418	0.403
						0.528	0.392	0.380
	$X_i$ (M$m^3$)	58.66	71.13	77.82	70.46
		56.00	68.89	74.25	66.34
	Harvest crops $({\displaystyle \frac{kg}{ha}})$	2304	3677	2983	3814
		2189	3505	2836	3682
Lenjanat						0.371	0.365	0.408
						0.369	0.366	0.382
	$X_{ i}$ (M$m^3$)	70.11	61.23	62.51	65.68
		68.98	58.70	60.70	62.09
	Harvest crops $({\displaystyle \frac{kg}{ha}})$	3896	2572	2709	4006
		3703	2418	2613	3879

3.4. Analysis of Conflict Domain with Regard to Water Distribution

Due to insufficient water resources to meet the requirements of various crops, there is conflict in the process of water distribution between multi-crops. Figure 6 presents the average volume of water distributed relative to the overall demand during seasonal crop scheduling. However, the water distribution in every sub-area exhibits substantial fluctuations at the beginning and end of the period. For instance, while the initial average water allocation for fodder in Isfahan exceeded 80 ${Mm}^3$, the corresponding volume for this crop in the other two sub-regions was substantially lower, falling below 60 ${Mm}^3$. In general, the rate of total water distribution for crops varies with their harvest periods and planting times, resulting in significant fluctuations in the rate of conflict.

Figure 6. Average distribution with regard to overall demand in seasonal crop scheduling.

As shown in Figure 7, the conflict domain value across all sub-areas averaged approximately $14.08\%$. In sub-regions such as Lenjanat, the conflict rate for a crop like fodder showed minor changes of $1\%$, while this rate for a crop like watermelon was recorded at $15\%$.

Figure 7. Conflict rate with regard to water distribution between multi-crops.

As drought conditions intensify, more water-intensive crops are increasingly challenged by water scarcity, highlighting the need to consider alternative cropping patterns.

4. Discussion

Although previous studies [30,31] have emphasized the optimal allocation of water in various methods, these studies have predominantly focused on fundamental economic-based models, such as trading water in exchange for more profit. Focusing solely on economic benefits while overlooking environmental challenges will exacerbate the rapid depletion of water resources. Due to the critical importance assigned to water conservation, a reevaluation of water supply strategies in response to anticipated challenges concerning wastage of water resources is necessary. The agricultural sector is known for significant water wastage. Consequently, this study presents the following findings:

Preposition 1: Reevaluating decision strategies with regard to water conservation policy.

The results of this study indicate that participants in this sector frequently prioritize economic gains over the varying water consumption levels of different crops, often neglecting the crucial importance of water conservation. Given the critical importance of water conservation, reevaluating decision-making strategies to address anticipated water loss challenges, adopting alternative crops with lower water consumption, and implementing new irrigation technologies are crucial steps toward providing a suitable and practical solution. Beyond that, to enhance resilience in addressing irrigation disparities, it is essential to predict spatial–temporal patterns of population density to predict food security and water conservation policy. This proactive approach to managing participants’ requirements will significantly help in reducing conflicts.

Preposition 2: Implementing water distribution policies that assign accountability to both participants and suppliers.

Given the rate of conflict identified in Section 3.4, it is important to acknowledge that drought is an ongoing issue that cannot be eradicated. In fact, concentrating exclusively on the distribution of scarce water resources while disregarding demand fluctuations results in significant contradictions, which ultimately expand the domain of conflict. Therefore, developing flexible decision-making strategies aimed at optimizing overall water distribution, while considering water demand governance, can significantly minimize disparity, thereby enhancing the domain of conflict.

5. Conclusions

A reliable multi-objective framework was proposed to track the disparity in water distribution between multi-crops under alternative perspectives. The major points derived from the water distribution within the irrigation system include (1) minimizing the imbalance between water demand and water supply in response to water conservation policies to optimize disparity within the irrigation system; (2) enhancing the domain of conflict arising from the two critical contradictions of irrigation timing and distribution space; and (3) various alternative perspectives that pursue the reliability and feasibility of the model under varying water requirements. Indeed, evaluating the disparity between multi-crops highlights the range of conflict domains, particularly with respect to surface waters. The results showed a trade-off between the objective functions and the reliability depending on the different levels of distributed water. The Zayandehroud watershed, a water-stressed watershed within the Iranian plateau, was considered as the study area to investigate the feasibility of the proposed model. The optimal results, considering various alternative perspectives, were compared and analyzed. Accordingly, the city of Isfahan recorded the worst disparity rate and showed the highest sensitivity to conflict in this respect, whereas the city of Lenjanat achieved optimal values, reflecting the least sensitivity to conflict. Additionally, implementing alternative perspectives, such as reductions in crop water requirements by 5% to 10%, directly influenced water distribution patterns and improved the disparity index by approximately 4% under the proposed objective functions.

To advance research in this field, optimal frameworks could be developed that incorporate groundwater resources, desalination and water treatment systems, water requirement uncertainty, and market-based models among users.