Emergency water supply decision-making of transboundary river basin considering government

Abstract

The emergency supply of transboundary water resources is a prominent problem affecting the social and economic development of basin countries. However, current water supply decisions on transboundary water resources may ignore the psychological perception of multi-stakeholders, and the evolution of emergencies increases the uncertainty of decision making. Both factors would lead to the low acceptance of water-related decisions. Utility satisfaction, perceived losses, and quantity satisfaction were selected in this paper to identify the perceived satisfaction of upstream governments, downstream governments, and the public, respectively, over multiple decision-making stages. A modeling framework combining prospect theory and the multi-stage multi-objective programming methodology was then developed to measure the perceived satisfaction of different stakeholders in a watershed under emergency. A two-stage NSGA-II and TOPSIS based approach was adopted to find the optimal compromise solution to solve the model. The framework was applied in the Lancang–Mekong River basin to provide suggestions to decision makers. Upstream decision makers must choose a moderate proportional fairness degree when making emergency decisions to maximize the perceived satisfaction of all stakeholders. Meanwhile, the perceived loss of downstream countries with low water demand should be considered first in the formulation of emergency water supply plans. Furthermore, although water supply from upstream countries can improve perceived water quantity satisfaction of downstream publics, additional actions must still be taken to change the traditional concepts of the public.

Keywords

Transboundary river basin emergency water supply decision government–public perceived satisfaction lancang–mekong river

1 Introduction

Large-scale water safety incidents due to natural disasters and social accidents frequently occur, making emergency water supply a prominent problem. Approximately 250 international rivers are found worldwide, covering more than one-half of the land surface of the globe and affecting 40% of its population [1]. Establishing a temporary joint working group to deal with bilateral or multilateral water supply or allocation issues in the basin is an international practice after an emergency [2]. However, bilateral or multilateral political negotiations involve the complex distribution of interests because of multi-stakeholders. In an up/downstream transboundary watershed, the following three main stakeholders are involved. The first one is the upstream government, who has the prior right to allocate emergency water to downstream countries due to geographical location and water storage projects. As a rational economic agent, the upstream government tends to make a balance between the input and output of a water supply plan. That is, high water supply costs will reduce the willingness of upstream countries to cooperate [3]. The second stakeholder is the downstream government, which provides additional attention to local social and economic benefits and attempts to minimize the loss caused by incidents. The third stakeholder is the public in the downstream basin, who is sensitive to obtainable water quantity under emergency [4]. If the obtainable water considerably varies from their psychological expectations, then this condition would ensue panic [5]. The increased water demand and limited water supply recently exacerbated the possibility of conflicts among multi-stakeholders [6]. Such conflicts require a water supply plan that satisfies most demands of stakeholders and encourages their acceptance of water-related decisions. Therefore, emergency water supply in a transboundary river basin is a multi-objective decision-making problem, and multi-stakeholders with different backgrounds highlight the importance of a rational water supply scheme.

Multi-objective optimization methods can be effective tools for addressing water supply or allocation under multiple conflicting objectives in a water system [7]. Many studies focus on water allocation decision-making in a transboundary watershed from social and economic perspectives [8]. However, each stakeholder would prefer criteria or principles that most supported his claims [9]. If the preferred criteria of one stakeholder are not adopted, then this stakeholder will be dissatisfied with the water decisions, and the resulting irrational behaviors will hinder the compromise of multi-objective conflicts. That is, the social and economic methods cannot fully solve the multi-criteria disputes, and the psychological behavior of stakeholders is not comprehensively analyzed. Human beings, with their beliefs and perceptions, are not an external but an inherent part of the water system that should be studied [10]. Perceived satisfaction, a psychology concept used to reflect the beliefs or perceptions of humans under uncertainty [11], provides a new perspective for this multi-criterion decision-making dilemma. The extension and connotation of this concept are constantly expanding and widely used in various fields. For example, the relationship between human satisfaction and perceived value [12], perceived decision quality [13], and perceived benefits [14] has been studied. An understanding of the processes that influence human perception of water decisions can contribute to improvements in water management [15]. In addition, transboundary water resource supply is not only a multi-objective optimization problem but also a dynamic optimization process because dynamic evolution of disaster increases the uncertainty of decision making [16, 17]. Decision makers should adjust the water allocation strategy over multiple stages to reduce the errors and improve the perceived satisfaction of multiple stakeholders. Another reason for multi-stage decision-making is that water resources distribution is spatially and seasonally uneven [18]. Therefore, conceptualizing emergency water supply problems in a multi-objective multi-stage model that fully considers the perceived satisfaction of the upstream and downstream governments and the public is appropriate. Unfortunately, studies that considered the combination of perceived satisfaction and multi-objective multi-stage decision-making process are limited.

Despite the establishment of cooperative organizations and temporary working groups to achieve a rational supply of transboundary water under emergency, water resource supply schemes that consider the perceived satisfaction of multi-stakeholders over multiple stages are still lacking. Hence, a multi-objective multi-stage water supply model, which aims to improve the perceived satisfaction of upstream governments, downstream governments, and the public in different stages, is necessary. In modeling, the first step is to quantify the satisfaction degree of multi-stakeholders over multiple stages. Different methods, such as fuzzy clustering model [19], minimum and difference satisfaction functions [20], or coordination satisfaction function [21, 22], were proposed to measure the satisfaction of agents on a water-related decision. Based on the above literature, the perceived utility and losses of upstream and downstream governments, respectively, have been proposed to quantify the satisfaction of up/downstream governments in different stages. The perception of the government and the public is generally different when facing a risk [23], and the measurement methods for satisfaction are also different. Usually, the quantitative measures of public perceived satisfaction included the utility function in expect utility theory (EUT) [24, 25] and the value function in prospect theory (PT) [26 –28]. The utility function deduced that the risky prospect is linear in outcome probability based on the hypothesis of rational economic man. However, the value function in PT indicated that people have nonlinear preferences and tend to take risks to avoid losses. The public in a transboundary basin, as a bounded rationality group, tends to pursue their own interests by overexploitation if they are unsatisfied with the water decisions [29]. Therefore, compared with the utility function in EUT, the value function in PT can effectively reflect the loss aversion characteristic of the public. Overall, perceived utility, losses, and water quantity (by the value function in PT) were applied to study the satisfaction of multi-stakeholders at different stages. A multi-objective multi-stage decision-making model was established on the basis of the preceding analysis, providing a comprehensive overview of the transboundary watershed system.

Second, obtaining the optimal solution of the aforementioned multi-objective multi-stage model is vital for the following water supply schemes. The genetic algorithm (GA) is proven to be an effective method for solving multi-objective optimization problems. Non-dominated sorting GA II (NSGA-II) [30] was applied to solve the model because it generates a set of non-dominated solutions (Pareto solutions), which perform better on multi-criterion than the other solutions [31]. A ranking procedure called technique for order preference by similarity to ideal solution (TOPSIS) [32] has been adopted because identifying the best compromise solution in each stage from the Pareto set under emergency is necessary for decision makers. The basic principle of TOPSIS is to find a solution that has the shortest and farthest distances from the positive and the negative ideal solutions, respectively. The general procedures of the original TOPSIS method are: (1) Obtain a decision matrix and normalize it. (2) Construct a weighted normalized decision matrix. (3) Find the positive ideal solution and the negative ideal solution. (4) Calculate the distance between each alternative solution and positive ideal solution, and negative ideal solution. (5) Calculate the relative closeness to the ideal solution and rank the preference order. The original TOPSIS method is effective in dealing with numerical value-based information. Then, the extended TOPSIS methods were developed to handle uncertain information, such as interval-valued fuzzy TOPSIS [33 –35] and fuzzy linguistic TOPSIS [36, 37]. The original TOPSIS method is adopted in this paper because the Pareto solutions are composed of numerical values. Many studies introduced the application of numerical value-based TOPSIS in Pareto sorting [38], where the Pareto solutions were obtained by NSGA-II [39] to prioritize the efficient optimal solutions [40]. Finally, taking the Lancang–Mekong River as an example, several numerical analyses were conducted to demonstrate that NSGA-II determines the Pareto set and TOPSIS finds the best compromise solutions for different scenarios.

The structure of this paper is as follows. Section 2 presents the literature review. Section 3 establishes a multi-objective multi-stage model considering the perceived satisfaction of multi-stakeholders under emergency in a transboundary watershed. Section 4 analyzes the case of emergency water supply in the Lancang–Mekong River Basin. Section 5 concludes this study and introduces future work.

2 Literature review

Many researchers have studied the transboundary emergency water supply problem and proposed different hydrology methods, including hydrological modeling [41], probabilistic forecasts [42], and space and time analysis [43], to solve the emergency water supply problem. However, although transboundary emergency water resource supply is an issue of resources, it is considered a typical decision-making problem [44]. The above studies mainly focused on hydrological impacts and ignored the acceptance of decision recipients. Perceived satisfaction is a human pleasure or the feeling of contentment when individuals perform a required or desired action and experience the result [45]. This feeling provides a direct way to measure the policy acceptance of stakeholders.

The study on human perceived satisfaction began with a psychology concept called perception need satisfaction of employees [11]. The concept of perceived satisfaction has been used by many researchers in different fields, endowing it with different connotations. Neal applied this concept in the tourism field and studied the perceived satisfaction of tourists with service quantity [46]. Liaw and Huang applied it in the education field and investigated the perceived satisfaction of students with the e-learning system [47]. Park and Park introduced this concept into the public administration field and examined the perceived satisfaction of patients with community-based case management services [48]. This paper defined perceived satisfaction as stakeholder acceptance of water-related decisions and the degree of comfort involved in using these decisions.

The existing literature of the research on the factors that influence the perceived satisfaction of humans mainly focuses on the fairness of resource allocation, the timeliness of emergency response, and the effectiveness of resource utilization. For example, Meng et al proposed a resource allocation scheme aiming at the max–min fairness of user satisfaction [49]. Cao et al studied victim satisfaction considering emergency responses from the perspective of time and quantity attributes [50]. Tang et al established a multi-objective programming model by maximizing the time satisfaction degree of resources and dispatching and minimizing the total cost [51]. Bozorgi-Amiri & Khorsi aimed at minimizing the maximum amount of shortages among the affected areas in all periods, including the total travel time, and the summation of pre- and post-disaster costs [52]. Mcdougall & Levesque revealed that the perceived value was the most important driver of human satisfaction [53]. In addition, the social position and cultural background of stakeholders affect their perceived satisfaction [54]. The above literature on influence factors of the perceived satisfaction mainly focused on the allocation of emergency resources within a region or country, while water resources in transboundary river basins are quasi-public resources involving many countries. Moreover, downstream countries are active recipients during this quasi-public resource distribution process, and they can find a satisfactory solution through political or military action. Measuring the response and perceived satisfaction of multinational stakeholders is necessary to make reasonable decisions.

Different methods were proposed to study the satisfaction of stakeholders with water under risk. These methods include the structural equation model [55], relational theory of risk [56], risk-based framework [57], and logistic regression analysis [58]. However, these methods have some limitations. Transboundary emergency water supply is the distribution of water-involved benefits among different stakeholders, and the key to solving this problem is to set up an integrated model that satisfies most demands of stakeholders [44]. The above models mainly focus on the social or economic satisfaction of certain stakeholders, such as the economic satisfaction of local water practitioners and the societal stability satisfaction of regional governments. Transboundary river basins have many stakeholders, but the public is also an important stakeholder. The public would overexploit water resources if they are unsatisfied with the water decisions, even if punished [29]. That is, the public is a loss aversion group instead of a risk aversion group. Therefore, the measurement of the public’s perceived satisfaction is particularly important. PT could be an effective method to address this problem by quantitatively measuring the perceived satisfaction of stakeholders and intuitively providing a display of loss aversion psychology using the value function.

Table 1
Symbols and definitions

Symbol Definition Symbol Definition

i Affected countries, i = 1, 2, 3 … n β Concave degree of loss function

j Decision stages, j = 1, 2, 3 … m λ Publics’ sensitivity between losses and gains

d_ij Water demand of affected country i at stage j π Proportional fairness degree

x_ij Obtained water quantity of country i at stage j η Available supply water ratio for public

w_ij Weight of country i at stage j h Upstream governments supplied water quantity

w_ri Importance of water resource for country i a Fix water supply cost

w_li Vulnerability of affected country i b Flexible cost coefficient

α Convexity degree of profit function C ₀ Supplied water cost

Symbol	Definition	Symbol	Definition
i	Affected countries, i = 1, 2, 3 … n	β	Concave degree of loss function
j	Decision stages, j = 1, 2, 3 … m	λ	Publics’ sensitivity between losses and gains
d_ij	Water demand of affected country i at stage j	π	Proportional fairness degree
x_ij	Obtained water quantity of country i at stage j	η	Available supply water ratio for public
w_ij	Weight of country i at stage j	h	Upstream governments supplied water quantity
w_ri	Importance of water resource for country i	a	Fix water supply cost
w_li	Vulnerability of affected country i	b	Flexible cost coefficient
α	Convexity degree of profit function	C ₀	Supplied water cost

PT was proposed by Kahneman and Tversky for decision analysis under risk [59]. Tversky and Kahneman later developed cumulative PT, which captures the psychological aspects of decision making under risk [60]. In PT, the outcomes are expressed through gains and losses from a reference alternative [61]. The value function in PT assumes an S-shape concave above the reference alternative, which reflects the aversion of risk in the face of gains, and the convex part below the reference alternative reflects the propensity to risk in case of losses [62]. PT addresses the decision process and the factors that influence decisions, including values, emotions, and experiences [63], making PT an excellent choice in describing the psychological activity of stakeholders. In the past decades, PT has been widely applied in behavioral economics [64], political decision-making [65], and transportation research [66]. PT also has potential implications for natural hazards and disaster planning, which involve the coordinated efforts of governments, private individuals, and corporations. Unfortunately, research works on the application of PT in water supply decisions under risk are limited.

Overall, the innovations of this paper are mainly reflected in the following three aspects. First, different from the traditional hydrological methods used to deal with the emergency supply of transboundary water resources, this paper attempts to maximize the perceived satisfaction of multi-stakeholders in the early stage of disasters to improve the acceptance of water supply decisions. Second, minimum proportional fairness is proposed because the water demand of upstream countries is prioritized in accordance with their geographical location. This approach aims to ensure the fairness of water supply decisions, which is important for the countries located in the estuary. Third, public satisfaction with water supply is considered from the perspective of psychology and history by PT. Thus, this paper establishes a fair and reasonable water resource supply decision model to improve the acceptance of multi-stakeholders for emergency water supply decision-making.

3 Multi-stakeholders perceived satisfaction model of the water resource supply in transboundary river basin

Section 3 describes the formulation of the model. First, the definition of symbols and basic assumptions are introduced to provide the basis of modeling. Second, the decision-making programmer and the methodology framework are concluded on the basis of emergency decision processes in a transboundary basin to provide a comprehensive overview of the system. Third, perceived utility, loss, and quantity are selected to identify the satisfaction of multi-stakeholders. An integrated model is also established. Finally, NSGA-II is used to obtain Pareto solutions of the model, and TOPSIS is applied to find the best compromise solutions for different scenarios.

3.1 Definition of symbols and variables

The transboundary river in this paper refers to the typical upstream and downstream international rivers. The geographical location determines the water use priorities in each country in the basin. Upstream countries are always in favorable positions, which affect the flow of rivers in downstream countries. The upstream countries can use water resources in various ways, such as power generation, agricultural irrigation projects, water transfer, and water storage projects, thereby reducing the available water resources in downstream countries and directly impacting their economic or social development [67].

Table 1 shows all the symbols and variables used in the model.

3.2 Basic assumptions

Assumption 1: The first assumption is that upstream countries have the capability to rescue the downstream countries in the early stage of the disaster.

This paper assumes the existence of a large hydropower station in an upstream country. The upstream government can rescue the downstream countries by adjusting the storage capacity and discharge volume. According to the International Water Law regarding the principle of “Equitable and Reasonable Utilization,” upstream countries must consider the water demand of downstream countries to achieve the coordinated development of the entire basin. Therefore, the discharge flow of the hydropower stations in upstream countries can be divided into two parts: the domestic and downstream water demands. In addition, the most urgent decision-making problem is only considered in the early stage of the disaster. The follow-up political negotiation or mechanism design is generally disregarded in this paper.

Assumption 2: Each country has guaranteed its minimum ecological water demand.

According to the Tennant method, this paper assumes that 10% of the average annual flow obtained from the upstream hydrological station closest to the border is the minimum ecological flow of the river from this station to the border [68].

Assumption 3: Agricultural irrigation water in the downstream countries is the main consumer of supplied water resources.

The water resource supply of transboundary rivers involves many aspects, such as river navigation, agricultural irrigation, hydropower, and ecology of the environment. However, agricultural water accounts for the largest proportion in the world. Irrigation is the largest water use in most of the transboundary river basins. Therefore, agricultural irrigation water is the main consumer of supplied emergency water resources in this paper.

Assumption 4: The public mainly refers to farmers.

The proportion of residents’ domestic water use is small in all sectors, and the priority is satisfied; thus, this factor is not considered in this paper. FAO states that the agriculture sector is still the main economic activity in the riparian countries, especially in the downstream ones [69]. As the main user of agricultural water, the satisfaction of farmers on emergency water supply directly reflects the rationality of water decisions. Overall, the public mainly refers to farmers in this paper.

3.3 Decision-making programmer and methodology framework

In this paper, the disaster information grasped by upstream decision makers in the early stage is incomplete and must be gradually improved in decision making. Therefore, a multi-stage emergency water supply is a Bayesian sequential decision-making process, which has effective adaptability to the distribution of emergency resources in the case of uncertain information [70].

Fig.1

Multi-stage decision-making process of emergency water supply.

Figure 2 illustrates the methodology framework of this study. This framework combines PT with the emergency resource supply model within the modeling framework while considering the perceived satisfaction of different stakeholders.

Fig.2

Model formulation.

3.4 Model of the water resource supply of transboundary rivers

3.4.1 Perceived utility satisfaction of upstream governments

The International Water Law regarding the principle of “Equitable and Reasonable Utilization” states that preparing an emergency water supply plan considering the social, economic, and ecological factors is necessary to maximize the overall interests of water resources in transboundary rivers [71]. During the process of dynamic water supply decisions, upstream governments must not only consider the water demand of downstream countries but also their emergency water supply capacity and cost. The emergency water supply capacity herein is mainly the reserved water of the hydropower station in the upper reaches; the cost includes the water supply and labor costs. Limited resources require consideration of the input and output utilities of funds in the emergency decision-making process. Otherwise, upstream governments may be negatively involved in water supply decision-making. Therefore, a rational emergency water supply decision must fully consider the interest of upstream governments and improve their satisfaction with the input–output of water supply. This study uses the perceived utility to depict the satisfaction of upstream governments with water supply decisions: $max f (x_{ij}) = 1 - \frac{\sum_{i = 1}^{n} \sum_{j = 1}^{m} c_{ij} x_{ij}}{C_{0}}$ (1) $s . t . {\begin{matrix} \sum_{i = 1}^{n} x_{ij} \leq h_{j}, \forall j \in J \\ \sum_{j = 1}^{m} h_{j} = h, \forall j \in J \\ x_{ij} \geq 0, \forall i \in I, j \in J \end{matrix}$ (2) where C₀ is the budget of upstream country; c_ij =a+0.5b x_ij. This function represents the water supply cost. In constraint (2), $\sum_{i = 1}^{n} x_{ij} \leq h_{j}$ prevents the water supply at stage j from exceeding the reserved water; $\sum_{j = 1}^{m} h_{j} = h$ requires all supplied water quantities at different stages to be equal to the reserved water provided by upstream country; x_ij ≥ 0 requires the supplied water quantity at the j stages of the affected area i to be larger than 0.

3.4.2 Perceived loss and water decision satisfaction of downstream governments

Two main challenges are encountered by downstream governments after the outbreak of emergencies: minimized social and economic losses. Social loss herein mainly pertains to the risk of social stability caused by water scarcity, while economic loss refers to the crop yield reduction due to drought. Meanwhile, the relationship between perceived loss and satisfaction of agents with policy or service has also been verified by many scholars [72, 73]. Hence, the satisfaction of downstream governments with water supply decisions can only be improved by minimizing the economic and social losses of downstream countries. In this study, losses are mainly caused by unmet water demand. Thus, the perceived loss of all downstream governments can be defined as follows: $min \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} L (x_{ij})$ (3) $s . t . {\begin{matrix} 0 \leq \sum_{j = 1}^{m} (x_{ij} + Q_{ij}) \leq d_{i}, \forall i \in I \\ \sum_{j = 1}^{m} (x_{ij} + Q_{ij}) \geq φ d_{i}, \forall i \in I \\ φ = π \cdot \sum_{j = 1}^{m} (h_{j} + Q_{ij}) / - \sum_{i = 1}^{n} d_{i}, \forall i \in I, j \in J \\ L (x_{ij}) = \frac{w_{rli}}{d_{ij}^{δ}} (d_{ij} - x_{ij} - Q_{ij})^{δ} \end{matrix}$ (4) where L(x_ij) is the loss function of affected area i at stage j; w_ij is the weight of affected area i at stage j; Q_ij is the self-produced water of area i at stage j; w_rli =w_ri×w_li is the combined coefficient of the supplied water resource importance (w_ri) and the vulnerability of affected areas (w_li). In Constraint (4), the first inequality prevents the water supplied to area i from exceeding its water demand; the second inequality is the minimum degree of proportional fairness; φ herein is the minimum demand satisfaction rate, which is necessary for the equality of “material distribution” under emergency [74]; π is the proportional fairness degree, π∈[0,1]. If π is near 0, then the proportional fairness is low. If π is near 1, then the proportional fairness is high. δ is the emergency index of affected areas; when the value of δ is large, the disaster in the downstream countries is serious.

3.4.3 Perceived water quantity satisfaction of downstream publics

The public, as a group of limited rationality, tends to panic and worry because of resource scarcity after emergencies [75]. In this study, the public will have an intuitive perception of the water policy only when the water supply is as near as possible to their psychological expectations. Referring to Wang & Dong, the expected water quantity of the public is calculated on the basis of locally supplied water quantity in history [76]. In addition, optimizing the water supply path in a short time is difficult due to the fixity of waterways. That is, the arrival time of water resources is disregarded in this paper. According to PT, the perceived satisfaction model of the public in area I at stage j can be obtained as follows: $V (x_{ij}) = {\begin{matrix} (x_{ij} - x_{ij 0})^{α}, x_{ij} \geq x_{ij 0} \\ - λ [- (x_{ij} - x_{ij 0})]^{β}, x_{ij} < x_{ij 0} \end{matrix}$ (5) where x_ij₀ is the expected water supply for the public of area i at stage j; $x_{ij 0} = \sum_{r = 1}^{R} \frac{x_{ijr}^{'}}{R}$ ; r = 1,2,3 ... R; $x_{ijr}^{'}$ herein is the supplied water quantity of area i at stage j in the last R years. If x_ij ≥ x_ij0, which means that the supplied water quantity is more than the psychological expectation of the public, then they will be satisfied with the policy; if x_ij < x_ij0, which means that the supplied water is less than the psychological expectation of the public, then they will be dissatisfied with the policy. Thus, the perceived water quantity satisfaction of the public can be expressed as follows: $max \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} V (x_{ij})$ (6) $s . t . {\begin{matrix} \sum_{i = 1}^{n} \sum_{j = 1}^{m} x_{ij} \leq η \cdot h, & \forall i \in I, j \in J \\ x_{ij} \geq 0, & \forall i \in I, j \in J \end{matrix}$ (7)

Equation (6) maximizes the water quantity satisfaction of the public in affected areas at all stages. In constraint (7), the first inequality indicates the actual available water for the public, while the second inequality requires all supplied water quantities in area i at stage j to be larger than or equal to 0.

3.4.4 Transboundary emergency water resource supply model

A multi-stage transboundary emergency water supply model considering perceived satisfaction of multi-stakeholders can be synthesized as follows: ${\begin{matrix} max f (x_{ij}) \\ min \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} L (x_{ij}) \\ max \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} V (x_{ij}) \end{matrix}$ (8) $s . t . {\begin{matrix} 0 \leq \sum_{i = 1}^{n} x_{ij} \leq h_{j} \forall j \in J \\ 0 \leq \sum_{j = 1}^{m} (x_{ij} + Q_{ij}) \leq d_{i}, \forall i \in I \\ \sum_{j = 1}^{m} (x_{ij} + Q_{ij}) \geq φ d_{i}, \forall i \in I \\ φ = π \cdot \sum_{j = 1}^{m} (h_{j} + Q_{ij}) / - \sum_{i = 1}^{n} d_{i}, \forall i \in I, j \in J \\ \sum_{i = 1}^{n} \sum_{j = 1}^{m} x_{ij} \leq η h, \forall i \in I, j \in J \\ f (x_{ij}) = 1 - \frac{\sum_{i = 1}^{n} \sum_{j = 1}^{m} c_{ij} x_{ij}}{C_{0}} \\ L (x_{ij}) = \frac{w_{rli}}{d_{ij}^{δ}} (d_{ij} - x_{ij} - Q_{ij})^{δ} \\ V (x_{ij}) = {\begin{matrix} (x_{ij} - x_{ij 0})^{α}, x_{ij} \geq x_{ij 0} \\ - λ [- (x_{ij} - x_{ij 0})]^{β}, x_{ij} < x_{ij 0} \end{matrix} \\ x_{ij} \geq 0, \forall i \in I, j \in J \end{matrix}$ (9) where max f (x_ij) maximizes the utility satisfaction of upstream government with emergency water supplement; $min \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} L (x_{ij})$ minimizes the perceived loss of downstream governments; $max \sum_{i = 1}^{n} \sum_{j = 1}^{m} w_{ij} V (x_{ij})$ maximizes public satisfaction on the quantity of water supply. In Constraint (9), the first inequality prevents the water supplement at stage j from exceeding the reserved water at stage j; the second inequality prevents the supplied water in area i from exceeding its water demand; the third inequality ensures the minimum demand satisfaction rate of affected areas; the fourth formula is minimum demand satisfaction rate; η is the available supply water ratio for public; the last inequality is a non-negative constraint.

3.4.5 Model solution and decision-making strategy

A two-stage NSGA-II and TOPSIS based approach is applied to find the optimal compromise solution (Fig. 3). In stage 1, “gamultiobj” toolbox in MATLAB R2016b was used to find a Pareto set, namely, 70 sets of non-dominated solutions in Table 10. “gamultiobj” toolbox is an improved multi-objective optimization algorithm based on NSGA-II [77, 78]. A brief introduction of the application of NSGA-II in model solving is presented (Stage 1 in Fig. 3).

Fig.3

Two-stage NSGA-II and TOPSIS approach for model solving.

A single solution is preferred by the decision maker to compare Pareto and GA to facilitate and amalgamate a range of solutions. Ranking methods can be applied to trim down the non-dominated solution sets to a single solution [79]. In stage 2, a ranking method called TOPSIS was selected to assist decision makers to find a single solution among non-dominated solution sets. Many researchers have adopted this method to rank the given alternatives to the Pareto solutions obtained by NSGA-II [80, 81].

Note1

In general, several methods have been reported to assist decision maker to find the best compromise solution among non-dominated solution sets, such as weighted sum method [82], pareto uncertainty index [83], weighted stress function method [84] and pareto filter concept [85]. In particular, the proposed numerical value-based TOPSIS method is widely adopted to rank the non-dominated solutions [86 , 88] due to its rationality, comprehensibility, and simple computation [89]. Inspired by above literature, we applied the numerical value-based TOPSIS method to find the best compromise solution in this paper, too. Moreover, we argue that it is very interesting in the future to apply other methods to find the best compromise solution.

Fig.4

Lancang–Mekong River basin (Mekong River Commission, 2016).

4 Case study

Section 4 describes the application of the established model in the Lancang–Mekong River basin. First, a general description of the Lancang–Mekong River basin, including social and natural overviews, and the drought in 2016, is presented. Second, optimal model solutions are obtained by NSGA-II and TOPSIS methods, and decision makers can select among solutions based on their preference. Third, two sets of sensitivity analyses are conducted to identify the sensitive factors for decision making. Finally, three scenarios are set to verify the model. The result shows that the model proposed in this paper can promote the coordinated development of the entire basin.

Fig.5

Pareto front.

4.1 Description of the study area

Figure 4 shows that the Lancang–Mekong River is a transboundary river that originates from Tibetan Plateau and flows through China to Indochina Peninsula. The part of the river in China is known as the Lancang River, while the downstream part is known as the Mekong River. Internationally, the portion of the river in China and Myanmar is commonly referred to as the Upper Mekong River, while the downstream portion in Laos, Cambodia, Thailand, and Vietnam is referred to as the Lower Mekong River [90]. The Upper Mekong drains an area of over 190,000 km², with 22,000 km² in Myanmar and the remainder in China. The total length of the Upper Mekong is 2395 km and extends more than 4700 m over the distance. Its length covers 2130 km in China; 31 km along the China–Myanmar border, and 234 km along the Myanmar–Laos border. The Lower Mekong has a catchment area of over 617,000 km² [91]. Its length is 2485 km with a fall of ca. 400 m, which includes 777, 502, 230, and 976 km in Laos, Cambodia, Vietnam, and along the Laos–Thai border, respectively.

The rainfall in the Lancang–Mekong River basin has dramatically reduced since the end of 2015 because of El Nino. China and the lower Mekong countries were seriously affected. The worst-hit area was Vietnam in the southernmost of the Mekong River; that is, approximately 139,000 ha of rice cultivation area and 575,000 people suffered from water scarcity [92]. Consequently, the Vietnam government turned to China for help. Then, the Chinese government conducted a three-stage emergency water supplement from Lancang to the Mekong River. Specifically, JingHong hydropower station of China has increased the outflow volume by 2000 m3/s per day from March 15 to April 10, 2016, from the perspective of hydrology [93].

Although the Lao and Vietnamese governments were grateful for the emergency water supply of China, the Ministry of Water Resources of Cambodia was not amenable to the plan, stating that the water supply is unlikely to have a substantial impact. The official media of Thailand exerted public opinion pressure on the Chinese government through comments on the upstream dam construction. Some farmers in the downstream countries also stated that emergency water supply cannot fully meet their needs [94]. Hence, studying stakeholder satisfaction on emergency water supply and formulating a scheme that considers the interests of most stakeholders are necessary to promote the coordinated development of the Lancang–Mekong River basins.

4.2 Results and discussion

4.2.1 Optimal model results

A total of 70 sets of non-inferior solutions were obtained by the “gamultiobj” toolbox in MATLAB R2016b. Figure 5 shows that all Pareto fronts are evenly distributed, and a contrary relationship exists between upstream and downstream satisfaction and upstream and public satisfaction. Meanwhile, a proportional relationship exists between downstream and public satisfaction.

Then, the numerical value-based TOPSIS method was used to calculate the closeness degree between each solution and the ideal one. Subsequently, the top seven solutions with the closest distance to the ideal solution were obtained and presented in Table 2. Decision makers can choose a satisfactory solution based on their preference. For example, if decision makers provide additional attention to their own interest, then #37 solution will be the best choice. If they emphasize on the response to the decision making of the public, then #69 solution is the best. If they tend to maintain a good relationship with downstream governments, then #37 solution is a viable solution.

Seven other solutions were selected on average among 70 non-inferior solutions according to the TOPSIS sequence to verify the validity of the entire model. These TOPSIS sequence numbers are #10, #20, #30, #40, #50, #60, and #70, which correspond to #40, #7, #6, #60, #25, #39, and #53 in Table 8, respectively. Then, a comparative analysis of the water demand satisfaction rates in different countries is presented in Fig. 6.

Figure 6 shows the relationship between water demand satisfaction rates and solutions. With the decline in closeness degree, the water demand satisfaction rates of Thailand and Vietnam tend to stabilize, thereby ranging from 54.16% to 60.56%. Meanwhile, a similar variation trend between the two countries is observed. However, the water demand satisfaction of Laos and Cambodia has experienced considerable fluctuations ranging from 58.68% to 95.70%. With the decrease in closeness degree, the water demand satisfaction rate of countries with large demands, such as Thailand and Vietnam, maintains a stable trend despite minor fluctuations. Meanwhile, countries with low water demand, such as Laos and Cambodia, have a similar fluctuation trend as that of Thailand and Vietnam, but the fluctuation range is large. The above variation trend indicates that the water demand of downstream countries is an important factor that should be considered. Therefore, a sensitivity analysis of the water demand of downstream countries is conducted and discussed in the next chapter.

Table 2
Top seven solutions for decision makers

TOPSIS Model Upstream Downstream Public

sequence solutions satisfaction satisfaction satisfaction

(Z₁) (Z₂) (Z₃)

1 #10 1.14389 0.55038 –0.08422

2 #64 1.13360 0.49859 –0.08091

3 #17 1.10729 0.68006 –0.07904

4 #69 1.12107 0.53635 –0.07903

5 #56 1.11725 0.63140 –0.08037

6 #31 1.13501 0.54521 –0.08286

7 #37 1.15728 0.36080 –0.08494

TOPSIS	Model	Upstream	Downstream	Public
1	#10	1.14389	0.55038	–0.08422
2	#64	1.13360	0.49859	–0.08091
3	#17	1.10729	0.68006	–0.07904
4	#69	1.12107	0.53635	–0.07903
5	#56	1.11725	0.63140	–0.08037
6	#31	1.13501	0.54521	–0.08286
7	#37	1.15728	0.36080	–0.08494

Fig.6

Water demand satisfaction rates in different solutions.

Fig.7

Pareto fronts under different water demands.

Table 3

Stakeholder satisfaction under different water demands

	Upstream	\|ΔZ₁\|/	Downstream	\|ΔZ₂\|/	Public	\|ΔZ₃\|/
	satisfaction	Volatility	satisfaction	Volatility	satisfaction	Volatility
	(Z₁)		(Z₂)		(Z₃)
d=397.95	1.14375	0.12882/ 11.26%	0.47465	0.07975/ 16.80%	–0.03722	0.0039/9.48%
d=467.63	1.22986		0.55440		–0.04019
d=555.31	1.27257		0.54489		–0.04112

Meanwhile, countries with different distances from the upstream water supply center also show diverse water demand satisfaction rates with the decrease in closeness degree. Laos is the nearest country to the upstream water supply center, and its water demand satisfaction rate ranges from 68.53% to 96.30%. This finding means that regardless of the solution selected by the upstream government, the water demand satisfaction rate of Laos remains high. By contrast, Vietnam is the farthest country from the upstream water supply center, and its water demand satisfaction rate ranges from 54.16% to 57.30%, which is the lowest among the four countries. The above analysis indicates that distance is another factor that affects water demand satisfaction rates. The proportional fairness degree parameter is used in this study to ensure the water supply quantity of remote areas. Hence, choosing a suitable proportional fairness degree for decision-makers is necessary. A sensitivity analysis of the proportional fairness degree is also conducted and discussed in the next chapter.

4.2.2 Sensitivity analysis

(1) Sensitivity analysis of water demand

With other parameters unchanged, the water demand of each affected area i at j stages (d_ij) increased by 30%, 60%, and 90% to study the impact of water demand on the perceived satisfaction of stakeholders. Overall, the corresponding water demand of all downstream countries is increased to 397.95, 467.63, and 555.31 million m³. All Pareto fronts are shown in Fig. 7, and the corresponding function value of the best compromise solution can be calculated by the TOPSIS method in Table 3.

Figure 7 shows that all Pareto fronts are uniformly distributed, and an inverse relationship exists between the upstream and downstream satisfaction and the upstream and public satisfaction. Moreover, downstream satisfaction is proportional to public satisfaction. Furthermore, low water demand leads to a small satisfaction value. Table 3 shows that the upstream satisfaction value increases with the demand, while the public satisfaction value maintains a decreasing trend. Table 3 also demonstrates that the volatility of public satisfaction is less than that of the upstream and downstream satisfaction with the increase in water demand.

Figure 8 describes the water demand satisfaction rates of different countries with an increase in water demand. Countries with large water demands, such as Thailand and Vietnam, show a slight fluctuation in demand ranging from 54.06% to 56.71% with the increase in water demand. This finding indicates that the change in demand has less impact on countries with large demands. By contrast, the water demand satisfaction rates of countries with low water demands are high and fluctuate between 71.04% and 87.82%, demonstrating that the change in demand has a considerable impact on countries with low demands. Typically, the perceived satisfaction of downstream countries with low water demands should be considered first when formulating an emergency water resource supply plan.

Fig.8

Water demand satisfaction rates under different water demands.

Fig.9

Pareto fronts under different proportional fairness degrees.

Table 4

Stakeholder satisfaction under different proportional fairness degrees

	Upstream	\|ΔZ₁\|/	Downstream	\|ΔZ₂\|/	Public	\|ΔZ₃\|/
	satisfaction	Volatility	satisfaction	Volatility	satisfaction	Volatility
	(Z₁)		(Z₂)		(Z₃)
π=0.2	1.03330	0.09540/ 9.40%	0.67054	0.14234 18.76%	–0.03304	0.00358/ 9.84%
π=0.4	1.01532		0.75890		–0.03279
π=0.6	1.11076		0.61656		–0.03637

(2) Sensitivity analysis on proportional fairness degree

A sensitivity analysis of proportional fairness degree (π) was conducted to verify the feasibility of the model in different situations. Three situations are presented: π= 0.2, π= 0.4, and π= 0.6. All Pareto fronts are shown in Fig. 9, and the corresponding function value of each situation can be calculated by the TOPSIS method presented in Table 4.

Figure 9 shows the same relationship among all stakeholders as that in Fig. 7. However, some differences can be observed. The highest proportional fairness degree always corresponds to the longest Pareto front. Table 4 also shows that upstream and downstream satisfaction values decrease first and then increase with the proportional fairness degree, while public satisfaction increases first and then decreases.

Figure 10 shows the water demand satisfaction rates of four countries under different proportional fairness degrees. When π=0.2, the water demand satisfaction rates of Laos, Thailand, Cambodia, and Vietnam are 98.58%, 50.86%, 61.47%, and 50.52%, respectively. When π=0.6, the water demand satisfaction rates of Laos, Thailand, Cambodia, and Vietnam are 70.08%, 55.43%, 64.22%, and 54.64%, respectively. The data show that with the increase in proportional fairness degree, the water demand satisfaction rates of the countries with large water demands and long distance from the origin supply reservoir, such as Thailand, Cambodia, and Vietnam, increase first and then decrease. By contrast, the nearest country with low water demand, such as Laos, maintains a decreasing trend. The above analysis indicates that a moderate proportional fairness degree, such as π=0.4, may be beneficial for countries located farther from the original water reserve center, which is necessary for the fairness of water allocation. In the calculation, an excessive proportional fairness degree (π> 0.7) would lead to infeasible solutions due to the feasibility reduction. Therefore, upstream decision makers should maintain a moderate proportional fairness degree when making decisions. That is, a low proportional fairness degree can adversely affect remote areas, while an excessive proportional fairness degree may result in infeasible solutions. Overall, a moderate degree would benefit most stakeholders.

Fig.10

Water demand satisfaction rates under different proportional fairness degrees.

4.2.3 Scenario analysis

(1) Scenario setting

Table 5
Irrigated area and water allocation data of downstream countries in scenario 2

Laos Thailand Cambodia Vietnam

Irrigated area (Hectare) 166476 1411807 504245 1919623

Irrigated area percentage (%) 4.16 35.28 12.60 47.96

Allocated water quantity (million m³) 3.65 31.24 11.16 42.47

	Laos	Thailand	Cambodia	Vietnam
Irrigated area (Hectare)	166476	1411807	504245	1919623
Irrigated area percentage (%)	4.16	35.28	12.60	47.96
Allocated water quantity (million m³)	3.65	31.24	11.16	42.47

Table 6

Stakeholder satisfaction in different scenarios

	Upstream	\|ΔZ₁\|	Downstream	\|ΔZ₂\|	Public	\|ΔZ₃\|
	satisfaction		satisfaction		satisfaction
	(Z₁)		(Z₂)		(Z₃)
Scenario 1	1.00000	0.6264	0.79245	0.6823	–30.83160	30.7474
Scenario 2	0.51749		0.11019		–15.89170
Scenario 3	1.14389		0.55038		–0.08422

Three scenarios were set to verify the optimal model. In the first scenario, the upstream government does not implement an emergency water supply plan, and the available water quantity of each country is 50% of its maximum water demand. In the second scenario, the upstream government implements an emergency water supplement through the traditional hydrological approach without considering the perceived satisfaction of stakeholders. In this scenario, 70% of the supplied water can be acquired by downstream stakeholders. Meanwhile, all supplied water is distributed by the proportion of irrigated areas. All data in this scenario are listed in Table 5. In the third scenario, an optimal supply water allocation scheme that considers the perceived satisfaction of stakeholders is implemented. Four downstream countries are assumed to cooperate with each other. Then, the perceived satisfaction values of the different stakeholders in the three scenarios are compared.

(2) Scenario analysis

Table 6 describes the perceived satisfaction of stakeholders in three scenarios. In scenario 1, the upstream government has no water supply plan, and downstream government and public satisfaction values are at their lowest because of low water supply quantity. In scenario 2, the water supply plan was conducted in accordance with the irrigation area of four downstream countries. The satisfaction of the upstream government is the lowest because the water supply quantity herein is the largest one among the three scenarios. Meanwhile, the satisfaction of downstream governments is the highest due to the largest water supply.

In scenario 3, the perceived satisfaction values of the upstream government and the public are high. For the upstream government, the water quantity supplied downstream is lower than that in Scenario 2, while its perceived satisfaction is higher than that in Scenario 2. For downstream governments, receiving additional water leads to less water loss, which demonstrates the changing trend of their perceived satisfaction in Table 6. For the downstream public, although the water quantity in Scenario 3 is lower than the traditional supply model, such as Scenarios 1 and 2, their perceived satisfaction dramatically increases. This finding indicates that the water supply from the upstream country plays an important role in improving the perceived satisfaction of the downstream public. Moreover, public satisfaction on water policy is always negative in any scenario, which is consistent with the actual situation, that is, the limited rational public tends to question the water supply of the upstream countries if the available water is lower than the historical average. This problem may be solved by increasing the water supply quantity or providing subsidies.

Compared with other studies on transboundary water resource supply, this work integrates water resources management and psychological factors of stakeholders in the analysis. Therefore, the results are practical. Moreover, supply schemes of optimal emergency water resources are obtained on the basis of the perceived satisfaction of all stakeholders, which would help promote the coordinated development of the entire basin. This study also provides supply plans for different emergency water resources and decision makers with different alternatives according to their preferences.

5 Conclusion and future research

A modeling framework combining the transboundary water resources supply with PT was developed in this study to optimize emergency water supply schemes among different stakeholders under water scarcity. The perceived satisfaction of all stakeholders on water policy was defined, and a multi-stage multi-objective model was developed. A two-stage NSGA-II and TOPSIS based approach was then applied to find the optimal compromise solution. Subsequently, a sensitivity analysis was performed on water demand, and the proportional fairness degree was conducted to identify sensitive factors for decision making. Finally, three scenarios were established to compare previous decisions with optimal results.

A case study in the Lancang–Mekong River basin between China and four downstream countries was conducted to demonstrate the methodology. Considering the multi-objective model results and the previous emergency water resource supply policy, upstream decision makers are urged to provide additional attention to the perceived satisfaction of downstream stakeholders on water policies from the psychological perspective. Upstream decision makers should prioritize downstream countries farther from the original water supply center or those with low water demands to achieve sustainable development. The analysis of stakeholder satisfaction in three scenarios indicates that although the emergency water supply decision of upstream governments can improve the perceived satisfaction of the downstream public, additional actions must still be taken to change the traditional concepts of the public. The integration of PT within the multi-stage multi-objective water supply modeling framework would provide a sound basis for decision making.

Studying the normalized transboundary water resource allocation mechanism considering climate change is necessary for the future. The establishment of a normalized transboundary water resource allocation mechanism involving multi-stakeholders should still consider other stakeholders, such as non-government organizations and external interest-related countries. Clarification of the interactive behavior and realization of the equilibrium of interests are notable problems that must be considered [95]. Meanwhile, consensus-reaching mechanism [96], water-related benefits game [97], and multi-agents conflict analysis [98] may also be potential topics in a transboundary river basin. Therefore, the mechanism for transboundary water resource allocation involving different stakeholders is suggested for future study.

Footnotes

Appendix

Table 10

The value of Z_ω1, Z_ω2, Z_ω3 in Table 10 was calculated by the “gamultiobj” toolbox in MATLAB R2016b, and the TOPSIS sequence was obtained by TOPSIS method [80, 81]

ω	Z _ω ₁	Z _ω ₂	Z _ω ₃	TOPSIS	ω	Z _ω ₁	Z _ω ₂	Z _ω ₃	TOPSIS
				sequence					sequence
#1	1.09151	0.61327	–0.07521	#34	#36	1.22924	0.14174	–0.09518	#56
#2	1.10486	0.46390	–0.07494	#24	#37	1.13437	0.49442	–0.08163	#7
#3	1.20249	0.26643	–0.09103	#66	#38	1.12344	0.58653	–0.08021	#23
#4	1.21885	0.18717	–0.09344	#62	#39	1.21003	0.22109	–0.09252	#60
#5	1.24710	0.15976	–0.09878	#37	#40	1.15732	0.50554	–0.08521	#10
#6	1.23518	0.21935	–0.09711	#30	#41	1.16653	0.42288	–0.08604	#38
#7	1.10837	0.63967	–0.07815	#20	#42	1.17142	0.32139	–0.08657	#59
#8	1.24050	0.17091	–0.09759	#43	#43	1.13522	0.44883	–0.08097	#28
#9	1.22880	0.14285	–0.09514	#55	#44	1.16082	0.27418	–0.08409	#48
#10	1.14389	0.55038	–0.08422	#1	#45	1.17652	0.28524	–0.08702	#61
#11	1.22656	0.23569	–0.09581	#36	#46	1.17908	0.36915	–0.08925	#46
#12	1.09726	0.66504	–0.07702	#16	#47	1.19380	0.24221	–0.08993	#67
#13	1.16740	0.31314	–0.08626	#63	#48	1.13201	0.57161	–0.08189	#12
#14	1.19293	0.33447	–0.09236	#22	#49	1.22641	0.20652	–0.09461	#51
#15	1.16128	0.37474	–0.08534	#49	#50	1.12946	0.48078	–0.08000	#19
#16	1.18258	0.35034	–0.08859	#69	#51	1.19130	0.25088	–0.08946	#68
#17	1.10728	0.68006	–0.07904	#3	#52	1.14497	0.39233	–0.08241	#41
#18	1.09574	0.67381	–0.07689	#13	#53	1.17681	0.34274	–0.08806	#70
#19	1.21514	0.25813	–0.09439	#39	#54	1.13267	0.55683	–0.08128	#29
#20	1.12445	0.53300	–0.08095	#21	#55	1.18555	0.29729	–0.08794	#57
#21	1.09592	0.67323	–0.07689	#14	#56	1.11725	0.63140	–0.08037	#5
#22	1.10216	0.65580	–0.07748	#17	#57	1.18138	0.40971	–0.09054	#8
#23	1.14252	0.42442	–0.08079	#25	#58	1.12792	0.43527	–0.07873	#27
#24	1.13872	0.52451	–0.08304	#26	#59	1.16414	0.36456	–0.08555	#47
#25	1.16317	0.40417	–0.08602	#50	#60	1.20597	0.29116	–0.09289	#40
#26	1.21889	0.21000	–0.09508	#44	#61	1.18896	0.23200	–0.08860	#65
#27	1.13359	0.51787	–0.08269	#64	#62	1.19825	0.30445	–0.09182	#45
#28	1.19391	0.33006	–0.09054	#52	#63	1.13619	0.39905	–0.08063	#35
#29	1.22836	0.15109	–0.09510	#54	#64	1.13360	0.49859	–0.08091	#2
#30	1.10627	0.64819	–0.07809	#15	#65	1.11544	0.51023	–0.07773	#9
#31	1.13501	0.54521	–0.08286	#6	#66	1.09976	0.65750	–0.07720	#18
#32	1.15728	0.36080	–0.08494	#53	#67	1.23834	0.19367	–0.09763	#33
#33	1.12117	0.61999	–0.08014	#11	#68	1.09164	0.61243	–0.07523	#32
#34	1.12017	0.57503	–0.07925	#58	#69	1.12107	0.53635	–0.07903	#4
#35	1.10678	0.60925	–0.07803	#31	#70	1.23862	0.17728	–0.09734	#42

Acknowledgments

This research was supported by Major Program of National Social Science Fund of China (Grants No. 16ZDA046, 19ZDA084), National Natural Science Fund of China (Grants No. 71974053), Rolling Support Program for Changjiang Scholars and Innovative Research Team in University (Grants No. IRT_17R35), and the Fundamental Research Funds for the Central Universities (Grants No.2018B20214, No.2019B30414, No2019B34014).

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Emergency water supply decision-making of transboundary river basin considering government–public perceived satisfaction

Abstract

Keywords

1 Introduction

2 Literature review

3.1 Definition of symbols and variables

3.2 Basic assumptions

3.3 Decision-making programmer and methodology framework

3.4.1 Perceived utility satisfaction of upstream governments

4.2 Results and discussion

4.2.1 Optimal model results

Table 5 Irrigated area and water allocation data of downstream countries in scenario 2 Laos Thailand Cambodia Vietnam Irrigated area (Hectare) 166476 1411807 504245 1919623 Irrigated area percentage (%) 4.16 35.28 12.60 47.96 Allocated water quantity (million m3) 3.65 31.24 11.16 42.47

Footnotes

Appendix

Acknowledgments

References

Table 5
Irrigated area and water allocation data of downstream countries in scenario 2

Laos Thailand Cambodia Vietnam

Irrigated area (Hectare) 166476 1411807 504245 1919623

Irrigated area percentage (%) 4.16 35.28 12.60 47.96

Allocated water quantity (million m³) 3.65 31.24 11.16 42.47