Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games

In recent years, uneven distribution of available water resources as well as increasing water demands and overexploiting the water resources have brought severe need for transferring water from basins having sufficient water to basins facing water shortages. Therefore, optimal allocation of shared water resources in water transfer projects, considering the utilities of different stakeholders, physical limitations of the system and socioeconomic criteria is an important task. In this paper, a new methodology based on crisp and fuzzy Shapley games is developed for optimal allocation of inter-basin water resources. In the proposed methodology, initial water allocations are obtained using an optimization model considering an equity criterion. In the second step, the stakeholders form crisp coalitions to increase the total net benefit of the system as well as their own benefits and a crisp Shapley Value game is used to reallocate the benefits produced in the crisp coalitions. Lastly, to provide maximum total net benefit, fuzzy coalitions are constituted and the participation rates of water users to fuzzy coalitions are optimized. Then, the total net benefit is reallocated to water users in a rational and equitable way using Fuzzy Shapley Value game. The effectiveness of this method is examined by applying it to a large scale case study of water transfer from the Karoon river basin in southern Iran to the Rafsanjan plain in central Iran.     

A Fuzzy Variable Least Core Game for Inter-basin Water Resources Allocation Under Uncertainty

In this paper, a new solution concept, called Fuzzy Variable Least Core (FVLC), is developed for fuzzy cooperative games. The FVLC is able to incorporate fuzzy input variables and result in fuzzy benefit shares of players participating in a coalition. This solution concept is used for water and benefit allocation to water users in inter-basin water transfer systems considering the uncertainties associated with their benefit coefficients. In the proposed water allocation methodology, an Integrated Stochastic Dynamic Programming (ISDP) model is developed to obtain the water rights of players and economic water allocation policies. In the next step, the total net fuzzy benefit of the system is reallocated to water users in an equitable and rational way using a FVLC-based model. In this model, a new algorithm is proposed for converting a multilateral cooperative game with fuzzy variables to some fuzzy bilateral cooperative games, which are solved using the FLVC solution concept. The applicability and efficiency of the proposed methodology is examined by applying it to a large scale inter-basin water transfer project in Iran.     

Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions

In this paper, two fuzzy cooperative games are utilized for modeling equitable and efficient water allocation among water users in both inter-basin and intra-basin water allocation problems. The proposed all-inclusive water allocation approach consists of three main steps, following Sadegh et al. (Water Resour Manage 24(12):2991?C2310, 2010). In the first step, an initial water allocation is carried out using an optimization model taking into account an equity criterion. In the second step, the water users form crisp coalitions with fuzzy characteristic functions to increase the total net benefit of the system and also their own benefits. In the methodology used in this step, the water users do not need to have exact information about their payoffs and they can evaluate their payoffs as fuzzy numbers. In the second step, based on the Hukuhara difference of fuzzy numbers, optimum water allocation strategies are determined using a game with fuzzy characteristic function. In the third step, we applied another methodology which considers a class of fuzzy games with fuzzy characteristic functions and also fuzzy coalitions for water allocation. The methodology of this step is on the basis of the Hukuhara difference and the Choquet integral. The usefulness of the mentioned methodologies is studied by applying them to three defined real life scenarios in a case study of water allocation in Iran. The results showed that the proposed methodologies are professionally appropriate to real-world uncertain problems of equitable and economic inter-basin and intra-basin water resources allocations.     

Optimizing Multiple-Pollutant Waste Load Allocation in Rivers: An Interval Parameter Game Theoretic Model

In this paper, a new methodology is developed for optimal multiple-pollutant waste load allocation (MPWLA) in rivers considering the main existing uncertainties. An interval optimization method is used to solve the MPWLA problem. Different possible scenarios for treatment of pollution loads are defined and corresponding treatment costs are taken into account in an interval parameter optimization model. A QUAL2Kw-based water quality simulation model is developed and calibrated to estimate the concentration of the water quality variables along the river. Two non-cooperative and cooperative multiple-pollutant scenario-based models are proposed for determining waste load allocation policies in rivers. Finally, a new fuzzy interval solution concept for cooperative games, namely, Fuzzy Boundary Interval Variable Least Core (FIVLC), is developed for reallocating the total fuzzy benefit obtained from discharge permit trading among waste load dischargers. The results of applying the proposed methodology to the Zarjub River in Iran illustrate its effectiveness and applicability in multiple-pollutant waste load allocation in rivers.     

A multi-weight fuzzy Methodological Framework for Allocating Coalition Payoffs of Joint Water Environment Governance in Transboundary River Basins

To ensure transboundary river basins are protected as a system, forming water environment governance coalitions is important. However, accurate determination and allocation of the payoffs of joint environment governance under uncertain conditions is a challenging task. This study used a triangular fuzzy number to describe the payoff and solve the fuzzy allocation problem. The article also considered the importance of different coalitions and the effectiveness of the distribution. In addition, the authors constructed a multi-weight fuzzy allocation quadratic programming model and proposed an analytical solution to determine the triangular fuzzy allocation payoffs. These contributions were used to allocate the coalition payoff of basin-wide environment governance, and the Zhanghe River Basin is used as a case study. The results showed that the model produces outputs comparable with the Shapley value allocation method. Therefore, the proposed methodological framework can be used as an alternative allocation scheme that provides a reasonable solution during uncertainty.

     

Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis

This paper presents a new game theoretic methodology for water and discharge permit allocation to agricultural zones in shared rivers. The methodology consists of four main steps: (1) initial allocation of water rights and pollutant discharge permits, (2) forming possible coalitions and optimal water and discharge permit reallocation to water users participating in a coalition to increase their total net benefit, (3) equitable benefit reallocation by utilizing some solution concepts in cooperative game theory, and (4) identifying the best water and pollutant discharge permit allocation strategies by minimizing the maximum regret in the system. A new linear form for crop water production function is used in the objective function of the water allocation optimization models. To show the efficiency and applicability of the methodology, it is applied to the Karoon-Dez river system in Iran.     

Equitable Waste Load Allocation in Rivers Using Fuzzy Bi-matrix Games

This paper presents a new game theoretic methodology for equitable waste load allocation in rivers utilizing fuzzy bi-matrix games, Non-dominated Sorting Genetic Algorithms II (NSGA-II), cooperative game theory, Bayesian Networks (BNs) and Probabilistic Support Vector Machines (PSVMs). In this methodology, at first, a trade-off curve between objectives, which are average treatment level of dischargers and fuzzy risk of low water quality, is obtained using NSGA-II. Then, the best non-dominated solution is selected using a non-zero-sum bi-matrix game with fuzzy goals. In the next step, to have an equitable waste load allocation, some possible coalitions among dischargers are formed and treatment costs are reallocated to discharges and side payments are calculated. To develop probabilistic rules for real-time waste load allocation, the proposed model is applied considering several scenarios of pollution loads and the results are used for training and testing BNs and PSVMs. The applicability and efficiency of the methodology are examined in a real-world case study of the Zarjub River in the northern part of Iran. The results show that the average relative errors of the proposed rules in estimating the treatment levels of dischargers are less than 5?%.     

A Nonlinear Interval Model for Water and Waste Load Allocation in River Basins

In this paper, a new methodology is proposed for simultaneous allocation of water and waste load in river basins. A nonlinear interval number optimization model is used to incorporate the uncertainties of model inputs and parameters. In this methodology, the bounds of the uncertain inputs are only required, not necessarily knowing their probability density or fuzzy membership functions. In the proposed model, the existing uncertainties in water demands and monthly available water are considered in the optimization model. Also the economic and environmental impacts of water allocation to the agricultural water users are taken into account. To have an equitable water and waste load allocation, benefits are reallocated to water users using some solution concepts of the cooperative game theory. Results of applying the methodology to the Dez river system in south-western part of Iran show its effectiveness and applicability for water and waste load allocation in an uncertain environment.     

A Fuzzy Stochastic Dynamic Nash Game Analysis of Policies for Managing Water Allocation in a Reservoir System

In this paper a fuzzy dynamic Nash game model of interactions between water users in a reservoir system is presented. The model represents a fuzzy stochastic non-cooperative game in which water users are grouped into four players, where each player in game chooses its individual policies to maximize expected utility. The model is used to present empirical results about a real case water allocation from a reservoir, considering player (water user) non-cooperative behavior and also same level of information availability for individual players. According to the results an optimal allocation policy for each water user can be developed in addition to the optimal policy of the reservoir system. Also the proposed model is compared with two alternative dynamic models of reservoir optimization, namely Stochastic Dynamic Programming (SDP) and Fuzzy-State Stochastic Dynamic programming (FSDP). The proposed modeling procedures can be applied as an appropriate tool for reservoir operation, considering the interaction among the water users as well as the water users and reservoir operator.     

Editorial Comments on the World Commission on Water for the 21stCentury

Abstract

In this study, in order to create a decision-making model on water resources projects, a hierarchy of criteria has been developed by public participation. The Value Management methodology has been used for extraction of the effective criteria and attributes in the scope of Integrated Water Resources Management (IWRM). The hierarchy is generic for water resources management in the Islamic Republic of Iran. Since the evaluations of alternatives with respect to some attributes are uncertain and vague, fuzzy set theory has been used. By merging fuzzy set theory and multi-attribute decision-making a new Decision Support System (DSS), namely FDM, has been developed to compare different alternatives. As an innovation, FDM accepts evaluations of alternatives with respect to the attributes as crisp variables, fuzzy variables, and linguistic variables. FDM embodies an expert system whose duty is to choose an appropriate method among the SAW, Fuzzy SAW, TOPSIS or Fuzzy TOPSIS based on the characteristics of the problem.

The central and Southeastern regions of Iran are considered arid regions, suffering from water shortages. In this paper, water transfers to the Zayanderud basin in Iran have been modeled by FDM. Successful application of this DSS in this study allows for its application by water authorities in other case studies.     

地下水补给影响下的河流水质模糊模拟

摘 要：基于河流水环境系统的模糊性、不精确性，采用三角模糊数描述和表征沿岸地下水水文地质参数，建立了计算地下水补给量和补给强度的模糊模型。在将水质模型参数定义为三角模糊数的基础上，构建了考虑地下水补给影响的一维稳态河流水质模糊模拟模型。作为案例，将上述模型应用于淮河流域某支流水质模拟研究。采用-截集技术，计算得到各控制断面模糊数形式的污染物浓度值，并与确定性模型计算结果进行比较。实例研究表明，以三角模糊数原理模拟和表征考虑地下水补给影响的河流水体污染物浓度变化规律，理论上可行，计算结果可信，较好地弥补了传统确定性模型的不足。     

Intelligent Water Management: a Triangular Type-2 Intuitionistic Fuzzy Matrix Games Approach

Matrix games with fuzzy payoffs have spread itself nowadays in diverse fields. Fuzzy game theory with triangular type-1 fuzzy numbers are visited more by researchers. In this paper, we consider matrix games with payoffs as triangular type-2 intuitionistic fuzzy numbers, i.e., Triangular Type-2 Intuitionistic Fuzzy Matrix Game (TT2IFMG) as a new and rare concept. A new ranking function is used to get relevant solutions of TT2IFMG. We are living in times of unprecedented scientific-technical advancement, yet facing several critical global problems that threaten human welfare and our ecosystem. Water management, a burning problem of the Earth now-a-days, is treated here under the scanner of TT2IFMG environment where we discuss some policy-management toward the free and fair accession of water against its limited resources.     

Asymmetry and Equity in Water Resources Management; Critical Institutional Issues for Southern Africa

Water users wish to achieve the highest benefits from water resources. Rules limit the manner in which water users may utilise the water resources occurring within their constituencies or territories. However an asymmetrical situation exists whereby downstream users may not affect upstream users but upstream users do cause downstream impacts. Because of this asymmetry the equitable sharing of water resources between upstream and downstream users will always imply that upstream users have to forego some potential water benefits. The general question that this paper addresses is: which institutional arrangements can be devised to (re-)establish an equilibrium between up- and downstream entities within a catchment area or river basin? The paper addresses this question by first focusing on some local and national water allocation arrangements. After briefly reviewing the different management regimes, customary and colonial, that co-evolved in Southern Africa, it assesses the water management principles that are currently being espoused. The focus then turns to the principles in international water law that deal with the allocation of water in transboundary river basins. It is concluded that it often proves difficult to reach agreement over how to share the scarce resource. The paper then discusses the current trend to look beyond water and beyond the river basin when seeking peaceful means to share a common water resource. The concept of “hydrosolidarity” emerges as a normative value that may help to recreate a balance between the various (asymmetrical) interests that exist within a river basin. The paper concludes that water resources can only be governed wisely is there is capacity to understand and monitor the water fluxes within a river basin. If such capacity is wanting, priority should be given to strengthen it.     

Water Allocation in Transboundary River Basins under Water Scarcity: a Cooperative Bargaining Approach

Transboundary river basins are one of the main sources of fresh water which are facing water scarcity. When transboundary water is contested not only the allocation outcomes matter but also the allocation process should possess a certain desirable properties such as flexibility and sustainability. Therefore designing a mechanism that possesses these desirable characteristics and allocates the contested water resource is important as well. This article proposed a water allocation framework by combining the bankruptcy theory with asymmetric Nash bargaining solution concept for solving the water sharing problem in transboundary river basins under scarcity. Furthermore, the allocation framework was applied to the Nile river basin and to a hypothetical water scarce transboundary river basin. The results obtained were then compared with the allocation outcomes from classical bankruptcy allocation rules. The results showed that the proposed method can provide insights which could be useful for obtaining water allocation outcomes which are easier to implement and enforce under water scarce conditions.

     

A Game Theoretic Approach to Assess the Impacts of Major Investments on Transboundary Water Resources: The Case of the Euphrates and Tigris

There are varying and inconsistent claims among countries sharing the same river basins. While upstream countries are asserting that they regulate flows through built-up reservoirs (enabling flood prevention) and reduce seasonal flow variations (providing water during drought seasons), downstream countries criticize upstream countries for excessive withdrawals and declining annual flows. Behind the scene, almost every basin country unilaterally envisions of ambitious projects demanding extensive water withdrawals for their prospective development and growth. This study establishes a methodology to measure the rational economic and political impacts of extensive reservoir projects throughout a basin, using the case of the Euphrates and Tigris. This methodology uses both linear programming applications calculating country and coalition benefits, and game theory concepts (core and Shapley value) for evaluating the impacts of reservoirs. The Euphrates and Tigris River Basin Model (ETRBM) is extended by adding the time dimension. In conjunction with time, reservoir capacities are incorporated into the model as a new set of parameters enabling resources allocations over multiple periods. In a rational economic view, the existence of reservoirs, while providing certain advantages in allocating water overtime, provides varying geopolitical powers to upstream and downstream basin countries. As a result of model applications, it is observed that basin-wide coalitions may potentially eliminate construction of excessive reservoir capacities, and, therefore, unnecessary investment costs and evaporation losses. It is also observed that assuming the absence of downstream reservoirs, the upstream reservoirs provide significant, first, economic benefit to the all forms of coalitions with upstream country and associated parties and, second, power to the country having the reservoirs in any coalition scenario. However, again in a game theoretic perspective, the power of upstream countries looses some of its weight when downstream reservoirs are incorporated. During drought years, the availability of reservoirs ensures extensive core solutions and encourages a grand coalition among all parties.     

A Coupled Water Quantity–Quality Model for Water Allocation Analysis

As the demand for water continuously increases with population growth and economic development, the gap between water supply and demand in China has become increasingly wide. In recent years worsening water pollution has caused this gap to become much more serious. Conventional allocation pattern, which mainly considers water quantity as the key factor, is no longer satisfying the water allocation need. A coupled water quantity–quality model in a river basin is presented in this paper to provide a tool for water allocation schemes analysis. The pollutants transport and hydrological cycling processes in a river basin are involved in the model. A river network is divided into different reaches. According to the division of river network, the areas out of the river are divided into a series of tanks. In each tank, hydrologic processes, pollutant loading production, water demand of users and water supply are calculated. In river network, hydrodynamics processes and water quality are simulated. Water quantity and quality exchanges between each tank and river are also considered. The time step of water quality calculation is 24 h, the same with that of water quantity calculation. In each time step period, the connections of river reaches and tanks are realized through the exchange of water quantity and quality between rivers and tanks: pollutants discharge from tanks to rivers and water intake from rivers to satisfy water demand in tanks. The water use in each tank includes three types: domestic, industrial and agricultural water use. Water allocation schemes are one of the input conditions of the model. Using the proposed model, in each tank, water demand and deficit of different uses, in both water quantity and quality, can be obtained under different water allocation schemes. According to the water deficit, water allocation schemes are analyzed to make proper allocation schemes. In this aspect, the proposed model can also be thought as a water allocation model. The model is tested and applied to the Jiaojiang River basin, Zhejiang Province, China, to analyze the different water resource allocation schemes.     

不同水权模式下流域水资源配置博弈的一般性解释

文中运用博弈论中的经典分析案例结合流域水资源配置特点对不同水权模式下参与人的用水行为作出合理解释。分析表明,在公共水权模式下,由于个体理性以及水资源负外部性的存在,容易使水资源利用产生“公有地悲剧”的结果。同时证明,在缺乏排他性水权或水权制度设计不尽完善的情况下,流域水资源不仅可能被过度利用,而且全流域社会福利将不能达到最优。上游用水主体因具备先动优势而恣意用水,由此给下游用水主体带来利益损害。在个体理性的作用下,试图通过全局优化实现流域水资源配置的帕雷托改进是无法实现的。     

Irrigation Planning Under Uncertainty—A Multi Objective Fuzzy Linear Programming Approach

The problem of irrigation planning becomes more complex by considering an uncertainty. The uncertainties can be tackled by formulating the problem of irrigation planning as Fuzzy Linear Programming (FLP). FLP models can incorporate the scenario of real world problem. In the present study, Multi Objective Fuzzy Linear Programming (MOFLP) irrigation planning model is formulated for deriving the optimal cropping pattern plan for the case study of Jayakwadi project in the Godavari river sub basin in Maharashtra State, India. Four conflicting objectives are considered such as Net Benefits (NB), Crop/Yield Production (CP), Employment Generation/Labour Requirement (EG) and Manure Utilization (MU). Four different cases are considered to incorporate the uncertainty in MOFLP model. To include the uncertainty in irrigation planning problem only objectives are taken as fuzzy and constraints are crisp in nature in Case-I. To consider the uncertainty involved in availability of resources, in Case-II the stipulations are fuzzy. The technological coefficients are fuzzy in Case-III. The Case-IV includes both technological coefficients and stipulations fuzzy. The level of satisfaction (λ) works out to be 0.58, 0.50, 0.50 and 0.28 respectively for Case-I to IV. The results obtained in Case-IV are more realistic and promising as it involves the uncertainty in technological coefficients and stipulations simultaneously.     

基于规则的水资源配置模型应用研究

为了将多层次、多工程、多用户、多水源的复杂水资源配置系统转换成计算机模型,合理有效地模拟水资源系统,进而完成区域或流域水资源从多水源向多用户的水量分配过程,着重介绍了水资源系统的系统概化规则和模型配置规则,在此基础上提出了基于规则的水资源配置模型,并将该模型应用在滹沱河流域.应用结果表明,模型的构建合理可行,规则的确定切合实际,模拟计算的结果合理可靠,该模型具有良好的实用性.     

探讨适合长江流域特点的水量分配研究框架

长江流域水资源相对丰富,但存在降水时空分布不均、自然灾害频繁、城市需水增长快、供求矛盾加剧、水污染加重、用水效率低下等水资源问题.三峡水库的建设运用,外流域调水工程的实施打破了长江原有的水平衡.保证流域水资源的合理开发利用与调配对流域社会经济的发展极其重要,了解流域本身的水资源特点和问题,研究河流生态用水,分析不同功能、不同区域的水量分配额度,提出区域社会经济发展的水量分配方案,是水资源管理的基础,也是保障流域水资源的合理调配和可持续开发利用,维护河流健康发展的需求和根本.对适合长江流域特点的水量分配研究框架进行了探讨.