Agricultural Multi-Water Source Allocation Model Based on Interval Two-Stage Stochastic Robust Programming under Uncertainty

Numerous uncertainties and complexities exist in the agricultural irrigation water allocation system, that must be considered in the optimization of water resources allocation. In this paper, an agricultural multi-water source allocation model, consisting of stochastic robust programming and two-stage random programming and introducing interval numbers and random variables to represent the uncertainties, was proposed for the optimization of irrigation water allocation in Jiamusi City of Heilongjiang Province, China. The model could optimize the water allocaton to different crops of groundwater and surface water. Then, the optimal target value and the optimal water allocation of different water sources distributed to different crops could be obtained. The model optimized the economic benefits and stability of the agricultural irrigation water allocation system via the introduction of a the penalty cost variable measurement to the objective function. The results revealed that the total water shortage changed from [18.6, 32.3]?×?10⁸ m³ to [15.7, 26.2]?×?10⁸ m³ at a risk level ω from zero to five, indicating that the water shortage decreased and the reliability improved in the agricultural irrigation water allocation system. Additionally, the net economic benefits of irrigation changed from [287.21, 357.86]?×?10⁸ yuan to [253.23, 301.32]?×?10⁸ yuan, indicating that the economic benefit difference was reduced. Therefore, the model can be used by decision makers to develop appropriate water distribution schemes based on the rational consideration of the economic benefit, stability and risk of the agricultural irrigation water allocation system.     

Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework

Water Resources Management - This paper shows the utility of a new interval cooperative game theory as an effective water diplomacy tool to resolve competing and conflicting needs of water users...     

A Multi-objective Linear Programming Model with Interval Parameters for Water Resources Allocation in Dalian City

Water resources management has been of concern for many researchers since the contradiction between increased water demand and decreased water supply has become obvious. In the real world, water resources systems usually have complexities among social, economic, natural resources and environmental aspects, which leads to multi-objective problems with significant uncertainties in system parameters, objectives, and their interactions. In this paper, a multi-objective linear programming model with interval parameters has been developed wherein an interactive compromising algorithm has been introduced. Through interactive compromising conflicts among multi-objectives, a feasible solution vector can be obtained. The developed model is then applied to allocation of multi-source water resources with different water qualities to multiple users with different water quality requirements for the Dalian city for 2010, 2015 and 2020 planning years. The model pursues the maximum synthesis benefits of economy, society and the environment. The results indicate that the proportion of reused water to the total water amount is gradually increasing, and the proportion of agricultural water consumption to the total water consumption is gradually decreasing. The allocation of multi-source water resources to multiple users is improved due to incorporation of uncertain factors into the model that provide useful decision support to water management authorities.     

Fractional Stochastic Interval Programming for Optimal Low Impact Development Facility Category Selection under Uncertainty

Uncertainties in nature and human society influence low impact development (LID) facility category selection during LID facility optimization distribution, however the investigation of this area is seldom. There are still two problems with uncertainty which influence LID facility distribution 1) how uncertainty factors affect LID facility selection and 2) in the case of a number of LID facilities of multiple categories are to be set, how to construct the LID facility optimization distribution model for LID facility category selection under uncertainty. To handle the problems, this study develops a fractional stochastic interval programming model to process LID facility category selection under the influence of uncertainty. The model can either process multiple objectives via objective maximization and minimization or process the stochastic uncertainty and interval uncertainty. The study shows that the uncertainties which influence LID facility category selection exist in rainfall, infiltration rate, release coefficient, unit price and budget. and the study reveal that the key constraint of LID facility category selection is the uncertainty parameter characteristic of the LID facility, in which different parameters lead to various LID facility optimization schemes. Results of the model include a series of LID facility optimization distribution schemes in multiple scenarios.Results also provide a series of feasible schemes for decision makers, and the manager can select the most appropriate scheme according to water processing level or budget. The developed model could 1) identifying the uncertainty which impact the LID facility distribution. 2) processing the LID facility category selection under interval uncertainty and stochastic uncertainty during LID facility optimization distribution. The method can also be used to estimate the rationality of the LID facility optimization scheme. Moreover, the proposed method is universal and could be extended to other cases of LID facility category selection under uncertainty.

     

IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty

In this study, an inventory-theory-based inexact chance-constrained multi-stage stochastic programming (IB-ICCMSP) model under multi-uncertainties is developed. IB-ICCMSP integrates inventory theory into an inexact chance-constrained multi-stage stochastic optimization framework. This method can not only effectively address system multiple uncertainties (e.g. discrete intervals and probability density functions) and dynamic features, but also provide water transferring and allocating schemes among multiple stages. The developed model is applied to irrigation water allocation optimization system in Zhangye City, Gansu province, China. Based on the runoff simulation prediction of Yingluo Gorge and water supply–demand balance analysis of the 12 irrigation areas in Zhangye City, different optimal irrigation water measures are generated under different flow levels and different probabilities in the planning year. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identifying desired water-allocation plans for irrigation under multi-uncertainties.     

Interval-parameter Two-stage Stochastic Nonlinear Programming for Water Resources Management under Uncertainty

Over the past decades, controversial and conflict-laden water allocation issues among competing interests have raised increasing concerns. In this research, an interval-parameter two-stage stochastic nonlinear programming (ITNP) method is developed for supporting decisions of water-resources allocation within a multi-reservoir system. The ITNP can handle uncertainties expressed as both probability distributions and discrete intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised allocation targets are violated. Moreover, it can deal with nonlinearities in the objective function such that the economies-of-scale effects in the stochastic program can be quantified. The proposed method is applied to a case study of water-resources allocation within a multi-user, multi-region and multi-reservoir context for demonstrating its applicability. The results indicate that reasonable solutions have been generated, which present as combined interval and distributional information. They provide desired water allocation plans with a maximized economic benefit and a minimized system-disruption risk. The results also demonstrate that a proper policy for water allocation can help not only mitigate the penalty due to insufficient supply but also reduce the waste of water resources.     

Optimization of Nebhana Reservoir Water Allocation by Stochastic Dynamic Programming

This study is devoted to the identification of an optimal rule that would permit to improve the water resources management of dam in arid condition. The Nebhana dam is considered in this study as a representative of a set dams situated in such condition. The water storage is used for irrigation purpose. The identification of an optimal rule is based on two opposite objectives: the satisfaction of the irrigation water demand and the safeguard of a minimal water storage in the dam. By considering different weights for these objectives, the stochastic dynamic programming technique was lead to various optimal rules for the water resources management of the Nebhana dam. This technique takes into account the variability of the volume of water inflow to the dam on the basis of their occurrence probability; the water losses by means of forecasting models and the water resources goals using weight coefficients. The identified optimal rule would permit to estimate the necessary water release volume for irrigation by considering the water storage and the decision period.     

A New Interval Two-stage Stochastic Programming with CVaR for Water Resources Management

Water Resources Management - In area of water resources management, decision-makers usually need to make plans under various uncertainties in order to achieve the maximal total net benefits and...     

An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of λ in SSM. The risk preference degree of λ could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers’ net benefit reaches to [8.949, 12.442]?×?10⁸ RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.     

灌区优化配水研究进展

针对我国水资源缺乏、农业灌溉用水低效的现象,介绍了非充分灌溉优化配水技术、灌区水库调度的国内外研究状况,分析了存在的有关问题,提出了可能的解决途径。     

Two-Stage Multi-Water Sources Allocation Model in Regional Water Resources Management under Uncertainty

Water Resources Management - Water shortages are common in society, and the effective allocation of limited water resources to each competitive sector has become one of the urgent concerns for...     

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.     

Socially-Optimal and Nash Pareto-Based Alternatives for Water Allocation under Uncertainty: an Approach and Application

This study has proposed a methodology by enhancing an interactive algorithm to multi-objective optimization problems with interval parameters, in an attempt to reach the tradeoff between quality and reliability of the resultant optimum solutions. The earlier algorithm could turn into a prolonged procedure that deals with several players with different aspirations at different reliability, or risk, levels under non-deterministic conditions. Hence, it is not a pertinent approach to solve problems of water allocation between competing parties. The enhanced methodology aims to alleviate the burdens of the procedure and generate a unique set of solutions (i.e., near-Pareto-optimal alternatives), instead of a myriad of compromise solution sets. We have investigated a real-world hydro-environmental problem, the allocation of water between Dorudzan-Korbal irrigation networks and Bakhtegan Lake in Fars Province, Iran to assess feasibility of this methodology. In order to reach a consensus concerning the stakeholders’ individual preferences, we identified the compromise alternatives from the obtained sets of non-dominated solutions by taking advantage of various social choice rules and the Nash bargaining model. The results demonstrated that the developed methodology could incorporate the risk of system constraints violations (i.e., planning reliability under uncertainty) into the process of approximating the optimal tradeoff set of solutions. It also gave policymakers a chance to acquire perception into the potentially best compromise for land and water allocation schemes regarding the preference profiles of the involved interest groups.     

Improved Water Allocation under Limited Water Supplies Using Integrated Soil-Moisture Balance Calculations and Nonlinear Programming

Water allocation under limited water supplies is becoming more important as water becomes scarcer. Optimization models are frequently used to provide decision support to enhance water allocation under limited water supplies. Correct modelling of the underlying soil-moisture balance calculations at the field scale, which governs optimal allocation of water is a necessity for decision-making. Research shows that the mathematical programming formulation of soil-moisture balance calculations presented by Ghahraman and Sepaskhah (2004) may malfunction under limited water supplies. A new model formulation is presented in this research that explicitly models deep percolation and evapotranspiration as a function of soil-moisture content. The new formulation also allows for the explicit modelling of inefficiencies resulting from nonuniform irrigation. Modelling inefficiencies are key to the evaluation of the economic profitability of deficit irrigation. Ignoring increasing efficiencies resulting from deficit irrigation may render deficit irrigation unprofitable. The results show that ignoring increasing efficiencies may overestimate the impact of deficit irrigation on maize yields by a maximum of 2.2 tons per hectare.

     

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.     

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.     

Variable Sets and Fuzzy Rating Interval for Water Allocation Options Assessment

Optimal water allocation is an important means of improving water use efficiency. However, since water allocation options are usually characterized by multi-region, multi-principle and multi-criterion factors, decision-makers often have difficulty in making objective decisions using them because the many available water allocation options often make the ratings of the options so close to be ranked. This study present a hierarchy variable sets (VS) model, based on the single-layer variable sets model, for ranking the water allocation options of Jining City, China. The ratings of the options are evaluated using a fuzzy rating interval (FRI) that can overcome homogenization in the ratings. The structure of the model presented in this study is clear with a simple procedure of computation and the result is rational. The case study used illustrates that this model can help decision-makers know the rating of water allocation options partially and overall. The computed result from this model appears more convincing than a previous water allocation approach for the city based on the maximum entropy principle.     

Investment in Irrigation Systems under Precipitation Uncertainty

Efficient agricultural water management is indispensable in meeting future food demands. The European Water Framework Directive promotes several measures such as the adoption of adequate water pricing mechanisms or the promotion of water-saving irrigation technologies. We apply a stochastic dynamic programming model (SDPM) to analyze a farmer??s optimal investment strategy to adopt a water-efficient drip irrigation system or a sprinkler irrigation system under uncertainty about future production conditions, i.e. about future precipitation patterns. We assess the optimal timing to invest into either irrigation system in the planning period 2010 to 2040. We then investigate how alternative policies, (a) irrigation water pricing, and (b) equipment subsidies for drip irrigation, affect the investment strategy. We perform the analysis for the semi-arid agricultural production region Marchfeld in Austria, and use data from the bio-physical process simulation model EPIC (Environmental Policy Integrated Climate) which takes into account site and management related characteristics as well as weather parameters from a statistical climate change model. We find that investment in drip irrigation is unlikely unless subsidies for equipment cost are granted. Also water prices do not increase the probability to adopt a drip irrigation system, but rather delay the timing to invest into either irrigation system.     

Modeling of Water Resources Allocation and Water Quality Management for Supporting Regional Sustainability under Uncertainty in an Arid Region

In this study, a scenario-based interval-stochastic fraticle optimization with Laplace criterion (SISFL) method is developed for sustainable water resources allocation and water quality management (WAQM) under multiple uncertainties. SISFL can tackle uncertainties presented as interval parameters and probability distributions; meanwhile, it can also quantify artificial fuzziness such as risk-averse attitude in a decision-making issue. Besides, it can reflect random scenario occurrence under the supposition of no data available. The developed method is applied to a real case of water resources allocation and water quality management in the Kaidu-kongque River Basin, where encounter serve water deficit and water quality degradation simultaneously in Northwest China. Results of water allocation pattern, pollution mitigation scheme, and system benefit under various scenarios are analyzed. The tradeoff between economic activity and water-environment protection with interval necessity levels and Laplace criterions can support policymakers generating an effective and robust manner associated with risk control for WAQM under multiple uncertainties. These discoveries avail local policymakers gain insight into the capacity planning of water-environment to satisfy the basin’s integrity of socio-economic development and eco-environmental sustainability.     

基于不确定性的渠系水资源优化配置

在以渠灌为主的灌区,设计合理的渠系工作制度,将水资源在渠系间进行高效配置具有重要意义。在实际灌溉中,同级渠道的灌水时间往往存在较大差异。为此,在灌区渠系建立0-1线性整数规划优化配水模型,并考虑了此过程中的不确定性,将模型运用到汾东灌区,进行求解。首先将支渠划分为两个灌溉组同时进行灌水,然后对每个灌溉组内的斗渠划分轮灌组,最后再将斗渠下的农渠划分为若干个轮灌组,实现在某次灌溉过程中的轮流输水。这样就缩短了各条渠道的输水时间,有利于提高灌水效率,且因不确定性信息的加入,结果更符合实际。通过上述优化过程,可以得到整个灌区的渠系工作制度,为决策者提供决策参考。