Planning Agricultural Water Resources System Associated With Fuzzy and Random Features1

Li, Y.P. and G.H. Huang, 2011. Planning Agricultural Water Resources System Associated With Fuzzy and Random Features. Journal of the American Water Resources Association (JAWRA) 47(4):841‐860. DOI: 10.1111/j.1752‐1688.2011.00558.x Abstract: More and more regions where demand outstrips water resources availability have suffered from chronic severe shortages. It is particularly aggravated for agricultural irrigation systems where more water is necessary to support the rapidly increasing population and speedily developing economy. In this study, a two‐stage fuzzy‐stochastic programming (TFSP) method is developed for planning agricultural water resources management system in more efficient and sustainable ways. The developed method can address uncertain parameters described as probability distributions and fuzzy sets. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences since penalties are exercised with recourse actions against any infeasibility. The developed method is applied to agricultural water‐resources management planning of the Zhangweinan River Basin, China. Solutions under various α‐cut levels and fuzzy dominance indices can be generated by solving a series of deterministic submodels, which can help determine optimized crop‐target values that could hedge appropriately against future available water levels. The results are helpful for water resources managers in not only making decisions of crop irrigation but also gaining insight into the tradeoffs between economic objective and system‐failure risk.     

Inexact multistage stochastic integer programming for water resources management under uncertainty

In this study, an inexact multistage stochastic integer programming (IMSIP) method is developed for water resources management under uncertainty. This method incorporates techniques of inexact optimization and multistage stochastic programming within an integer programming framework. It can deal with uncertainties expressed as both probabilities and discrete intervals, and reflect the dynamics in terms of decisions for water allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the IMSIP can facilitate analyses of the multiple policy scenarios that are associated with economic penalties when the promised targets are violated as well as the economies-of-scale in the costs for surplus water diversion. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that reasonable solutions have been generated for both binary and continuous variables. For all scenarios under consideration, corrective actions can be undertaken dynamically under various pre-regulated policies and can thus help minimize the penalties and costs. The IMSIP can help water resources managers to identify desired system designs against water shortage and for flood control with maximized economic benefit and minimized system-failure risk.     

Interactive two-stage stochastic fuzzy programming for water resources management

In this study, an interactive two-stage stochastic fuzzy programming (ITSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact two-stage stochastic programming (ITSP) framework. ITSFP can not only tackle dual uncertainties presented as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints, but also permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers (DMs) to conduct in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints (i.e., risk of constraint violation).     

Two-stage planning for sustainable water-quality management under uncertainty

In water-quality management problems, uncertainties may exist in a number of impact factors and pollution-related processes (e.g., the volume and strength of industrial wastewater and their variations can be presented as random events through identifying a statistical distribution for each source); moreover, nonlinear relationships may exist among many system components (e.g., cost parameters may be functions of wastewater-discharge levels). In this study, an inexact two-stage stochastic quadratic programming (ITQP) method is developed for water-quality management under uncertainty. It is a hybrid of inexact quadratic programming (IQP) and two-stage stochastic programming (TSP) methods. The developed ITQP can handle not only uncertainties expressed as probability distributions and interval values but also nonlinearities in the objective function. It can be used for analyzing various scenarios that are associated with different levels of economic penalties or opportunity losses caused by improper policies. The ITQP is applied to a case of water-quality management to deal with uncertainties presented in terms of probabilities and intervals and to reflect dynamic interactions between pollutant loading and water quality. Interactive and derivative algorithms are employed for solving the ITQP model. The solutions are presented as combinations of deterministic, interval and distributional information, and can thus facilitate communications for different forms of uncertainties. They are helpful for managers in not only making decisions regarding wastewater discharge but also gaining insight into the tradeoff between the system benefit and the environmental requirement.     

A two-stage inexact joint-probabilistic programming method for air quality management under uncertainty

A two-stage inexact joint-probabilistic programming (TIJP) method is developed for planning a regional air quality management system with multiple pollutants and multiple sources. The TIJP method incorporates the techniques of two-stage stochastic programming, joint-probabilistic constraint programming and interval mathematical programming, where uncertainties expressed as probability distributions and interval values can be addressed. Moreover, it can not only examine the risk of violating joint-probability constraints, but also account for economic penalties as corrective measures against any infeasibility. The developed TIJP method is applied to a case study of a regional air pollution control problem, where the air quality index (AQI) is introduced for evaluation of the integrated air quality management system associated with multiple pollutants. The joint-probability exists in the environmental constraints for AQI, such that individual probabilistic constraints for each pollutant can be efficiently incorporated within the TIJP model. The results indicate that useful solutions for air quality management practices have been generated; they can help decision makers to identify desired pollution abatement strategies with minimized system cost and maximized environmental efficiency.     

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

In this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.     

An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina

In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management.     

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk.     

Irrigation Water Allocation Using an Inexact Two‐Stage Quadratic Programming with Fuzzy Input under Climate Change

Agricultural irrigation accounts for nearly 70% of the total water use around the world. Uncertainties and climate change together exacerbate the complexity of optimal allocation of water resources for irrigation. An interval‐fuzzy two‐stage stochastic quadratic programming model is developed for determining the plans for water allocation for irrigation with maximum benefits. The model is shown to be applicable when inputs are expressed as discrete, fuzzy or random. In order to reflect the effect of marginal utility on benefit and cost, the model can also deal with nonlinearities in the objective function. Results from applying the model to a case study in the middle reaches of the Heihe River basin, China, show schemes for water allocation for irrigation of different crops in every month of the crop growth period under various flow levels are effective for achieving high economic benefits. Different climate change scenarios are used to analyze the impact of changing water requirement and water availability on irrigation water allocation. The proposed model can aid the decision maker in formulating desired irrigation water management policies in the wake of uncertainties and changing environment.     

The Use of an Ecologic Classification to Improve Water Resource Planning in New Zealand

The Resource Management Act (RMA) legislates the management of most natural resources in New Zealand. The RMA invokes ecosystem-based management by requiring that regulation be based on managing the effects of resource according to “the life supporting capacity” of the environment. The management of water resources under the RMA is carried out at the regional level by regional councils. Regional councils can develop regional water plans to establish objectives and criteria for water management. Regional water planning under the RMA has been problematic, and regional plan objectives developed under the RMA have been criticized as too broad and not sufficiently quantified. As a consequence, many resource users are unconvinced of the need for the regulatory criteria promulgated by plans, whereas other groups are concerned that the environment is inadequately protected. This article proposes that a lack of ecologically relevant management units has prevented regional water plans from fulfilling their intended function under the RMA. Then it introduces the use of River Environment Classification as a means of defining units for assessment and management, and provides three case studies that demonstrate its potential to support regional water management planning. The discussion shows that the specificity of regional assessments can be increased if ecologic variation is stratified into distinctive units (i.e., units within which variation in the characteristics of interest is reduced) as part of the assessment process. The increased specificity of the assessments increases the possibility that regional objectives and criteria for water management can be derived that are quantitative and justifiable and that provide certainty for stakeholders. The authors conclude that greater choice and meaning can be generated in regional planning processes if regional variation in ecologic characteristics is stratified using a classification, and if classes are used as units for assessment and management.     

Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management – Part A: Methodology

In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada.     

Systematic regional planning for multiple objective natural resource management

On-ground natural resource management actions such as revegetation and remnant vegetation management can simultaneously affect multiple objectives including land, water and biodiversity resources. Hence, planning for the sustainable management of natural resources requires consideration of these multiple objectives. However, planning the location of management actions in the landscape often treats these objectives individually to reduce the process and spatial complexity inherent in human-modified and natural landscapes. This can be inefficient and potentially counterproductive given the linkages and trade-offs involved. We develop and apply a systematic regional planning approach to identify geographic priorities for on-ground natural resource management actions that most cost-effectively meet multiple natural resource management objectives. Our systematic regional planning approach utilises integer programming within a structured multi-criteria decision analysis framework. Intelligent siting can capitalise on the multiple benefits of on-ground actions and achieve natural resource management objectives more efficiently. The focus of this study is the human-modified landscape of the River Murray, South Australia. However, the methodology and analyses presented here can be adapted to other regions requiring more efficient and integrated planning for the management of natural resources.     

Violation analysis for solid waste management systems: an interval fuzzy programming approach

This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approach, several given levels of tolerable violation for system constraints are permitted. This is realized through a relaxation of the critical constraints using violation variables, such that the model's decision space can be expanded. Thus, solutions from the violation analysis will not necessarily satisfy all of the model's original constraints. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions can be generated through this approach. Considerable information regarding decisions of facility expansion and waste flow allocation within the waste management system were generated. The modeling results help to generate a number of decision alternatives under various system conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability.     

An interval-based regret-analysis method for identifying long-term municipal solid waste management policy under uncertainty

In this study, an interval-based regret-analysis (IBRA) model is developed for supporting long-term planning of municipal solid waste (MSW) management activities in the City of Changchun, the capital of Jilin Province, China. The developed IBRA model incorporates approaches of interval–parameter programming (IPP) and minimax–regret (MMR) analysis within an integer programming framework, such that uncertainties expressed as both interval values and random variables can be reflected. The IBRA can account for economic consequences under all possible scenarios associated with different system costs and risk levels without making assumptions on probabilistic distributions for random variables. A regret matrix with interval elements is generated based on a matrix of interval system costs, such that desired decision alternatives can be identified according to the interval minimax regret (IMMR) criterion. The results indicate that reasonable solutions have been generated. They can help decision makers identify the desired alternatives regarding long-term MSW management with a compromise between minimized system cost and minimized system-failure risk.     

Flexible interval mixed-integer bi-infinite programming for environmental systems management under uncertainty

A number of inexact programming methods have been developed for municipal solid waste management under uncertainty. However, most of them do not allow the parameters in the objective and constraints of a programming problem to be functional intervals (i.e., the lower and upper bounds of the intervals are functions of impact factors). In this study, a flexible interval mixed-integer bi-infinite programming (FIMIBIP) method is developed in response to the above concern. A case study is also conducted; the solutions are then compared with those obtained from interval mixed-integer bi-infinite programming (IMIBIP) and fuzzy interval mixed-integer programming (FIMIP) methods. It is indicated that the solutions through FIMIBIP can provide decision support for cost-effectively diverting municipal solid waste, and for sizing, timing and siting the facilities’ expansion during the entire planning horizon. These schemes are more flexible than those identified through IMIBIP since the tolerance intervals are introduced to measure the level of constraints satisfaction. The FIMIBIP schemes may also be robust since the solutions are “globally-optimal” under all scenarios caused by the fluctuation of gas/energy prices, while the conventional ones are merely “locally-optimal” under a certain scenario.     

Pragmatic Approaches for Water Management Under Climate Change Uncertainty1

Stakhiv, Eugene Z., 2011. Pragmatic Approaches for Water Management Under Climate Change Uncertainty. Journal of the American Water Resources Association (JAWRA) 47(6):1183–1196. DOI: 10.1111/j.1752‐1688.2011.00589.x Abstract: Water resources management is in a difficult transition phase, trying to accommodate large uncertainties associated with climate change while struggling to implement a difficult set of principles and institutional changes associated with integrated water resources management. Water management is the principal medium through which projected impacts of global warming will be felt and ameliorated. Many standard hydrological practices, based on assumptions of a stationary climate, can be extended to accommodate numerous aspects of climate uncertainty. Classical engineering risk and reliability strategies developed by the water management profession to cope with contemporary climate uncertainties can also be effectively employed during this transition period, while a new family of hydrological tools and better climate change models are developed. An expansion of the concept of “robust decision making,” coupled with existing analytical tools and techniques, is the basis for a new approach advocated for planning and designing water resources infrastructure under climate uncertainty. Ultimately, it is not the tools and methods that need to be revamped as much as the suite of decision rules and evaluation principles used for project justification. They need to be aligned to be more compatible with the implications of a highly uncertain future climate trajectory, so that the hydrologic effects of that uncertainty are correctly reflected in the design of water infrastructure.     

OPTIMIZING NONPOINT SOURCE CONTROLS IN WATER QUALITY REGULATION1

ABSTRACT: A stochastic programming framework is developed to evaluate the economic implications of reliability criteria and multiple effluent controls on nonpoint source pollution. An integrated watershed simulation model is used to generate probability distributions for agricultural effluents in surface and ground water resulting from agricultural practices. Results from the planning model indicate that reliability and multiple effluent constraints significantly increase the cost of nonpoint controls but the effects vary by control alternative. The analysis indicates that an evaluation of multiple water quality objectives can be an important planning tool for designing nonpoint source controls for innovative programs to promote cost-effective water quality regulation.     

ONE APPROACH TO IRRIGATION MODELING UNDER RISK1

Recent progress in operations research has refined stochastic programming with recourse sufficiently to significantly increase its potential for use in water resource planning. To demonstrate its strengths and weaknesses this paper considers an irrigation planning problem and illustrates how more and more refined variants of this problem are successively cast into stochastic programming with recourse forms. The result is an outline of the state of the art with method limitations and demands on model formulation clearly indicated.     

Integrated urban water management modelling under climate change scenarios

The concept of integrated water management is uncommon in urban areas, unless there is a shortage of supply and severe conflicts among the users competing for limited water resources. Further, problem of water management in urban areas will aggravate due to uncertain climatic events. Therefore, an Integrated Urban Water Management Model considering Climate Change (IUWMCC) has been presented which is suitable for optimum allocation of water from multiple sources to satisfy the demands of different users under different climate change scenarios. Effect of climate change has been incorporated in non-linear mathematical model of resource allocation in term of climate change factors. These factors have been developed using runoff responses corresponding to base and future scenario of climate. Future scenarios have been simulated using stochastic weather generator (LARS-WG) for different IPCC climate change scenarios i.e. A1B, A2 and B1. Further, application of model has been demonstrated for a realistic water supply system of Ajmer urban fringe (India). Developed model is capable in developing adaptation strategies for optimum water resources planning and utilization in urban areas under different climate change scenarios.     

Policy planning under uncertainty: efficient starting populations for simulation-optimization methods applied to municipal solid waste management

Evolutionary simulation-optimization (ESO) techniques can be adapted to model a wide variety of problem types in which system components are stochastic. Grey programming (GP) methods have been previously applied to numerous environmental planning problems containing uncertain information. In this paper, ESO is combined with GP for policy planning to create a hybrid solution approach named GESO. It can be shown that multiple policy alternatives meeting required system criteria, or modelling-to-generate-alternatives (MGA), can be quickly and efficiently created by applying GESO to this case data. The efficacy of GESO is illustrated using a municipal solid waste management case taken from the regional municipality of Hamilton-Wentworth in the Province of Ontario, Canada. The MGA capability of GESO is especially meaningful for large-scale real-world planning problems and the practicality of this procedure can easily be extended from MSW systems to many other planning applications containing significant sources of uncertainty.