An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

DECISION SUPPORT FOR ALLOCATION OF WATERSHED POLLUTION LOAD USING GREY FUZZY MULTIOBJECTIVE PROGRAMMING1

ABSTRACT: This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water quality models, water quality standards, wastewater treatment costs, and potential benefits gained via in‐stream water quality improvement. While fuzzy sets are characterized based on semantic and cognitive vagueness in decision making, grey numbers can delineate measurement errors in data collection. By employing three distinct set theoretic fuzzy operators, the synergy of grey and fuzzy implications may smoothly characterize the prescribed management complexity. With the aid of genetic algorithm in the solution procedure, the modeling outputs contribute to the development of an effective waste load allocation and reduction scheme for tributaries in this subwatershed located in the lower Tseng‐Wen River Basin, South Taiwan. Research findings indicate that the inclusion of three fuzzy set theoretic operators in decision analysis may delineate different tradeoffs in decision making due to varying changes, transformations, and movements of waste load in association with land use pattern within the watershed.     

MULTIOBJECTWE ALLOCATION OF WATER SHORTAGE IN THE SVARTA RIVER,SWEDEN1

ABSTRACT: A model is proposed for allocation of water shortages among competing water uses in the Svarta River basin in Sweden. The three major competing uses in the basin are hydroelectricity generation, irrigation water supply, and urban water supply. Minor uses that impact upon the allocation are minimum river flow requirements for fishlife and for dilution of treated wastewater, and storage level restrictions for recreation purposes in the main storage facility, Lake Sommen. Analysis of the competing demands on the water are modeled through the method-of-weights multiobjective technique using a deterministic mixed-integer optimization formulation. The (0–1) variables in the formulation are required to synthesize the restricted validity of permits for withdrawal of irrigation water from the river and to simulate the complex operating rules of the major regulation facility on the river. Due to the deterministic nature of the formulation, the model is used on a hydrologic scenario basis. Use of the model is demonstrated by application to the Svarta River.     

IFRP: a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

In this study, an interval-parameter fuzzy-robust programming (IFRP) model is developed and applied to the planning of solid waste management systems under uncertainty. As an extension of the existing fuzzy-robust programming and interval-parameter linear programming methods, the IFRP can explicitly address system uncertainties with complex presentations. Parameters in the IFRP model can be represented as interval numbers and/or fuzzy membership functions, such that the uncertainties can be directly communicated into the optimization process and resulting solution. Furthermore, highly uncertain information for the lower and upper bounds of interval parameters that exist due to the complexity of the real world can be effectively handled through introducing the concept of fuzzy boundary interval. Consequently, robustness of the optimization process and solution can be enhanced. Results of the case study indicate that useful solutions for planning municipal solid waste management practices can be generated. They reflect a compromise between optimality and stability of the study system. Willingness to pay higher costs will guarantee the system stability; however, a desire to reduce the costs will run the risk of potential instability of the system. The results also suggest that the proposed hybrid methodology is applicable to practical problems that are associated with highly complex and uncertain information.     

WATER QUALITY ALLOCATED COST FOR MULTIPURPOSE RESERVOIRS1

ABSTRACT: Low flow augmentation from multipurpose reservoirs may yield significant water quality benefits. Cost allocation assigns a portion of reservoir expense to water quality consumers, waste water dischargers who benefit from increased receiving flow. Whereas such allocation currently is not authorized for Federal projects, the procedure is increasingly appropriate for efficient multiobjective management. Waste water treatment costs, multipurpose reservoir costs, and water quality are modeled for Oregon's Willamette River. Water quality is expressed as a function of treatment and augmentation levels. Treatment cost necessary to achieve a given water quality without augmentation less treatment cost with augmentation is an alternative cost of water quality maintenance. With a cost allocation procedure, this alternative cost is used to determine water quality's share of reservoir cost. Under current conditions, water quality beneficiaries could be charged approximately seven percent of annualized reservoir expense. This charge is one-fourth the expense of additional treatment facilities required were augmentation not provided.     

Sustainable pattern analysis of a publicly owned Material Recovery Facility in a fast-growing urban setting under uncertainty

Sustainable development goals are achievable through the installation of Material Recovery Facilities (MRFs) in certain solid waste management systems, especially those in rapidly expanding multi-district urban areas. MRFs are a cost-effective alternative when curbside recycling does not demonstrate long-term success. Previous capacity planning uses mixed integer programming optimization for the urban center of the city of San Antonio, Texas to establish that a publicly owned material recovery facility is preferable to a privatized facility. As a companion study, this analysis demonstrates that a MRF alleviates economic, political, and social pressures facing solid waste management under uncertainty. It explores the impact of uncertainty in decision alternatives in an urban environmental system. From this unique angle, waste generation, incidence of recyclables in the waste stream, routing distances, recycling participation, and other planning components are taken as intervals to expand upon previous deterministic integer-programming models. The information incorporated into the optimization objectives includes economic impacts for recycling income and cost components in waste management. The constraint set consists of mass balance, capacity limitation, recycling limitation, scale economy, conditionality, and relevant screening restrictions. Due to the fragmented data set, a grey integer programming modeling approach quantifies the consequences of inexact information as it propagates through the final solutions in the optimization process. The grey algorithm screens optimal shipping patterns and an ideal MRF location and capacity. Two case settings compare MRF selection policies where optimal solutions exemplify the value of grey programming in the context of integrated solid waste 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.     

An Interval-Parameter Waste-Load-Allocation Model for River Water Quality Management Under Uncertainty

A simulation-based interval quadratic waste load allocation (IQWLA) model was developed for supporting river water quality management. A multi-segment simulation model was developed to generate water-quality transformation matrices and vectors under steady-state river flow conditions. The established matrices and vectors were then used to establish the water-quality constraints that were included in a water quality management model. Uncertainties associated with water quality parameters, cost functions, and environmental guidelines were described as intervals. The cost functions of wastewater treatment units were expressed in quadratic forms. A water-quality planning problem in the Changsha section of Xiangjiang River in China was used as a study case to demonstrate applicability of the proposed method. The study results demonstrated that IQWLA model could effectively communicate the interval-format uncertainties into optimization process, and generate inexact solutions that contain a spectrum of potential wastewater treatment options. Decision alternatives can be generated by adjusting different combinations of the decision variables within their solution intervals. The results are valuable for supporting local decision makers in generating cost-effective water quality management strategies.     

COST-EFFECTIVE REGULATORY OPTIONS FOR WATER QUALITY LIMITED STREAMS1

With the pressure from industries and municipalities to reduce the waste water treatment costs associated with the permit limits needed to attain the goals of the Clean Water Act, attention has turned ways of introducing flexibility into the regulations without sacrificing the water quality goals. Wisconsin is the first state to have adopted a variety of options from which dischargers may choose when meeting their water quality requirements. These options were developed for the express purpose of minimizing the costs and maximizing the flexibility of the point source water quality regulations while ensuring that permitted discharge would not violate the water quality standards. This paper presents five options that the state has made available to dischargers, as well as one the state did not adopt. The conclusion is that a mix of options can substantially increase the flexibility and reduce the costs of meeting water quality standards on effluent limited streams.     

多级模糊模式识别方法用于河流水质评价

应用多级模糊模式识别模型进行水质量分类评价,克服了最大隶属度原则所不适用的地方,而且以相对隶属度、隶属函数为基础理论,使隶属度、隶属函数的计算更容易。建立了多级模糊模式识别模型,并应用于汾河水质分类评价中,应用结果表明,该方法合理、可行。     

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.     

Comparison of Two Spatial Optimization Techniques: A Framework to Solve Multiobjective Land Use Distribution Problems

Two spatial optimization approaches, developed from the opposing perspectives of ecological economics and landscape planning and aimed at the definition of new distributions of farming systems and of land use elements, are compared and integrated into a general framework. The first approach, applied to a small river catchment in southwestern France, uses SWAT (Soil and Water Assessment Tool) and a weighted goal programming model in combination with a geographical information system (GIS) for the determination of optimal farming system patterns, based on selected objective functions to minimize deviations from the goals of reducing nitrogen and maintaining income. The second approach, demonstrated in a suburban landscape near Leipzig, Germany, defines a GIS-based predictive habitat model for the search of unfragmented regions suitable for hare populations (Lepus europaeus), followed by compromise optimization with the aim of planning a new habitat structure distribution for the hare. The multifunctional problem is solved by the integration of the three landscape functions (“production of cereals,” “resistance to soil erosion by water,” and “landscape water retention”). Through the comparison, we propose a framework for the definition of optimal land use patterns based on optimization techniques. The framework includes the main aspects to solve land use distribution problems with the aim of finding the optimal or best land use decisions. It integrates indicators, goals of spatial developments and stakeholders, including weighting, and model tools for the prediction of objective functions and risk assessments. Methodological limits of the uncertainty of data and model outcomes are stressed. The framework clarifies the use of optimization techniques in spatial planning.     

MULTIOBJECTIVE REAL‐TIME RESERVOIR OPERATION WITH A NETWORK FLOW ALGORITHM1

ABSTRACT: A network flow algorithm has been developed for the optimization of real‐time operation of a multiple reservoir system. Two purposes have been considered in the operation: flood control and hydropower generation. A special network structure was developed which allows the consideration of river routing. A multiobjective formulation is utilized thus allowing generation of a non‐dominated curve. The effect of imperfect forecast on the performance of the real‐time operation model is also evaluated. An application is made to a subsystem of the Brazilian hydroelectric system, located in the Paranapanema river basin. In this case study, the model showed good performance under the largest flood of the historical records.     

The influence of metal source uncertainty on cost-effective allocation of mine water pollution abatement in catchments

In mine water pollution abatement, it is commonly assumed that known mine waste sites are the major pollution sources, thus neglecting the possibility of significant contribution from other old and diffuse sources within a catchment. We investigate the influence of different types of pollution source uncertainty on cost-effective allocation of abatement measures for mine water pollution. A catchment-scale cost-minimization model is developed and applied to the catchment of the river Dalälven, Sweden, in order to exemplify important effects of such source uncertainty. Results indicate that, if the pollution distribution between point and diffuse sources is partly unknown, downstream abatement measures, such as constructed wetlands, at given compliance boundaries are often cost-effective. If downstream abatement measures are not practically feasible, the pollution source distribution between point and diffuse mine water sources is critical for cost-effective solutions to abatement measure allocation in catchments. In contrast, cost-effective solutions are relatively insensitive to uncertainty in total pollutant discharge from mine water sources.     

Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints

The existing inexact optimization methods based on interval-parameter linear programming can hardly address problems where coefficients in objective functions are subject to dual uncertainties. In this study, a superiority–inferiority-based inexact fuzzy two-stage mixed-integer linear programming (SI-IFTMILP) model was developed for supporting municipal solid waste management under uncertainty. The developed SI-IFTMILP approach is capable of tackling dual uncertainties presented as fuzzy boundary intervals (FuBIs) in not only constraints, but also objective functions. Uncertainties expressed as a combination of intervals and random variables could also be explicitly reflected. An algorithm with high computational efficiency was provided to solve SI-IFTMILP. SI-IFTMILP was then applied to a long-term waste management case to demonstrate its applicability. Useful interval solutions were obtained. SI-IFTMILP could help generate dynamic facility-expansion and waste-allocation plans, as well as provide corrective actions when anticipated waste management plans are violated. It could also greatly reduce system-violation risk and enhance system robustness through examining two sets of penalties resulting from variations in fuzziness and randomness. Moreover, four possible alternative models were formulated to solve the same problem; solutions from them were then compared with those from SI-IFTMILP. The results indicate that SI-IFTMILP could provide more reliable solutions than the alternatives.     

UNCERTAINTY IN ESTIMATING BANKFULL CONDITIONS1

ABSTRACT: Bankfull depth and discharge are basic input parameters to stream planform, stream restoration, and highway crossing designs, as well as to the development of hydraulic geometry relationships and the classification of streams. Unfortunately, there are a wide variety of definitions for bankfull that provide a range of values, and the actual selection of bankfull is subjective. In this paper, the relative uncertainty in determining the bankfull depth and discharge is quantified, first by examining the variability in the estimates of bankfull and second by using fuzzy numbers to describe bankfull depth. Fuzzy numbers are used to incorporate uncertainty due to vagueness in the definition of bankfull and subjectivity in the selection of bankfull. Examples are provided that demonstrate the use of a fuzzy bankfull depth in sediment trans. port and in stream classification. Using fuzzy numbers to describe bankfull depth rather than a deterministic value allows the engineer to base designs and decisions on a range of possible values and associated degrees of belief that the bankfull depths take on each value in that range.     

Process design for the environment: A multi-objective framework under uncertainty

Designing chemical processes for the environment requires consideration of several indexes of environmental impact including ozone depletion, global warming potentials, human and aquatic toxicity, photochemical oxidation, and acid rain potentials. Current methodologies, such as the generalized waste reduction algorithm (WAR), provide a first step towards evaluating these impacts. However, to address the issues of accuracy and the relative weights of these impact indexes, one must consider the problem of uncertainties. Environmental impacts must also be weighted and balanced against other concerns, such as their cost and long-term sustainability. These multiple, often conflicting, goals pose a challenging and complex optimization problem, requiring multi-objective optimization under uncertainty. This paper will address the problem of quantifying and analyzing the various objectives involved in process design for the environment. Towards this goal, we proposed a novel multi-objective optimization framework under uncertainty. This framework is based on new and efficient algorithms for multi-objective optimization and for uncertainty analysis. This approach finds a set of potentially optimal designs where trade-offs can be explicitly identified, unlike cost-benefit analysis, which deals with multiple objectives by identifying a single fundamental objective and then converting all the other objectives into this single currency. A benchmark process for hydrodealkylation (HDA) of toluene to produce benzene modeled in the ASPEN simulator is used to illustrate the usefulness of the approach in finding environmentally friendly and cost-effective designs under uncertainty.     

A MULTIOBJECTIVE MODEL FOR REGIONAL WATER QUALITY MANAGEMENT1

ABSTRACT: Linear programming is the simplest of all the optimization techniques used in regional water quality management studies; but the technique can optimize only one goal. When there are multiple goals with the same or different priorities, goal programming is a useful decisionmaking tool. This paper illustrates the application of goal programming to a regional water quality management problem where the following two goals are considered: (1) minimize the total cost of waste treatment, and (2) maintain the water quality goals (dissolved oxygen) close to the minimum level stated in the stream standards.     

AN EVALUATION OF EIGHT WASTELOAD ALLOCATION METHODS1

Evidence suggests that there is no superior wasteload allocation method. Eight allocation strategies have been evaluated based on: total cost of implementation, equity in distributing costs and loads among dischargers, effectiveness in use of available waste assimilative capacity, and sensitivity to changes in water-quality-related variables. One method, which allocated equal percentages of the maximum allowable dissolved oxygen deficit, was eliminated as a feasible strategy because it led to excessive costs and overly conservative load estimates. The other seven methods remained viable alternatives. Two methods proved to be insensitive to changes in the water-quality-related variables tested, which may be advantageous in certain applications. This report presents seven workable alternatives that may be used in wasteload allocation and demonstrates a procedure to determine the practicability of other methods.