An inexact optimization approach for river water-quality management

A previously developed fuzzy waste load allocation model (FWLAM) for a river system is extended to address uncertainty involved in fixing the membership functions for the fuzzy goals of the pollution control agency (PCA) and the dischargers using the concept of grey systems. The model provides flexibility for the PCA and the dischargers to specify their goals independently, as the parameters for membership functions are considered as interval grey numbers instead of deterministic real numbers. An inexact or a grey fuzzy optimization model is developed in a multiobjective framework, to maximize the width of the interval valued fractional removal levels for providing latitude in decision-making and to minimize the width of the goal fulfillment level for reducing the system uncertainty. The concept of an acceptability index for order relation between two partially or fully overlapping intervals is used to get a deterministic equivalent of the grey fuzzy optimization model developed. The improvement of the optimal solutions over a previously developed grey fuzzy waste load allocation model (GFWLAM) is shown through an application to a hypothetical river system. The fuzzy multiobjective optimization and fuzzy goal programming techniques are used to solve the deterministic equivalent of the GFWLAM.     

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.     

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.     

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.     

ANALYSIS OF A KARSTIC AQUIFER MANAGEMENT PROBLEM BY FUZZY COMPOSITE PROGRAMMING1

ABSTRACT: A multiple objective framework for water resources problems possessing uncertain or imprecise elements is provided using distance-based concepts, fuzzy set theory, and fuzzy arithmetic. The case of regional management of a karstic aquifer in Hungary in which six conflicting objectives and six alternatives have been identified illustrates the methodology The objectives are classified into three groups of two objectives each, namely: (1) environmental (aesthetics, thermal springs temperature), (2) economic (mining, tourism), and (3) water quality (nitrates, phosphates). Both environmental objectives are formulated under fuzziness, and all objectives are scaled using the extension principle. Fuzzy compromise programming (FCP-I) is then applied; here, all six objectives are entered in a single l_p norm measuring the distance between each alternative and an ideal point. Next, fuzzy composite programming (FCP-II) is developed; here, a trade off is first made within each group of objectives, and then an upper level trade-off takes place between the three groups. The fuzzy numbers describing each alternative as a result from applying these techniques are ranked to yield an ordering of the alternatives. The results of applying FCP.I, FCP-II, and two different ordering techniques are compared. The FCP-II technique appears to provide a relatively simple approach at hierarchical or multilevel multiple objective decision-making, where uncertainty is described by fuzziness. (KEY TERMS: compromise programming; fuzzy arithmetic; fuzzy sets; hierarchical criteria; karstic aquifer; l_p, norms; mining; multiple objectives; thermal springs.)     

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.     

OPTIMIZATION OF MULTIPURPOSE RESERVOIR SYSTEM OPERATION1

ABSTRACT: The goal programming approach for multipurpose reservoir operation has been proposed and applied to the Bhadra reservoir system, having irrigation and hydropower production as dual purposes, in India. The objective of the model is to satisfy sequentially a series of operating criteria. Two goal programming models, one with the objective function as minimizing the deviations from storage targets and the other with the objective function as minimizing the deviations from release targets, have been formulated and applied to the reservoir system under study. The results proved that the model with release targets is preferred over the model with storage targets for determining operational policies for multipurpose reservoir system.     

NONLINEAR PROGRAMMING IN RIVER BASIN MODELING1

ABSTRACT: This paper explores the use of nonlinear programming in river basin water quality modelling. Applications recently reported in the literature, along with the author's experience with nonlinear programming, are reviewed. Results obtained using nonlinear programming are compared with the results obtained by other researchers using linear and dynamic programming to solve river basin water quality optimization problems. These water quality models have objective functions with continuous first partial derivatives, several inequality and variable bound constraints, and are of the form: minizie Σ^j=n_j=1Y_j(X_j) subject to Σ^j=n_j=1a_ijX_jb_i, i=1,2, …, m c_jX_jd_j, j= 1,2, …, n The variable X_i is the maximum allowable ratio of the BOD (biochemical oxygen demand) of the effluent outflow to the BOD of the wastewater inflow for treatment plant j, in the range c_j to d_j. The a_ijd and b_i are constants in the DO (dissolved oxygen) and BOD constraints. The resuks show, given certain assumptions about the data, that nonlinear programming is a better solution method for these problems than is either linear programming or dynamic programming.     

A stochastic fuzzy chance-constrained programming model for energy–environment system planning and management in the City of Beijing

A stochastic and fuzzy chance-constrained programming (SFCCP) model was developed in this study for supporting energy–environment management in the city of Beijing, China. SFCCP was capable of tackling the variables in constraints as fuzzy random variables, which were integration of randomness and vagueness. SFCCP was applied to an energy–environment management system in the city of Beijing. The study results indicated that SFCCP was useful in helping decision makers gain in-depth insights into proposed management system and establish environment-friendly energy allocation alternatives. The application of SFCCP is expected to provide a good demonstration to energy–environment management problems under complex uncertainties.     

A Hierarchical Fuzzy Decision Support System for the Environmental Rehabilitation of Lake Koronia,Greece

This article presents the design of a fuzzy decision support system (DSS) for the assessment of alternative strategies proposed for the restoration of Lake Koronia, Greece. Fuzzy estimates for the critical characteristics of the possible strategies, such as feasibility, environmental impact, implementation time, and costs are evaluated and supplied to the fuzzy DSS. Different weighting factors are assigned to the critical characteristics and the proposed strategies are ordered with respect to the system responses. The best strategies are selected and their expected impact on the ecosystem is evaluated with the aid of a fuzzy model of the lake. Sensitivity analysis and simulation results have shown that the proposed fuzzy DSS can serve as a valuable tool for the selection and evaluation of appropriate management actions. Note: This version was published online in June 2005 with the cover date of August 2004.     

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 Environmental “Risky” Region: Identifying Land Degradation Processes Through Integration of Socio-Economic and Ecological Indicators in a Multivariate Regionalization Model

The economic policy needs to pay increasingly more attention to the environmental issues, which requires the development of methodologies able to incorporate environmental, as well as macroeconomic, goals in the design of public policies. Starting from this observation, this article proposes a methodology based upon a Simonian satisficing logic made operational with the help of goal programming (GP) models, to address the joint design of macroeconomic and environmental policies. The methodology is applied to the Spanish economy, where a joint policy is elicited, taking into consideration macroeconomic goals (economic growth, inflation, unemployment, public deficit) and environmental goals (CO₂, NO _x and SO _x emissions) within the context of a computable general equilibrium model. The results show how the government can “fine-tune” its policy according to different criteria using GP models. The resulting policies aggregate the environmental and the economic goals in different ways: maximum aggregate performance, maximum balance and a lexicographic hierarchy of the goals.     

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).     

Fuzzy pricing for urban water resources: model construction and application

A rational water price system plays a crucial role in the optimal allocation of water resources. In this paper, a fuzzy pricing model for urban water resources is presented, which consists of a multi-criteria fuzzy evaluation model and a water resources price (WRP) computation model. Various factors affecting WRP are comprehensively evaluated with multiple levels and objectives in the multi-criteria fuzzy evaluation model, while the price vectors of water resources are constructed in the WRP computation model according to the definition of the bearing water price index, and then WRP is calculated. With the incorporation of an operator's knowledge, it considers iterative weights and subjective preference of operators for weight-assessment. The weights determined are more rational and the evaluation results are more realistic. Particularly, dual water supply is considered in the study. Different prices being fixed for water resources with different qualities conforms to the law of water resources value (WRV) itself. A high-quality groundwater price computation model is also proposed to provide optimal water allocation and to meet higher living standards. The developed model is applied in Jinan for evaluating its validity. The method presented in this paper offers some new directions in the research of WRP.     

Emergy-based fuzzy optimization approach for water reuse in an eco-industrial park

The establishment of an eco-industrial park (EIP) provides opportunity for individual plants to cooperate with each other in order to utilize resources efficiently and thus reduce waste. The goal of an EIP is to “close the loop” through recycling and reuse of material and energy streams. Studies show with current freshwater consumption trends there would be water stress aggravated by global warming in the near future. This paper presents a model to design an EIP water reuse network that considers overall system sustainability as measured with emergy, as well as cost saving desired by individual plants. Case studies from literature are then solved to illustrate the advantage of this method in decision making. The illustrative examples show how the model achieves a compromise among the potentially conflicting fuzzy goals of the various EIP stakeholders.     

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.     

A multi-period optimization model for energy planning with CO2 emission consideration

A novel deterministic multi-period mixed-integer linear programming (MILP) model for the power generation planning of electric systems is described and evaluated in this paper. The model is developed with the objective of determining the optimal mix of energy supply sources and pollutant mitigation options that meet a specified electricity demand and CO₂ emission targets at minimum cost. Several time-dependent parameters are included in the model formulation; they include forecasted energy demand, fuel price variability, construction lead time, conservation initiatives, and increase in fixed operational and maintenance costs over time. The developed model is applied to two case studies. The objective of the case studies is to examine the economical, structural, and environmental effects that would result if the electricity sector was required to reduce its CO₂ emissions to a specified limit.     

SCREENING THE RELOCATION STRATEGIES OF WATER QUALITY MONITORING STATIONS BY COMPROMISE PROGRAMMING1

Water quality monitoring network designs historically have tended to use experience, intuition, and subjective judgment in siting monitoring stations only sporadically. Better design procedures for optimizing monitoring systems with respect to multiple criteria decision analysis had rarely been put into practice up front when the needs for intensive monitoring became critical. This paper describes a systematic relocation strategy that is organized to identify several significant planning objectives and consider a series of inherent constraints simultaneously. The planning objectives considered in this analysis are designed to enhance the detection possibility for lower compliance areas, reflect the emphasis for different attainable water uses at different locations, promote the potential detection for the lower degradation areas of pollutants, increase the protection degree of those areas with higher population density in the proximity of the river system, and strengthen the pre‐warning capability of water quality for water intakes. The constraint set contains the limitations of budget, the equity implication, and the detection sensitivity in the water environment. A case study in the Kao‐Ping River Basin, South Taiwan, demonstrates the application potential of this methodology based on a seamless integration between the optimization and the simulation models. It enables identification of the optimal locational pattern stepwise using the embedded screening and sequencing capacity in a compromise programming model. However, a well calibrated and verified water quality model is an indispensable tool in support of this multiobjective evaluation. Extra sampling procedures become necessary for the sites with sparse environmental information. Comparison of planning outcomes of compromise programming is made against previously achieved analyses by using weighted programming and fuzzy programming.     

Book reviews

Urban Europe: A Study of Growth and Decline. Vol. 1

L. van den Berg, R. Drewett, L. H. Klaassen, A. Rossi and C. H. T. Vijverberg

European Coordination Centre for Research and Documentation in Social Science, Vienna.

Pergamon Press, 1982, 162 pp. £18.00 Hardback.

Working Party on New Towns

"New Towns in National Development"

International Federation for Housing and Planning, 1980, 292 pages.

Plans and Diagrams. No price stated.     

THE ROLE OF AGRICULTURAL GROUNDWATER CONSERVATION IN ACHIEVING ZERO OVERDRAFT IN ARIZONA1

ABSTRACT: The elimination of groundwater overdraft was a key feature of the 1980 Arizona Groundwater Management Act. To achieve this goal, the Arizona Department of Water Resources identified several Active Management Areas and developed urban, industrial, and agricultural water conservation plans. This study examines the reductions in groundwater use through agricultural water conservation in the Phoenix Active Management Area (AMA). Linear programming models are developed to analyze changes in groundwater use and net returns to agriculture over a 38-year period, 1990 to 2025, for farming areas in the Phoenix AMA. Results indicate that the agricultural conservation program provides only modest groundwater savings under a wide range of scenarios. The low level of savings is partly due to the current economically efficient use of water. Other policy measures such as retiring agricultural land may be necessary if the Phoenix AMA is to meet its overdraft reduction goals; even if urban water conservation goals are met.