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.     

POLITICAL RESOLUTION OF ENVIRONMENTAL CONFLICTS1

ABSTRACT Many water resources management problems ultimately require a political decision in order to formulate a course of action to follow. Metagame analysis is a nonquantitative technique that can model the decision-making process and is used in this article to arrive at a politically feasible solution to a typical water pollution problem. The output from the linear programming formulation of the problem is used as input to the “political” metagame analysis. This allows a solution to the pollution conflict that is not only physically and economically feasible according to the linear programming analysis, but politically feasible as well.     

Economies of scale in global iron-making

In this paper, we investigate the presence of economies of scale in the global iron-making industry for integrated steel plants, iron making being the first stage in the steel-making process. Iron making depends on basic commodities, such as iron ore, coke and various forms of energy, required in the operation of the blast furnace, which can be classified as essential inputs and used in fixed proportions to produce iron. A generalized Leontief cost function is estimated using panel data for 69 integrated plants, such a specification being appropriate for technologies with essential inputs that are used in fixed proportions in production. A significant scale effect is observed due to the existence of fixed costs and a linear dependence of the cost function on production. Under a simple linear cost function, a rough estimate of the breakeven scale of plant, where costs equal revenue, is 4.5 Mt per year. Competitiveness, as measured by the ratio of plant average cost per tonne to best practice cost per tonne, can be shown to be positively related to the scale of production as well as the cost of essential inputs. Therefore, low-cost producers are also often producers with low raw material costs and production levels below the estimated breakeven scale of operation. Labor costs, although significant, are comparatively less important as a driver towards low costs.     

SOLID SET IRRIGATION SYSTEM DESIGN USING LINEAR PROGRAMMING1

: Irrigation systems can be formulated to enable linear programming to be used to obtain optimal systems. Linear programming is a readily available technique in most scientific and technical centers which have computer facilities. The objective function towards a minimal cost is based on a suggested classification of the system components, and the constraints mainly refer to required pressures and discharges. A case study in which linear programming is used to determine optimal pipe diameters is given for the solution of a solid set under tree sprinkler system.     

GROUND WATER MANAGEMENT OPTIMIZATION USING GENETIC ALGORITHMS AND SIMULATED ANNEALING: FORMULATION AND COMPARISON1

ABSTRACT: Genetic algorithms (GA) and simulated annealing (SA), two global search techniques, are coupled with MODFLOW, a commonly used groundwater flow simulation code, for optimal management of ground water resources under general conditions. The coupled simulation-optimization models allow for multiple management periods in which optimal pumping rates vary with time to reflect the changing flow conditions. The objective functions of the management models are of a very general nature, incorporating multiple cost terms such as the drilling cost, the installation cost, and the pumping cost. The models are first applied to two-dimensional maximum yield and minimum cost water supply problems with a single management period, and then to a multiple management period problem. The strengths and limitations of the GA and SA based models are evaluated by comparing the results with those obtained using linear programming, nonlinear programming, and differential dynamic programming. For the three example problems examined in this study, the GA and SA based models yield nearly identical or better solutions than the various programming methods. While SA tends to outperform GA in terms of the number of forward simulations needed, it uses more empirical control parameters which have significant impact on solution efficiency but are difficult to determine.     

OPTIMAL MANAGEMENT AND DESIGN OF HYDRAULIC SYSTEMS1

ABSTRACT: A possible methodology is developed to deal with the problem of designing complex pipeline systems, when they are subject to different rates of demand, and when a hypothesis of the flow distribution in different branches is not allowed. The mathematical algorithm used in linear programming. The problem, which is not linear, is dealt with by means of an iterative method; that is, by starting with a possible solution and inserting at each iteration the solution found in the preceding iteration. By taking as variables of the problem the piezometric heads of the ends for each branch of the network, the piezometric gradients and flows, and by thus considering the diameter as a derived variable, it is possible to isolate the nonlinearity in the cost function of the network. The latter is linearized each time close to the solution found in the preceding iteration.     

ON THE CAPACITY-EXPANSION OF DESALINATION PLANTS AND STORAGE TANKS1

ABSTRACT A mathematical programming model is structured to find the optimal time and capacity expansion path of desalination plants and storage tanks for a hypothetical community which depends on desalination as its sole, or major, water supply source. The objective is to determine the least costly combination of sues and times of installation (of both desalting plants and storage tanks) which can meet a rising water demand over a finite planning horizon. The optimality criterion used in the model is based on two major economic elements: the economies of scale inherent in such facilities and the time-value of money represented by the interest rate, the former favoring large capacities and the latter small capacities. The model is applied using three population growth patterns and two interest rates. The water demand components for every year in the planning period are computed using empirical formulas which are based on population and other basic data. The model is solved for each of the above cases with the aid of a computer program based on the method of feasible conjugate directions. The results clearly reflect the balance between the economies of scale and the time-value of money under every demand growth function.     

ECONOMIC DESIGN OF CENTRAL WATER SUPPLY SYSTEMS FOR MEDIUM SIZED TOWNS1

ABSTRACT. Adequate and good-quality water supply for medium sized towns is costly when there are insufficient quantity and low quality of groundwater or surface water. In a central water supply system serving a number of towns, the economies of scale may permit a sufficient and good-quality supply at lesser rates. Such a system has the flexibility of supplying rural population through small service lines. The system may be an interbasin or intrabasin conveyance depending on the location of a suitable water source and the economics of the supply network. Seven cost elements are pertinent to the optimum or least-cost design of network consisting of pipelines and pumping stations. The relevant cost functions are based on the available data gathered from various sources. Water conveyance costs are calculated for various flow rates, pipeline diameters, flow variabilities, static heads, and interest rates, thus providing a measure of sensitivity of the conveyance cost to such variations. The economies of scale, the sensitivity of optimum unit conveyance costs, and variations in unit costs with change in cost functions are useful in making a feasibility study for a proposed conveyance system.     

ON THE CENTRALIZATION OF WASTEWATER TREATMENT FACILITIES1

ABSTRACT. Two factors affecting the centralization of wastewater treatment facilities were investigated; the cost of collection and treatment systems and the performance of treatment plants. Based on computer-generated minimum cost designs, wastewater collection networks were found to be characterized by diseconomies of scale of magnitude similar to the reported economies of scale for wastewater treatment works. The combined costs of collection and treatment are U-shaped functions from which the least cost size of collection and treatment systems were found for particular values of population density. Examination of the day-to-day performance of five metropoitan-area waste-water treatment plants revealed that, for time series shorter than one month, the day-to-day variation in effluent quality was random, although the variation in quantity discharged was distinctly non-random. The performances of all five plants on any given day showed little correlation. This suggests that the decentralization of treatment facilities can produce benefits both through the reduction in quantities of waste discharged at a given point and through in-stream averaging of the varying performances of several treatment plants. Since the cost function of collection and treatment combined is generally flat in the region of the minimum-cost size, little penalty is invoked to gain the potential benefits of treatment plant decentralization.     

OPTIMAL CAPACITIES OF WATER SUPPLY RESERVOIRS IN SERIES AND PARALLEL1

ABSTRACT: The planning of water supply reservoirs has traditionally been based on the Rippl or sequent peak analysis which applies to the design of a single reservoir. This paper incorporates the sequent peak method as the central feature in establishing a procedure for determining the sizes of several potential reservoirs located in a system of one or more rivers. Separate algorithms are developed for sites on parallel streams and for sites on the same stream. In both cases the approach is to find the combination of reservoirs which can satisfy a given constant monthly demand at a minimum total construction cost. It is shown that both problems can be cast in the form of a dynamic programming problem. A more complex system is then a combination of reservoirs in parallel and in series. An extension is given if the monthly demand is not constant but each reservoir satisfies a constant fraction of the monthly demand.     

How Widely Applicable is River Basin Management? An Analysis of Wastewater Management in an Arid Transboundary Case

The basin scale has been promoted universally as the optimal management unit that allows for the internalization of all external effects caused by multiple water uses. However, the basin scale has been put forward largely on the basis of experience in temperate zones. Hence whether the basin scale is the best scale for management in other settings remains questionable. To address these questions this paper analyzes the economic viability and the political feasibility of alternative management options in the Kidron/Wadi Nar region. The Kidron/Wadi Nar is a small basin in which wastewater from eastern Jerusalem flows through the desert to the Dead Sea. Various options for managing these wastewater flows were analyzed ex ante on the basis of both a cost benefit and a multi-criteria analysis. The paper finds that due to economies of scale, a pure basin approach is not desirable from a physical and economic perspective. Furthermore, in terms of political feasibility, it seems that the option which prompts the fewest objections from influential stakeholder groups in the two entities under the current asymmetrical political setting is not a basin solution either, but a two plant solution based on an outsourcing arrangement. These findings imply that the river basin management approach can not be considered the best management approach for the arid transboundary case at hand, and hence is not unequivocally universally applicable.     

OPTIMIZATION OF WATER RESOURCES FOR IRRIGATION IN EAST JORDAN1

The paper describes an approach towards optimal allocation of surface and ground water resources to three agricultural areas in the Jordan Valley under conditions of scarce water supply. The optimizing model allocates water from three main rivers, each with reservoir storage, and from two ground water sources to three irrigation regions. Productivity of irrigation water, expressed as the net present value of the regional agricultural output, but allowing for crop water deficits, is first maximized using nonlinear programming. The allocation process then adopts techniques of linear programming to determine the least cost alternative based on the unit cost of water from each resource at each destination, as it varies with time.     

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.     

AN ANALYSIS OF WATER RESOURCES CONSTRAINTS ON POWER PLANT SITING IN THE MID-ATLANTIC STATES1

ABSTRACT: Expansion of the electrical generation system in the Pennsylvania-Jersey-Maryland power pool will impact, and be constrained by, inland water availability. Future interpretations of the Federal Water Pollution Control Act Amendments of 1972 regarding evaporative cooling towers for coastal power plants, offshore siting and energy centers, and the policies and public acceptability of low flow augmentation reservoirs are some of the issues examined in this paper using scenarios generated by the Brookhaven National Laboratory Regional Energy Facility Siting Model (REFS). REFS is a multicommodity, transshipment-location linear programming model used here to allocate power plants among counties in a power pool under a minimization of cost objectives. The solutions are sensitive to the water resources assumptions in the model. For the year 2000, the amount of low flow augmentation allowed in the region's river basins and whether off-shore siting becomes a reality are the two water resources related issues which most affect the scenarios. The results show that decisions regarding specific water problems can have region wide implications for water and nonwater related issues.     

A CODED ALGORITHM FOR CAPACITY EXPANSION OF A WATER QUALITY MANAGEMENT SYSTEM1

ABSTRACT: This paper describes a mathematical model, an algorithm and a computer program that were specially developed to study the problem of a water quality management system undergoing a rapidly increasing environmental stress. The model output will determine the locations, sizes and the timing of construction of new treatment plants plus an overall treatment plant operating policy so that environmental standards are maintained at a minimum cost. The model, as formulated, is a 0-1 mixed integer programming problem which is solved by decomposing it into a capital budgeting problem (solved by Little's branch and bound algorithm) and an operational policy problem (solved by linear programming). The coded algorithm (in FORTRAN 10) has been tested with a semi-realistic example.     

LINEAR PROGRAMMING APPLICATIONS IN WATER RESOURCES1

Applications of linear programming to water quality and water quantity problems are discussed, and a fairly comprehensive sample of recent literature in these areas is reviewed. Basic elements of linear programming are also discussed. Emphasis is placed on the elements of linear programming that make it a useful tool for analyzing water resource problems and the basic features of various water resource problems that render them amenable to meaningful analysis by linear programming.     

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.     

A LINEAR ANALYSIS OF AN URBAN WATER SUPPLY SYSTEM1

The use of linear programming as a planning tool for determining the optimal long-range development of an urban water supply system was explored. A stochastic trace of water demand was synthesized and used as an input to the model. This permitted evaluating the feasibility of imposing demand restrictions as an effective cost reduction mechanism. The City of Lincoln, Nebraska, was used as the urban model. The fundamental problem was to allocate limited water supplies from several sources to an urban load center to minimize costs and comply with system constraints. The study period covered twenty years, and findings indicate the planning direction for stage development during this period. Sensitivity analyses were performed on cost coefficients and demands. Thirteen sources were included in the initial computations. Conclusions were that linear programming and generated demand traces are useful tools for both short- and long-term urban water supply planning. Lowering peak demands results in long-range development of fewer sources of supply and more economic and efficient use of the supplies developed.     

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.     

ITERATIVE EVALUATION OF A LAKE WATER QUALITY MANAGEMENT PROGRAM1

ABSTRACT: Local governments often face environmental problems that cross political boundaries. The onus for solution usually falls on the moat severely affected jurisdiction, others do nothing until impacted. Resolution of these problems requires cooperation across political boundaries which means that local governments must be persuaded first that there is a problem, and second that action is required to solve it. This paper presents a method to supply low cost, credible information that can be used to achieve consensus on problem solution. A case study of a lake water quality management problem is described. Formative evaluation techniques was adapted to provide a minimum of evidence which was then used to persuade less impacted local jurisdictions to cooperate in the problem solution.