Optimal Location and Management of Waste Disposal Facilities Affecting Ground Water Quality1

ABSTRACT: Numerical simulation of ground water solute transport is combined with linear programming to optimize waste disposal. A discretized form of the equation governing solute transport is included as a set of constraints in a linear program. Two problems are described. First, the management model is used to maximize ground water waste disposal. The model constrains disposal activities so that the quality of local ground water supplies is protected. Parametric programming is shown to be important in evaluating waste disposal tradeoffs at the various facilities. Changes in the velocity field induced by waste water injection cause a nonlinearity in the solute transport equation which is dealt with by employing an iterative procedure. The second problem is aimed at identifying all sites which are suitable for waste disposal in the subsurface. The management model is manipulated so that the optimal value of the dual variables are “unit source impact indicators.” This physical interpretation is valuable in identifying feasible disposal sites. The joint simulation and optimization approach permits the management of complex ground water systems where the aquifer is used simultaneously for waste disposal and water supply.     

OPTIMAL GROUND WATER MANAGEMENT IN TWO-AQUIFER SYSTEMS1

ABSTRACT; This paper presents a numerical model for the prediction of optimal ground water withdrawal from a two-aquifer system by observing a set of constraints determined by the ecological conditions of the ground water basin. The aquifer system consists of an upper unconfined and a lower confined aquifer with a leaky stratum between them. It is assumed that water is withdrawn from the confined aquifer only, but the unconfined aquifer will also be affected due to the leakiness of the layer separating the upper and lower aquifers. Simulation and linear programming are employed for developing a computer model for the optimal management of such systems, with the objectives of determining withdrawal rates for predetermined ground water levels.     

COMPARISON OF RESERVOIR LINEAR OPERATION RULES USING LINEAR AND DYNAMIC PROGRAMMING1

ABSTRACT: Mathematical optimization techniques are used to study the operation and design of a single, multi-purpose reservoir system. Optimal monthly release policies are derived for Hoover Reservoir, located in Central Ohio, using chance-constrained linear programming and dynamic programming-regression methodologies. Important characteristics of the former approach are derived, discussed, and graphically illustrated using Hoover Reservoir as a case example. Simulation procedures are used to examine and compare the overall performance of the optimal monthly reservoir release policies derived under the two approaches. Results indicate that, for the mean detention time and the corresponding safe yield target water supply release under existing design of Hoover Reservoir, the dynamic programming policies produce lower average annual losses (as defined by a two-sided quadratic loss function) while achieving at least as high reliability levels when compared to policies derived under the chance-constrained linear programming method. In making this comparison, the reservoir release policies, although not identical, are assumed to be linear. This restricted form of the release policy is necessary to make the chance-constrained programming method mathematically tractable.     

STOCHASTIC DYNAMIC PROGRAMMING FOR OPTIMUM RESERVOIR OPERATION1

ABSTRACT. For a multipurpose single reservoir a deterministic optimal operating policy can be readily devised by the dynamic programming method. However, this method can only be applied to sets of deterministic stream flows as might be used repetitively in a Monte Carlo study or possibly in a historical study. This paper reports a study in which an optimal operating policy for a multipurpose reservoir was determined, where the optimal operating policy is stated in terms of the state of the reservoir indicated by the storage volume and the river flow in the preceding month and uses a stochastic dynamic programming approach. Such a policy could be implemented in real time operation on a monthly basis or it could be used in a design study. As contrasted with deterministic dynamic programming, this method avoids the artificiality of using a single set of stream flows. The data for this study are the conditional probabilities of the stream flow in successive months, the physical features of the reservoir in question, and the return functions and constraints under which the system operates.     

SOLUTION OF A WATER RESOURCES PROBLEM WITH ECONOMIES OF SCALE BY LINEAR PROGRAMMING1

ABSTRACT Both because of its effectiveness and ease in use, linear programming has become progressively popular in water resources planning problems. Yet, the assumptions of linear construction costs can be misleading. Diseconomies of scale in construction can be handled by successive approximations to the cost function but problems with economies of scale yield paradoxical results when piecewise approximations are used. If significant economies of scale exist in only one facility, the solution to problems of this nature can be found using normal linear programming codes by successively adjusting the unit construction cost on that single facility to iteratively work toward the true optimal solution.     

AN ARCHETYPAL LINEAR PROGRAMMING MODEL FOR OPTIMAL INTERTEMPORAL ALLOCATION OF GROUNDWATR TO AGRICULTURAL ACTIVITIES1

ABSTRACT: In the past, researchers have applied a variety of analytical techniques for maximizing the present value of a stock resource - simulation, calculus of variations, stochastic dynamic programming, and optimal control theory. This paper presents a more operational approach - linear programming. A simplified, broadly drawn example from Southwest agriculture is used for demonstrating the model's structure and output. The method is based on a set of state transformation operations that prevent the additivity assumption of linear programming from being violated.     

MODELS FOR WATER AND POWER SCHEDULING FOR THE CALIFORNIA STATE WATER PROJECT1

ABSTRACT: A large-scale simulation/optimization model provides schedules for operation of water and power for the California State Water Project (SWP). The SWP consists of a series of reservoirs linked by rivers, pumping plants, canals, tunnels, and generating plants and is operated by the California Department of Water Resources. The Department provides water to municipal and agricultural users, and manages its electrical loads and resources. The model, therefore, performs hydraulic and electrical computations leading to optimal operation of the entire system. It consists of hydraulic network programming components to meet the storage objectives at all the reservoirs, a linear programming component to determine the schedules at pumping and generating plants, an electrical network programming component to balance electrical loads and resources, and a number of other simulation components. It operates on yearly, weekly, and daily bases. It is primarily used for real-time operation of the SWP and can provide hourly detail schedules which are implemented by the SWP staff via a computerized system.     

IDENTIFICATION OF AN OPTIMAL GROUNDWATER MANAGEMENT STRATEGY IN A CONTAMINATED AQUIFER1

A groundwater hydraulic management model is used to identify the optimal strategy for allocating limited fresh-water supplies and containing wastes in a hypothetical aquifer affected by brine contamination from surface disposal ponds. The present cost of pumping from a network of potential supply and interception wells is minimized over a five-year planning period, subject to a set of hydraulic, institutional, and legal constraints. Hydraulic constraints are formulated using linear systems theory to describe drawdown and velocity variables as linear functions of supply and interception well discharge decision variables. Successful validation of the optimal management strategy suggests that the model formulation can feasibly be applied to define management options for locally contaminated aquifer systems which are used to fulfill fresh-water demands.     

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.     

THE EFFECTS OF RISK AND RELIABILITY ON OPTIMAL RESERVOIR DESIGN1

A chance-constrained linear programming model, which utilizes multiple linear decision rules and is useful for river basin planning, is used to evaluate the effects of risk and reliability on optimal reservoir design. Streamflow forecasts or predictions can be explicitly included in the linear program. The risk associated with the predictions is included in the model through the use of cumulative distribution functions (CDF) of streamflows which are conditioned on the predictions. A multiple-purpose reservoir on the Gunpowder River in Maryland is used to illustrate the effectiveness of the model. In order to provide the decision makers with complete and useful information, trade-off curves relating minimum reservoir capacity (a surrogate for dam costs), water supply and flood control targets, and the reliability of achieving the targets are developed. The trade-off curves may enhance the decision maker's ability to select the best dam capacity, considering technological and financial constraints as well as the trade-offs between targets, risks, and costs.     

An inexact dynamic optimization model for municipal solid waste management in association with greenhouse gas emission control

Municipal solid waste (MSW) should be properly disposed in order to help protect environmental quality and human health, as well as to preserve natural resources. During MSW disposal processes, a large amount of greenhouse gas (GHG) is emitted, leading to a significant impact on climate change. In this study, an inexact dynamic optimization model (IDOM) is developed for MSW-management systems under uncertainty. It grounds upon conventional mixed-integer linear programming (MILP) approaches, and integrates GHG components into the modeling framework. Compared with the existing models, IDOM can not only deal with the complex tradeoff between system cost minimization and GHG-emission mitigation, but also provide optimal allocation strategies under various emission-control standards. A case study is then provided for demonstrating applicability of the developed model. The results indicate that desired waste-flow patterns with a minimized system cost and GHG-emission amount can be obtained. Of more importance, the IDOM solution is associated with over 5.5 million tonnes of TEC reduction, which is of significant economic implication for real implementations. Therefore, the proposed model could be regarded as a useful tool for realizing comprehensive MSW management with regard to mitigating climate-change impacts.     

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 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.     

AQUIFER MANAGEMENT UNDER TRANSIENT AND STEADY-STATE CONDITIONS1

ABSTRACT: The equations of transient and steady-state flow in two-dimensional artesian aquifers are approximated using finite differences. The resulting linear difference equations, combined with other linear physical and management constraints and a linear objective function, comprise a linear programming (LP) formulation. Solutions of such LP models are used to determine optimal well distributions and pumping rates to meet given management objectives for a hypothetical transient problem and for a steady-state field problem.     

APPLICATION OF LINEAR SYSTEM'S THEORY AND LINEAR PROGRAMMING TO GROUND WATER MANAGEMENT IN KANSAS1

ABSTRACT: A ground water management model based on the linear systems theory and the use of linear programming is formulated and solved. The model maximizes the total amount of pound water that can be pumped from the system subject to the physical capability of the system and institutional constraints. The results are compared With analytical and numerical solutions. Then, this model is applied to the Pawnee Valley area of south-central Kansas. The results of this application support the previous studies about the future ground water resources of the Valley. These results provide a guide for the ground water resources management of the area over the next ten years.     

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.     

A MODELLING METHOD FOR EVALUATING WATER QUALITY POLICIES IN NONSERIAL RIVER SYSTEMS1

ABSTRACT: This paper describes a modelling method which simplifies the evaluation of water quality policies for nonserial (branching) river systems. The method introduces dummy facilities at the junctions of the major tributary branches with the mainstream as replacements for the facilities and activities on the tributaries. The cost functions for the dummy facilities and the DO and BOD concentrations at the junctions as determined for each tributary are introduced into the mainstream serial system model which is then solved for the optimal values of the mainstream treatment plant efficiencies, the dummy facility effeciencies, and the tributary system DO and BOD concentrations using nonlinear programming. Given the optimum values for the dummy facility efficiencies and the values for the tributary system DO and BOD concentrations, the optimum values for the tributary treatment plant efficiencies are found using nonlinear programming. The method is applied to a river system with a mainstream and one major tributary which contain industrial and municipal organic and thermal polluters and their associated wastewater treatment plants.     

ASSESSMENT ANALYSIS FOR WATER SUPPLY ALTERNATIVES1

ABSTRACT Providing adequate water supplies of good quality is becoming a serious problem in many areas of the United States. Some of the alternatives proposed for meeting the growing shortage of clean-water or cheap-water are reallocation, reuse, and importation. This paper outlines a methodology to assess all of these water supply alternatives by examining the amount and time-staging for development of water sources. In conceptualizing the problem, sources of supply are classified in three categories: primary or base supplies, secondary or effluent supplies, and supplementary or imported supplies. A model of the water system is formulated as a “transportation problem” in linear programming depicting the possible sources of supply which can be used to satisfy the requirements of various water users. The optimizing objective in the model is to minimize the cost of water under various assumptions for operating the system. A case study of the Salt Lake Qty, Utah, area is used to illustrate the application of the model in obtaining optimal water supply allocations for projected future demands. Assessment of alternatives in the study include redistribution of supplies, time-staging of supplies and related treatment facilities, and sensitivity of allocations to changes in costs.     

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.     

CO2 emissions reduction from the power system in India

The power system in India accounts for nearly one-third of CO₂ emissions of the country as a whole. A comparison of some of the technical options to reduce CO₂ emissions is presented in this paper. A linear programming framework is used to simulate the integrated optimal operation of the three regional grids, and it is shown that such operations lead to lower fuel costs and to lower CO₂ emissions. The same framework is used to see how a rise in thermal efficiency translates into a CO₂ emissions reduction. Reduced fuel requirements also lead to reductions in other pollutants ie SO₂, NO_x and fly ash. The reductions in CO₂ emissions and other pollutants are at far lower cost in the case of integrated optimal operations as compared to reductions due to gas fuelled generation or thermal efficiency improvements. However, thermal efficiency improvements under optimal integrated operations result in much higher reductions in operating costs, coal consumption and total emissions of all pollutants.