OPTIMAL OPERATION OF SHELBYVILLE AND CARLYLE LAKES1

ABSTRACT: Dams were built by the U. S. Army Corps of Engineers on the Kaskaskia River at Shelbyville and Carlyle in Illinois, in 1969 and 1967, respectively. The operation of the Shelbyville and Carlyle Lakes has changed over the years because of considerably lower bankfull channel capacities downstream of the dams than were adopted in the project designs. This study was conducted to review the present operation policy. Intent was to derive a policy for maximizing the overall benefits (or minimizing the overall damages) and to compare these benefits or damages with those with the present policy. The operating rules were optimized through a simulation model which was structured considering the physical nature of the system and the desirable operation in the best interest of various beneficial uses. The expected annual value of overall benefits from recreation and agriculture is shown to increase by $0.2 million with the optimal policy. With the optimal operation, the overall damages are reduced by 76 percent on the average over the 24 years of flow record at Shelbyville and Carlyle.     

A MULTILEVEL MODEL AND ALGORITHM FOR SOME MULTIOBJECTIVE PROBLEMS1

This paper presents a solution method for a class of multiobjective problems characterized by a hierarchical structure of decisionmaking and a large number of alternatives. The method, consisting of a multilevel problem formulation and an interactive algorithm, has distinct advantages for identifying preferred solutions to problems having those characteristics. The method is illustrated to a problem involving waste water treatment in the chemical industry.     

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.     

CAPACITY EXPANSION PLANNING MODEL FOR WASTE WATER TREATMENT AND I/I CONTROL1

ABSTRACT: A dynamic programming model is presented for planning the optimal capacity expansion sequence of waste water treatment plants servicing sewerage systems with infiltration/inflow. The model employs a nonlinear deterministic demand function for waste water treatment plant capacity. Model output provides the optimal timing, size, and sequence for treatment plant capacity expansion projects and infiltration/inflow removal projects. An example problem is presented and solved.     

CONTROLLING GROUND WATER DEGRADATION IN THE TULARE LAKE BASIN1

ABSTRACT This study examined the feasibility of extending the Accelerated Salt Transport (ASTRAN) method of groud water quality control to a complex, closed basin which is experiencing ground water quality degradation from irrigated agriculture (e.g., the Tulare Lake Basin in the Southern portion of the California Central Valley). A linear programming model was constructed and parametric analysis conducted which produced results with a “general appraisal” (or “level B”) degree of accuracy. The study concluded that a drainage water export drain is required in order to implement a long-term solution but that ground water degradation can be mitigated by a combination of the ASTRAN method and other measures even with existing entitlements and legal constraints.     

PRIVATIZING THE GROUND WATER RESOURCE: INDIVIDUAL USE AND ALTERNATIVE SPECIFICATIONS1

ABSTRACT: While most inquiries into improving the efficiency of ground water allocation have focused upon various schemes involving centralized management, recently the focus has shifted towards exploring private property solutions to these problems. However, most of these studies, when modeling ground water use, have equated behavior under private property to that under common property conditions. This leads to the possibly mistaken conclusion that private property rights do not promote more efficient ground water use, because these models assume that producers ignore the future effects of current pumping. This paper attempts to correct this deficiency by formally modeling ground water use under common property, central management, and private property scenarios. Moreover, there are many ways that property rights can be defined over ground water, some establishing more exclusivity over the resource than others. Four specifications of property rights are analyzed for their likely effects on allocative efficiency: full stock-flow, partial stock-flow, limited stock-flow, and pure flow rights.     

MODELING AND CONTROL OF THE POLLUTION OF WATER RESOURCES SYSTEMS VIA MULTILEVEL APPROACH1

ABSTRACT. The problem of modeling and control of water pollution is considered. A general mathematical model, where the pollution effluent is discharged directly into the river, into the lake, or into a bypass pipe leading to an advanced Waste Water Treatment (AWT) plant, is developed. The Water Resource System (WRS) under consideration is decomposed into N subsystems. The pollution effluent input vector to each subsystem includes the water quantity and different water characteristics such as BOD, DO, pH, conductivity, temperature, algae, phosphates, nitrates, etc. Treatment cost functions and quality transition functions as well as system model constraints are introduced, where all functions can be nonlinear. A system Lagrangian is formed to incorporate the system constraints and coupling. The Lagrangian is decomposed into N independent subsystems, and a two level optimization methodology is introduced. Each subsystem is independently and separately minimized at the first level assuming known Lagrange multipliers. At the second level, the total Lagrangian is maximized with respect to the Lagrange multipliers using optimal values for effluent inputs from all subsystems obtained from the first level. Economic interpretation on the Lagrange multipliers reveals that they are merely prices imposed by the central authority (second level) for the pollution caused by the subsystems. Advantages of the multilevel approach are discussed.     

CONJUNCTIVE USE OF SEA AND FRESH WATER RESOURCES: AN INTEGER PROGRAMMING APPROACH1

ABSTRACT Mathematical models are formulated for selection of water resources projects to meet the future additional water requirements of a given region at the minimum present worth cost. The projects available are surface water reservoirs and desalination plants. The modles are used for selecting both the development sequence of projects and their optimum sizes. Decisions with regard to planning time horizon and discount rates are made outside of the mathematical model. The algorithm used for solving these models is an integer programming routine using the implicit enumeration technique. Some computational results are presented for a hypothetical case.     

OPTIMIZATION IN MUNICIPAL WATER SUPPLY SYSTEM DESIGN1

ABSTRACT. The design of a municipal water supply system may involve utilizing singly or in combination a conventional water supply, a desalted water supply, and a supply from a recharged aquifer reservoir. Optimization of the design requires a model formulated in a way that modern methods of systems analysis can be used. This study concerns the formulation, solution, and evaluation of a mathematical model of a municipal water supply system that includes a supply from a variable quality output desalting plant. The combined system is operated in conjunction with an artificially recharged aquifer reservoir. Also considered are short periods of water shortages. The model is set up in an approximate linear programming format, and the optimum solution (minimum cost) is found. The model is tested by applying it to the design of a supply system to meet the 1985 estimated water demand of the city of Lincoln, Nebraska. Results of this test indicate that the artificial reservoir and the existing conventional supply system are capable of supplying that demand during all but the peak period. An electrodialysis desalting system is used in this analysis. It is competitive only when the length of transmission pipeline for a conventional supply system approaches 90 miles. The model is formulated in a general way so that it can be applied to almost all situations encountered in municipal water supply design, as well as to the specific system designated for this study.     

THE EFFECT OF PRICE ON LONG RUN WATER SUPPLY BENEFITS AND COSTS1

ABSTRACT The long-term effects of presently used and alternatively proposed water pricing policies were studied using some tools of operations research and economics. A discrete deterministic dynamic programming model was structured and operated to determine the optimal water supply capacity expansion paths for a hypothetical residential community with a given water pricing policy. The objective of the model was the maximization of future discounted consumers'surpluses plus producer's revenues net of the long-run cost of supply. State variables were the size of system capacity in MGD and stage variables were the times of feasible capacity increase in years. Demand curves, population sizes, and growth rates for various economic sectors of the community were assumed known, as well as short-run production and capital construction costs. Several policies, including constant unit rates, decreasing or increasing block rates and summer differential rates were tested. It was concluded that price plays a major role in the short-run allocation and long-run planning and conservation of water supplies. Conservational pricing policies were advocated as means of lowering the long-run cost of water, using the water price-demand function as a planning tool. Further research in these areas was recommended.