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 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.     

A PARTITIONING PROCEDURE FOR WATER QUALITY MANAGEMENT MODELS1

ABSTRACT: An improved computational procedure for solving water quality management models containing interacting pollutants and control policies is presented. The method is developed with respect to the specific problem of minimizing the costs of basin-wide thermal and organic pollution control to meet water quality standards. It views the problem in partitioned form where a master problem is used to find cooling levels for thermal polluters while subproblems determine optimal organic pollutant reductions for fixed cooling levels. A gradient based search procedure is used to solve the master problem. Computational results for several river systems are presented. Application of the method to other water quality management models is suggested.     

A VIABLE METHODOLOGY TO IMPLEMENT THE PRINCIPLES AND STANDARDS1

ABSTRACT: The “principles and standards for planning water and related land resources” were made effective October 25, 1973. The document was noticeably deficient in suggestions for the necessary implementing procedures to ensure its success. Current implementing procedures are based on an incorrect premise of maximizing a single objective subject to non-quantified constraints. A successful implementation of multiple objective planning requires optimizing simultaneously several competitive goals. A system of goal programming has been developed and applied to decisionmaking situations as a test of its usefulness in planning for multiple objective water resources projects. The result is a project planning process which can be replicated for adjustments in expected resource supplies or demands to provide a tradeoff matrix between economic and environmental objectives as well as traditional functional purposes. This procedure, tested on the Cross Florida Barge Canal, is an integrated analysis of economic and environmental values which may be as effective in implementing multiple objective planning as the “Green Book” was in developing the now inappropriate benefit cost analysis.     

A RESERVOIR OPERATING MODEL WITH INORGANIC QUALITY CONSTRAINTS FOR THE TRUCKEE RIVER1

ABSTRACT: This study investigated low flow augmentation as a means of meeting inorganic water quality standards for the Truckee River at the California-Nevada state line. A digital inorganic water quality model was combined with a deterministic dynamic reservoir operating model in an iterative process which allowed the optimization of releases subject to selected inorganic water quality constraints as well as downstream demands. Results from model runs with varied flow and river loading data indicate that flow augmentation may be a feasible and relatively inexpensive way of meeting standards for this system except in time of severe drought.     

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.     

FLOOD CONTROL STORAGE ALLOCATIONS BY LINEAR PROGRAMMING1

ABSTRACT. The setting of rule curves for reservoirs or lakes operation requires balancing the flood control storages reserved against the storage requirements for various conservation uses. In this study, a linear programming model is developed to perform single purpose analysis that minimizes flood damages of a multi-lake river system under various initial and input conditions. A flood control utility measure function is arrived from the resulting analysis, and the inclusion of the function in conservation analysis could provide the total functional analysis. The river-system transition function involving time-lags of short duration is described. The function constitutes the basis for the optimization model, and also provides the transformation to reduce significantly the size of the problem. The application to a critical subsystem in the Oswego River System is reported.     

PEAKING STORAGE TANKS FOR WATER SUPPLY SYSTEMS1

ABSTRACT: Construction of a “peaking storage tank” may reduce the operational cost of municipal water in the availability of a time-of-use energy rate. A peaking storage tank is used for storing water that is pumped from wells or other sources of supply during off-peak periods when energy costs are less for use during periods of on-peak water demand. The optimal size of a peaking storage tank is that which results in the minimum total cost, which includes both the storage construction cost and the cost of operation of the pumps. The operational cost for a given time-of-use rate is determined by help of a pipe network simulation model solved by the Newton-Raphson technique and a dynamic programming optimization model. A more simplified method is also introduced. Analyses show that low off-peak energy costs make the construction of peaking storage tanks economically attractive and reduce on-peak energy use, which results in electrical load leveling.     

VALUATION OF IMPROVED IRRIGATION EFFICIENCY FROM AN EXHAUSTIBLE GROUNDWATER SOURCE1

This paper presents estimates made via a recursive linear programming model of the net benefits of improving irrigation application efficiency from an exhaustible groundwater source. Net benefits were derived for different application efficiency levels under furrow, sprinkler, and LEPA irrigation systems. In addition, net benefit estimates were obtained for the transition across irrigation systems. Solutions from the model indicate that low crop prices have a differential impact on net benefits across irrigation application efficiencies and irrigation systems. Also, the more limited groundwater situations consistently reduce the economic incentive to adopt improved irrigation application techniques across all irrigation systems.     

A STOCHASTIC DYNAMIC PROGRAMMING BASED APPROACH TO THE OPERATION OF A MULTI-RESERVOIR SYSTEM1

ABSTRACT: An heuristic iterative technique based upon stochastic dynamic programming is presented for the analysis of the operation of a three reservoir ‘Y’ shaped hydroelectric system. The technique is initiated using historical inflow data for the downstream reservoir. At each iteration the optimal policies for the downstream hydroelectric generating unit are used to provide relative weightings or targets for operation of upstream reservoirs. New input inflows to the downstream reservoir are then obtained by running the historical streamflow record through the optimal policies for the upstream reservoirs. These flows are then used to develop a new operating policy for the downstream reservoir and hence new targets for the upstream reservoirs. The process is continued until the operating policies for each reservoir provide the same overall system benefit for two successive iterations. Results obtained from the procedure are compared to the results obtained by historical operation of the system. The procedure is shown to develop operating policies which give benefits which are as close to the historical benefits as can be expected given the choice of the number of storage state variables.