COST MINIMIZATION OF NUTRIENT REDUCTION IN WATERSHED MANAGEMENT USING LINEAR PROGRAMMING1

ABSTRACT: Linear programming is applied to identify the least cost strategy for reaching politically specified phosphorus and total suspended solids reduction targets for the Fox-Wolf river basin in Northeast Wisconsin. The programming model uses data collected on annualized unit reduction costs associated with five categories of sources of phosphorus and total suspended solids discharge in each of the 41 sub-watersheds in the basin to determine the least cost management strategy. Results indicate that: (1) cost-effective nutrient reduction requires careful selection of geographic areas and source categories to address throughout the watershed; (2) agricultural sources are the most cost-effective to address in the basin; and (3) care should be exercised in setting nutrient reduction targets, given that there are likely to be significantly increasing marginal costs of nutrient reduction; the model predicts that lowering the most restrictive target by 33 percent would cut reduction expenditures by about 75 percent. Policy implications of the model include support for the investigation and potential development of institutional arrangements that enable cost-effective nutrient reduction activities to occur, such as the creation of an agency with authority over a given watershed, coordinated watershed management activities, or nutrient trading programs.     

Forest planning in an Oregon case study: Defining the problem and attempting to meet goals with a spatial-analysis technique

Five major management goals were identified for the upper Grande Ronde River Basin on the Wallowa-Whitman National Forest in northeastern Oregon: to produce high-quality fish habitat, to maintain elk habitat, to restore and maintain forest conditions within the natural range of viability, and to contribute to community economic stability. From the broad goals, specific goals for stream temperature, habitat effectiveness index (HEI), habitat corridors, maintenance of land in late or old seral stages, and a nondeclining even flow of timber were selected. A case study was undertaken in a small watershed that is under typical societal constraints to determine whether one decisionsupport tool, SNAP II+, could evaluate the selected goals in a single planning exercise. Three riparian management strategies and two forest road scenarios were used. The exclusion of harvest and road-building from riparian zones in order to increase habitat protection decreased harvest levels and net present value but maintained preactivity stream temperatures. Other resources were generally maintained within prescribed management levels. Although the technique has limitations (e.g., it does not account for riparian zones in calculations of forage and cover for HEI, and it can use the maximum but not minimum acreage goal for some resources), it shows promise for evaluating management tradeoffs in watershed analysis.This is Paper 3069 of the Forest Research Laboratory, Oregon State University, Corvallis, Oregon.     

OPTIMIZING THE PROBABILITIES OF WATER YIELD FOR THE RIDAURA AQUIFER (SPAIN)1

ABSTRACT: Aquifer pumping represents, in many geographical locations, an alternative and/or a complementary source of water to surface water supplies. Several Catalonian coastal towns in the northeastern corner of Spain are in this situation. Also, since pumped water is used to supply drinking water, the main purpose in managing these water resources is to supply, no matter the cost, the amount needed at every moment. In other words, the managers of these aquifers attempt to optimize firm water yield. If we think of these aquifers as underground reservoirs with fixed storage capacity, most of the techniques which are applied to surface reservoirs can be implemented. In this paper we use a Stochastic Dynamic Programming model to optimize the yield from the aquifer of the Ridaura River. The objective function in this model was chosen with the aim of maximizing the reliability of the target yields in each of four seasons.     

REGIONAL WATER SUPPLY PLANNING BY INTERACTIVE SYSTEMS ANALYSIS1

Abstract: This paper describes an interactive data and model generator that is intended to bridge the gap between the water resource enginner and planner and the mathematical progrmming systems approach to regional water supply planning. The optimization objective is to minimize total annual cost with respect to capital investment and operation and maintenance costs. The matrix generator formulates the necessary hydrologic, demographic and programming problem for system optimization. The interactive program guides the user through the input and optimization segments, totally eliminates the chore of manually structuring the model matrix aides in eliminating errors, and allows use by planners without skill in mathematical programming.     

APPLICATION OF A SINGLE RESERVOIR OPERATION POLICY TO A RAIN WATER CISTERN SYSTEM1

The operation policy for a single reservoir is applied to a rain water cistern system because the functions of a cistern are similar to a simple single reservoir. Since the cistern is a closed system, water loss is negligible. In this study, a dynamic programming analysis has been made to study the effects of the probable weekly rainfall and the water storage in the cistern towards the water consumption policy. The result of this study indicates that the water consumption rate should be adjusted into a lower rate when the water storage in the cistern is low and/or when the expected probable weekly rainfall is low if the owner of the cistern does not want to risk the chance of an empty cistern. The demand for a reliable method for forecasting weekly rainfall is evident in this study.     

Timber harvest planning—A combined optimization/simulation model

A special cascading fixed charge structure can be used to characterize a forest management planning problem in which the objectives are to identify the optimal shape of forest harvest cutting units and simultaneously to assign facilities for logging those units. We describe a four-part methodology that has been developed to assist forest managers in analyzing areas proposed for harvesting. This methodology performs an analysis of harvesting feasibility, computes the optimal solution to the cascading fixed charge problem, undertakes a GASP IV simulation to provide additional information about the proposed harvesting operation, and permits the forest manager to perform a time-cost analysis that may lead to a more realistic, and thus improved, solution.     

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.     

A METHOD FOR INCORPORATING AGRICULTURAL RISK INTO A WATER RESOURCE SYSTEM PLANNING MODEL1

ABSTRACT Prior studies of water resource systems have considered risk from the point of view that only the system planners could react to the effects of the risk elements. However, users of water from a system also react to risk. When the quantity of water that a system can supply is subject to considerable variation, the reactions of the users of the water will often effect the benefits generated by the system and thus its optimal design characteristics. A simulation model of a reservoir-irrigation system is developed which incorporates the water users' reactions to risk in such a manner as to reflect their influence on the optimal design characteristics. A risk (convex) programming algorithm is incorporated into the model to reflect the water users' reactions to various levels of aversion to risk and degree of uncertainty in water deliveries. Response surfaces are generated as a result of performing the simulation at different levels of the design variables. An examination of these surfaces reveals the importance of including water users' reactions to risk in water resource system planning. The effects of different levels of risk aversion on the irrigation farmers' choice of crop enterprises are also examined.     

LINEAR PROGRAMMING USE FOR EVALUATING WATER RESOURCES AND COST AND BENEFIT ALLOCATION1

ABSTRACT A linear programming model for a river basin was developed to include almost all water-related economic activity both for consumers and producers. The model was so designated that the entire basin or basin sub-division could be analyzed. The model included seven sectors, nine objective function criteria, and three river-flow levels. Economic basis for conflicts among sectors over incidence of cost allocation and level of economic activity can be traced to some chosen objective. The disposal of untreated household waste water, particularly from the rural household, directly into the river was consistent with maximizing net benefits and minimizing costs. The optimum resource allocation, water-treatment plants, farms and industry activities would change with flow level. For each of the three industries analyzed separately, paper, wool and tanning, public treatment of industrial waste water was the optimal treatment process in one or more of the solutions. Lake shoreline was the dominant feature determining lake-resource valuation. Implied capital value varied from $126 per shoreline foot to over $250 depending on discount rate. Implied prices on lake surface ranged from $42 to $147 per acre. Strong economic forces encouraged small lot sizes for vacation cottages.     

AN APPLICATION OF NETWORK THEORY TO WATER MANAGEMENT IN POULTRY PROCESSING1

ABSTRACT This paper summarizes a study employing a systems approach for analyzing one class of modifications within a poultry processing plant. The modifications considered were changes in water-flow arrangements and process characteristics to reduce water intake of the plant and waste-treatment costs. The object of the study was to develop a technique or techniques by which a combination of proposed modifications could be chosen to minimize water flow through the plant. Existing and proposed flows were represented as a network, and linear programming was used to solve the minimum-flow problem for the network. Application of the technique was made to an existing, typical plant in Durham, N.C. Results of the application showed fresh water intake could be reduced by 45% to 51%, and furthermore that annual returns of 62% to 494% could be obtained on investment in the optimum modification sets, as fresh water costs varying from 10 cents to $1.00 per 1000 gal. Types of modifications of a poultry processing plant are classified by types, and the relative importance and effectiveness of each type are discussed.