In water planning activities, major emphasis has been placed on the development of procedures for devising “optimum plans.” These plans are defined as those which meet prespecified demands for water at “minimum cost.” However, all plans are developed subject to postulated conditions regarding the state of the physical system and of nature. Because planning takes place in a dynamic and uncertain environment in which postulated conditions are known to change, it is imperative that the planner be apprised in the planning phase of the effect of changes which can occur. Using “this information, a planner can temper his judgment with a knowledge of the effect of the uncertainty resulting from changes in the system state variables. This paper presents results of the use of a computer simulation and optimization model to quantify possible variations in system response which could occur as a result of uncertainty in the postulated physical and economic conditions under which the proposed water development system was to perform. The possible effects of these variable responses on planning decision‐making is discussed.
Traditional water use forecasting methodologies have been based primarily upon extrapolation of historical trends into the future, using either single or multidimensional regression analysis. However mathematically eloquent, these techniques are in many cases today totally inadequate for providing planners and decision makers with meaningful guidance on expected future water use. The primary reason for this lies with the pure and simple fact that in more and more cases within the United States, the ‘limits to growth’ concepts are beginning to be felt in both the heavy water using portions of the economy and the portions not related to water. The direct and indirect effects of this on future water use are impossible to predict with any confidence by using forecasting techniques based on the analysis and extrapolation of historical trends. To correct this, the following basic concepts should guide the development and utilization of future water use forecasting procedures.
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.
ABSTRACT. The purpose of this paper is to present and discuss a procedure for finding an optimal staging plan for implementing a multi‐basin water resource system‐a system that must meet, with tolerable shortages, pre‐specified but highly variable demands for water that increase over time‐a system such as the proposed Texas Water System. The paper stresses that, in the past, planners have paid little attention to quantifying explicitly the impact that uncertainty has on the decision process, and in that context, presents a means for explicitly evaluating the impact that uncertainty has on finding and evaluating the performance of the optimal and several alternate staging plans. The procedure presented evaluates the impact that uncertainty, in both the hydrologic and the economic variables, has on the decisions that need to be made. The decisions requiring resolution are (1) which of an over‐specified set of facilities should be constructed, (2) how large each of the facilities should be at various points in time, and (3) how should the system be operated so as to minimize the capital plus operational costs over the planning period.
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