Optimal expansion of a water resources system

How to carry out an optimal expansion of an existing water resources system is of continuing importance because of the rising demand for and limited supply of water in many areas of the world, particularly in the southwestern part of the United States of America. Governmental agencies in the U.S.A. and elsewhere have made large public investments in the field of water resources in the past and will continue to do so in the future. Whenever investment in a water resource project is under consideration, important questions such as what is the economic value of the project(s), what is the optimal scale of development of the project(s), and when the project should be constructed need to be answered? It is only through the use of an analytical economic evaluation that competitive uses for capital can be quantitatively evaluated. This monograph describes a methodology that can be used in water resources planning taking into account both water quantity and quality while still remaining computationally tractable. It is concerned with the optimal expansion of a realistic water resources system to meet an increasing demand for municipal and industrial use, irrigation, energy, and recreation over a planning horizon of the next years. Although the problem of quantitatively describing a water resources system in a realistic fashion is forbidding, the outlook for quantitative analysis is good. Some of the problems of describing a river basin include: 1. We have only a fragmentary knowledge of the relevant parameters to include in a river basin model. 2. We do not know how important some of the variables are in relation to others. 3. We do not know which are the most significant parameters in any model in influencing the model outputs. Nevertheless, by formulating models of river basins that mesh successfully with the available optimization techniques, and by analyzing and improving the models, these difficulties can be ameliorated. In formulating the model of the river basin it is assumed that a number of possible dam sites are available for the further regulation of imported waters into the basin. The model has been limited to systems that have (1) deterministic inputs, (2) a network configuration, (3) linear constraints, and (4) capital investment and operating decisions made on a yearly and a monthly basis, respectively, so that the operating policy and construction policy could be optimized. The model of the system did not include (1) stochastic effects or (2) intangible benefits and costs that could not be quantified. Emphasis in the preparation of the model has been placed on the diversity of applicability rather than a specific river basin. After discussion of the criteria for and scope of the problem of expanding an existing water resources system in Chapter 1, a water resources system model is developed and explained in Chapter 2. In Chapter 3 an optimization strategy is developed to maximize, over the set of alternative projects, the sum of the discounted present value of net earnings of the system subject to the water demands and various institutional, physical, and budgetary limits. The optimization problem is posed as a 0-1 mixed integer programming problem that is decomposed into the set of all feasible combinations, a capital budgeting problem; and the economic return is determined for each combination, an operating policy problem. In Chapter 4 an example problem is formulated, solved, and discussed. The efficacy of the optimization algorithm is demonstrated by applying it to the solution of a capital investment problem in a model river basin that resembles a real river basin (the Maule River Basin in central Chile). Chapters 5 briefly shows how to carry out a sensitivity analysis on a water resources system to discover the critical parameters and inputs in the model, parameters whose values in principle have to be obtained with the greatest accuracy. Chapter 6 indicates how water quality can be incorporated into the water quantity model. A FORTRAN listing of the computer program to execute the optimization algorithm will be found in Appendix A. For those not familiar with or who desire more information about existing techniques in optimization, we provide references at appropriate places in this text to the introductory book by Beveridge and Schechter, "Optimization Theory and Practice," McGraw-Hill, New York, 1970. The approach and methodology developed in this monograph are intended to provide guidance to policy and decision makers. It is intended to isolate the economic effects of interrelated factors of water quantity and quality more explicitly to the end that water resources planning may more effectively and efficiently serve the needs of society. Probably one of the major flaws in the systems approach to water resources development is the inability of the scientist and engineer to provide the political decision makers with meaningful plans. It is hoped that this m