A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.     

ON THE ECONOMIC IMPACT OF LARGE DIVERSIONS OF SNAKE RIVER WATERS1

ABSTRACT. This work evaluates the economic losses due to diversion from the Snake River during the relatively low-flow year May 1928-April 1929. The results determine the losses due to pollution abatement and power generation for several different patterns and volumes of diversion, and the tool of analysis is dynamic programming.     

OPTIMAL CAPITAL INVESTMENT IN THE EXPANSION OF AN EXISTING WATER RESOURCES SYSTEMS1

The study of the optimal expansion of existing water resources systems is of continuing importance because of the rising demand and limited supply of water in many areas of the world, particularly in the southwestern part of the United States of America. This study is concerned with the investigation of 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 T years. A number of possible dam sites are available for the further regulation of river (canal) flows in the basin and/or the regulation of imported waters into the basin. To maximize, over the set of alternative projects, the sum of discounted present value of net earnings subject to the demands and various institutional, physical and budgetary limits, an optimization problem (Problem I) was formed as a 0-1 mixed integer programming problem and was decomposed into the set of all feasible combinations (Problem II). The economic return was determined for each combination (Problem III). Problem II was solved by a branch and bound procedure which selected each feasible combination of dams while the optimal return for each such combination (Problem III) was found by a network analysis code.     

THE CENTRAL ARIZONA WATER CONTROL STUDY: A CASE FOR MULTIOBJECTIVE PLANNING AND PUBLIC INVOLVEMENT1

This paper describes the successful application of a multiobjective planning framework, incorporating substantial public involvement, to a major water resources decision involving intense confilcts. The study was initiated to help resolve more than a decade of controversy over a project proposed to control flooding and provide regulatory storage in the Phoenix, Arizona, area. The public was actively involved in the development of study goals and the specification of acceptable tradeoffs between multiple objectives. A wide range of structural and nonstructural alternatives was formulated and evaluated in relation to these objectives, and broad-based support was developed for a new plan. Reasons for the successful outcome are discussed, as well as implications for water resources planning under the new Federal Principles and Guidelines.     

AN APPLICATION OF MATHEMATICAL PROGRAMMING TO WATER RESOURCES PLANNING: AN ECONOMIC VIEW1

ABSTRACT: Individuals involved in state water resource planning generally have avoided any development of a comprehensive public water planning investment model that would set the stage for quantitative recommendations of a “what ought to be” tone for future water strategies. Three New Hampshire towns were selected to illustrate the usefulness of a mixed integer multiperiod programming model that utilizes hydrologic and economic data for identifying the discounted least cost of water supply, distribution, and scheduling. Comparisons are made regarding the feasibility of a regional water system approach versus independent “town by town” water supplies that presently prevail. To analyze the sensitivity of optimal water planning solutions to projected water demands, variations in these demands are made.     

Designing a conservation reserve network with minimal fragmentation: A linear integer programming approach

In the biological conservation literature, the optimum reserve site selection problem has often been addressed by using the prototype set covering and maximal covering formulations, assuming that representation of species is the only criterion in site selection. This approach usually results in a small but highly fragmented reserve, which is not useful for practical conservation planning. To improve the chances of species' persistence, it may be desirable to reduce habitat fragmentation. This paper presents a linear integer programming formulation to minimize spatial gaps between selected sites in a reserve network, which is applied to a data set on breeding birds. The authors express their willingness to share the database used in this study. Those readers who wish to have access to the data may contact Robert A. Briers at r.briers@napier.ac.uk.     

Mathematical Methods for Spatially Cohesive Reserve Design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.     

平原河网地区双向生态补偿机制与核算方法

针对平原河网地区地势平坦、水流流向不定、上下游关系不明确的特点,以太湖流域为例,根据“十二五”期间流域内各区域COD和NH₃-N两种污染物的削减量和削减成本,运用非线性回归获得各区域的污染物削减成本函数.根据污染物削减成本函数,以流域污染物削减总成本最小为规划目标,以区域间污染物转移量不超过30%为约束条件,构建基于单目标非线性规划方程组的流域污染物削减总成本最小化模型,求解模型获得太湖流域各区域间的污染物削减成本优化配额方案,计算行政指令配额方案与成本优化配额方案下各区域污染物削减成本的差额,以此为依据,核算生态补偿金额并确定生态补偿方向.核算结果表明,相比行政指令配额方案,太湖流域的成本优化配额方案能够节省9 897.03×104元的污染物削减总成本,根据成本优化配额方案,江苏省需要向浙江省和上海市提供10 577.86×104元的生态补偿费用,浙江省和上海市可分别获得8 909.12×104和1 668.74×104元的生态补偿费用.这种基于流域污染物削减成本最小化的生态补偿机制,根据污染物削减成本函数核算生态补偿金额并确定补偿方向,由于污染物削减成本函数有一定的变动性,因此,允许两个区域间根据成本变动情况改变补偿方向,是一种双向生态补偿机制.      

水污染防治规划理论方法综述

我国的水污染防治规划工作起于20世纪70年代，经过几十年的发展，目前已初成体系，一些成熟的规划方法得到了较为广泛的应用。然而传统方法本身的缺陷、水环境新问题的提出、计算机技术的发展都要求和促使更多新理论方法应用到实践中来。本文在回顾我国水污染防治规划的发展历程和现有规划方法的基础上，对水污染防治规划理论方法的发展趋势进行了展望。