Methodology for systematic planning of regional water management

Abstract

The purpose of this dissertation is to present methodology for systematic planning of regional water management. The text is divided into four major sections. The first section presents stochastic formulation for obtaining an optimal operating policy to single multi-purpose reservoirs. The stochastic formulation is based on a material balance equation, random inflow and demand, and chance constraints. The chance constraints are converted to an equivalent linear and quadratic objective functions are appended to the linear constraint set. In the second section methodology is presented for the analysis of time phasing of reservoir system operations with capacity expansion. The objective is to select reservoir capacities, construction timing and to establish an operating policy such that the total cost of the linked reservoir system is minimized. The formulation of this problem is a mixed integer-continuous linear programming problem. The analyst defines the feasible reservoir segments and capacity for each time period where expansion is possible. The resulting problem size and general structure lends itself to Benders' decomposition technique. Benders' method allows for the problem to be separated into a pure linear program and an almost pure integer program. Benders' approach greatly enhances the solution to this type of problem. In the third section the stochastic nature of streamflow is considered for the development of a water resource system. An existing river basin serves as a model for design and formulation. The model is designed to meet a demand placed on a particular reservoir. The flow into the reservoir is not known with absolute certainly. This uncertainty leads to a set of stochastic constraints are converted to their equivalent deterministic constraints. Two types of objective function forms are appended to the linear constraint set, linear and quadratic. The resulting linear and quadratic problems are solved by two solution techniques. The first technique is linear (quadratic) programming and contraction mapping. The second procedure is parametric linear (quadratic) programming. In the final section application of postoptimal analysis is used to illustrate how the analyst could obtain a set of optimal solutions. The analysis includes all the additional variations in the cost function associated with certain decision variables. From the resulting set of solutions, the analyst can select the solution which best meets his budget requirements. He can then eliminate the variables which will produce little or no return for additional expenditures. The relative importance of the decision variables whose returns cannot be changed by additional expenditures can also be determined.