Factorial multi-stage stochastic programming methods for water resources management

The constantly increasing demand for water, in terms of both sufficient quantity and satisfactory quality, has forced decision makers to contemplate and propose more comprehensive, complex and ambitious plans for water resources systems. A wide range of mathematical techniques have been developed to aid planners or decision makers in formulating and generating effective water-resources management policies. However, water resources management systems are always associated with a variety of uncertainties due to water managers' vague attitudes as well as inexact information obtained for many system components; this leads to complicated planning efforts with uncertain parameters as well as their interactions. Therefore, in order to facilitate more robust water resources management and planning, innovative optimization methodologies, with the ability to reflect various combinations of these uncertainties and complexities, are desired.;This study is a first attempt to integrate multivariate factorial analysis with inexact two- and multi-stage stochastic programming. By introducing multivariate factorial analysis into the inexact optimization process, the developed methods are able to not only tackle uncertainties properly and provide water managers with reasonable solutions, but are also capable of analyzing the detailed effects from individual inputs on system performance and reflecting multi-level interactions among various modeling parameters as well as their combined effects on the system.;In this thesis, a Factorial Two-Stage Stochastic Programming (FTSP) method is firstly developed to support water resources management under uncertainty. The developed FTSP improves upon conventional inexact two-stage stochastic programming (ITSP) methods. It well inherits the merits of the conventional ITSP method and can provide the detailed effects of uncertain parameters and their interactions on system performance. The developed FTSP approach is applied to a hypothetical case study of water resources system analysis. The results indicate that significant system inputs and their interactions can be identified. Reasonable water-allocation schemes can also be formulated based upon the resulting information regarding detailed effects from various impact factors and their interactions. Next, in order to reflect dynamic features of water resources management system and provide water managers with more decision options within a multi-stage context, a Factorial Multi-Stage Stochastic Programming (FMSP) method is developed in this thesis. A set of scenarios which could possibly reflect the universe of possible outcomes are constructed using a multi-layer scenario tree. Based on the conventional method for solving inexact multi-stage stochastic programming problems, five alternatives are proposed and incorporated within the conventional algorithm, constructing a general approach to address inexact multi-stage issues. The bundled approach can better reflect water managers' various attitudes toward system objectives and constraints. Based on water managers' major concerns, a series of policies can be generated to assist them in making decisions. Moreover, through factorial analysis, parameters and interactions which have influential effects on system performance could be identified. The results can assist water managers in characterizing the system and support their decision making. This method is applied to a hypothetical case study of water resources management. The results afford water managers with an in-depth characterization of the system and provide useful decision support.