Development of Stochastic Factorial Programming Methods for Water Resources Management Under Uncertainty

Abstract

Freshwater is a limited and vital natural resource on earth. It also plays a key role in advancing social and economic development. Despite its importance, freshwater is still one of the most vulnerable resources that have not been managed in a proper manner. There is growing recognition in public and private sectors that freshwater resource needs to be effectively conserved, managed, and distributed. This aspiration makes water resources management a prevalent topic from regional to national levels. The need for sustainable water resources management has become even more urgent with the status quo of global water scarcity. In this dissertation, a set of factorial-analysis-based mathematical programming methods has been proposed to support water resources management under uncertainty. The proposed methods include: (1) the factorial fuzzy programming (FFP) method which can deal with uncertain parameters with fuzzy information and quantify the main and interactive effects of fuzzy parameters on system responses, (2) the dual factorial fuzzy programming (DFFP) method which can deal with dual uncertainties in terms of the fuzziness in modelling parameters and the variability in α-cut levels, (3) the factorial dual-objective two-stage stochastic programming (FDTSP) method which can address dual-objective optimization problems under uncertainty and provide detailed uncertainty analysis, and (4) the multi-level factorial dual-objective programming (MFDP) method which can investigate the non-linear effects of uncertain parameters on system responses and help decision makers gain improved insight into a system. The main contributions of this research include: (1) the development of a set of innovative methods for supporting integrated and sustainable water resources management under uncertainty and (2) the development of regional planning models with regard to the economic efficiency of water use for rural counties in China. The FFP and DFFP methods improve existing fuzzy mathematical programming methods by enabling factorial analysis and the fuzzy vertex method to be seamlessly integrated within a general modelling framework. The two methods are applied to illustrative flood diversion planning and water resources management cases respectively to demonstrate the applicability of the methods. The FDTSP and MFDP methods improve existing linear fractional programming methods by allowing data uncertainty to be considered in the modelling process and the effects of uncertain parameters to be quantified in systems analysis. The two methods are applied to develop regional planning models for Makit County and Xingshan County, China respectively to support rural sustainable development.