Water Network Design and Management via Stochastic Programming

Abstract

Water is an essential natural resource for life and economic activities. Water resources management is facing major challenges due to increasing demands caused by population growth, increased industrial and agricultural use, and depletion of fresh water sources around the world. In addition to putting stress on our civilization, factors such as water supply availability, spatial population changes, industrial growth, etc. are all sources of major uncertainty in water resources management. There are also uncertainties regarding climate variability and how it affects both water demands and supplies. Stochastic programming is a mathematical tool to help make decisions under uncertainty that models the uncertain parameters using probability distributions and incorporates probabilistic statements in mathematical optimization. This dissertation applies stochastic programming to water resources management. In particular, we focus on reclaimed water distribution network design to effectively reuse water in a municipal system and a water allocation problem in an integrated water system under uncertainty. We first present a two-stage stochastic integer program with recourse for cost- effective reclaimed water network design. Unlike other formulations, uncertain demands, temporal, and spatial population changes are explicitly considered in our model. Selection of pipe and pump sizes are modeled using binary variables in order to linearize the nonlinear hydraulic equations and objective function terms. We then develop preprocessing methods to significantly reduce the problem dimension by exploiting the problem characteristics and network structure. We analyze the sensitivity of the network design under varying model parameters, present computational results, and discuss when the stochastic solution is most valuable. Next, we investigate the use of risk-averse approach in water resources management using the so-called conditional value-at-risk as a risk measure. We develop a multistage risk-averse stochastic program with recourse for long-term water allocation under uncertain demands and water supply variability. We propose a specialized decomposition-based algorithm to solve multistage risk-averse stochastic programs, and present both the single-cut and the multicut version of the algorithm. We then compare the solution methodologies with different ways of decomposing the resulting problem. We solve the multistage risk-averse water allocation problem with different risk aversion levels and model assumptions, present computational results to demonstrate the potential benefits of risk-averse approach, and provide a guideline for risk aversion level selection.