Robust Water Resource Planning at River Basins

Freshwater is a fundamental, but scarce resource vital for life. Uncertainty is one of the significant factors in water resource systems planning and management problems. We consider the problem of water resource systems planning at river basins when there are competing demands and different operating policies. Firstly, we provide a mathematical model using the minimum cost network flow problem, in which the system is represented as a directed multi-graph. Arc coefficients are introduced for modeling gain/loss in the system. Multiple arcs are used to create of the system priorities. Secondly, we reformulate the aforementioned problem using cardinality-constrained robust optimization to address uncertainty when there is an agreement amongst decision makers about uncertainty sets. A set of experiments is conducted to demonstrate the trade-off between the level of robustness and the cost of robustness. We also use Monte-Carlo simulation to analyze the performance of the model in terms of its feasibility in the presence of uncertainty. Thirdly, we employ robust decision making (RDM) to address uncertainty when there is not an agreement amongst decision makers. RDM is applied to analyze the system performance under evaporation/ precipitation uncertainty. Monte-Carlo simulation is used to take samples from the uncertain future ranges. To evaluate the policies multiple attribute decision making (MADM) methodology is used. We have shown that the combination of RDM and MADM is a suitable approach for dealing with deep uncertainty and selecting the most suitable robust strategy. This thesis provides insight into modeling uncertainty in river basins systems.