Abstract

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.