Robust optimization for incorporating risk and uncertainty in sustainable water resources planning

Robust optimization (RO) is introduced as a framework for incorporating risk and uncertainty in water resources planning models. To model uncertainty, a number of scenarios representing possible future hydrological sequences are considered. The goal of RO is to find solu­ tions which are sufficiently robust (i.e. optimal or at least acceptable over-all scenarios) in light of the decision maker's preferences towards risk. To demonstrate RO, a small but representative conjunctive use model is developed. The model is a two-stage capacity expansion model, with investment decisions made in the first stage and operating decisions made in the second stage. The resulting stochastic mixed-integer non­ linear programming model is solved using Generalized Benders Decom­ position, and the trade-offs among various planning goals are briefly investigated. It is concluded that RO is a promising tool for water resources planning under uncertainty, but work is needed to solve large- scale, practical problems.