Optimal multi-year management of a regional Water Supply System under uncertainty: The Affine Adjustable Robust Counterpart (AARC) approach

In this study a regional Water Supply System (WSS), fed from natural sources which depend on uncertain recharge, and from desalination plants with fixed capacity, is to be operated over years. The water is transported through a network to meet consumers' demands. The requirement is to decide dynamically on the optimal operating policy, based on the revealed uncertainty up to the decision point, for minimizing the total operation cost of the system while fulfilling operational constraints at multiple time decision points. The Robust Counterpart (RC) methodology [Ben-Tal et al., 2009] is adopted, which uses a min-max approach assuming that the uncertain parameters reside within a user-defined uncertainty set. The dynamic version of RC is called Adjustable Robust Counterpart (ARC). One of its special tractable versions is the Affine Adjustable Robust Counterpart (AARC) in which the dependence of future decision variables on revealed uncertain data is restricted to be linear. The AARC solution provides a non-probabilistic analysis for multiyear management of WSS under uncertain conditions.