Adjustable robust strategies for flood protection

Flood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management often requires determining a cost-efficient protection strategy, i.e., one which has the lowest possible long run cost and which satisfies flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges that complicate the modeling: (i) uncertainty - many of the important parameters on which the strategies are based (e.g. the sea level rise) are uncertain, and will be known only in the future, and (ii) adjustability - decisions implemented at later time stages need to adapt to the realized uncertainty values. We develop a new mathematical model addressing both issues, based on recent advances in integer robust optimization, and we apply it to the Rhine Estuary - Drechtsteden area in the Netherlands. Our approach shows, among others, that (i) considering 40% uncertainty about the sea level rise leads to a solution with less than 10% increase in the total cost, (ii) solutions taking the uncertainty into account are cheaper in the long run if the 'bad scenarios' for the uncertainty materialize, even if the 'optimistic solutions' are allowed to be repaired later on, and (iii) the optimal here-and-now investment decisions change when uncertainty and adjustability are included in the model.