Safe dike heights at minimal costs Part II: the inhomogeneous case Ruud Brekelmans * , Carel Eijgenraam † , Dick den Hertog ‡ , Kees Roos § February, 2010 1 Background Protection against flooding is an important issue in the Netherlands, and in several other countries in the world. In Part I of this paper we described the history of dike height optimization in the Netherlands. The Dutch government is going to correct the safety standards for all dikes by changing the Dutch Act on the Water Defences. We were asked to develop a mathematical model for the trade-off between investment costs for heightening dikes and benefits from avoiding floods and therefore damage costs. Moreover, the government asked to develop a solution method such that optimal solutions and optimal safety standards for each of the 53 dike rings in the Netherlands can be calculated. In Part I we described the model and the Dynamic Programming approach that we developed. Both the model and the DP approach assumed that the dike ring is homogeneous, which means that all dikes in the dike ring have the same characteristics with respect to investment costs, flood probabilities, etc. However, many of the dike rings in the Netherlands are inhomogeneous, because such dike rings consist of different dike segments, each of them with different characteristics. Differences occur, e.g., if a dike ring contains a sluice, or if the dike ring protects against more than one river, each with different characteristics. The DP approach cannot be used for dike rings with multiple dike segments, since the number of states at each stage explodes. In this Part II, we therefore develop a Mixed Integer Nonlinear Programming (MINLP) model for the inhomogeneous case, and describe a method to find the optimal solution. Since several parameters in the model are uncertain, much attention is paid in this part to find robust solutions. 2 Research problem The research problem is to extend the model in Part 1 to the inhomogeneous case (for cases up to ten different segments) and to develop a solution method that can compute solutions for all dike rings, preferably with a global optimality guarantee. Moreover, since several parameters in this model are uncertain, e.g., the discount factor, sea-level rise, and economic growth, it was asked to include robustness into the model, so that the final solution is robust against the uncertainty in these parameters. The final goal is to find the right safety standards for the inhomogeneous dike rings, so that the Dutch Act on the Water Defences can be adapted accordingly. * Department of Econometrics and Operations Research, CentER, Tilburg University, Tilburg, The Netherlands † Netherlands Bureau for Economic Policy Analysis (CPB), The Hague, The Netherlands ‡ Department of Econometrics and Operations Research, CentER, Tilburg University, Tilburg, The Netherlands § Department of Information Systems and Algorithms, Delft University of Technology, Delft, The Netherlands 1