Safe dike heights at minimal costs: An integer programming approach

Optimal dike heights are of crucial importance to the Netherlands as almost 60% of its surface is under threat of flooding from sea, lakes, or rivers. This area is protected by more than 3500 kilometres of dunes and dikes. These dunes and dikes require substantial annual investments of over 1 billion euro. In this paper we propose an integer programming model for a cost-benefit analysis to determine optimal dike heights. We improve upon the model proposed by Brekelmans, den Hertog, Roos and Eijgenraam (2012). Our model provides an alternative approach with almost complete flexibility towards input-parameters for flood probabilities, damage costs and investment costs for dike heightening. We present an easy-to-implement algorithm that provides an optimal solution to the problem. The method has been implemented and tested for the most recent data on flood probabilities, damage and investment costs, which were recently used by the government to determine the new safety standards in the Dutch Water Act.