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 3,500 kilometres of dunes and dikes. These dunes and dikes require substantial yearly investments of more than 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 et al. (2012), which is in turn an improvement of the model by Van Dantzig (1956). The model by Van Dantzig (1956) was introduced after a devastating flood in the Netherlands in 1953. Our model provides an alternative approach with almost complete flexibility towards input-parameters for flood probabilities, damage costs and investment costs for dike heightening. In contrast to Brekelmans et al. (2012), who present a dedicated approach with no optimality guarantee, we present an easy-to-implement algorithm that provides an optimal solution to the problem. We briefly discuss robust optimization approaches to deal with uncertainty, e.g. climate change. The method has been implemented and tested for the most recent data on flood probabilities, damage and investment costs, which are presently being used by the government to determine how the safety standards in the Dutch Water Act should be changed.