Safe dike heights at minimal costs: An integer programming approach

Abstract

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.

Optimal investment and location decisions of a firm in a flood risk area using impulse control theory

“…Economic approaches are cost-effectiveness analyses, multi-criteria analyses, robust-decisionmaking approaches and dynamic programming (Zwaneveld and Verweij 2014;Eijgenraam et al 2012Eijgenraam et al , 2014. The most popular tool is cost-benefit analysis applied to cities (Lichfield 1960;Hunt and Watkiss 2011), regions, and countries [e.g.…”

Economically optimal safety targets for interdependent flood defences in a graph-based approach with an efficient evaluation of expected annual damage estimates

“…Typically, the time between improvements in flood defences is large (on the order of 50 years) due to either high (fixed and variable) costs associated with investments in flood defences or long planning periods (Zwaneveld and Verweij, 2014b). Therefore, if one or multiple flood defences have been strengthened recently, the adjacency list can be reduced to only contain vertices that keep the recently strengthened flood defence(s) at the current level(s).…”

“…Recent publications regarding economically optimal safety targets for the Netherlands can be found in the publications by Eijgenraam (2006), Brekelmans et al (2012) and Zwaneveld and Verweij (2014b, a). In Eijgenraam (2006) and Eijgenraam et al (2016), a set of equations was derived which describe the economically optimal safety target for a single homogeneous flood defence system (i.e.…”

“…A common choice to present optimisation problems is to use graph algorithms (Cormen, 2009). Regarding the economic optimisation of flood defences, this choice was also made in Zwaneveld and Verweij (2014b). An example of a graph for a single flood defence is shown in Fig.…”

“…In Brekelmans et al (2012), a possible heuristic solution is given by modelling the problem as a mixed-integer nonlinear programming problem. Zwaneveld and Verweij (2014b) developing a graph-based modelling approach to solve the nonhomogeneous case to proven optimality. Eijgenraam (2006), Brekelmans et al (2012) and Zwaneveld and Verweij (2014b) assess independent flood-prone areas in which individual flood defences within a dike ring area fail under identical circumstances.…”