Safe Dike Heights at Minimal Costs: The Nonhomogeneous Case

• Published in: Operations research 2012-11, Vol.60 (6), p.1342-1355
• Main Authors: Brekelmans, Ruud, den Hertog, Dick, Roos, Kees, Eijgenraam, Carel
• Format: Article
• Language: English
• Subjects: Analysis; Applied sciences; Approximation; Buildings. Public works; Cost benefit analysis; Cost functions; CROSSCUTTING AREAS; Dams and subsidiary installations; Default; Earth sciences; Earth, ocean, space; Evaluation; Exact sciences and technology; Flood control; Flood damage; flood prevention; Floods; Hydraulic constructions; Hydrology; Hydrology. Hydrogeology; Investment plans; Levees; Management science; Mathematical optimization; Mathematical programming; Minimization of cost; MINLP; Nonlinear programming; Operating costs; Operational research and scientific management; Operational research. Management science; Optimization; Optimization techniques; Parametric models; Reliability theory. Replacement problems; Robust optimization; Studies
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1110.1028

Dike height optimization is of major importance to the Netherlands because a large part of the country lies below sea level, and high water levels in rivers can cause floods. Recently impovements have been made on the cost-benefit model introduced by van Dantzig after the devastating flood in the Netherlands in 1953. We consider the extension of this model to nonhomogeneous dike rings, which may also be applicable to other deltas in the world. A nonhomogeneous dike ring consists of different segments with different characteristics with respect to flooding and investment costs. The individual segments can be heightened independently at different moments in time and by different amounts, making the problem considerably more complex than the homogeneous case. We show how the problem can be modeled as a mixed-integer nonlinear programming problem, and we present an iterative algorithm that can be used to solve the problem. Moreover, we consider a robust optimization approach to deal with uncertainty in the model parameters. The method has been implemented and integrated in software, which is used by the government to determine how the safety standards in the Dutch Water Act should be changed.