Safe dike heights at minimal costs

The nonhomogeneous case

R.C.M. Brekelmans, D. den Hertog, C. Roos, C. Eijgenraam

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)1342-1355
JournalOperations Research
Volume60
Issue number6
Publication statusPublished - 2012

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Levees
Costs
Sea level
Nonlinear programming
Water levels
Rivers
Water
The Netherlands

Cite this

Brekelmans, R.C.M. ; den Hertog, D. ; Roos, C. ; Eijgenraam, C. / Safe dike heights at minimal costs : The nonhomogeneous case. In: Operations Research. 2012 ; Vol. 60, No. 6. pp. 1342-1355.
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Safe dike heights at minimal costs : The nonhomogeneous case. / Brekelmans, R.C.M.; den Hertog, D.; Roos, C.; Eijgenraam, C.

In: Operations Research, Vol. 60, No. 6, 2012, p. 1342-1355.

Research output: Contribution to journalArticleScientificpeer-review

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T2 - The nonhomogeneous case

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AB - 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.

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