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A Mathematical Approach to Living on Sinking Ground

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Numerical Analysis and Optimization (NAO 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 235))

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Abstract

Many regions in the world are protected against flooding by a dike, which may be either natural or artificial. We deal with a model for finding the optimal height of such a dike in the future. The model minimizes the sum of investment costs and expected damage costs. It is highly nonlinear, nonconvex, and infinite-dimensional. Despite this, it is shown that the model can be solved analytically. Our model has been used in the Netherlands to define legal safety standards for the coming decades.

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References

  1. Brekelmans, R.C.M., den Hertog, D., Roos, C., Eijgenraam, C.J.J.: Safe dike heights at minimal costs: the nonhomogeneous case. Oper. Res. 60(6), 1342–1355 (2012)

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  2. Eijgenraam, C.J.J., Brekelmans, R.C.M., den Hertog, D., Roos, C.: Optimal strategies for flood prevention. Manage. Sci. pp. 1 – 15 (2016). https://doi.org/10.1287/mnsc.2015.2395

  3. Eijgenraam, C.J.J., Kind, J., Bak, C., Brekelmans, R.C.M., den Hertog, D., Duits, M., Roos, C., Vermeer, P., Kuijken, W.: Economically efficient standards to protect the Netherlands against flooding. Interfaces 44(1), 7–21 (2014)

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  4. van Dantzig, D.: Economic decision problems for flood prevention. Econometrica 24(3), 276–287 (1956)

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Author information

Authors and Affiliations

  1. Delft University of Technology, P.O. Box 5031, 2600, GA Delft, The Netherlands

    Kees Roos

Authors
  1. Kees Roos
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Corresponding author

Correspondence to Kees Roos .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  2. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Calabria University, Arcavacata, Italy

    Lucio Grandinetti

  3. Department Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

    Anton Purnama

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Roos, K. (2018). A Mathematical Approach to Living on Sinking Ground. In: Al-Baali, M., Grandinetti, L., Purnama, A. (eds) Numerical Analysis and Optimization. NAO 2017. Springer Proceedings in Mathematics & Statistics, vol 235. Springer, Cham. https://doi.org/10.1007/978-3-319-90026-1_13

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