On the complexity of solving a decision problem with flow-depending costs: The case of the IJsselmeer dikes

A. Abiad, S. Gribling, D. Lahaye, M. Mnich, G. Regts, L. Vena (Corresponding author), G. Verweij, P. Zwaneveld

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Samenvatting

We consider a fundamental integer programming (IP) model for cost–benefit analysis and flood protection through dike building in the Netherlands, due to Zwaneveld and Verweij (2017). Experimental analysis with data for the IJsselmeer shows that the solution of the linear programming relaxation of the IP model is integral. This naturally leads to question whether the polytope associated to the IP is always integral. In this paper we first give a negative answer to this question by proving the non-integrality of the polytope. Secondly, we establish natural conditions that guarantee the linear programming relaxation of the IP model is integral. We show that these conditions are indeed satisfied by the recent data on flood probabilities, damage and investment costs of IJsselmeer. Finally, we show that the IP model can be solved in polynomial time when the number of dike segments, or the number of feasible barrier heights, are bounded.

Originele taal-2Engels
Artikelnummer100565
Aantal pagina's27
TijdschriftDiscrete Optimization
Volume37
DOI's
StatusGepubliceerd - aug. 2020

Financiering

We thank Kees Roos for helpful discussions in an early stage of this work, André Woning from Rijkswaterstaat for useful background information and Gary Greaves for reading the manuscript. Parts of our results were obtained in the 2017 Study Group Mathematics with Industry , for which we thank the organizers. M. Mnich is supported by a DFG, Germany grant MN 59/4-1 . L. Vena is supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement 339109 , and by the project 18-13685Y of the Czech Science Foundation (GAČR). We thank two anonymous referees whose comments and suggestions have enhanced the accessibility of this article and made the proofs easier to follow. Appendix

FinanciersFinanciernummer
Seventh Framework Programme339109
European Research Council18-13685Y
Deutsche ForschungsgemeinschaftMN 59/4-1
Grantová Agentura České Republiky
Seventh Framework Programme
Rijkswaterst./Water, Verkeer Leefomg.

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