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

Aida Abiad, Sander Gribling, Domenico Lahaye, Matthias Mnich, Guus Regts, Lluis Vena, Gerard Verweij and Peter Zwaneveld

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Abstract: We consider a fundamental integer programming (IP) model for cost-benefit analysis flood protection through dike building in the Netherlands, due to Verweij and Zwaneveld. Experimental analysis with data for the Ijsselmeer lead to integral optimal solution of the linear programming relaxation of the IP model. This naturally led to the question of integrality of the polytope associated with the IP model. In this paper we first give a negative answer to this question by establishing non-integrality of the polytope. Second, we establish natural conditions that guarantee the linear programming relaxation of the IP model to be integral. We then test the most recent data on flood probabilities, damage and investment costs of the IJsselmeer for these conditions. Third, 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 constant.

Date: 2018-04
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