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