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

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...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Abiad, Aida, Sander Gribling, Lahaye, Domenico, Mnich, Matthias, Regts, Guus, Vena, Lluis, Verweij, Gerard, Zwaneveld, Peter
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.04.2018
Subjects
Cost benefit analysis
Dikes
Flood management
Integer programming
Integrals
Linear programming
Polynomials
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422