Optimal Flood Levee Designs by Dynamic Programming

Bogardi, I., Casti, A., Casti, J.L., & Duckstein, L. (1977). Optimal Flood Levee Designs by Dynamic Programming. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-77-012

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Abstract

An economic optimal development of a levee system along a river is investigated and a dynamic programming (DP) approach is used to find the optima under various conditions. The system consists of a number of levee reaches or stages. A random input of flood wave is regarded at the upstream point of the system. There are two failure modes considered and, consequently, two parameters of the flood wave (state variables) to trigger failure modes in every stage. Stochastic DP is used since the state transition functions (flood routing along the stages) are random functions. Three methods are discussed. In Method I, the expected value of the objective function is taken first, then DP is used as a numerical technique. In Method II, a fixed design flood is chosen as an input under which both optimum cost and policy is determined. In Method III, the value of the expected optimum objective function is calculated. It is shown that the full power of DP cannot be used if Method I is applied. Future research involves comparing the solutions of the three methods.

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