Flood Control Reservoir System Design Using Stochastic Programming

Mathematically a natural river system is a rooted directed tree where the orientations of the edges coincide with the directions of the streamflows. Assume that in some of the river valleys it is possible to build reservoirs the purpose of which will be to retain the flood, once a year, say. The problem is to find optimal reservoir capacities by minimizing total building cost eventually plus a penalty, where a reliability type constraint, further lower and upper bounds for the capacities are prescribed. The solution of the obtained nonlinear programming problem is based on the supporting hyperplane method of Veinott combined with simulation of multivariate probability distributions. Numerical illustrations are given.