Numerical experiments on discretization of the random inflow to a nonseasonal reservoir

We performed a series of numerical experiments in order to study the effect of discretizing the probability distribution of the natural inflows, on the accuracy of the optimal solution of a stochastic dynamic programming model, for the management of a hydroelectric reservoir with a piecewise linear revenue function. We evaluated the error obtained as a function of the coarseness of the discretization on a regular grid, and we compared it with the error of a method based on Gaussian quadrature. We find that the relative error of the Gaussian quadrature method is almost as large as with the deterministic solution.