The joint optimization of the input flow and the size of the storehouse

In the structure of water supply costs for the non-gravitational system the costs of energy exceed the costs of investment. Let us study the case in which the cost of electric energy differ periodically during the day and according to the total power of working pumps. We know the periodical behaviour of demand in each hour per day (more generally in each element of period). We have to control the switching of pumps in the way that we minimize the total costs of electric energy. This control is limited by the size of the reservoir and by the level of the investment, and therefore the size of the reservoir must be included in the optimization process. Because of stochastic demand it is advisable to vary the level of confidence and to choose the optimal solution according to this variation.