The short-term hydropower optimization problem proposed in this talk consists in computing the optimal plan for production in order to maximize energy. The optimization variables are the reservoir volumes, the water discharges and the actual turbines in operation, for every turbine, powerplant and period in the planning horizon. Hydropower production functions are nonconvex and nonlinear and this talk proposes two formulations of the short-term problem to tackle the problem, more precisely one for deregulated energy markets and a second for regulated markets. A stochastic linear integer model and a mixed-integer nonlinear model are detailed in this talk.