This paper presents a linear mixed-integer formulation to solve the short-term unit commitment problem. It determines the pair of maximum efficiency points of water discharge and the power produced at the maximal storage for all possible combinations of turbines. The goal is to maximize total energy for all periods. The objective function is calculated using the correction between the power produced at the current volume and the maximal storage and penalizes unit start-ups. Constraints on the maximal number of turbine changes are imposed to find a viable solution in practice. Numerical results are conducted on thirty cases for two powerhouses with five turbines each located in the Saguenay Lac-St-Jean region in the province of Quebec.