The feasible control problem is presented for the day-operation of the Three-Gorge Caseade Hydropower Station. The significance of the problem is explained. Basic propetties ofthe problem and the approaches to study it are discussed. Two methfods are given for solving theproblem. which are calculus of variation and linear programming. In the former. the Euler equationwith time-lag and the generalised two-point boundary conditions are obtained and the correspondingpractical implication is interpreted. In the latter. the rationality for the discrete model is exptainedand the computalional details are given for the implement software. some questions which should bepaid much attentfon and the corresponding propeels are prasented based on the numerical results andtheoretical analysis