With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the plants in hydro valleys is called the hydro unit commitment problem. This problem consists in finding the optimal power production schedule of a set of hydro units while meeting several technical, physical, and strategic constraints. The hydro unit commitment has always been a crucial and challenging optimization problem, not only because of its strong nonlinear and combinatorial aspects, but also because it is a large-scale problem that has to be solved to (near) optimality in a reasonable amount of time. This paper presents a review on mathematical programming approaches for the deterministic hydro unit commitment problem. We first provide a survey of the different variants of the problem by exposing a variety of the assumptions, objectives, and constraints considered in the literature. Then, we review the main contributions on resolution approaches with a particular focus on methods based on mathematical programming techniques.

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