Extended formulation for the discrete Hydro Unit Commitment problem

In order to schedule their hydraulic plants, electricity producers solve each day a problem known as the Hydro Unit Commitment. In this talk, we present a variant of this problem, the discrete Hydro Unit Commitment, inspired by the one solved at EDF. We propose a mixed-integer linear programming model for this variant and then introduce an extended formulation that enables cuts which significantly strengthen its linear relaxation. Finally, we discuss ways to reduce the size of the formulation while preserving a strong linear relaxation, and we present preliminary experimental results.