A stochastic program with time series and affine decision rules for the reservoir management problem

This paper proposes a multi-stage stochastic programming formulation for the reservoir management problem. Our problem specifically consists in minimizing the risk of floods over a fixed time horizon for a multi-reservoir hydro-electrical complex. We consider well-studied linear time series models and enhance the approach to consider heteroscedasticity. Using these stochastic processes under very general distributional assumptions, we efficiently model the support of the joint conditional distribution of the random inflows and update these sets as new data are assimilated. Using robust optimization techniques and affine decision rules, we embed these time series in a tractable convex program. This allows us to obtain good quality solutions rapidly and test our model in a realistic simulation framework using a rolling horizon approach. Finally, we study a river system in western Québec and perform various numerical experiments based on different inflow generators.