We investigate the hydropower scheduling problem, in which a price-taking producer determines a reservoir management strategy that maximises the present value of revenues from selling the produced electricity in a well-functioning market. Uncertainty is present both in market prices and in reservoir inflows. To solve the problem, we apply linear decision rules, which is an approximation method for solving multistage stochastic linear programming problems. Traditional methods for solving these types of problems suffer from computational efforts that grow exponentially with the number of stages and state variables. By restricting the decision variables to be affine functions of the realisations of the uncertain parameters, the original intractable problem is transformed into a problem with short computational time. The aim is to investigate feasibility of the framework. The approach is demonstrated on four Norwegian hydropower plants using recent inflow and price data over a ten year time horizon. We obtain flexible reservoir management strategies, providing feasible solutions where a deterministic approach fails, and otherwise improving expected profits by up to 4.5% compared to a deterministic approach. Solutions times are in the order of minutes.