Reservoir management with risk aversion

We consider the problem faced by a manager planning the operation of a mixed hydro/thermal system, where the manager controls the reservoir release made in each week (single reservoir), as well as the generation from other sources. Demand is deterministic and must be met in each period, while the inflows experienced in each week are uncertain. Stochastic Dynamic Programming (SDP) is a technique often applied to reservoir management problems, with the scheduling horizon divided naturally into discrete time periods, storage as the state variable, and release as the decision variable. If the objective is to minimise the expected annual cost, then a large number of observations with low costs can cancel out a few observations with large costs (because all outcomes are weighted equally). In reality, the manager might want to be able to trade-off a reduction in extremely good outcomes for an improvement in extremely bad outcomes ie, putting more ‘weight’ on the bad outcomes, but this invalidates the standard dynamic programming recursive relationship. We describe a SDP formulation which accommodates a non-linear end-of-horizon utility function by augmenting the state space. We describe some simple algorithmic modifications which significantly reduce the computational requirements of the optimisation, and illustrate the impact of risk averse attitudes on system performance.