Optimal scenario tree reductions for the stochastic Unit Commitment Problem

Scenario tree reductions of multi-period stochastic processes have been used as an important technique in obtaining good approximate solutions of multi-period convex stochastic programs. The scenario reduction step is aimed often at optimal approximation of the underlying stochastic process. We provide a new fast computationally cheap scenario tree reduction procedure and describe its approximation capabilities. Our context is the stochastic Unit Commitment Problem, the stochastic version of a problem that is at the heart of many modern energy markets. Its solution determines wholesale contracts between energy producers and energy consumers a day before actual transactions. We show that the new technique performs better than earlier prescriptions in obtaining approximations to the original program. However, these techniques of approximating only the underlying distributions without attention to the cost functions may produce weaker approximations of the optimal solution value; we provide a couple of illustrations to this point.