Journées de l'optimisation 2009 Optimizations days

In market equilibrium models with continuous variables, prices are usually extracted as dual variables of constraints. However, many models require some binary variables -- e.g., build/don't build decisions in capacity planning models. There is no established way to define prices of discrete activities, so equilibrium cannot be defined. A two-part pricing approach can resolve some difficulties.

The natural inflow to a hydroelectric reservoir is computed using the water balance equation. At the hourly rate, the resulting inflow appears quite noisy. To improve the inflow evaluation, a linear programming approach is proposed, which consists in disaggregating the information from longer time scales.

We consider the hydro-power "generate vs store" problem. At each moment, a manager can generate power, or store energy for future use. One main difficulty is to correctly account for the inherent value of optionality while modelling the forward-looking storage constraint. The control problem is solved by adapting Longstaff and Schwartz's popular "simulations/regressions" option pricing technique.

La fonction de Bellman solution d'une équation de programmation dynamique n'est pas généralement décomposable. Nous proposons une méthode combinant à la fois les techniques de décomposition en optimisation et de régression en statistique afin de contourner ce problème. Nous appliquons notre approche à la gestion d'équilibre offre demande en électricité.