Periodical Multistage Stochastic Programs

In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analog of the so-called Bellman equations for discounted infinite horizon problems, used in Markov Decision Processes and Stochastic Optimal Control. Furthermore, we describe a variant of the Stochastic Dual Dynamic Programming algorithm, applied to the constructed periodical Bellman equations, and provide numerical experiments for the Brazilian interconnected power system problem.


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