Decomposition of Multistage Stochastic Programs with Recombining Scenario Trees

This paper presents a decomposition approach for linear multistage stochastic programs, that is based on the concept of recombining scenario trees. The latter, widely applied in Mathematical Finance, may prevent the node number of the scenario tree to grow exponentially with the number of time stages. It is shown how this property may be exploited within a non-Markovian framework and under time-coupling constraints. Being close to the well-established Nested Benders Decomposition, our approach uses the special structure of recombining trees for simultaneous cutting plane approximations. Convergence is proved and stopping criteria are deduced. Techniques for the generation of suitable scenario trees and some numerical examples are presented.