A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure

A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The structure of the uncertain parameters described by a scenario tree. At each node this tree, an ambiguity set defined conditional moment constraints to guarantee consistency. This employs idea nested Benders decomposition that incorporates forward and backward steps. steps solve some conic programming problems approximate cost-to-go function at node, while are used generate additional trial points. new framework convergence analysis establish global approximation procedure, which does not depend on assumption polyhedral original problem. Numerical results practical inventory model reported demonstrate effectiveness proposed method.