Refinement Issues in Stochastic Multistage Linear Programming

Abstract

Linear stochastic multistage programs are considered with uncertain data evolving as a multidimensional discrete-time stochastic process. The associated conditional probability measures are supposed to depend linearly on the past. This ensures convexity of the problem and allows application of barycentric scenario trees. These approximate the discrete-time stochastic process, and provide inner and outer approximation of the value functions. The main issue is to reene the discretization of the stochastic process eeciently, using the nested optimization and integration of the dynamic, implicitely given value functions. We analyze and illustrate how errors evolve across nodes of the scenario trees.