A branch-and-price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems

In this paper we present a branch-and-price method to solve special structured multi-stage stochastic integer programming problems. We validate our method on two different versions of a multi-stage stochastic batch-sizing problem. One version adopts a recourse formulation, and the other is based on probabilistic constraints. Our algorithmic approach is applicable to both formulations. Our computational results suggest that both classes of problems can be solved using relatively few nodes of a branch-and-price tree. The success of our approach calls for extensions in methodology as well as applications