BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems

Abstract

We present an exact algorithmic framework, so-called BFC-MSMIP, for optimizing multistage stochastic mixed 0–1 problems with complete recourse. The uncertainty is represented by using a scenario tree and lies anywhere in the model. The problem is modeled by a splitting variable representation of the Deterministic Equivalent Model of the stochastic problem, where the 0–1 variables and the continuous variables appear at any stage. The approach uses the Twin Node Family concept within the algorithmic framework, so-called Branch-and-Fix Coordination, for satisfying the nonanticipativity constraints in the 0–1 variables. Some blocks of additional strategies are used in order to show the performance of the proposed approach. The blocks are related to the scenario clustering, the starting branching and the branching order strategies, among others. Some computational experience is reported. It shows that the new approach obtains the optimal solution in all instances under consideration.