Partial Decomposition Strategies for Two-Stage Stochastic Integer Programs

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates how it may be applied to any stochastic integer program with continuous recourse. Such programs are used to model many practical applications such as the one considered in this paper, network design. They are also useful for solving problems with integer recourse as many solution methods for such problems also solve one of its linear relaxations. With an extensive computational study, we have shown the significant advantages of using a partial decomposition, greatly reducing the number of optimality and feasibility cuts generated when solving a stochastic program with a Benders-based algorithm. We also show that how the partial decomposition is performed has a significant impact and point to the most performant strategy.