Hyperrectangular partition schemes for two-stage stochastic linear mixed integer programming problems

A new exact algorithm is developed in this paper for solving two-stage stochastic linear mixed integer programming problems with pure integer variables in the first stage and continuous variables in the second stage. By combining Benders' decomposition method with hyperrectangular cut and partition technique, we can cut off some hyperrectangulars where there is no optimal solution of the original problem. Integrating such solution scheme into a branch-and-bound framework, the proposed solution method reduces the optimality gap successively in the solution iterations. Furthermore, the proposed solution method can find the optimal solution within a finite number of iterations. The computational results show the solution method is promising.