Finitely Convergent Decomposition Algorithms For

We study a class of two-stage stochastic integer programs with general integer vari4 ables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ 5 method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Go6 mory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision 7 variables, i.e., they are valid for any feasible first-stage solutions. In addition, we propose an al8 ternative implementation that incorporates Benders’ decomposition into a branch-and-cut process 9 in the first stage. We prove the finite convergence of the proposed algorithms. We also report our 10 preliminary computations with a rudimentary implementation of our algorithms to illustrate their 11 effectiveness. 12