Cutting planes for multi-stage stochastic integer programs

Abstract

This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.We give a general method for generating cutting planes for multi-stage stochastic integer programs basedon combining inequalities that are valid for the individual scenarios. We apply the method to generatecuts for a stochastic version of a dynamic knapsack problem and to stochastic lot sizing problems. Wegive computational results which show that these new inequalities are very effective in a branch-and-cutalgorithm.