Convex approximations for complete integer recourse models

We consider convex approximations of the expected value function of a two-stage integer recourse problem. The convex approximations are obtained by perturbing the distribution of the random right-hand side vector. It is shown that the approximation is optimal for the class of problems with totally unimodular recourse matrices. For problems not in this class, the result is a convex lower bound that is strictly better than the one obtained from the LP relaxation.This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.Key words.integer recourse – convex approximationMathematics Subject Classification (1991):90C15, 90C11