Latin-American Conference on Combinatorics,  Graphs and Applications                  George Nemhauser (Georgia Institute of Technology, USA)         ·······················································································         Stochastic Integer Programming Polyhedra                   This is joint work with Yongpei Guan and Shabbir Ahmed. We begin by presenting a new method for combining linear inequalities for (mixed) 0-1 integer programming to obtain new inequalities. We then present an application of this procedure to multi-stage stochastic integer programming. The basic idea is that inequalities for individual scenarios can be combined to obtain new inequalities for many scenarios. In stochastic programming terminology we extend inequalities for paths in a scenario tree to subtrees. These new inequalities are very useful computationally in a branch-and-cut algorithm. We demonstrate this by providing computational results for solving stochastic uncapacitated lot-sizing problems.         ::