Finiteness theorems in stochastic integer programming

We study Graver test sets for families of linear multistage stochastic integer programs with a varying number of scenarios. We show that these test sets can be decomposed into finitely many "building blocks," independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to Nash-Williams' theory of better-quasi-orderings, which is used to show termination of our algorithm. We also apply this theory to finiteness results for Hilbert functions.