Solving Stochastic Programs with Complete Integer Recourse : A Framework Using Gröbner Bases

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grabner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the integer expected recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest possible improvements to economize on the number of function evalutations needed.