Solving stochastic programs with integer recourse by enumeration: A framework using Grobner basis reductions

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grobner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer 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 improvements to reduce the number of function evaluations needed. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.