Single-ratio fractional integer programs with stochastic right-hand sides

Abstract

ABSTRACTWe present an equivalent value function reformulation for a class of single-ratio Fractional Integer Programs (FIPs) with stochastic right-hand sides and propose a two-phase solution approach. The first phase constructs the value functions of FIPs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of the value functions of FIPs and utilize them in our algorithms. We show that in certain cases our approach can solve instances whose extensive forms have the same order of magnitude as the largest stochastic quadratic integer programs solved in the literature.